Author name code: frisch
ADS astronomy entries on 2022-09-14
author:"Frisch, Helene" 
------------------------------------------------------------------------  

Title: Effects of Angle-Dependent Partial Frequency Redistribution
    on Polarized Line Profiles
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.; Stenflo, J. O.
Bibcode: 2019ASPC..519..109S
Altcode:
  Scattering of the solar limb-darkened radiation field on atoms and
  molecules produces linearly polarized spectrum of the Sun (Second Solar
  Spectrum). Partial frequency redistribution (PFR) plays a fundamental
  role in shaping the wings of linearly polarized profiles of strong
  resonance lines. Here we present the effects of the angle-dependent
  (AD) PFR on resonance polarization both in the presence and absence
  of magnetic fields. We consider scattering on a two-level atom with
  unpolarized lower level, and a one-dimensional isothermal atmosphere.

Title: Non-conservative Rayleigh Scattering. A Perturbation Approach
Authors: Frisch, H.
Bibcode: 2019ASPC..519..101F
Altcode:
  The continuous spectra of stellar and planetary atmospheres may be
  linearly polarized by Rayleigh or Thomson scattering. The polarization
  rate follows the Chandrasekhar's law for the Milne or diffuse
  reflection problems, if scattering processes are the only source
  of absorption and emission. Deviations from the Chandrasekhar's law
  due to true absorptions by bound-free or free-free transitions are
  derived from a perturbation analysis of the polarized radiative
  transfer equation, using as expansion parameter the ratio ɛ =
  κ<SUB>c</SUB>/(κ<SUB>c</SUB> + σ<SUB>c</SUB>), with κ<SUB>c</SUB>
  and σ<SUB>c</SUB> the true absorption and scattering absorption
  coefficients. An expansion in powers of ɛ is proposed for the
  polarization rate. A comparison with numerical results shows
  an excellent fit for ɛ up to 10<SUP>-3</SUP> but a systematic
  underestimation above this value.

Title: Nonconservative Rayleigh scattering. A perturbation approach
Authors: Frisch, H.
Bibcode: 2019A&A...625A.125F
Altcode:
  Context. The continuous spectrum of stellar and planetary atmospheres
  can be linearly polarized by Rayleigh or Thomson scattering. The
  polarization rate depends on the ratio κ<SUB>c</SUB>/(κ<SUB>c</SUB> +
  σ<SUB>c</SUB>), κ<SUB>c</SUB> and σ<SUB>c</SUB> being the absorption
  coefficients due to photo-ionizations and scattering processes,
  respectively. The scattering process is conservative if κ<SUB>c</SUB>
  = 0, and in this case the center-to-limb variation of the polarization
  rate follows Chandrasekhar's law. Deviations from this law appear
  if the scattering is nonconservative, that is, if photons have a
  probability ɛ = κ<SUB>c</SUB>/(κ<SUB>c</SUB> + σ<SUB>c</SUB>)
  of being destroyed at each scattering. <BR /> Aims: Nonconservative
  Rayleigh scattering is addressed here with a perturbation point of view,
  using ɛ, assumed to be a constant, as an expansion parameter. The
  goal is to obtain a perturbation expansion of the polarized radiation
  field that can be used to measure of the effects of a nonzero ɛ on
  the polarization rate of the emergent radiation and to check the
  accuracy of numerical codes. <BR /> Methods: The expansion method
  is an application to Rayleigh scattering of a general perturbation
  approach developed for scalar monochromatic transport equations. The
  introduction of a space variable, rescaled by a factor √ɛ, transforms
  the radiative transfer equation into a new equation from which one can
  extract simpler equations to describe the field in the interior of the
  medium and in boundary layers. <BR /> Results: The perturbation method
  is applied to a plane-parallel slab with no incident radiation and an
  unpolarized primary source of photons. The interior and boundary layer
  fields are expanded in powers of √ɛ. The expansion of the interior
  radiation field shows that it is unpolarized at leading order, with
  an intensity i<SUB>0</SUB>(τ∼) satisfying a diffusion equation,
  and that the polarization appears at order ɛ. The emergent radiation
  is calculated up to and including order ɛ. The leading term yields
  the polarization rate of the Chandrasekhar's law. The following one,
  of order √ɛ, accurately predicts the decrease of the polarization
  rate for values of ɛ up to 10<SUP>-3</SUP> and shows that it varies
  roughly as (1 - μ) for any unpolarized primary source. Methods for
  testing the accuracy of numerical schemes are proposed. The perturbation
  method is also applied to a slab with an incident radiation field and
  a polarized primary source of photons.

Title: Analytic Results for Rayleigh Scattering and Resonance
    Polarization
Authors: Frisch, H.
Bibcode: 2019ASPC..526...19F
Altcode:
  In a plane parallel semi-infinite atmosphere, where the scattering
  of photons follows the Rayleigh scattering law and all the absorbed
  photons are reemitted (conservative scattering), the polarized radiation
  field can be expressed in terms of two functions H<SUB>l</SUB>(μ) and
  H<SUB>r</SUB>(μ) introduced by Chandrasekhar. It will be shown how the
  vector radiative transfer problem for the polarized radiation field can
  be decomposed into two scalar equations leading to exact expressions
  for H<SUB>l</SUB>(μ) and H<SUB>r</SUB>(μ). For non conservative
  Rayleigh scattering, the radiation field can be expressed in terms of
  a matrix H(μ) satisfying a numerically solvable nonlinear integral
  equation. The method of construction of this nonlinear equation and
  its generalization to resonance scattering of spectral lines formed
  with complete frequency redistribution is outlined.

Title: Large Area Flat Panel Imaging Detectors for Astronomy and
    Night Time Sensing
Authors: Siegmund, O.; McPhate, J.; Frisch, H.; Elam, J.; Mane, A.;
   Wagner, R.; Varner, G.
Bibcode: 2013amos.confE.105S
Altcode:
  Sealed tube photo-sensing detectors for optical/IR detection have
  applications in astronomy, nighttime remote reconnaissance, and
  airborne/space situational awareness. The potential development
  of large area photon counting, imaging, timing detectors has
  significance for these applications and a number of other areas
  (High energy particle detection (RICH), biological single-molecule
  fluorescence lifetime imaging microscopy, neutron imaging, time of
  flight mass spectroscopy, diffraction imaging). We will present details
  of progress towards the development of a 20 cm sealed tube optical
  detector with nanoengineered microchannel plates for photon counting,
  imaging and sub-ns event time stamping. In the operational scheme of
  the photodetector incoming light passes through an entrance window
  and interacts with a semitransparent photocathode on the inside of the
  window. The photoelectrons emitted are accelerated across a proximity
  gap and are detected by an MCP pair. The pair of novel borosilicate
  substrate MCPs are functionalized by atomic layer deposition (ALD),
  and amplify the signal and the resulting electron cloud is detected
  by a conductive strip line anode for determination of the event
  positions and the time of arrival. The physical package is ~ 25 x 25
  cm but only 1.5 cm thick. Development of such a device in a square 20
  cm format presents challenges: hermetic sealing to a large entrance
  window, a 20 cm semitransparent photocathode with good efficiency
  and uniformity, 20 cm MCPs with reasonable cost and performance,
  robust construction to preserve high vacuum and withstand an atmosphere
  pressure differential. We will discuss the schemes developed to address
  these issues and present the results for the first test devices. The
  novel microchannel plates employing borosilicate micro-capillary arrays
  provide many performance characteristics typical of conventional MCPs,
  but have been made in sizes up to 20 cm, have low intrinsic background
  (0.08 events cm2 s-1) and have very stable gain behavior over &gt;
  7 C cm2 of charge extracted. They are high temperature compatible
  and have minimal outgassing, which shortens and simplifies the sealed
  tube production process and should improve overall lifetimes. Bialkali
  (NaKSb) semitransparent photocathodes with &gt; 20% quantum efficiency
  have also been made on 20 cm borosilicate windows compatible with the
  window seals for the large sealed tube device. The photocathodes have
  good response uniformity and have been stable for &gt; 5 months in
  testing. Tests with a 20 cm detector with a cross delay line readout
  have achieved ~50µm FWHM imaging with single photon sub-ns timing and
  MHz event rates, and tests with a 10 x 10cm detector with cross strip
  readout has achieved ~20µm FWHM imaging with &gt;4 MHz event rates
  with ~10% deadtime. We will discuss the details and implications of
  these novel detector implementations and their potential applications.

Title: Performance characteristics of atomic layer functionalized
    microchannel plates
Authors: Siegmund, O. H. W.; Richner, N.; Gunjala, G.; McPhate, J. B.;
   Tremsin, A. S.; Frisch, H. J.; Elam, J.; Mane, A.; Wagner, R.; Craven,
   C. A.; Minot, M. J.
Bibcode: 2013SPIE.8859E..0YS
Altcode:
  Microchannel plates that have been constructed by atomic layer
  deposition of resistive and secondary emissive layers, onto
  borosilicate glass microcapillary arrays provide a novel alternative
  to conventional microchannel plates for detection of radiation and
  particles. Conventional microchannel plates can also benefit from
  atomic layer deposition of highly efficient secondary emissive
  layers. Our evaluations of these techniques have revealed unique
  features of atomic layer functionalized microchannel plates, including
  enhanced stability and lifetime, low background rates, and low levels of
  adsorbed gas. In addition borosilicate glass microcapillary arrays show
  enhanced physical and thermal robustness, which makes it possible to
  successfully fabricate large area devices (20 cm) with good uniformity
  of operational characteristics.

Title: Latest Advancements in Microchannel Plate Detectors
Authors: Vallerga, John; Siegmund, O.; McPhate, J. B.; Tremsin, A.;
   Welsh, B.; Frisch, H.; Wagner, R. G.; Elam, J.; Mane, A.; Varner, G.
Bibcode: 2013HEAD...1312315V
Altcode:
  Microchannel plate (MCP) detectors have been used in space-based
  astronomical detectors for decades (e.g. EUVE, ROSAT, Chandra, COS on
  Hubble) and their performance continues to improve. We will present
  the latest technological developments in MCP detectors, including
  very large format MCPs made from low background borosilicate glass
  (20cm x 20cm MCPs); functionalized by atomic layer deposition of
  semiconductor layers and high electron emission coefficient layers
  which substantially increase the lifetime of the output gain; high
  speed cross strip readouts (&gt; 4MHz count rate at 10% deadtime); and
  photocathode development for increased QE in the UV and x-ray bands. We
  will also present our efforts to raise the technology readiness level
  of our cross-strip electronics to level 6 by developing low power and
  low mass ASICs that can be space qualified. This work is supported by
  NASA Grants NNX12AF46A, NNG11AD54G and DOE grant #DE-AC02-06CH11357.

Title: Large Area and High Efficiency Photon Counting Imaging
    Detectors with High Time and Spatial Resolution for Night Time
    Sensing and Astronomy
Authors: Siegmund, O.; Vallerga, J.; Tremsin, A.; McPhate, J.; Frisch,
   H.; Elam, J.; Mane, A.; Wagner, R.; Varner, G.
Bibcode: 2012amos.confE..92S
Altcode:
  The development of large area photon counting, imaging, timing detectors
  with high performance has significance for applications in astronomy
  (such as our sensor on the SAAO SALT 10m telescope), night time remote
  reconnaissance, airborne/space situational awareness, and high-speed
  adaptive optics. Sealed tube configurations for optical/IR sensing also
  have applications in detection of Cherenkov light (RICH), biological
  single-molecule fluorescence lifetime imaging microscopy and neutron
  imaging applications. In open faced configurations these devices are
  important for UV and particle detection in space astrophysics, mass
  spectroscopy and many time-of flight applications. Currently available
  devices are limited to sizes of about 5 cm and use either conventional
  microchannel plates, or dynode multipliers for amplification, coupled
  coarse pad array readouts. Extension of these schemes to devices
  as large as 20 cm with high spatial resolution presents significant
  problems and potentially considerable cost. A collaboration (Large
  Area Picosecond Photon Detector) of the U. Chicago, Argonne National
  Laboratory, U.C. Berkeley, U. Hawaii and a number of other institutions
  has developed novel technologies to realize 20 cm format detectors
  in open face or sealed tube configurations. One critical component of
  this development is novel microchannel plates employing borosilicate
  micro-capillary arrays. The microchannel plates are based on a
  novel concept where the substrate is constructed from a borosilicate
  micro-capillary array that is made to function as a microchannel plate
  by deposition of resistive and secondary emissive layers using atomic
  layer deposition. The process is relatively inexpensive compared with
  conventional microchannel plates and allows very large microchannel
  plates to be produced with pore sizes as small as 10 microns. These
  provide many performance characteristics typical of conventional
  microchannel plates, but have been made in sizes up to 20 cm, have
  low intrinsic background (&lt;0.1 events/sq-cm/sec) and high stability
  with no observed gain degradation behavior over at least 5 Coul/sq-cm
  of charge extraction. Initial tests in a 20 cm detector with a cross
  strip electronic readout have achieved 4k x 4k pixel imaging with
  single photon sub-ns timing and MHz event rates. In concert with this
  effort we have made stable, uniform 20 cm bialkali photocathodes with
  &gt;20% quantum efficiency on borosilicate windows compatible with
  a large sealed tube device. Other related efforts have also produced
  small sealed tubes with 30% quantum efficiency GaAs sealed tubes with
  high resolution imaging and timing that are immediately applicable
  to current applications, and opaque GaN UV photocathodes directly
  deposited onto these novel microchannel plates. We will discuss the
  details and implications of these novel microchannel plates with
  respect to the realization of novel detectors up to 20 cm format with
  reasonable cost and performance, robust construction, high flexibility
  of format and readout, reduction of fabrication effort, dramatically
  increased lifetime and stability, and their potential applications.

Title: Forward-scattering Hanle effect in the solar Ca I 4227 Å line
Authors: Frisch, H.; Anusha, L. S.; Bianda, M.; Holzreuter, R.;
   Nagendra, K. N.; Ramelli, R.; Sampoorna, M.; Smitha, H. N.; Stenflo,
   J. O.
Bibcode: 2012EAS....55...59F
Altcode:
  High sensitivity spectropolarimetric observations of the four Stokes
  parameters of the solar Ca I 4227 Å line have been performed in
  October 2010 at IRSOL with the ZIMPOL polarimeter, near the disk center,
  outside an active region (Bianda et al. 2011). They were analyzed in
  Anusha et al. 2011 with a combination of detailed radiative transfer
  modelling of the Hanle effect for the linear polarization and weak
  field Zeeman approximation for the circular polarization. This approach
  made possible a unique determination of the magnetic field vector at
  various positions along the slit of the spectrograph. A summary of
  the observations and of their analysis is presented here.

Title: Search for anomalous production of multiple leptons in
    association with W and Z bosons at CDF
Authors: Aaltonen, T.; Álvarez González, B.; Amerio, S.; Amidei, D.;
   Anastassov, A.; Annovi, A.; Antos, J.; Apollinari, G.; Appel, J. A.;
   Arisawa, T.; Artikov, A.; Asaadi, J.; Ashmanskas, W.; Auerbach, B.;
   Aurisano, A.; Azfar, F.; Badgett, W.; Bae, T.; Barbaro-Galtieri, A.;
   Barnes, V. E.; Barnett, B. A.; Barria, P.; Bartos, P.; Bauce, M.;
   Bedeschi, F.; Behari, S.; Bellettini, G.; Bellinger, J.; Benjamin,
   D.; Beretvas, A.; Bhatti, A.; Bisello, D.; Bizjak, I.; Bland, K. R.;
   Blumenfeld, B.; Bocci, A.; Bodek, A.; Bortoletto, D.; Boudreau, J.;
   Boveia, A.; Brigliadori, L.; Bromberg, C.; Brucken, E.; Budagov,
   J.; Budd, H. S.; Burkett, K.; Busetto, G.; Bussey, P.; Buzatu, A.;
   Calamba, A.; Calancha, C.; Camarda, S.; Campanelli, M.; Campbell,
   M.; Canelli, F.; Carls, B.; Carlsmith, D.; Carosi, R.; Carrillo, S.;
   Carron, S.; Casal, B.; Casarsa, M.; Castro, A.; Catastini, P.; Cauz,
   D.; Cavaliere, V.; Cavalli-Sforza, M.; Cerri, A.; Cerrito, L.; Chen,
   Y. C.; Chertok, M.; Chiarelli, G.; Chlachidze, G.; Chlebana, F.; Cho,
   K.; Chokheli, D.; Chung, W. H.; Chung, Y. S.; Ciocci, M. A.; Clark,
   A.; Clarke, C.; Compostella, G.; Convery, M. E.; Conway, J.; Corbo,
   M.; Cordelli, M.; Cox, C. A.; Cox, D. J.; Crescioli, F.; Cuevas, J.;
   Culbertson, R.; Dagenhart, D.; d'Ascenzo, N.; Datta, M.; de Barbaro,
   P.; Dell'Orso, M.; Demortier, L.; Deninno, M.; Devoto, F.; d'Errico,
   M.; Di Canto, A.; Di Ruzza, B.; Dittmann, J. R.; D'Onofrio, M.; Donati,
   S.; Dong, P.; Dorigo, M.; Dorigo, T.; Ebina, K.; Elagin, A.; Eppig,
   A.; Erbacher, R.; Errede, S.; Ershaidat, N.; Eusebi, R.; Farrington,
   S.; Feindt, M.; Fernandez, J. P.; Field, R.; Flanagan, G.; Forrest, R.;
   Frank, M. J.; Franklin, M.; Freeman, J. C.; Frisch, H.; Funakoshi, Y.;
   Furic, I.; Gallinaro, M.; Garcia, J. E.; Garfinkel, A. F.; Garosi, P.;
   Gerberich, H.; Gerchtein, E.; Giagu, S.; Giakoumopoulou, V.; Giannetti,
   P.; Gibson, K.; Ginsburg, C. M.; Giokaris, N.; Giromini, P.; Giurgiu,
   G.; Glagolev, V.; Glenzinski, D.; Gold, M.; Goldin, D.; Goldschmidt,
   N.; Golossanov, A.; Gomez, G.; Gomez-Ceballos, G.; Goncharov, M.;
   González, O.; Gorelov, I.; Goshaw, A. T.; Goulianos, K.; Grinstein,
   S.; Grosso-Pilcher, C.; Group, R. C.; Guimaraes da Costa, J.; Hahn,
   S. R.; Halkiadakis, E.; Hamaguchi, A.; Han, J. Y.; Happacher, F.; Hara,
   K.; Hare, D.; Hare, M.; Harr, R. F.; Hatakeyama, K.; Hays, C.; Heck,
   M.; Heinrich, J.; Herndon, M.; Hewamanage, S.; Hocker, A.; Hopkins,
   W.; Horn, D.; Hou, S.; Hughes, R. E.; Hurwitz, M.; Husemann, U.;
   Hussain, N.; Hussein, M.; Huston, J.; Introzzi, G.; Iori, M.; Ivanov,
   A.; James, E.; Jang, D.; Jayatilaka, B.; Jeon, E. J.; Jindariani, S.;
   Jones, M.; Joo, K. K.; Jun, S. Y.; Junk, T. R.; Kamon, T.; Karchin,
   P. E.; Kasmi, A.; Kato, Y.; Ketchum, W.; Keung, J.; Khotilovich, V.;
   Kilminster, B.; Kim, D. H.; Kim, H. S.; Kim, J. E.; Kim, M. J.; Kim,
   S. B.; Kim, S. H.; Kim, Y. K.; Kim, Y. J.; Kimura, N.; Kirby, M.;
   Klimenko, S.; Knoepfel, K.; Kondo, K.; Kong, D. J.; Konigsberg, J.;
   Kotwal, A. V.; Kreps, M.; Kroll, J.; Krop, D.; Kruse, M.; Krutelyov,
   V.; Kuhr, T.; Kurata, M.; Kwang, S.; Laasanen, A. T.; Lami, S.; Lammel,
   S.; Lancaster, M.; Lander, R. L.; Lannon, K.; Lath, A.; Latino, G.;
   LeCompte, T.; Lee, E.; Lee, H. S.; Lee, J. S.; Lee, S. W.; Leo, S.;
   Leone, S.; Lewis, J. D.; Limosani, A.; Lin, C. -J.; Lindgren, M.;
   Lipeles, E.; Lister, A.; Litvintsev, D. O.; Liu, C.; Liu, H.; Liu, Q.;
   Liu, T.; Lockwitz, S.; Loginov, A.; Lucchesi, D.; Lueck, J.; Lujan,
   P.; Lukens, P.; Lungu, G.; Lys, J.; Lysak, R.; Madrak, R.; Maeshima,
   K.; Maestro, P.; Malik, S.; Manca, G.; Manousakis-Katsikakis, A.;
   Margaroli, F.; Marino, C.; Martínez, M.; Mastrandrea, P.; Matera,
   K.; Mattson, M. E.; Mazzacane, A.; Mazzanti, P.; McFarland, K. S.;
   McIntyre, P.; McNulty, R.; Mehta, A.; Mehtala, P.; Mesropian, C.;
   Miao, T.; Mietlicki, D.; Mitra, A.; Miyake, H.; Moed, S.; Moggi, N.;
   Mondragon, M. N.; Moon, C. S.; Moore, R.; Morello, M. J.; Morlock, J.;
   Movilla Fernandez, P.; Mukherjee, A.; Muller, Th.; Murat, P.; Mussini,
   M.; Nachtman, J.; Nagai, Y.; Naganoma, J.; Nakano, I.; Napier, A.;
   Nett, J.; Neu, C.; Neubauer, M. S.; Nielsen, J.; Nodulman, L.; Noh,
   S. Y.; Norniella, O.; Oakes, L.; Oh, S. H.; Oh, Y. D.; Oksuzian, I.;
   Okusawa, T.; Orava, R.; Ortolan, L.; Pagan Griso, S.; Pagliarone,
   C.; Palencia, E.; Papadimitriou, V.; Paramonov, A. A.; Patrick,
   J.; Pauletta, G.; Paulini, M.; Paus, C.; Pellett, D. E.; Penzo, A.;
   Phillips, T. J.; Piacentino, G.; Pianori, E.; Pilot, J.; Pitts, K.;
   Plager, C.; Pondrom, L.; Poprocki, S.; Potamianos, K.; Prokoshin,
   F.; Pranko, A.; Ptohos, F.; Punzi, G.; Rahaman, A.; Ramakrishnan,
   V.; Ranjan, N.; Redondo, I.; Renton, P.; Rescigno, M.; Riddick, T.;
   Rimondi, F.; Ristori, L.; Robson, A.; Rodrigo, T.; Rodriguez, T.;
   Rogers, E.; Rolli, S.; Roser, R.; Ruffini, F.; Ruiz, A.; Russ, J.;
   Rusu, V.; Safonov, A.; Sakumoto, W. K.; Sakurai, Y.; Santi, L.; Sato,
   K.; Saveliev, V.; Savoy-Navarro, A.; Schlabach, P.; Schmidt, A.;
   Schmidt, E. E.; Schwarz, T.; Scodellaro, L.; Scribano, A.; Scuri,
   F.; Seidel, S.; Seiya, Y.; Semenov, A.; Sforza, F.; Shalhout,
   S. Z.; Shears, T.; Shepard, P. F.; Shimojima, M.; Shochet, M.;
   Shreyber-Tecker, I.; Simonenko, A.; Sinervo, P.; Sliwa, K.; Smith,
   J. R.; Snider, F. D.; Soha, A.; Sorin, V.; Song, H.; Squillacioti,
   P.; Stancari, M.; St. Denis, R.; Stelzer, B.; Stelzer-Chilton, O.;
   Stentz, D.; Strologas, J.; Strycker, G. L.; Sudo, Y.; Sukhanov, A.;
   Suslov, I.; Takemasa, K.; Takeuchi, Y.; Tang, J.; Tecchio, M.; Teng,
   P. K.; Thom, J.; Thome, J.; Thompson, G. A.; Thomson, E.; Toback,
   D.; Tokar, S.; Tollefson, K.; Tomura, T.; Tonelli, D.; Torre, S.;
   Torretta, D.; Totaro, P.; Trovato, M.; Ukegawa, F.; Uozumi, S.;
   Varganov, A.; Vázquez, F.; Velev, G.; Vellidis, C.; Vidal, M.; Vila,
   I.; Vilar, R.; Vizán, J.; Vogel, M.; Volpi, G.; Wagner, P.; Wagner,
   R. L.; Wakisaka, T.; Wallny, R.; Wang, S. M.; Warburton, A.; Waters,
   D.; Wester, W. C., III; Whiteson, D.; Wicklund, A. B.; Wicklund, E.;
   Wilbur, S.; Wick, F.; Williams, H. H.; Wilson, J. S.; Wilson, P.;
   Winer, B. L.; Wittich, P.; Wolbers, S.; Wolfe, H.; Wright, T.; Wu,
   X.; Wu, Z.; Yamamoto, K.; Yamato, D.; Yang, T.; Yang, U. K.; Yang,
   Y. C.; Yao, W. -M.; Yeh, G. P.; Yi, K.; Yoh, J.; Yorita, K.; Yoshida,
   T.; Yu, G. B.; Yu, I.; Yu, S. S.; Yun, J. C.; Zanetti, A.; Zeng, Y.;
   Zucchelli, S.
Bibcode: 2012PhRvD..85i2001A
Altcode: 2012arXiv1202.1260T
  This paper presents a search for anomalous production of multiple
  low-energy leptons in association with a W or Z boson using events
  collected at the CDF experiment corresponding to 5.1fb<SUP>-1</SUP>
  of integrated luminosity. This search is sensitive to a wide range
  of topologies with low-momentum leptons, including those with
  the leptons near one another. The observed rates of production of
  additional electrons and muons are compared with the standard model
  predictions. No indications of phenomena beyond the standard model are
  found. A 95% confidence level limit is presented on the production cross
  section for a benchmark model of supersymmetric hidden-valley Higgs
  production. Particle identification efficiencies are also provided to
  enable the calculation of limits on additional models.

Title: Advances in microchannel plates and photocathodes for
    ultraviolet photon counting detectors
Authors: Siegmund, O. H. W.; Fujiwara, K.; Hemphill, R.; Jelinsky,
   S. R.; McPhate, J. B.; Tremsin, A. S.; Vallerga, J. V.; Frisch, H. J.;
   Elam, J.; Mane, A.; Bennis, D. C.; Craven, C. A.; Deterando, M. A.;
   Escolas, J. R.; Minot, M. J.; Renaud, J. M.
Bibcode: 2011SPIE.8145E..0JS
Altcode: 2011SPIE.8145E.251S
  A new method of fabricating microchannel plates has been investigated,
  employing microcapillary arrays of borosilicate glass that are
  deposited with resistive and secondary emissive layers using atomic
  layer deposition. Microchannel plates of this kind have been made in
  sizes from 33 mm to 200 mm, with pore sizes of 40 μm and 20 μm, pore
  length to diameter ratios of 60:1, bias angles of 8°, and open areas
  from 60% to 83%. Tests with single MCPs and MCP pairs have been done
  and show good imaging quality, gain comparable to conventional MCPs, low
  background rates (~ 0.085 events sec<SUP>-1</SUP> cm<SUP>-2</SUP>), fast
  pulse response, and good ageing characteristics. The quantum efficiency
  for bare and alkali halide coated MCPs is similar to conventional MCPs,
  and we have also been able to deposit opaque GaN(Mg) cathodes directly
  onto these MCPs.

Title: Analysis of the Forward-scattering Hanle Effect in the Ca I
    4227 Å Line
Authors: Anusha, L. S.; Nagendra, K. N.; Bianda, M.; Stenflo, J. O.;
   Holzreuter, R.; Sampoorna, M.; Frisch, H.; Ramelli, R.; Smitha, H. N.
Bibcode: 2011ApJ...737...95A
Altcode:
  Coherent scattering of limb-darkened radiation is responsible for the
  generation of the linearly polarized spectrum of the Sun (the Second
  Solar Spectrum). This Second Solar Spectrum is usually observed near the
  limb of the Sun, where the polarization amplitudes are largest. At the
  center of the solar disk the linear polarization is zero for an axially
  symmetric atmosphere. Any mechanism that breaks the axial symmetry (like
  the presence of an oriented magnetic field, or resolved inhomogeneities
  in the atmosphere) can generate a non-zero linear polarization. In the
  present paper we study the linear polarization near the disk center
  in a weakly magnetized region, where the axisymmetry is broken. We
  present polarimetric (I, Q/I, U/I, and V/I) observations of the Ca
  I 4227 Å line recorded around μ = cos θ = 0.9 (where θ is the
  heliocentric angle) and a modeling of these observations. The high
  sensitivity of the instrument (ZIMPOL-3) makes it possible to measure
  the weak polarimetric signals with great accuracy. The modeling of
  these high-quality observations requires the solution of the polarized
  radiative transfer equation in the presence of a magnetic field. For
  this we use standard one-dimensional model atmospheres. We show that the
  linear polarization is mainly produced by the Hanle effect (rather than
  by the transverse Zeeman effect), while the circular polarization is due
  to the longitudinal Zeeman effect. A unique determination of the full
  \bm {B} vector may be achieved when both effects are accounted for. The
  field strengths required for the simultaneous fitting of Q/I, U/I, and
  V/I are in the range 10-50 G. The shapes and signs of the Q/I and U/I
  profiles are highly sensitive to the orientation of the magnetic field.

Title: Observations of the forward scattering Hanle effect in the
    Ca I 4227 Å line
Authors: Bianda, M.; Ramelli, R.; Anusha, L. S.; Stenflo, J. O.;
   Nagendra, K. N.; Holzreuter, R.; Sampoorna, M.; Frisch, H.; Smitha,
   H. N.
Bibcode: 2011A&A...530L..13B
Altcode: 2011arXiv1105.2157B
  Chromospheric magnetic fields are notoriously difficult to measure. The
  chromospheric lines are broad, while the fields are producing
  a minuscule Zeeman-effect polarization. A promising diagnostic
  alternative is provided by the forward-scattering Hanle effect, which
  can be recorded in chromospheric lines such as the He i 10 830 Å
  and the Ca i 4227 Å lines. We present a set of spectropolarimetric
  observations of the full Stokes vector obtained near the center of the
  solar disk in the Ca i 4227 Å line with the ZIMPOL polarimeter at the
  IRSOL observatory. We detect a number of interesting forward-scattering
  Hanle effect signatures, which we model successfully using polarized
  radiative transfer. Here we focus on the observational aspects, while
  a separate companion paper deals with the theoretical modeling.

Title: Linear Polarization of the Solar Ca I 4227 Å Line: Modeling
    with Radiative Transfer and Last Scattering Approximation
Authors: Anusha, L. S.; Stenflo, J. O.; Frisch, H.; Bianda, M.;
   Holzreuter, R.; Nagendra, K. N.; Sampoorna, M.; Ramelli, R.
Bibcode: 2011ASPC..437...57A
Altcode:
  To model the Ca I 4227 Å line polarization, radiative transfer
  effects with partial frequency redistribution (PRD) must be taken into
  account. The numerical solution of the relevant polarized radiative
  transfer (RT) equations is computationally very demanding. The
  “last scattering approximation” (LSA) is a concept allowing
  faster methods to be devised. It is based on the remark that a single
  scattering of the radiation field is sufficient for creating most
  of the polarization. Its key ingredient is the anisotropy of the
  radiation field. If the anisotropy is extracted from the observed
  center to limb variation of the intensity profile, only the wings
  of the Q/I spectrum can be modeled (Sampoorna et al. 2009). We show
  here that the core region may be modeled as well if one takes into
  account the depth variation of the anisotropy which is obtained from
  an unpolarized multilevel RT (Anusha et al. 2010). After a validation
  of the LSA approach by comparison with a polarized RT calculation, we
  apply both approaches to model recent observations of the Ca I 4227 Å
  line polarization taken on the quiet Sun. Apart from a global scaling
  factor, both approaches give a very good fit to the Q/I spectrum for
  all the wavelengths. As the LSA is 8 times faster than the RT approach,
  we can recommend it as an efficient method to analyze other strong
  resonance lines in the second solar spectrum.

Title: Observations of the Solar Ca I 4227 Å Line
Authors: Bianda, M.; Ramelli, R.; Stenflo, J. O.; Anusha, L. S.;
   Nagendra, K. N.; Sampoorna, M.; Holzreuter, R.; Frisch, H.
Bibcode: 2011ASPC..437...67B
Altcode:
  Our aim is to understand some interesting polarization features
  observed in the solar Ca I 4277 Å line. Here we only discuss the
  observational aspects. Observations have also been made in other
  chromospheric lines within a few hours of those in the Ca I 4227 Å
  line, in the same region near the north solar limb, to illustrate the
  potential of simultaneous observations in different lines.

Title: Spectral line polarization with angle-dependent partial
    frequency redistribution. II. Accelerated lambda iteration and
    scattering expansion methods for the Rayleigh scattering
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.
Bibcode: 2011A&A...527A..89S
Altcode:
  Context. The linear polarization of strong resonance lines observed in
  the solar spectrum is created by the scattering of the photospheric
  radiation field. This polarization is sensitive to the form of
  the partial frequency redistribution (PRD) function used in the
  line radiative transfer equation. Observations have been analyzed
  until now with angle-averaged PRD functions. With an increase in
  the polarimetric sensitivity and resolving power of the present-day
  telescopes, it will become possible to detect finer effects caused
  by the angle dependence of the PRD functions. <BR /> Aims: We devise
  new efficient numerical methods to solve the polarized line transfer
  equation with angle-dependent PRD, in plane-parallel cylindrically
  symmetrical media. We try to bring out the essential differences
  between the polarized spectra formed under angle-averaged and the
  more realistic case of angle-dependent PRD functions. <BR /> Methods:
  We use a recently developed Stokes vector decomposition technique to
  formulate three different iterative methods tailored for angle-dependent
  PRD functions. Two of them are of the accelerated lambda iteration
  type, one is based on the core-wing approach, and the other one on
  the frequency by frequency approach suitably generalized to handle
  angle-dependent PRD. The third one is based on a series expansion in
  the mean number of scattering events (Neumann series expansion). <BR />
  Results: We show that all these methods work well on this difficult
  problem of polarized line formation with angle-dependent PRD. We
  present several benchmark solutions with isothermal atmospheres to
  show the performance of the three numerical methods and to analyze the
  role of the angle-dependent PRD effects. For weak lines, we find no
  significant effects when the angle-dependence of the PRD functions is
  taken into account. For strong lines, we find a significant decrease in
  the polarization, the largest effect occurring in the near wing maxima.

Title: Polymers in Constrained Ceramic Environments
Authors: Frisch, H. L.; Huang, L.
Bibcode: 2011emst.book.7684F
Altcode:
  There is a great deal of interest in the preparation and
  characterization of organic-inorganic nanocomposites, particularly in
  those materials in which an organic phase is ceramic constrained in
  such a way as to produce novel structures, frequently at the molecular
  level. Such ceramic-constrained environments include zeolites, clay
  galleries, and mesoporous silica. In some cases, a polymer is directly
  introduced into a constraining structure (clay galleries), while in
  others a constrained monomer is polymerized subsequently, for example
  in pores, to obtain the final composite material. This review focuses
  on some specific aspects of the morphology of organic-inorganic
  nanocomposites and how the confinement affects the properties of
  the polymer.

Title: Spectral line polarization with angle-dependent partial
    frequency redistribution. I. A Stokes parameters decomposition for
    Rayleigh scattering
Authors: Frisch, H.
Bibcode: 2010A&A...522A..41F
Altcode:
  Context. The linear polarization of a strong resonance lines observed
  near the solar limb is created by a multiple-scattering process. Partial
  frequency redistribution (PRD) effects must be accounted for to explain
  the polarization profiles. The redistribution matrix describing the
  scattering process is a sum of terms, each containing a PRD function
  multiplied by a Rayleigh type phase matrix. A standard approximation
  made in calculating the polarization is to average the PRD functions
  over all the scattering angles, because the numerical work needed to
  take the angle-dependence of the PRD functions into account is large and
  not always needed for reasonable evaluations of the polarization. <BR />
  Aims: This paper describes a Stokes parameters decomposition method,
  that is applicable in plane-parallel cylindrically symmetrical media,
  which aims at simplifying the numerical work needed to overcome
  the angle-average approximation. <BR /> Methods: The decomposition
  method relies on an azimuthal Fourier expansion of the PRD functions
  associated to a decomposition of the phase matrices in terms of the
  Landi Degl'Innocenti irreducible spherical tensors for polarimetry
  T^K_Q(i, Ω) (i Stokes parameter index, Ω ray direction). The terms
  that depend on the azimuth of the scattering angle are retained in the
  phase matrices. <BR /> Results: It is shown that the Stokes parameters
  I and Q, which have the same cylindrical symmetry as the medium, can be
  expressed in terms of four cylindrically symmetrical components I_Q^K (K
  = Q = 0, K = 2, Q = 0, 1, 2). The components with Q = 1, 2 are created
  by the angular dependence of the PRD functions. They go to zero at
  disk center, ensuring that Stokes Q also goes to zero. Each component
  I_Q^K is a solution to a standard radiative transfer equation. The
  source term S_Q^K are significantly simpler than the source terms
  corresponding to I and Q. They satisfy a set of integral equations
  that can be solved by an accelerated lambda iteration (ALI) method.

Title: Generalization of the Last Scattering Approximation for the
Second Solar Spectrum Modeling: The Ca I 4227 Å Line as a Case Study
Authors: Anusha, L. S.; Nagendra, K. N.; Stenflo, J. O.; Bianda, M.;
   Sampoorna, M.; Frisch, H.; Holzreuter, R.; Ramelli, R.
Bibcode: 2010ApJ...718..988A
Altcode:
  To model the second solar spectrum (the linearly polarized spectrum
  of the Sun that is due to coherent scattering processes), one needs
  to solve the polarized radiative transfer (RT) equation. For strong
  resonance lines, partial frequency redistribution (PRD) effects must be
  accounted for, which make the problem computationally demanding. The
  "last scattering approximation" (LSA) is a concept that has been
  introduced to make this highly complex problem more tractable. An
  earlier application of a simple LSA version could successfully model
  the wings of the strong Ca I 4227 Å resonance line in Stokes Q/I
  (fractional linear polarization), but completely failed to reproduce
  the observed Q/I peak in the line core. Since the magnetic field
  signatures from the Hanle effect only occur in the line core, we need
  to generalize the existing LSA approach if it is to be useful for the
  diagnostics of chromospheric and turbulent magnetic fields. In this
  paper, we explore three different approximation levels for LSA and
  compare each of them with the benchmark represented by the solution of
  the full polarized RT, including PRD effects. The simplest approximation
  level is LSA-1, which uses the observed center-to-limb variation of
  the intensity profile to obtain the anisotropy of the radiation field
  at the surface, without solving any transfer equation. In contrast,
  the next two approximation levels use the solution of the unpolarized
  transfer equation to derive the anisotropy of the incident radiation
  field and use it as an input. In the case of LSA-2, the anisotropy
  at level τ<SUB>λ</SUB> = μ, the atmospheric level from which an
  observed photon is most likely to originate, is used. LSA-3, on the
  other hand, makes use of the full depth dependence of the radiation
  anisotropy. The Q/I formula for LSA-3 is obtained by keeping the
  first term in a series expansion of the Q-source function in powers
  of the mean number of scattering events. Computationally, LSA-1 is 21
  times faster than LSA-2, which is 5 times faster than the more general
  LSA-3, which itself is 8 times faster than the polarized RT approach. A
  comparison of the calculated Q/I spectra with the RT benchmark shows
  excellent agreement for LSA-3, including good modeling of the Q/I
  core region with its PRD effects. In contrast, both LSA-1 and LSA-2
  fail to model the core region. The RT and LSA-3 approaches are then
  applied to model the recently observed Q/I profile of the Ca I 4227
  Å line in quiet regions of the Sun. Apart from a global scale factor
  both give a very good fit to the Q/I spectra for all the wavelengths,
  including the core peak and blend line depolarizations. We conclude
  that LSA-3 is an excellent substitute for the full polarized RT and
  can be used to interpret the second solar spectrum, including the
  Hanle effect with PRD. It also allows the techniques developed for
  unpolarized three-dimensional RT to be applied to the modeling of the
  second solar spectrum.

Title: The Hanle Effect as Diagnostic Tool for Turbulent Magnetic
    Fields
Authors: Anusha, L. S.; Sampoorna, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 2010ASSP...19..390A
Altcode: 2010mcia.conf..390A
  The Hanle effect is calculated for a random magnetic field characterized
  by a finite correlation length and a probability density function
  of the magnetic field vector. It is shown that linear polarization
  is essentially independent of the magnetic field correlation length,
  but strongly depends on the distribution of the field strength.

Title: The quiet Sun magnetic field observed with ZIMPOL on
    THEMIS. I. The probability density function
Authors: Bommier, V.; Martínez González, M.; Bianda, M.; Frisch,
   H.; Asensio Ramos, A.; Gelly, B.; Landi Degl'Innocenti, E.
Bibcode: 2009A&A...506.1415B
Altcode:
  Context: The quiet Sun magnetic field probability density function (PDF)
  remains poorly known. Modeling this field also introduces a magnetic
  filling factor that is also poorly known. With these two quantities,
  PDF and filling factor, the statistical description of the quiet Sun
  magnetic field is complex and needs to be clarified. <BR />Aims:
  In the present paper, we propose a procedure that combines direct
  determinations and inversion results to derive the magnetic field
  vector and filling factor, and their PDFs. <BR />Methods: We used
  spectro-polarimetric observations taken with the ZIMPOL polarimeter
  mounted on the THEMIS telescope. The target was a quiet region at disk
  center. We analyzed the data by means of the UNNOFIT inversion code,
  with which we inferred the distribution of the mean magnetic field α
  B, α being the magnetic filling factor. The distribution of α was
  derived by an independent method, directly from the spectro-polarimetric
  data. The magnetic field PDF p(B) could then be inferred. By introducing
  a joint PDF for the filling factor and the magnetic field strength, we
  have clarified the definition of the PDF of the quiet Sun magnetic field
  when the latter is assumed not to be volume-filling. <BR />Results: The
  most frequent local average magnetic field strength is found to be 13
  G. We find that the magnetic filling factor is related to the magnetic
  field strength by the simple law α = B_1/B with B<SUB>1</SUB> = 15
  G. This result is compatible with the Hanle weak-field determinations,
  as well as with the stronger field determinations from the Zeeman effect
  (kGauss field filling 1-2% of space). From linear fits, we obtain the
  analytical dependence of the magnetic field PDF. Our analysis has also
  revealed that the magnetic field in the quiet Sun is isotropically
  distributed in direction. <BR />Conclusions: We conclude that the
  quiet Sun is a complex medium where magnetic fields having different
  field strengths and filling factors coexist. Further observations
  with a better polarimetric accuracy are, however, needed to confirm
  the results obtained in the present work. <P />Based on observations
  made with the French-Italian telescope THEMIS operated by the CNRS
  and CNR on the island of Tenerife in the Spanish Observatorio del
  Teide of the Instituto de Astrofísica de Canarias. Present address:
  Instituto de Astrofísica de Canarias, vía Láctea s/n, 38205 La
  Laguna, Tenerife, Spain.

Title: The Hanle effect in a random magnetic field. Dependence of
    the polarization on statistical properties of the magnetic field
Authors: Frisch, H.; Anusha, L. S.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2009A&A...501..335F
Altcode:
  Context: The Hanle effect is used to determine weak turbulent magnetic
  fields in the solar atmosphere, usually assuming that the angular
  distribution is isotropic, the magnetic field strength constant, and
  that micro-turbulence holds, i.e. that the magnetic field correlation
  length is much less than a photon mean free path. <BR />Aims: To
  examine the sensitivity of turbulent magnetic field measurements
  to these assumptions, we study the dependence of Hanle effect on
  the magnetic field correlation length, its angular, and strength
  distributions. <BR />Methods: We introduce a fairly general random
  magnetic field model characterized by a correlation length and a
  magnetic field vector distribution. Micro-turbulence is recovered
  when the correlation length goes to zero and macro-turbulence when it
  goes to infinity. Radiative transfer equations are established for
  the calculation of the mean Stokes parameters and they are solved
  numerically by a polarized approximate lambda iteration method. <BR
  />Results: We show that optically thin spectral lines and optically
  very thick ones are insensitive to the correlation length of the
  magnetic field, while spectral lines with intermediate optical depths
  (around 10-100) show some sensitivity to this parameter. The result is
  interpreted in terms of the mean number of scattering events needed to
  create the surface polarization. It is shown that the single-scattering
  approximation holds good for thin and thick lines but may fail for lines
  with intermediate thickness. The dependence of the polarization on the
  magnetic field vector probability density function (PDF) is examined
  in the micro-turbulent limit. A few PDFs with different angular and
  strength distributions, but equal mean value of the magnetic field,
  are considered. It is found that the polarization is in general quite
  sensitive to the shape of the magnetic field strength PDF and somewhat
  to the angular distribution. <BR />Conclusions: The mean field derived
  from Hanle effect analysis of polarimetric data strongly depends on
  the choice of the field strength distribution used in the analysis. It
  is shown that micro-turbulence is in general a safe approximation.

Title: The Hanle Effect. Angle-dependent Frequency Redistribution
    Function. Decomposition of the Stokes Parameters in Irreducible
    Components.
Authors: Frisch, H.
Bibcode: 2009ASPC..405...87F
Altcode:
  We show that the spherical tensor decomposition of the Stokes
  parameters developed for angle-averaged frequency redistribution
  functions can be extended to angle-dependent frequency redistribution
  functions. The irreducible components of the Stokes parameters loose
  their cylindrical symmetry but one can still write an integral equation
  for the irreducible components of the source vector. Numerical solution
  of this equation may be simplified by the introduction of an azimuthal
  Fourier expansion of the frequency redistribution function.

Title: The CDF level 2 calorimetric trigger upgrade
Authors: Bhatti, A.; Canepa, A.; Casarsa, M.; Convery, M.; Cortiana,
   G.; Dell'Orso, M.; Donati, S.; Flanagan, G.; Frisch, H.; Fukun, T.;
   Krop, D.; Giannetti, P.; Greco, V.; Jones, M.; Liu, T.; Lucchesi, D.;
   Pagan-Griso, S.; Pantano, D.; Pianori, E.; Piendibene, M.; Pilcher,
   C.; Ristori, L.; Rogondino, L.; Rusu, V.; Sartori, L.; Schmidt, M.;
   Veszpremi, V.; Vidal, M.; Zhou, L.
Bibcode: 2009NIMPA.598..331B
Altcode:
  CDF II upgraded the calorimeter trigger to cope with the higher detector
  occupancy due to the increased Tevatron instantaneous luminosity
  (∼2.8×10<SUP></SUP>cm<SUP></SUP>s<SUP></SUP>). While the original
  system was implemented in custom hardware and provided to the L2 trigger
  a limited-quality jet clustering performed using a reduced resolution
  measurement of the transverse energy in the calorimeter trigger towers,
  the upgraded system provides offline-quality jet reconstruction of the
  full resolution calorimeter data. This allows to keep better under
  control the dependence of the trigger rates on the instantaneous
  luminosity and to improve the efficiency and purity of the trigger
  selections. The upgraded calorimeter trigger uses the general purpose
  VME board Pulsar, developed at CDF II and already widely used to
  upgrade the L2 tracking and L2 decision systems. A battery of Pulsars
  is used to merge and send the calorimeter data to the L2 CPUs, where
  software-implemented algorithms perform offline-like clustering. In this
  paper we review the design and the performance of the upgraded system.

Title: Zeeman line formation in solar magnetic fields. Studies with
    empirical probability distribution functions
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.; Stenflo, J. O.
Bibcode: 2008A&A...485..275S
Altcode:
  Context: Numerical simulations of magneto-convection and analysis
  of solar magnetograms provide probability distribution functions
  (PDFs) for the magnetic field strength. <BR />Aims: In the paper,
  we explore the effects of these PDFs on Zeeman line formation. <BR
  />Methods: We calculate the mean Stokes parameters for a Milne-Eddington
  atmosphere in the limit of optically thin (micro-turbulent) and thick
  (macro-turbulent) magnetic structures and also the dispersion around
  the mean profiles in the optically thick limit. Several types of PDFs
  are considered: (a) Voigt function and stretched exponential type
  PDFs for fields with fixed direction but fluctuating strength; (b)
  a cylindrically symmetrical power law for the angular distribution of
  magnetic fields with given field strength; (c) composite PDFs accounting
  for randomness in both strength and direction obtained by combining a
  Voigt function or a stretched exponential with an angular power law. For
  optically thin structures, explicit expressions are given for the mean
  values of the Zeeman absorption matrix elements. We also describe how
  the averaging technique for a normal Zeeman triplet may be generalized
  to the more common case of anomalous Zeeman splitting patterns. <BR
  />Results: We show that, for magnetic field rms fluctuations of
  the order of 6 G, consistent with observational data, Stokes I is
  essentially independent of the shapes of the PDFs but Stokes Q, U, and
  V and also the dispersion around the mean values are quite sensitive
  to the tail behavior of the PDF. We confirm a previous result that
  Stokes V is less sensitive to the scale of the magnetic structures
  than Stokes Q and U. The composite PDF proposed for the fluctuations of
  the magnetic field vector has an angular distribution peaked about the
  vertical direction for strong fields, and is isotropically distributed
  for weak fields; it can be used to mimic solar surface random fields.

Title: Some aspects of polarized line formation in magneto-turbulent
    media
Authors: Sampoorna, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 2008NewA...13..233S
Altcode:
  Observations and numerical simulations of magneto-convection show a
  highly variable solar magnetic field. Using a statistical approach,
  we analyze the effects of random magnetic fields on Stokes profiles of
  spectral lines. We consider the micro and macro-turbulent regimes,
  which provide bounds for more general random fields with finite
  scales of variations. The mean Stokes parameters are obtained in the
  micro-turbulent regime, by first averaging the Zeeman propagation
  matrix Φ^ over the probability distribution function P( B) of the
  magnetic field and then solving the concerned radiative transfer
  equation. In the macro-turbulent regime, the mean solution is obtained
  by averaging the emergent solution over P( B). It is assumed that B has
  a Gaussian distribution defined by its mean field B<SUB>0</SUB>, angular
  distribution and dispersion. Fluctuations parallel and perpendicular
  to B<SUB>0</SUB> are considered. Spectral lines are parameterized by
  their strength β, which is varied over the range 1-10 <SUP>4</SUP>. A
  detailed comparison of micro and macro-turbulent limit with mean field
  solution shows that differences are important for β ⩾ 10. When β
  increases, the saturation behavior of micro-turbulent profiles are
  significantly different from that of mean field profiles. The Stokes
  profiles shapes are explained in terms of the non-linear β-dependence
  of the Unno-Rachkovsky solution using approximate expressions for the
  mean absorption coefficients. These expressions when inserted in the
  Unno-Rachkovsky solution can predict Stokes profiles that match with
  the numerical result to a good approximation.

Title: The Hanle effect. Decomposition of the Stokes parameters into
    irreducible components
Authors: Frisch, H.
Bibcode: 2007A&A...476..665F
Altcode:
  Context: It has been shown for the weak-field Hanle effect that the
  Stokes parameters I, Q, and U can be represented by a set of six
  cylindrically symmetrical functions. The proof relies on azimuthal
  Fourier expansions of the radiation field and of the Hanle phase
  matrix. It holds for a plane-parallel atmosphere and scattering
  processes that can be described by a redistribution matrix where
  redistribution in frequency is decoupled from angle redistribution and
  polarization. <BR />Aims: We give a simpler and more general proof of
  the Stokes parameter decomposition using powerful new tools introduced
  for polarimetry, in particular the Landi Degl'Innocenti spherical
  tensors T^K_Q(i,Ω). <BR />Methods: The elements of the Hanle phase
  matrix are written as a sum of terms that depend separately on the
  magnetic field vector and the directions Ω and Ω' of the incoming and
  scattered beams. The dependence on Ω and Ω' is expressed in terms
  of the spherical tensors T^K_Q(i,Ω) where i refers to the Stokes
  parameters (i=0,ldots,3). A multipolar expansion in terms of the
  T^K_Q(i,Ω) is then established for the source term in the transfer
  equation for the Stokes parameters. <BR />Results: We show that the
  Stokes parameters have a multipolar expansion that can be written
  as I_i(ν,Ω)= sum<SUB>KQ</SUB>T^K_Q(i,Ω)I_Q^K(ν,θ) (K=0,1,2,
  -K≤ Q≤ +K) where the I_Q<SUP>K</SUP> are nine cylindrically
  symmetrical, irreducible tensors, θ being the inclination of Ω with
  respect to the vertical in the atmosphere. The proof is generalized
  to frequency-dependent phase matrices. It is applied both to partial
  frequency redistribution with angle-averaged scalar frequency
  redistribution functions and to complete frequency redistribution
  with the Hanle effect in the line core and Rayleigh scattering in the
  wings. Non-LTE transfer equations for the I_Q<SUP>K</SUP> and integral
  equations for the associated source functions S_Q<SUP>K</SUP> are
  established. Formal vectors and matrices constructed with I_Q^K, S_Q^K,
  and T_Q<SUP>K</SUP> are introduced in order to present the results in
  a compact matrix notation. In particular, a simple factorized form is
  proposed for the Hanle phase matrix.

Title: Turbulent magnetic field averages for the Zeeman effect .
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2007MmSAI..78..142F
Altcode:
  Stokes parameters measured in the Solar atmosphere are in general
  time or space averages over a magnetic field probability distribution
  function. Here we show how to write the Zeeman propagation matrix in a
  reference frame defined with respect to the direction of a mean magnetic
  field and how to average over a random magnetic field distribution. We
  concentrate on the case of a normal Zeeman triplet but indicate how
  to treat general Zeeman patterns. Numerical results are presented
  for Gaussian distributions having cylindrical symmetry about a mean
  field. Different models of probability distribution functions (PDF),
  are compared.

Title: Polarized Spectral Line Formation in Turbulent Magnetic Fields:
    The Zeeman and Hanle Effects
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2006ASPC..358..126F
Altcode:
  We present a short summary of work carried out on the effects of
  random magnetic fields with finite correlation length on spectral line
  polarization. The magnetic field is modeled by a step-wise Markovian
  random process defined by a probability distribution and a correlation
  length. Micro- and macro-turbulent limits are recovered when this
  length goes to zero and infinity, respectively. For the Zeeman effect,
  explicit expressions have been obtained for the mean emergent Stokes
  parameters and for their r.m.s. fluctuations. Examples illustrate the
  dependence of the mean Zeeman propagation matrix on the magnetic field
  distribution, and the dependence of mean Stokes parameters and their
  r.m.s. fluctuations on the correlation length of the magnetic field. For
  the Hanle effect, explicit expressions have also been obtained for the
  mean Stokes parameters. We outline the approach and give an explicit
  expression for the mean value of Stokes Q.

Title: Stochastic polarized line formation. II. Zeeman line transfer
    in a random magnetic field
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2006A&A...453.1095F
Altcode:
  Context: .The Zeeman effect produced by a turbulent magnetic field
  or a random distribution of flux tubes is usually treated in the
  microturbulent or macroturbulent limits where the Zeeman propagation
  matrix or the Stokes parameters, respectively, are averaged over
  the probability distribution function of the magnetic field when
  computing polarized line profiles.<BR /> Aims: .To overcome these
  simplifying assumptions we consider the Zeeman effect from a random
  magnetic field which has a finite correlation length that can be
  varied from zero to infinity and thus made comparable to the photon
  mean free-path.<BR /> Methods: .The vector magnetic field is modeled
  by a Kubo-Anderson process, a piecewise constant Markov process
  characterized by a correlation length and a probability distribution
  function for the random values of the magnetic field. The micro and
  macro turbulent limits are recovered when the correlation goes to zero
  or infinity.<BR /> Results: .An integral equation is constructed for
  the mean propagation operator and explicit expressions are obtained
  for the mean values and second-order moments of the Stokes parameters
  at the surface of a Milne-Eddington type atmosphere. The expression
  given by Landi Degl'Innocenti (1994) for the mean Stokes parameters
  is recovered. Mean values and rms fluctuations around the mean values
  are calculated numerically for a random magnetic field with isotropic
  Gaussian fluctuations. The effects of a finite correlation length
  are discussed in detail. Various extensions of the Milne-Eddington
  and magnetic field model are considered and the corresponding
  integral equations for the mean propagation operator are given.<BR
  /> Conclusions: .The rms fluctuations of the Stokes parameters are
  shown to be very sensitive to the correlation length of the magnetic
  field. It is suggested to use them as a diagnostic tool to determine
  the scale of unresolved features in the solar atmosphere.

Title: The Hanle effect in a random medium
Authors: Frisch, H.
Bibcode: 2006A&A...446..403F
Altcode:
  This paper considers the Hanle effect produced by a turbulent magnetic
  field. To overcome the simplified microturbulent treatment whereby
  the Hanle phase matrix is locally averaged over some magnetic field
  distribution, we consider a turbulent magnetic field with a finite
  correlation length. We assume that the magnetic field along each
  individual photon path can be represented by a Kubo-Anderson process
  (KAP) and study the stationary solution as time goes to infinity. A
  KAP is a discontinuous Markov process. The random magnetic field is
  characterized by a correlation length and a distribution function
  of the magnetic field vector; both can be chosen arbitrarily. The
  microturbulent limit is recovered when the correlation length goes to
  zero. A non-stochastic integral equation of the Wiener-Hopf type is
  obtained for a mean conditional source vector. This integral equation
  yields explicit expressions for the mean Stokes parameters, provided
  one makes physically realistic approximations, namely neglect the
  effect of the magnetic field on Stokes I, keep only the contributions
  from I and Q in the source terms for Stokes Q and Stokes U and solve
  the integral equation for Q with a two-scattering approximation. The
  final expressions involve mean values and correlation functions of
  some of the elements of the Hanle phase matrix and show the dependence
  on the correlation length of the random magnetic field. The combined
  effects of a turbulent velocity field and a turbulent magnetic field
  with finite correlation lengths is also studied. The velocity field
  is represented by a KAP with the same correlation length as the
  magnetic field. Some of the velocity field effects are treated with
  an effective medium approximation as in Frisch &amp; Frisch (1976,
  MNRAS, 175, 157). Explicit expressions are obtained for the mean Stokes
  parameters. They can account for correlations between velocity field
  and magnetic field fluctuations.

Title: Stochastic polarized line formation. I. Zeeman propagation
    matrix in a random magnetic field
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
Bibcode: 2005A&A...442...11F
Altcode:
  This paper considers the effect of a random magnetic field on Zeeman
  line transfer, assuming that the scales of fluctuations of the random
  field are much smaller than photon mean free paths associated to
  the line formation (micro-turbulent limit). The mean absorption and
  anomalous dispersion coefficients are calculated for random fields with
  a given mean value, isotropic or anisotropic Gaussian distributions
  azimuthally invariant about the direction of the mean field. Following
  Domke &amp; Pavlov (1979, Ap&amp;SS, 66, 47), the averaging process
  is carried out in a reference frame defined by the direction of the
  mean field. The main steps are described in detail. They involve the
  writing of the Zeeman matrix in the polarization matrix representation
  of the radiation field and a rotation of the line of sight reference
  frame. Three types of fluctuations are considered : fluctuations along
  the direction of the mean field, fluctuations perpendicular to the
  mean field, and isotropic fluctuations. In each case, the averaging
  method is described in detail and fairly explicit expressions for the
  mean coefficients are established, most of which were given in Dolginov
  &amp; Pavlov (1972, Soviet Ast., 16, 450) or Domke &amp; Pavlov (1979,
  Ap&amp;SS, 66, 47). They include the effect of a microturbulent velocity
  field with zero mean and a Gaussian distribution. A detailed numerical
  investigation of the mean coefficients illustrates the two effects
  of magnetic field fluctuations: broadening of the σ-components by
  fluctuations of the magnetic field intensity, leaving the π-components
  unchanged, and averaging over the angular dependence of the π and σ
  components. For longitudinal fluctuations only the first effect is at
  play. For isotropic and perpendicular fluctuations, angular averaging
  can modify the frequency profiles of the mean coefficients quite
  drastically with the appearance of an unpolarized central component
  in the diagonal absorption coefficient, even when the mean field is in
  direction of the line of sight. A detailed comparison of the effects of
  the three types of fluctuation coefficients is performed. In general
  the magnetic field fluctuations induce a broadening of the absorption
  and anomalous dispersion coefficients together with a decrease of their
  values. Two different regimes can be distinguished depending on whether
  the broadening is larger or smaller than the Zeeman shift by the mean
  magnetic field. For isotropic fluctuations, the mean coefficients can
  be expressed in terms of generalized Voigt and Faraday-Voigt functions
  H<SUP>(n)</SUP> and F<SUP>(n)</SUP> introduced by Dolginov &amp;
  Pavlov (1972, Soviet Ast., 16, 450). These functions are related to
  the derivatives of the Voigt and Faraday-Voigt functions. A recursion
  relation is given in an Appendix for their calculation. A detailed
  analysis is carried out of the dependence of the mean coefficients
  on the intensity and direction of the mean magnetic field, on its
  root mean square fluctuations and on the Landé factor and damping
  parameter of the line.

Title: An operator perturbation method for polarized line
    transfer. VI. Generalized PALI method for Hanle effect with partial
    frequency redistribution and collisions
Authors: Fluri, D. M.; Nagendra, K. N.; Frisch, H.
Bibcode: 2003A&A...400..303F
Altcode:
  A generalized iteration method is presented to solve the polarized line
  transfer equation for a two-level-atom in an arbitrarily oriented,
  weak magnetic field. The polarized redistribution matrix employed
  accounts self-consistently for collisions as well as the presence of
  a weak magnetic field responsible for the Hanle effect. The proposed
  numerical method of solution is based on a Polarized Approximate Lambda
  Iteration (PALI) method. A Fourier decomposition of the radiation field
  and of the phase matrix with respect to the azimuthal angle reduces
  the complexity of the problem. A generalized core-wing technique is
  proposed, which permits an efficient implementation of the frequency
  domain structure inherent in the polarized redistribution matrix. The
  numerical method is tested for its accuracy and efficiency by comparing
  with the existing methods.

Title: Numerical Methods for Solving the Polarized Line Transfer
    Equations with Partial Frequency Redistribution
Authors: Nagendra, K. N.; Frisch, H.; Fluri, D. M.
Bibcode: 2003ASPC..307..227N
Altcode:
  No abstract at ADS

Title: Hanle effect with angle-dependent partial redistribution
Authors: Nagendra, K. N.; Frisch, H.; Faurobert, M.
Bibcode: 2002A&A...395..305N
Altcode:
  The polarized line transfer equation for the Hanle effect is solved in
  the framework of an exact partial frequency redistribution (PRD) theory
  developed by Bommier (1997a,b). In that theory the effect of collisions
  on the Hanle effect is considered self-consistently. We follow that
  approach in the line transfer computations presented here. The theory
  formulated by Bommier clearly recognizes two levels of approximations
  for exact PRD, in order to facilitate the solution of the line transfer
  equation. The second level employs angle-dependent redistribution
  functions, and numerically represents a more difficult problem compared
  to the third level, which involves only the use of angle-averaged
  frequency redistribution functions. We present a method which can
  solve the problem in both the levels of approximation. The method
  is based on a perturbative approach to line polarization. Although
  computationally expensive, it offers the only practical means of solving
  the angle-dependent Hanle PRD problem. We discuss the numerical aspects
  of assembling the so called ``frequency domain dependent redistribution
  matrices'', and also an efficient way of computing the scattering
  integral. Some examples are presented to illustrate the interesting
  aspects of the Hanle-PRD problem with angle-dependent frequency
  redistribution. A comparison of the emergent profiles computed under
  angle-averaged and angle-dependent redistribution is carried out, and
  the effect of collisions is investigated. We show that it is necessary
  to incorporate an angle-dependent redistribution mechanism especially
  in the computation of the Stokes U parameter. We demonstrate that the
  use of simple frequency domains is good enough in practical applications
  of the Hanle PRD theory.

Title: Investigation of weak solar magnetic fields. New observational
    results for the SrI 460.7 nm linear polarization and radiative
    transfer modeling
Authors: Faurobert, M.; Arnaud, J.; Vigneau, J.; Frisch, H.
Bibcode: 2001A&A...378..627F
Altcode:
  Scattering polarization measurements were obtained with THEMIS in July
  2000, close to the solar south Pole and to the east Equator and in
  a period of maximum solar activity. Using the THEMIS multi-lines
  spectro-polarimetric mode (MTR), we observed simultaneously
  four spectral domains containing the 460.7 nm Sr i line, several
  molecular lines around 515.9 nm and the Na i D<SUB>1</SUB> and Na i
  D<SUB>2</SUB> lines. This allows us to scan different altitudes in the
  solar atmosphere at the same time and provides us with a large set
  of constraints to study the behaviour of the magnetic field. This
  paper is devoted to the Sr i line which exhibits quite a strong
  linear polarization peak outside active regions. A detailed radiative
  transfer modeling is performed in order to interpret the observed
  center-to-limb variations of the line intensity and polarization. It
  was shown previously (Faurobert-Scholl \cite{Faurobert-Scholl1})
  that this line, which is sensitive to the Hanle effect, can be used
  as a diagnostic tool for the presence of weak turbulent magnetic
  fields in the solar photosphere outside active regions. The line
  polarization rates that we measured in July 2000 are 25% lower
  than what has been reported previously, for observations near the
  minimum, or in the increasing phase, of the activity cycle (Stenflo
  et al. \cite{Stenflo1}). They are in agreement with other observations
  performed with a different observational set-up in August 2000 (Bommier
  &amp; Molodij \cite{Bommier4}). We show that they are consistent with
  the presence of a weak turbulent magnetic field with an average strength
  between 20 G and 30 G in the upper solar photosphere. This is about
  twice the value which was derived from previous observations. This
  result raises the possiblity of a long-term variation of the turbulent
  photospheric magnetic field with the activity cycle.

Title: Scattering Polarization and Hanle Effect: On the Importance
    of Angle-Dependent Frequency Redistribution
Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 2001ASPC..248..145F
Altcode: 2001mfah.conf..145F
  No abstract at ADS

Title: The Hanle Effect with Angle Dependent Redistribution Functions
Authors: Frisch, H.; Faurobert, M.; Nagendra, K. N.
Bibcode: 2001ASPC..236..197F
Altcode: 2001aspt.conf..197F
  No abstract at ADS

Title: An Operator Perturbation Method of Polarized Line Transfer
    V. Diagnosis of Solar Weak Magnetic Fields
Authors: Nagendra, K. N.; Frisch, H.; Faurobeet-Scholl, M.; Paletou, F.
Bibcode: 2000JApA...21..255N
Altcode:
  No abstract at ADS

Title: Fast Numerical Methods for Polarized Line Radiative Transfer
    in the Presence of Hanle Effect
Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 1999ASPC..184...28F
Altcode:
  The Hanle effect provides a diagnostic tool for weak magnetic fields
  which do not give rise to a measurable Zeeman effect, such as turbulent
  fields or magnetic canopies. The lines which are sensitive to the
  Hanle effect are formed under non-LTE conditions, by scattering of
  photons. Inversion methods for such diagnostics require to solve the
  non-LTE polarized transfer equation for a large number of magnetic
  configurations. Fast numerical methods are thus highly required. We
  present an Approximate Lambda Iteration method to treat the Hanle effect
  for lines formed with complete frequency redistribution. Referred to
  as PALI-H, this method is an extension of ALI methods first developed
  for non polarized line transfer. The starting point is to recast the
  polarized transfer equation into a vectorial integral equation for a
  6-component source function. We show that the convergence of the method
  is independent of the strength and direction of the magnetic field. The
  method is very fast and allows to handle any type of depth-dependent
  magnetic field.

Title: An operator perturbation method for polarized line transfer IV:
    Applications to the Hanle effect with partial frequency redistribution
Authors: Nagendra, K. N.; Paletou, F.; Frisch, H.; Faurobert-Scholl, M.
Bibcode: 1999ASSL..243..127N
Altcode: 1999sopo.conf..127N
  No abstract at ADS

Title: Resonance polarization and Hanle effect: The integral equation
    formulation and some applications
Authors: Frisch, H.
Bibcode: 1999ASSL..243...97F
Altcode: 1999sopo.conf...97F
  No abstract at ADS

Title: The Hanle effect. The density matrix and scattering approaches
    to the protect sqrt epsilon -law
Authors: Frisch, H.
Bibcode: 1998A&A...338..683F
Altcode:
  A sqrt epsilon -law was demonstrated by Landi Degl'Innocenti &amp;
  Bommier (1994) for resonance polarization in a magnetic atmosphere
  where the primary source of photons is of thermal origin (isotropic and
  unpolarized). In this paper we propose a generalized form of this law by
  dropping the hypothesis on the primary source of photons. We restrict
  ourselves to the case of weak magnetic fields (Hanle effect). For
  spectral lines formed with complete redistribution, it has been shown
  by Landi Degl'Innocenti et al (1990), using the density matrix theory
  in its irreducible tensorial operator version, that the Hanle effect
  can be reduced to an integral equation of the convolution type for
  a six-component source vector. As shown by Faurobert-Scholl (1991),
  a similar equation can be obtained by performing an azimuthal Fourier
  decomposition of the transfer equation for the Stokes parameters. In the
  first part of the paper we recall the main steps of the two methods and
  establish the correspondence between the convolution equations that
  they provide. In the second part we use these equations to obtain
  a generalized sqrt epsilon -law. For the equation coming from the
  density matrix formalism, we essentially follow the original proof of
  Landi Degl'Innocenti &amp; Bommier (1994). For the equation coming from
  the Fourier decomposition, because of a lack of symmetry in operator
  describing the action of the magnetic field, we use as intermediate
  step the Hopf-Bronstein-Rybicki relation established by Ivanov (1995)
  for transport operators which are not self-adjoint.

Title: An operator perturbation method for polarized line
    transfer. III. Applications to the Hanle effect in 1D media
Authors: Nagendra, K. N.; Frisch, H.; Faurobert-Scholl, M.
Bibcode: 1998A&A...332..610N
Altcode:
  In this paper we present an Approximate Lambda Iteration method to
  treat the Hanle effect (resonance scattering in the presence of
  a weak magnetic field) for lines formed with complete frequency
  redistribution. The Hanle effect is maximum in the line core and
  goes to zero in the line wings. Referred to as PALI-H, this method is
  an extension to non-axisymmetric radiative transfer problems of the
  PALI method presented in Faurobert-Scholl et al. (1997), hereafter
  referred to as Paper I. It makes use of a Fourier decomposition of the
  radiation field with respect to the azimuthal angle which is somewhat
  more general than the decomposition introduced in Faurobert-Scholl
  (1991, hereafter referred to as FS91). The starting point of the
  method is a vector integral equation for a six-component source vector
  representing the non-axisymmetric polarized radiation field. As
  in Paper I, the Approximate Lambda operator is a block diagonal
  matrix. The convergence rate of the PALI-H method is independent
  of the polarization rate and hence of the strength and direction
  of the magnetic field. Also this method is more reliable than the
  perturbation method used in FS91. The PALI-H method can handle any
  type of depth-dependent magnetic field. Here it is used to examine
  the dependence of the six-component source vector on the co-latitude,
  azimuthal angle and strength of the magnetic field. The dependence of
  the surface polarization on the direction of the line-of-sight and on
  the magnetic field is illustrated with polarization diagrams showing
  Q/I versus U/I at line center. The analysis of the results show that
  the full six-dimension problem can be approximated by a two-component
  modified resonance polarization problem, producing errors of at most
  20% on the surface polarization at line center.

Title: An operator perturbation method for polarized line
    transfer. I. Non-magnetic regime in 1D media.
Authors: Faurobert-Scholl, M.; Frisch, H.; Nagendra, K. N.
Bibcode: 1997A&A...322..896F
Altcode:
  In this paper we generalize an Approximate Lambda Iteration (ALI)
  technique developed for scalar transfer problems to a vectorial transfer
  problem for polarized radiation. Scalar ALI techniques are based on a
  suitable decomposition of the Lambda operator governing the integral
  form of the transfer equation. Lambda operators for scalar transfer
  equations are diagonally dominant, offering thus the possibility to
  use iterative methods of the Jacobi type where the iteration process
  is based on the diagonal of the Lambda operator (Olson et al., 1986,
  JQSRT 35, 431). Here we consider resonance polarization, created by
  the scattering of an anisotropic radiation field, for spectral lines
  formed with complete frequency redistribution in a 1D axisymmetric
  medium. The problem can be formulated as an integral equation for a
  2-component vector (Rees, 1978PASJ...30..455R) or, as shown by Ivanov
  (1995A&amp;A...303..621I), as an integral equation for a (2x2) matrix
  source function which involves the same generalized Lambda operator as
  the vector integral equation. We find that this equation holds also in
  the presence of a weak turbulent magnetic field. The generalized Lambda
  operator is a (2x2) matrix operator. The element {11} describes the
  propagation of the intensity and is identical to the Lambda operator of
  non-polarized problems. The element {22} describes the propagation of
  the polarization. The off-diagonal terms weakly couple the intensity and
  the polarization. We propose a block Jacobi iterative method and show
  that its convergence properties are controlled by the propagator for
  the intensity. We also show that convergence can be accelerated by an
  Ng acceleration method applied to each element of the source matrix. We
  extend to polarized transfer a convergence criterion introduced by
  Auer et al. (1994A&amp;A...292..599A) based on the grid truncation
  error of the converged solution.

Title: Transfert de rayonnement hors-ETL et applications en physique
    solaire.
Authors: Faurobert-Scholl, M.; Paletou, F.; Frisch, H.
Bibcode: 1996JAF....53...24F
Altcode:
  No abstract at ADS

Title: Partial Frequency Redistribution of Polarized Radiation
Authors: Frisch, H.
Bibcode: 1996SoPh..164...49F
Altcode:
  Resonance polarization, which is created by the scattering of an
  anisotropic radiation field in regions of zero or weak magnetic
  fields, is strongly dependent on the frequency redistribution
  taking place during the scatterings. Here we discuss the frequency
  redistribution matrix relevant to resonance lines, concentrating on
  linear polarization. First we analyze in detail the redistribution
  matrix in a zero magnetic field given by the theory of Omont, Smith
  and Cooper (1972), revisited by Domke and Hubeny (1988). We explain
  that the linear polarization maxima which may appear in the wings
  of the Stokes Q profiles of strong resonances lines such as the Ca I
  4227 Å line are coherent frequency redistribution effects. Various
  approximate forms of the frequency redistribution matrix are also
  examined. For resonance polarization in a weak magnetic field, we
  suggest a new expression for the redistribution matrix which can be
  used at all line frequencies, and is consistent with the condition
  that the Hanle effect acts only in the line core.

Title: CDF Results on the W Mass and the Search for the Top
Authors: Frisch, H. J.
Bibcode: 1995psc..conf...81F
Altcode:
  No abstract at ADS

Title: Monte-Carlo simulation of a radiative transfer problem in a
random medium: application to a binary mixture.
Authors: Audic, S.; Frisch, H.
Bibcode: 1993JQSRT..50..127A
Altcode:
  This paper considers monochromatic radiative transfer in a diffusive
  three dimensional random binary mixture. The absorption coefficient,
  along any line-of-sight is a homogeneous Markoy process, which is
  described by a three-dimensional Kubo-Anderson process. The transfer
  equation is solved numerically by Monte-Carlo simulations on a massively
  parallel computer (a Connection Machine) by attaching one or several
  photons to each processor. The implementation of the simulations on
  the machine is discussed in detail, in particular the association
  between photons and processors and the storage of the data concerning
  the photons and the realizations of the statistics.

Title: Quelques problèmes de transfert en physique solaire.
Authors: Frisch, H.; Faurobert-Scholl, M.
Bibcode: 1991sed..conf..151F
Altcode:
  (1) Introduction. (2) Formation ETL des raies: (2.1) Intensité
  du rayonnement et équation de transfert. (2.2) Approximation
  de diffusion. (2.3) Equation de transfert ETL pour les raies. (3)
  Formation non-ETL des raies: (3.1) Fonction source d'un atome à deux
  niveaux. (3.2) Fonction de redistribution. (3.3) Equation de transfert
  non-ETL. (3.4) Analyse asymptotique. (3.5) Transfert non-ETL dans
  une couche plane. (3.6) Probabilité d'échappement. (3.7) Méthodes
  numériques en transfert non-ETL. (3.8) Construction de modèles
  d'atmosphères. (4) Transfert de rayonnement polarisé. (4.1)
  Les paramètres de Stokes. (4.2) Mécanismes de polarisation des
  raies spectrales. (4.3) Equation de transfert d'un rayonnement
  polarisé. (4.4) Effet Hanle. (4.5) Effet Zeeman.

Title: An exact analytical solution of a radiative transfer problem
    in a binary mixture.
Authors: Frisch, H.; Pomraning, G. C.; Zweifel, P. F.
Bibcode: 1990JQSRT..43..271F
Altcode:
  The authors give an exact analytical solution of a statistical
  radiative transfer problem. This problem consists of time-independent,
  non-scattering transport in a binary statistical mixture. The mixing
  statistics are taken as homogeneous. The chord-length distribution
  of each constituent is assumed to be representable as a Laplace
  transform. Markov statistics are a special (degenerate) case of
  the class of statistics the authors are able to treat. Two different
  techniques, a singular eigenfunction analysis and an integral equation
  method, are applied to the problem.

Title: Asymptotic analysis of resonance polarization and escape
    probability approximations
Authors: Faurobert-Scholl, M.; Frisch, H.
Bibcode: 1989A&A...219..338F
Altcode:
  Polarized transfer asymptotic and first order escape probability methods
  developed for the nonpolarized case are generalized to include linear
  polarization produced by the scattering of anisotropic radiation in
  the absence of magnetic fields. The analyses are based on a coupled
  integral equation for two-angle-dependent source functions. Some general
  properties, such as the order of magnitude of the surface polarization
  and approximations for the source functions, are deduced. The escape
  probability approximations are compared with exact solutions and found
  to be more accurate than first order perturbation techniques for lines
  of moderate optical thickness in solar isothermal prominences.

Title: A Model for the Penetration of Lyman Alpha in the Solar
    Chromosphere
Authors: Faurobert, M.; Frisch, H.; Skumanich, A.
Bibcode: 1988ApJ...328..856F
Altcode:
  A multilevel calculation of the hydrogen spectrum by Skumanich and
  Lites, followed by a two-level representation of each transition, shows
  that all the solar Lyα photons are created in an optically thick layer
  in the high chromosphere above τ<SUB>0</SUB> ≈ 10<SUP>2</SUP>. The
  authors give a simplified model that demonstrates the penetration of
  Lyα into the lower chromosphere below the creation region, i.e., for
  τ<SUB>0</SUB> &gt; 10<SUP>2</SUP>. A second-order escape probability
  approximation yields a simple analytical expression which accurately
  reproduces the behavior of the Lyα source function for 10<SUP>2</SUP>
  ⪉ τ<SUB>0</SUB> ⪉ 5×10<SUP>6</SUP> provided the destruction
  probability, ɛ is set close to 10<SUP>-6</SUP>.

Title: A Cauchy integral equation method for analytic solutions of
    half-space convolution equations.
Authors: Frisch, H.
Bibcode: 1988JQSRT..39..149F
Altcode:
  This paper is devoted to a method of Cauchy integral equation for
  the solution of half-space convolution equations. It was introduced
  by Frisch and Frisch to solve Wiener-Hopf integral equations with
  algebraically decreasing kernels, arising in non-coherent transfer with
  complete frequency redistribution. The author shows here that coherent
  transfer may also be treated by the Cauchy integral method. Various
  examples chosen among standard problems are used to illustrate the
  method.

Title: Radiation in moving gaseous media : eighteenth Advanced Course
    of the Swiss Society of Astrophysics and Astronomy
Authors: Kudritzki, R. P.; Yorke, H. W.; Frisch, Helene
Bibcode: 1988rmgm.book.....K
Altcode: 1988STIA...8950499K
  The propagation of EM radiation in gaseous media is characterized
  in chapters based on lectures presented at Leysin, Switzerland, on
  March 6-12, 1988. The emphases are on the fundamental astrophysics
  and the experimental and observational methods employed. Topics
  addressed include hot-star atmosphere models and their application
  to observations, radiation in diffuse matter (dust properties, gas
  microphysics, static nebula models, radiation hydrodynamics, and the
  formation and evolution of H II regions), and radiative transfer
  with frequency redistribution (asymptotic methods, scaling laws,
  and approximate solutions).

Title: Radiative Transfer with Frequency Redistribution - Asymptotic
    methods scaling laws and approximate solutions
Authors: Frisch, Hélène
Bibcode: 1988rmgm.conf..339F
Altcode: 1988SAAS...18..339F
  General Introduction Asymptotic methods. Some general ideas Outline
  of the lectures Diffusive and Non-Diffusive Large Scale Behaviour
  Introduction Asymptotic analysis of the integral equation for the source
  function Specific intensity in the interior Transfer with Partial
  Frequency Redistribution Introduction The ingredients of a partial
  redistribution problem The redistribution function The Asymptotic of
  Partial Redistribution Introduction R<SUB>I</SUB> and R<SUB>III</SUB>
  partial redistribution R<SUB>IV</SUB> partial redistribution Coherent
  scattering and R<SUB>II</SUB> partial redistribution Hints for
  the calculation of subordinate and resonance lines Boundary Layers
  Introduction Complete redistribution Diffusive type processes Transport
  of continuous radiation in stars Scaling Laws for Spectral Line
  Formation. A Summary Introduction Complete redistribution R<SUB>II</SUB>
  redistribution and coherent scattering Time-dependent transfer Escape
  Probabilties for Static and Moving Media Introduction Escape probability
  approximation procedures in a static medium Line formation in moving
  media Numerical Methods Introduction Iterative methods with exact
  operators Operator perturbation methods Preconditioning; necessity
  and technique Analytic Solutions of Half-Space Transport Equations
  Introduction A Cauchy integral equation method of solution Utilizations
  of exact analytical solutions Monochromatic scattering The H-function
  in the Wiener-Hopf type methods References

Title: The Lyman α line in the solar chromosphere: penetrative
    model andapproximations.
Authors: Faurobert, M.; Frisch, H.; Skumanich, A.
Bibcode: 1987PAICz..66..205F
Altcode: 1987eram....1..205F
  The authors present a model for the formation of Lyman α in the
  chromosphere below the creation region. The hydrogen atom is treated
  as a two-level atom and the chromosphere as a semi-infinite medium
  free of primary sources and illuminated by an isotropic and frequency
  independent radiation field at r<SUB>0</SUB> ≅ 10<SUP>2</SUP>.

Title: First results from a 1.1-m-diameter superconducting monopole
    detector
Authors: Incandela, J.; Frisch, H.; Somalwar, S.; Kuchnir, M.;
   Gustafson, H. R.
Bibcode: 1986PhRvD..34.2637I
Altcode:
  We present the design and performance of a superconducting induction
  magnetic-monopole detector with 1.1-m-diameter gradiometer loops. The
  detector demonstrates that gradiometers can be overlapped with no
  mutual inductance to yield high redundancy without increasing shield
  volume. One of two detector units was sensitive to the passage of
  monopoles through two overlapped gradiometers with 98% coincidence
  efficiency for 161 hours. The unit has a coincident sensitive area
  averaged over 4π sr of 4400 cm<SUP>2</SUP>. No candidate events were
  observed, setting an upper limit on the flux of cosmic-ray magnetic
  monopoles of f&lt;~7.1×10<SUP>-11</SUP> cm<SUP>-2</SUP> sr<SUP>-1</SUP>
  sec<SUP>-1</SUP> (90% C.L.). The detector was operated in ambient
  magnetic fields of ~5-125 mG.

Title: The status of searches for magnetic monopoles
Authors: Frisch, H. J.
Bibcode: 1986NYASA.461..652F
Altcode: 1986awph.conf..652F
  The fundamental principles, apparatus, procedures, and results of
  ongoing terrestrial searches for the superheavy magnetic monopoles
  (MMs) predicted by GUTs are reviewed. Approaches examined include
  methods based on the MM magnetic charge (Faraday induction experiments
  and the Parker bound from Galactic magnetic fields), MM ionization
  properties (MM velocity estimates; detection in scintillation and
  gas detectors), and the ability of MMs to catalyze nucleon decay
  (proton-decay experiments and cosmic-ray-shower hadronic cross section
  measurements). Diagrams, drawings, graphs, and tables of numerical
  data are provided, and plans for future MM detectors are indicated.

Title: Line transfer with complete frequency redistribution in an
    absorbing medium - Scaling laws and approximation
Authors: Faurobert, M.; Frisch, H.
Bibcode: 1985A&A...149..372F
Altcode:
  This paper discusses the influence of a continuous absorption
  produced by dust grains or photoionization on subordinate or weak
  resonance lines. The lines are being formed with complete Doppler or
  Voigt frequency redistribution in a one dimensional slab of finite
  thickness. An asymptotic analysis in the limit of small β (ratio
  of continuum to line opacity coefficient) shows that the large scale
  behaviour of the radiation field is described by a singular integral
  equation identical to that obtained by Frisch and Frisch (1977) for
  collisional destruction, but with an exponentially decreasing kernel
  in the case of the Voigt profile. Asymptotic scaling laws for the mean
  path length, the mean number of scatterings and the fraction of created
  photons which escapes the medium are given in the limits of weak and
  strong absorption. A first order escape probability method is used to
  evaluate net radiative brackets and line cooling rates, taking into
  account a possible emission by the continuum in the frequency domain
  of the line. Finally, a definition of the mean number of scatterings
  properly incorporating this emission term is proposed.

Title: Asymptotic properties of complete and partial frequency
    redistribution.
Authors: Frisch, H.
Bibcode: 1985ASIC..152...87F
Altcode: 1985pssl.proc...87F
  Radiative transfer problems with frequency redistribution may be
  investigated by asymptotic methods when the mean number of scatterings
  undergone by photons is very large. These methods provide scaling laws
  for characteristic parameters of the line radiation field. These methods
  also provide asymptotic transfer equations which describe the large
  scale behaviour of the radiation field away from boundaries. Complete
  redistribution and the four standard types of partial redistribution
  is discussed. Implications for numerical calculations are briefly
  considered.

Title: Pannel discussion on partial redistribution.
Authors: Freire Ferrero, R.; Frisch, H.; Linsky, J.; Oxenius, J.;
   Simonneau, E.
Bibcode: 1985ASIC..152..143F
Altcode: 1985pssl.proc..143F
  No abstract at ADS

Title: Flux limit on cosmic-ray magnetic monopoles from a large area
    induction detector
Authors: Incandela, J.; Campbell, M.; Frisch, H.; Somalwar, S.;
   Kuchnir, M.; Gustafson, H. R.
Bibcode: 1984PhRvL..53.2067I
Altcode:
  The design and performance of a superconducting induction detector
  with two 60-cm-diameter superconducting loops is presented. During
  eight months of data taking, no candidate events were observed,
  and an upper limit on the flux of cosmic-ray magnetic monopoles of
  about 6.7 x 10 to the -12th/sq cm sr sec (90-percent confidence level)
  is set. The detector demonstrates the possibility of operating large
  induction detectors in ambient magnetic fields greater than 1 mG.

Title: Boundary layer conditions for the transport of radiation
    in stars
Authors: Frisch, H.; Faurobert, M.
Bibcode: 1984A&A...140...57F
Altcode:
  An expansion technique used by Larsen et al. (1983) for
  describing coherent scattering is applied to characterizing an
  outer thermal boundary condition for radiation transport in stellar
  interiors. Modifications are introduced to cover conditions of non-gray
  radiative equilibrium, which is analyzed asymptotically. An expansion
  parameter is defined in terms of coupled transfer and energy equations
  and carried out to first order to obtain a ratio of the photon free
  path to the stellar characteristic dimension. The ratio provides a
  scale for the space variable with which a singular perturbation problem
  is solved for interior and boundary conditions, the latter being in
  the stellar atmosphere and the sum of the interior solution and the
  boundary layer correction. A Robin boundary condition results which
  is only 5 percent higher in temperature than the interior in the case
  of a gray opacity coefficient.

Title: Mean Escape Probabilities and Mean Numbers of Scatterings
    for Resonance Lines
Authors: Frisch, H.
Bibcode: 1984mrt..book...25F
Altcode:
  No abstract at ADS

Title: First results from the Chicago-Fermilab-Michigan cosmic ray
    magnetic monopole detector.
Authors: Incandela, J. R.; Campbell, M.; Frisch, H.; Somalwar, S.;
   Kuchnir, M.; Gustafson, H. R.
Bibcode: 1984mono.conf..461I
Altcode:
  No abstract at ADS

Title: Scaling laws for the scattering of resonance line photons.
Authors: Frisch, H.
Bibcode: 1984PhST....7..110F
Altcode: 1984PhyS....7..110F
  Resonance lines of ions with a large Z are broadened essentially by
  natural damping, and therefore photons with frequencies larger than a
  few Doppler widths are scattered almost coherently. This "coherent"
  scattering of resonance-line photons can be described by a space
  and frequency diffusion process when the mean number of scatterings
  undergone by the photons is sufficiently large.

Title: Mean escape probabilities and mean numbers of scatterings
    for resonance lines.
Authors: Frisch, H.
Bibcode: 1984mrt..book...65F
Altcode: 1984mrt..conf...65F
  A mean escape-probability approximation for resonance lines, which
  encompasses both the effectively thin and the effectively thick
  limits, is described. Global conservation of photons and the large
  scale diffusive behavior of the radiation field are reasonably well
  preserved in this approximation. This approximation is tested on a
  two-level atom by comparison with accurate numerical results.

Title: Dust-driven winds. I - A two-fluid model and its numerical
    solution
Authors: Berruyer, N.; Frisch, H.
Bibcode: 1983A&A...126..269B
Altcode:
  A model of dust-driven wind relevant to red giant stars is investigated,
  in which the usual hypothesis of 'momentum coupling' (amounting to
  neglect of grain particle mass) is relaxed. When the momentum coupling
  approximation is abandoned, the sonic point is shifted outwards, and the
  gas and grain expansion velocities are reduced. In the supersonic part
  of the wind the diminution is of the order of 30 percent, but it may
  reach several orders of magnitude below the sonic point. An asymptotic
  analysis of the flow at the base of the wind shows the existence of
  a boundary layer where the grains suffer a very strong acceleration,
  the gas velocity staying almost constant. The coupling between the
  grains and the gas is maximum just outside the boundary layer, and
  decreases gradually outwards. Beyond a thousand inner envelope radii
  the grains and the gas are fully uncoupled. The coupling is still very
  strong when the velocities have saturated the almost constant values.

Title: Escape probabilities, mean number of scatterings and net
    radiative bracket for resonance lines
Authors: Frisch, H.
Bibcode: 1982A&A...114..119F
Altcode:
  An examination of the multiple scattering of resonance-line photons
  in nonconservative media, where the photons have a small probability
  of destruction at each scattering, yields an approximation for the
  mean number of scatterings on the basis of scaling arguments which
  takes into account both the destruction of photons and escape through
  boundaries. The approximation is used to show that the fraction of
  the emitted energy escaping from the medium, known as the mean escape
  probability, is nearly independent of the value of the destruction
  probability. Analytical solutions which are valid deep within the
  medium, and accurate numerical solutions of the transfer problem,
  are used to check the validity of the stated results and examine the
  errors made when scaling laws for the mean escape probability are
  transformed into depth variation scaling laws.

Title: A method of Cauchy integral equation for noncoherent tranfer
    in half-space.
Authors: Frisch, H.; Frisch, U.
Bibcode: 1982JQSRT..28..361F
Altcode:
  No abstract at ADS

Title: Non-LTE transfer with complete redistribution. Scaling laws
    for a slab.
Authors: Frisch, H.
Bibcode: 1982JQSRT..28..377F
Altcode:
  No abstract at ADS

Title: Hydrogen line spectrum in quasars. I - Approximation procedures
    for line transfer versus an exact treatment
Authors: Collin-Souffrin, S.; Delache, Ph.; Frisch, H.; Dumont, S.
Bibcode: 1981A&A...104..264C
Altcode:
  Approximation procedures frequently used in handling self-absorption
  effects in the hydrogen emission lines of quasars are discussed and
  compared with an exact numerical treatment of line transfer. The model
  here is a finite slab with prescribed density and temperature. It
  is noted that if a medium has finite thickness and is such that
  subordinate lines are not thermalized, then a semi-infinite
  'local escape probability,' which implicitly assumes that photons
  emerge from only one surface of the slab, will overestimate the line
  fluxes. In this way, the intensity ratio H-alpha/H-beta can be greatly
  underestimated. A modified form of the 'local escape probability'
  is proposed which allows for the possibility of photons escaping from
  both sides of the medium. With this probability, it becomes possible
  to obtain much more accurate line ratios and fluxes. It is also found
  that natural broadening effects (representable by a Voigt profile)
  may be important in subordinate lines.

Title: Diffusion approximations for the scattering of resonance-line
photons: interior and boundary layer solutions.
Authors: Frisch, H.; Bardos, C.
Bibcode: 1981JQSRT..26..119F
Altcode:
  No abstract at ADS

Title: Broadening of non-LTE lines by a turbulent velocity field
    with a finite correlation length
Authors: Froeschle, Ch.; Frisch, H.
Bibcode: 1980A&A....91..202F
Altcode:
  Profiles of non-LTE lines broadened by a turbulent velocity field
  with a finite correlation length are computed by the 'effective source
  function' technique. This method can reformulate stochastic transfer
  as a standard non-LTE problem with an effective escape probability
  determined by averaging all realizations of velocity fields. Effective
  source functions and mean emergent profiles were calculated for a
  two-level atom with two choices of a thermal source, and choices between
  the Doppler and Voigt line profiles. It is concluded from correlations
  between the macroturbulent limit, the thermalization length, and
  variations of emergent profiles in isothermal and chromospheric
  atmospheres, that a micro-macroturbulent model cannot reproduce a
  turbulent velocity field with a finite correlation length.

Title: Scaling laws for resonance line photons in an absorbing medium
Authors: Frisch, H.
Bibcode: 1980A&A....87..357F
Altcode:
  Resonance line scattering in the presence of a source of continuous
  absorption is studied for very small values of the ratio of the
  continuous to line opacity, beta. Scaling laws for the thermalization
  length, the thermalization frequency, the mean number of scatterings
  and the mean path length are extracted from an asymptotic analysis
  of the equation of transfer in the limit as beta approaches 0. An
  interpretation is given for asymptotic scaling laws inferred from
  numerical data by Hummer and Kunasz (1978) and Bonilha et al. (1979).

Title: Non-LTE transfer. V - The asymptotics of partial redistribution
Authors: Frisch, H.
Bibcode: 1980A&A....83..166F
Altcode:
  The large-scale behavior of noncoherent radiative transfer with
  partial frequency redistribution is examined. Scaling laws for four
  basic scattering processes are extracted from an asymptotic analysis
  of the integral equation for the source function in the limit, epsilon
  approaches zero (where epsilon is the probability of photon destruction)
  to describe the dependence of characteristic lengths and frequencies on
  epsilon. It is shown that partial frequency redistribution simplifies
  drastically for small epsilon and angular redistribution is irrelevant
  in all cases. For all scattering processes the source function,
  after the rescaling of optical depths and frequencies, depends on
  fewer variables than the original source functions. The main results
  are discussed with reference to implications for numerical methods
  currently used in the astrophysical literature.

Title: Renormalization-group approach to noncoherent radiative
    transfer
Authors: Bell, Thomas L.; Frisch, U.; Frisch, H.
Bibcode: 1978PhRvA..17.1049B
Altcode:
  In noncoherent transfer, a photon undergoes multiple scattering
  with frequency changes, the frequency profile φ (0&lt;=φ&lt;=Λ)
  after each scattering is prescribed, the mean free path varies like
  φ<SUP>-1</SUP>, and there is a small probability of destruction ɛ. In
  contrast with the coherent (monochromatic) case, diffusive behavior is
  not obtained as ɛ--&gt;0. The scaling law of the intensity of radiation
  can be obtained with a technique suggested by the renormalization-group
  approach to critical phenomena. The equation of transfer for "core"
  photons (say, Λ&gt;=φ&gt;12Λ) is solved in terms of "wing" photons
  (Λ2&gt;=φ&gt;0). The solution is substituted wherever core photons
  appear in the equation for the wing photons. A closed equation for
  wing photons is thus obtained. After rescaling of the variables (wave
  number and φ) it resembles the original equation (φ again runs from
  0 to Λ) but has a nonlocal scattering operator. The procedure is
  iterated and the successive equations are found to approach a fixed
  form with suitable choice of the rescaling factors. This choice fixes
  the scaling law. It depends only on the asymptotic behavior of the
  profile at large frequencies. Known results for the dependence of the
  "thermalization length" on ɛ are recovered.

Title: Rapport d'activité de l'A.D.I.O.N. par le Secrétaire
    Général et rapport financier. Report 1975 and 1976.
Authors: Delache, P.; Schatzman, E.; Frisch, H.
Bibcode: 1978BONic..13...33D
Altcode:
  No abstract at ADS

Title: Non-LTE transfer - III. Asymptotic expansion for small
    epsilon .
Authors: Frisch, U.; Frisch, H.
Bibcode: 1977MNRAS.181..273F
Altcode:
  Radiative transfer with complete frequency redistribution in a
  one-dimensional full- or half-space with no incoming radiation
  is analyzed in the limit of small epsilon. It is shown that an
  asymptotic expansion can be performed in the case of complete frequency
  redistribution. The coherent-scattering problem is also discussed for
  purposes of comparison. An asymptotic expansion for specific intensity
  is derived from an asymptotic expansion for the source function.

Title: Non-LTE transfer - IV. A rapidly convergent iterative method
    for the Wiener-Hopf integral equations.
Authors: Frisch, H.; Froeschle, C.
Bibcode: 1977MNRAS.181..281F
Altcode:
  It is shown that a simple approximation previously derived for the
  source function in the isothermal case of non-LTE line transfer with
  complete frequency redistribution can be extended into a rapidly
  convergent iterative scheme for solving Wiener-Hopf integral
  equations. The convergence of the method and its numerization
  are discussed, and the iterative scheme is used for the singular
  integral equation of the interior asymptotic expansion as well as the
  homogeneous Wiener-Hopf equation for the boundary layer. Analogs for
  these equations based on the approximation for the source function
  are presented. Consideration is given to the extent to which the
  leading terms of the asymptotic expansions arising when epsilon tends
  to zero may be employed in practice to determine the source function
  for finite epsilon.

Title: Applications of Fourier analysis to broadening of stellar
line profiles. V: Effects of finite sized eddies on solar lines.
Authors: Smith, M. A.; Frisch, H.
Bibcode: 1976SoPh...47..461S
Altcode:
  Turbulence dominated by eddies of a finite size produces effects on
  a line profile which are similar to both macro- and micro-turbulence
  but which are at the same time neither. It is suggested that one of
  these effects in the Fourier transform domain, namely the narrowing
  of the first natural sidelobe relative to the width of the main lobe,
  can be used as an indicator of the dominance of finite-sized eddies
  (`mesoturbulence'). An examination of some existing solar data shows
  that finitesized eddy models fit the observed sidelobe widths better
  than do models computed with any reasonable combination of micro-
  and macro-turbulent broadenings (Paper III).

Title: Non-LTE transfer-11. Two-level atoms with stochastic velocity
    field
Authors: Frisch, H.; Frisch, U.
Bibcode: 1976MNRAS.175..157F
Altcode:
  Following previous work on LTE stochastic transfer (Auvergne et aL;
  sFrisch), transfer with incoherent scattering is considered for
  two-level satoms in the presence of turbulent velocity fields with
  finite seddy-size. Assuming that the velocity along each individual
  photon path smay be represented by a Markov Process in time, we
  obtain a snon-stochastic equation of transfer for the `mean conditional
  sintensity', from which the mean (observable) intensity may be recovered
  sby integration over the velocity distribution. An integral equation
  of sthe Wiener-Hopf type is obtained for the `mean conditional source
  sfunction' from which it is shown by techniques introduced in Paper I
  s(Frisch &amp; Frisch) that the rms surface source function assumes
  the susual value EB for uniform thermal source B. An `effective
  kernel and ssource function' approximation is introduced by which a
  standard stransfer problem is recovered and worked out explicitly in
  a special scase. It is shown that finite eddy-size effects can change
  the effective ssource function and the emergent profile by a factor
  z or more.

Title: LTE and non-LTE formation with turbulent velocity fields
Authors: Frisch, H.; Frisch, U.
Bibcode: 1976pmas.conf..113F
Altcode:
  No abstract at ADS

Title: On the inverse problem in statistical mechanics
Authors: Frisch, H. L.; Fesciyan, S.
Bibcode: 1976GReGr...7...83F
Altcode:
  We review briefly the status of some inverse problems in classical
  equilibrium statistical mechanics.

Title: Non-LTE transfer. V C revisited
Authors: Frisch, U.; Frisch, H.
Bibcode: 1975MNRAS.173..167F
Altcode:
  Assuming a semi-infinite atmosphere, a two-level atom and complete
  frequency redistribution, we give, in the isothermal case, a new
  derivation of the surface value of the source function based only
  on the integral equation for the source function. This derivation
  has a straightforward extension to the case where a uniform velocity
  gradient is included, to the time-dependent case (thermal source B
  switched on at time t = o) and to the determination of the mean number
  of scatterings undergone by an escaping photon (with Ambartsumian's
  definition). Our derivation suggests also a simple approximate
  differential equation for the complete source function = /2 B/ r where
  P = +(i- )K2(r) and K2(r) is the direct escape probability for outwards
  emitted photons. This approximation is tested both for isothermal and
  exponential atmosphere. As long as the scale of B is large compared to
  the photon mean free-path at the centre of the line, our approximation
  reproduces all the qualitative features and is usually slightly in
  excess of the exact solution. The approximation is easily extended to
  non-uniform E and multilevel atoms.

Title: Finite eddy-size effects on centre-to-limb variations; an
    alternative to anisotropic microturbulence.
Authors: Frisch, H.
Bibcode: 1975A&A....40..267F
Altcode:
  An attempt is presented to explain the center-to-limb increase in
  width of solar lines on the basis of the theory of line formation in a
  turbulent medium where finite eddy-size is taken into account (Auvergne
  et al., 1973). Hydrodynamic velocities along the line of sight are
  represented by a step-wise constant stochastic process (Kubo-Anderson
  Process), with Gaussian isotropic velocity distribution and an arbitrary
  variation of the eddy-size with the continuum optical depth. For the
  simplest case of constant geometrical eddy-size, the profiles are found
  to be wider at the limb than at the center; this is because the optical
  size of the eddies decreases towards the limb, bringing us closer to
  the microturbulent limit. An application to the forbidden Mg I 4571 A
  line shows that this effect accounts for much of the observed widening,
  without recourse to ad-hoc assumptions such as depth variation of the
  microturbulent velocity or anisotropic microturbulence.

Title: Spectral Line Formation in a Tur- bulent Atmosphere
Authors: Auvergne, M.; Frisch, H.; Frisch, U.; Froeschle, Ch.;
   Pouquet, A.
Bibcode: 1973A&A....29...93A
Altcode:
  . In order to bridge the gap between the usual microturbulent and
  macroturbulent approximations, we study the formation of spectral lines
  in a turbulent medium in which the eddies have a finite scale. The
  variation of the velocity along the line of sight is represented by a
  Kubo-Anderson process for which the probability distribution and the
  correlation length, or its inverse the eddy density n, can be adjusted
  arbitrarily. Exact analytical expressions are obtained for the mean
  line profile, its statistical dispersion, and also for the mean curve
  of growth. The macro- and microturbulent approximations are recovered
  respectively for n =0 and n = . It is found that in the far wings the
  mean profile becomes independent of the eddy density. It is shown that
  the position of the plateau of the curve of growth depends both on the
  eddy density and on the r.m.s. turbulent velocity a unique determination
  of the latter is therefore not possible. Key words: spectral line
  formation - turbulence - stochastic processes - radiative transfer

Title: Coupling between Thermal Conduction and Radiative Transfer
    in a Moving Atmosphere
Authors: Frisch, H.
Bibcode: 1973A&A....27..223F
Altcode:
  Summary. A singular perturbation expansion method commonly used in
  boundary layer analysis is applied to the study of the coupling between
  thermal conduction and radiative transfer in a moving atmosphere. The
  expansion parameter is the conduction coefficient assumed to be small
  in suitable dimensionless units. The model consists of a plane slab of
  finite thickness heated by thermal conduction and loosing energy through
  emission of radiation. Boundary temperatures, incoming intensities
  and matter flux are given. In order to bring out the essential ideas
  the asymptotic expansion is performed on a linearized version of the
  equations. This restriction is however not essential. Conditions under
  which the equations may be linearized are discussed. It is shown that
  thermal conduction is essentially limited to a boundary layer near the
  hot end. A separate equation is obtained for the exterior region which
  is then used to find the conditions under which convection dominates
  over radiative transfer. Matched interior and exterior asymptotic
  expansions are give in special cases. Key words: radiative transfer -
  thermal conduction - chromosphere - singular perturbation expansion

Title: The Solar Chromosphere and Its Transition to the Corona
Authors: Frisch, H.
Bibcode: 1972SSRv...13..455F
Altcode:
  Our present knowledge on the average physical properties of the
  chromosphere and of the transition region between chromosphere and
  corona is reviewed. It is recalled that shock wave dissipation is
  responsible for the high temperatures observed in the chromosphere and
  corona and that, due to the non-linear character of the dissipation
  mechanism, no satisfactory explanation of the structure of the outer
  solar layers has yet been given. In this paper, the main emphasis
  is on the observations and their interpretation. Evidence for the
  non-spherically symmetric structure of the atmosphere is given;
  the validity of interpreting the observations with the help of
  a fictitious spherically symmetric atmosphere is discussed. The
  chromosphere and the transition region are studied separately: for
  each region, the energy balance is considered and recent homogeneous
  models derived from ultra-violet, infrared and radio observations are
  discussed. It is stressed that although in the chromosphere, a study
  of the radiative losses may lead to the determination, as function of
  height, of the amount of mechanical energy dissipated as function of
  height, a more detailed analysis of the velocity field is necessary
  to find the periods and the wavelengths of the waves responsible for
  the heating. The methods used for wave detection and some results
  are presented. Observational and theoretical evidence is given for
  the non-validity of the assumption of hydrostatic equilibrium which
  is commonly used in modeling the transition region. We conclude that
  a better understanding of the heating mechanism will come through
  a higher spatial resolution (less than 0.2″) and more accurate
  absolute measurements, rather than from sophisticated hydrodynamical
  calculations.

Title: Ultraviolet effects on the chemical composition and optical
    properties of interstellar grains.
Authors: Greenberg, J. M.; Yencha, A. J.; Corbett, J. W.; Frisch, H. L.
Bibcode: 1972saim.conf..425G
Altcode:
  No abstract at ADS

Title: Non-linear Coupling between Thermal Conduction and Radiative
    Transfer
Authors: Frisch, H.
Bibcode: 1971A&A....13..359F
Altcode:
  The problem of coupled thermal conduction and radiative transfer is
  solved numerically for a plane slab, of finite thickness, heated by
  thermal conduction, the temperatures at the boundaries and the radiation
  entering the slab being given. The absorption coefficient is taken of
  the form T , where T is the temperature and n a positive number. An
  iterative method is used to solve this non-linear differential
  problem. Th the optically thick case a simple physical interpretation
  of the solution can be given in terms of a region of pure radiative
  equilibrium and transition regions where absorption (but not emission)
  of radiative energy is negligible. Key words: radiative transfer -
  thermal conduction - solar chromosphere.

Title: Growth, Distribution, and Chemical Composition of Interstellar
    Dust.
Authors: Greenberg, J. M.; Yencha, A. J.; Corbett, J.; Frisch, H. L.
Bibcode: 1971BAAS....3Q.250G
Altcode:
  No abstract at ADS

Title: Coupling between Radiative Transfer and Thermal Conduction
    in the Chromosphere
Authors: Frisch, H.
Bibcode: 1970A&A.....9..269F
Altcode:
  The influence of the transfer of radiative energy on the temperature
  structure of a plane slab of finite thickness heated by thermal
  conduction is studied. The temperatures at the boundaries and
  the radiation entering the slab are given. In some cases, constant
  absorption coefficient per cm and coefficient of thermal conductivity
  proportional to the third power of the temperature, the problem
  can be solved analytically. When the absorption coefficient goes
  to zero or infinity the temperature distribution in the slab becomes
  asymptotically identical to that of a slab heated by thermal conduction
  only. In intermediate cases the temperature inside the slab may become
  greatly inferior to that of the boundaries with very rapid variations
  in the vicinity of those boundaries. A generalization of the results
  to the case of a non-constant absorption coefficient is outlined.

Title: Couplage du transfert radiatif et de la conduction thermique
    dans la chromosphère solaire.
Authors: Frisch, H.
Bibcode: 1970CRASB.270..918F
Altcode:
  No abstract at ADS

Title: Contribution à l'étude de la température du surface du
soleil et de la remontée chomosphérique de température Title:
    Contribution à l'étude de la température du surface du soleil et
de la remontée chomosphérique de température Title: Contribution
    to the study of solar surface temperature and chomospheric temperature
    rise;
Authors: Frisch, Hélène
Bibcode: 1966PhDT........52F
Altcode:
  No abstract at ADS

