Numerical Method of Relativistic Fokker-Planck Equation for Energy Deposition of Fast Electrons

Abstract

Abstract: For energy deposition of fast electrons in high density plasma, a relativistic Fokker-Planck equation in three-dimensional momentum space is introduced. It includes both binary collision and contribution from plasma collective response. Numerical method as well as kinetic code of the equation is developed. Typical energy deposition cases are presented with comparison with stopping power model. Energy deposition of fast electrons with energy from 0.5 MeV to 3.5 MeV in 300 g·cm^-3 DT plasma are simulated. It shows that scattering angle ϕ plays minor role on range and penetration depth of energy deposition of fast electrons.

Key words: electron beam, energy deposition, relativistic Fokker-Planck equation

CLC Number:

ZHANG Hua, WU Sizhong, ZHOU Cangtao, HE Minqing, CAI Hongbo, CAO Lihua, ZHU Shaoping, HE Xiantu. Numerical Method of Relativistic Fokker-Planck Equation for Energy Deposition of Fast Electrons[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(5): 555-562.

References

[1] TABAK M, HAMMER J, GLINSKY M E, et al. Ignition and high gain with ultrapowerful lasers[J]. Physics of Plasmas, 1994, 1(5):1626-1634.
[2] BETTI R, ANDERSON K, BOEHLY T R, et al. Progress in hydrodynamics theory and experiments for direct-drive and fast ignition inertial confinement fusion[J]. Plasma Physics & Controlled Fusion, 2006, 48(12B):B153.
[3] SHIRAGA H, NAGATOMO H, THEOBALD W, et al. Fast ignition integrated experiments and high-gain point design[J]. Nuclear Fusion, 2014, 54(5):1464-1473.
[4] DEUTSCH C, FURUKAWA H, MIMA K, et al. The interaction physics of the fast ignitor concept[J]. Laser and Particle Beams, 1997, 256(4):2483-2486.
[5] LI C K, PETRASSO R D. Energy deposition of MeV electrons in compressed targets of fast-ignition inertial confinement fusion[J]. Physics of Plasmas, 2006, 13(5):1626.
[6] SOLODOV A A, BETTI R. Stopping power and range of energetic electrons in dense plasmas of fast-ignition fusion targets[J]. Physics of Plasmas, 2008, 15(4):042707-042707-5.
[7] ATZENI S, SCHIAVI A, DAVIES J R. Stopping and scattering of relativistic electron beams in dense plasmas and requirements for fast ignition[J]. Plasma Physics & Controlled Fusion, 2008, 51(1):015016.
[8] SOLODOV A A, ANDERSON K S, BETTI R, et al. Integrated simulations of implosion, electron transport, and heating for direct-drive fast-ignition targets[J]. Physics of Plasmas, 2009, 16(5):056309-056309-9.
[9] ROBICHE J, RAX J M. Relativistic kinetic theory of pitch angle scattering, slowing down, and energy deposition in a plasma[J]. Physics of Plasmas, 2004, 70(4):046405.
[10] TZOUFRAS M, BELL A R, NORREYS P A, et al. A Vlasov-Fokker-Planck code for high energy density physics[J]. Journal of Computational Physics, 2011, 230(17):6475-6494.
[11] YOKOTA T, NAKAO Y, JOHZAKI T, et al. Two-dimensional relativistic Fokker-Planck model for core plasma heating in fast ignition targets[J]. Physics of Plasmas, 2006, 13(2):022702.
[12] WU S Z, ZHOU C T, ZHU S P, et al. Relativistic kinetic model for energy deposition of intense laser-driven electrons in fast ignition scenario[J]. Physics of Plasmas, 2011, 18(2):1626.
[13] WU S Z, ZHANG H, ZHOU C T, et al. Kinetic model for energy deposition in fast ignition[J]. European Physical Journal, 2013,59(1):05021.
[14] 吴思忠, 张华, 周沧涛,等. 快点火中相对论电子束能量沉积的动理学研究[J]. 强激光与粒子束, 2015, 27(3):77-86.
[15] BRAAMS B J, KARNEY C F F. Differential form of the collision integral for a relativistic plasma[J]. Physical Review Letters, 2005, 59(16):1817-1820.
[16] BRAAMS B J, KARNEY C F F. Conductivity of a relativistic plasma[J]. Physics of Fluids, 1989, 1B(7):1355-1368.