Temperature equilibration rate with Fermi-Dirac statistics

Journal Article · Sat Dec 15 00:00:00 EST 2007 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.76.066404· OSTI ID:21101964

Brown, Lowell S; Singleton, Jr, Robert L ^[1]

---

1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We calculate analytically the electron-ion temperature equilibration rate in a fully ionized, weakly to moderately coupled plasma, using an exact treatment of the Fermi-Dirac electrons. The temperature is sufficiently high so that the quantum-mechanical Born approximation to the scattering is valid. It should be emphasized that we do not build a model of the energy exchange mechanism, but rather, we perform a systematic first principles calculation of the energy exchange. At the heart of this calculation lies the method of dimensional continuation, a technique that we borrow from quantum field theory and use in a different fashion to regulate the kinetic equations in a consistent manner. We can then perform a systematic perturbation expansion and thereby obtain a finite first-principles result to leading and next-to-leading order. Unlike model building, this systematic calculation yields an estimate of its own error and thus prescribes its domain of applicability. The calculational error is small for a weakly to moderately coupled plasma, for which our result is nearly exact. It should also be emphasized that our calculation becomes unreliable for a strongly coupled plasma, where the perturbative expansion that we employ breaks down, and one must then utilize model building and computer simulations. Besides providing different and potentially useful results, we use this calculation as an opportunity to explain the method of dimensional continuation in a pedagogical fashion. Interestingly, in the regime of relevance for many inertial confinement fusion experiments, the degeneracy corrections are comparable in size to the subleading quantum correction below the Born approximation. For consistency, we therefore present this subleading quantum-to-classical transition correction in addition to the degeneracy correction.

• OSTI ID: 21101964
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 76, Issue 6; Other Information: DOI: 10.1103/PhysRevE.76.066404; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BORN APPROXIMATION
COMPUTERIZED SIMULATION
CORRECTIONS
ELECTRON TEMPERATURE
ELECTRONS
ENERGY TRANSFER
ERRORS
FERMI STATISTICS
INERTIAL CONFINEMENT
ION TEMPERATURE
KINETIC EQUATIONS
PERTURBATION THEORY
PLASMA
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SCATTERING