Compton Fokker-Planck Equation for Hot Plasmas

Cooper, G.E.

doi:10.1103/physrevd.3.2312

Cited by 55 publications

(37 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We then use the result of angular averaging over the directions of p detailed in Appendix B and subsequently average over the direction between k and k ′ , the average over cos θ. To present the results in a compact form, we separately record the order v 2 result, the one that gives the Kompaneets equation, 6) and the order v 4 result which gives the leading relativistic correction to the Kompaneets equation…”

Section: Expansions and Angular Averagesmentioning

confidence: 99%

Leading relativistic corrections to the Kompaneets equation

Brown¹,

Preston²

2012

Astroparticle Physics

View full text Add to dashboard Cite

We calculate the first relativistic corrections to the Kompaneets equation for the evolution of the photon frequency distribution brought about by Compton scattering. The Lorentz invariant Boltzmann equation for electron-photon scattering is first specialized to isotropic electron and photon distributions, the squared scattering amplitude and the energy-momentum conserving delta function are each expanded to order v 4 /c 4 , averages over the directions of the electron and photon momenta are then carried out, and finally an integration over the photon energy yields our FokkerPlanck equation. The Kompaneets equation, which involves only first-and second-order derivatives with respect to the photon energy, results from the order v 2 /c 2 terms, while the first relativistic corrections of order v 4 /c 4 introduce third-and fourth-order derivatives. We emphasize that our result holds when neither the electrons nor the photons are in thermal equilibrium; two effective temperatures characterize a general, non-thermal electron distribution. When the electrons are in thermal equilibrium our relativistic Fokker-Planck equation is in complete agreement with the most recent published results, but we both disagree with older work.

show abstract

Section: Expansions and Angular Averagesmentioning

confidence: 99%

Leading relativistic corrections to the Kompaneets equation

Brown¹,

Preston²

2012

Astroparticle Physics

View full text Add to dashboard Cite

show abstract

“…Efficient routines for doing this calculation have been developed by Kershaw, Prasad and Beason [143]. Power-series expansions in the two small quantities h ẍ mc 2 and kT¨mc 2 have been developed for the differential cross section from which it has been shown that to first order in the two small parameters the moments are given by These expressions could be improved using the results for the relativistic regime obtained by Cooper [72]. The value for B, the mean square frequency shift, is not hard to derive from the non-relativistic Doppler effect formula without worrying about the Klein-Nishina corrections.…”

Section: Comptonizationmentioning

confidence: 99%

Radiation Hydrodynamics

Castor

2004

254

259

View full text Add to dashboard Cite

“…where C B and C C are the bremsstrahlung and Compton 19,20 collision operators, and we have taken here the nonrelativistic limit of the Compton operator. This form utilizes the dimensionless density of states, ϵ 8 T e 3 2 / h 3 c 3 .…”

Section: Photon Collision Operatorsmentioning

confidence: 99%

Photon coupling theory for plasmas with strong Compton scattering: Four temperature theory

et al. 2009

View full text Add to dashboard Cite

ARTICLES YOU MAY BE INTERESTED INStudy of the ion kinetic effects in ICF run-away burn using a quasi-1D hybrid model Physics of Plasmas 24, 022704 (2017) When an equimolar mixture of deuterium ͑D͒ and tritium ͑T͒ at high density undergoes fusion burn, the system becomes extremely nonequilibrium. The ion temperature rises much higher than the electron temperature which, in turn, is much higher than the radiation temperature. Accurately simulating this nonequilibrium burn process has previously required a multigroup representation of the radiation field. Although simulating this D-T burn with a simple three temperature model ͑3T͒ also results in significant departures from thermal equilibrium, the ion and electron temperature histories from the 3T simulations are much lower than from the multigroup simulations. In this paper, a theory that overcomes the deficiencies of the 3T model in simulating burn of high density D-T is developed. The primary deficiency of the 3T model for this physical system is with the treatment of the Compton scattering energy exchange. The theory here developed culminates in a four temperature model ͑4T͒ which describes the radiation field with two temperatures. These are T R , which is the standard radiation temperature of the 3T model ͑proportional to the fourth root of the radiation energy density͒, and T p , which is the true thermodynamic temperature of the photon distribution. This 4T theory gives excellent agreement with the multigroup model for the nonequilibrium burn of D-T. Further, the 4T model transitions smoothly to the 3T model when this is appropriate. Thus the kinetic theory derivation of the 4T model also provides a solid theoretical foundation for the 3T model. Extensions of the theory to inhomogeneous systems are under development to allow treatment of geometries where the computational efficiency of the 4T approach can convey a sizable advantage. There appear to be at least two important applications where the model can be applied. One is for inertial confinement fusion capsules that are optically thick and utilize volume ignition. The second application involves astrophysical accretion disks in the high temperature regime that also exhibit matter heating radiation, albeit without a fusion energy source. A reduced complexity radiation model with the associated reduced computer resource requirements has the potential to facilitate high resolution two dimensional and three dimensional simulations of these astrophysical objects.

show abstract

Compton Fokker-Planck Equation for Hot Plasmas

Cited by 55 publications

References 4 publications

Leading relativistic corrections to the Kompaneets equation

Leading relativistic corrections to the Kompaneets equation

Radiation Hydrodynamics

Photon coupling theory for plasmas with strong Compton scattering: Four temperature theory

Contact Info

Product

Resources

About