Fluctuations in a Plasma II: The Numerical Factor in the Coulomb Logarithm

抄録

Considering the binary collision effects and the many-body correlation effects simultaneously, one makes it unnecessary to introduce the cut-off procedure to avoid the divergence of cross sections. The energy loss rate P of a charged particle moving fast through the plasma is obtained as follows:
P=\fracq²ω₀²vln\frac2μv³γ|q|eω₀,
where lnγ=0.577, Euler’s constant, q, v are the charge, speed of the moving particle, and ω₀, μ, −e are the frequency of plasma oscillation, reduced mass, and charge of the electron, respectively. The rate R of the relaxation between ion and electron temperatures is
R=R₀ln\fracaT₂Ze²k₂,
R₀=\frac83(n₁+n₂)\fracm₂m₁\left(\fracZe²T₂\ ight)²\left(\frac2πT₂m₂\ ight)^1⁄2,
k₂=(4πn₂e²⁄T₂)^1⁄2,
lna=−1⁄2+2ln(2⁄γ)=−0.268,
where m₁, n₁, Ze are the mass, number density and charge of the ion, and m₂, n₂, T₂ are the mass, number density, and temperature of the electron.