Osamu Aono

UNIFIED THEORY OF RELAXATIONS IN PLASMAS. I. BASIC THEOREM

Two approximate theories–the impact theory and wave theory– of relaxation phenomena in hot plasmas are united into an exact theory, in which no cut-off procedure of the diverging integrals is needed, and which gives Coulomb logarithms with exact numerical factors in the arguments. When a relaxation rate is given by a diverging integral \({\int}B(b)db\) with respect to the impact parameter b in the impact theory and by a diverging integral \({\int}K(k)dk\) with respect to the wave number k in the wave theory, then the present theory gives the rate in the form \begin{aligned} \int_{0}^{\infty}B(b)\exp\left(-\frac{1}{2}b^{2}/{b_{0}}^{2}\right)db+\int_{0}^{\infty}K(k)\exp\left(-\frac{1}{2}k^{2}/{b_{0}}^{2}\right)dk. \end{aligned} Here b 0 is any length much longer than the close impact radius but much shorter than the Debye radius; and the final results are independent of b 0 . Simple examples are treated.

Unified Theory of Relaxations in Plasmas, II. Applications

The basic theorem proposed in Part I of the paper is applied to two-component plasmas. The relaxation between ion and electron temperatures, attenuation of low-frequency oscillations, diffusion and thermal conduction across a magnetic field, and relaxation of an anisotropic distribution of ion velocities are treated. The rates of these relaxations with exact numerical factors in the arguments of the Coulomb logarithms are obtained.

Energy Change of a Charged Particle Moving in a Plasma

The energy loss rate of a charged particle moving in a plasma is calculated without any cutoff procedure. The result is applicable to any velocity of the test particle.

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

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: \begin{aligned} P{=}\frac{q^{2}{\omega_{0}}^{2}}{v}\ln\frac{2\mu v^{3}}{\gamma|q|e\omega_{0}}, \end{aligned} where ln γ=0.577, Eulers constant, q , v are the charge, speed of the moving particle, and ω 0 , 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

Fluctuations in a Plasma III: Effect of the Magnetic Field on the Stopping Power

The rate of energy loss of a charged particle moving fast through a plasma in a magnetic field is obtained exactly without any cut-off procedures. The stopping power decreases as the magnetic field is increased. Some limiting cases are treated analytically, but general cases are investigated with numerical calculations.

Theory of Čerenkov and cyclotron radiations in plasmas

Radiation from a charge q moving in a helix in magnetoplasmas is investigated theoretically. When its speed ν is much larger than the thermal velocity, (m−1 kT)½, of the plasma electrons and the gyration frequency is much smaller than the plasma frequency ω0, the radiation power from the charge is (q2 ω02/2ν) ln (ν2/m−1 kT). Cyclotron radiation from an electron with nonrelativistic speed decreases to zero as plasma density increases. For a positron in a dilute plasma, however, the radiation is strengthened. This strengthened radiation from a positron again decreases with increasing ω02/ωH2 and becomes zero for ω02/ωH2 ≥ 2 (ωH = gyration frequency of the plasma electron). Damping of the Cerenkov radiation due to collisions of plasma electrons is also discussed.

Fluctuations in a Plasma I: Ion-Electron Temperature Relaxation

Fluctuations of the electric field in a plasma are treated on the basis of the fluctuation-dissipation theorem. The treatment is applied to the relaxation between ion and electron temperatures. The interaction between ion and electron which causes the relaxation is reduced to the interaction between the ion and the fluctuating electric field caused by the surrounding electrons. The short range encounters between electrons are neglected but the long range encounters are included through the dielectric permeability which is obtained use of the fluctuation–dissipation theorem. The rate of relaxation agrees with the result obtained Kihara et al. who considered that the ion interacts with the individual electrons.

Thermodynamic coupling of diffusion with chemical reaction

On the basis of the nonlocal phenomenological relation between thermodynamic fluxes and forces in continuous systems, it is shown that the vectorial flux couples with the scalar force even in an isotropic system. This result has application to active transport in living organisms and to thermonuclear fusion research.

Unified Theory of Relaxations in Plasmas. V. Formulation from Liouville Equation

From the Liouville equation a kinetic equation is derived which is exact in the sense that exact numerical factors can be given in the arguments of the Coulomb logarithms. The kinetic equation is written in the form of the connection formula obtained in Part I or Part III . The connection formula is generalized so as to make it possible to treat rapidly varying or inhomogeneous plasmas in external fields.

HIGH-FREQUENCY CONDUCTIVITY OF PLASMAS

The unified theory developed by Kihara and the present author is applied to oscillatory phenomena. As an example the response of two-component plasma to high-frequency electric fields is investigated. The increment of the plasma frequency and damping coefficient of the plasma oscillation are obtained.