Yukio Midzuno

Non-Stochastic Heating of Magnetized Plasma by Electrostatic Wave

When an electrostatic wave is suddenly applied, initially trapped particles suffer a rapid, large acceleration as well as the stochastic heating, while initially untrapped particles suffer only the stochastic heating. When the bounce frequency ω B is larger than (ω c ω) 1/2 , the initially trapped particles mainly absorb the wave energy and form a high energy tail. The results are applied to the problem of energetic ion creation in laser fusion plasma and of a high energy tail formation in a plasma heated by the lower hybrid wave.

Statistics of Two-Dimensional Lattices with Many Components

The statistics of the two-dimensional Ising lattice, for which each lattice site may take one of two states, has been partly generalized to the following model: each lattice site may take one of s states and each pair of neighboring sites in different states has a common excess energy, J , compared with a pair of neighboring sites in a same state. The partition function for the square lattice has a temperature symmetry and the Curie temperature, T c , is given by \begin{aligned} (s-1)\exp(-2J/kT_{c})+2\exp(-J/kT_{c})-1{=}0, \end{aligned} ( k is the Boltzmann constant). Although the partition function itself has only been obtained in the form of power series valid at low and high temperature regions, it is highly probable that for any finite s the specific heat is infinite at the Curie temperature. The transition is not the normal phase transition of the first order which the Bragg-Williams approximation predicts for our lattice with s ≧3.

Non-additive Intermolecular Potential in Gases I. van der Waals Interactions

The potential energy of van der Waals interactions between three spherically symmetric atoms at large separations has been investigated both by perturbation theory and by variation method. Without using any particular atomic models the van der Waals interaction is derived, from second and third-order perturbations, in the form \begin{aligned} -\mu_{12}{r_{12}}^{-6}-\mu_{23}{r_{23}}^{-6}-\mu_{31}{r_{31}}^{-6}+\nu(r_{12}r_{23}r_{31})^{-3}(3\cos\theta_{1}\cos\theta_{2}\cos\theta_{3}+1), \end{aligned} where r i j is the distance between i th and j th atoms, θ i s are inner angles of a triangle formed by the three atoms. An approximate relation between µ and ν is found by variation method: \begin{aligned} \nu{=}\frac{2R_{1}R_{2}R_{3}(R_{1}+R_{2}+R_{3})}{(R_{1}+R_{2})(R_{2}+R_{3})(R_{3}+R_{1})}, \end{aligned} in which \begin{aligned} \frac{1}{R_{1}}{=}\frac{1}{\mu_{12}\alpha_{3}}+\frac{1}{\mu_{31}\alpha_{2}}\frac{1}{\mu_{12}\alpha_{3}}-\frac{1}{\mu_{12}\alpha_{3}}\quad\text{etc}, \end{aligned} α i being the po...

Virial Coefficients and Intermolecular Potential of Helium

The intermolecular potential of helium has been determined from an analysis of the second and the third virial coefficients above the Boyle temperature, where the virial coefficients can be expanded into power series on h 2 , the square of Plancks constant. The series have been calculated up to the term proportional to the third power of h 2 in case of the second virial coefficient and up to the term proportional to the first power of h 2 in case of the third virial coefficient. The following conclusion has been drawn. The two-body system of He 4 atoms has a discrete energy level while the two-body system of He 3 atoms has no discrete level.

NONLINEAR BEHAVIORS OF WAVES IN A PLASMA IN THE VICINITY OF MARGINALLY STABLE STATE.

Nonlinear behaviors of monochromatic traveling waves are discussed by the use of an asymptotic method. The wave is assumed to be stationary in the first approximation and nonlinear interactions are taken into account only among the wave under consideration and its harmonics. It is shown that two cases are distinguished according as the frequency of the wave in the first approximation is given by a simple root or a double root of the dispersion relation. Characteristic behaviors of the wave in the latter case are investigated by discussing a model equation and special cases of two-beam instability. The behaviors of the complex amplitude of the wave are visualized in the form of “a motion of a particle in an axisymmetric potential field”. Various phenomena, such as amplitude oscillation, explosion of amplitude, amplitude-dependent frequency shift, are found to take place depending on the plasma and the initial condition.

Induction of DC Current by an RF Travelling Wave in a Strong Magnetic Field

On the basis of a simple model the DC current induced by an RF travelling wave is calculated. It is assumed that the initial velocity distribution of electrons is Maxwellian and that the electrons move adiabatically on a magnetic line of force. The average electron velocity attained when B w / B 0 ≪1 is found to be \({\ll}\nu_{z}{\gg}_{\text{L}}{=}1.639\nu_{\text{ph}}\exp\left(-\frac{1}{2}m_{\text{e}}\nu_{\text{ph}}^{2}/T_{\text{e}}\right)(B_{\text{w}}/B_{0})^{3/2}\), where the axial magnetic field is assumed of the form: B ( Z )= B 0 + B w cos k ( z -ν ph t ). An evaluation and discussion are made on the required RF power for sustaining the plasma current in Golovins model of the Tokamak fusion reactor.

Ion-Electron Relaxation of Plasmas in a Magnetic Field, II.

Relaxation between ion and electron temperatures, T 1 and T 2 , of dilute fully ionized gases in a magnetic field has been treated by force-correlation method. The rate R of the relaxation, defined by \begin{aligned} d(T_{2}-T_{1})/dt{=}-(T_{1}-T_{1})R, \end{aligned} increases with increasing magnetic field from

Transport Properties of Plasmas in a Strong Magnetic Field

Irreversible processes in plasmas in a strong magnetic field are discussed from both phenomenological and microscopic points of view. The thermodynamics of irreversible processes is applied and it is shown that the Onsager-Casimir reciprocity relation takes a symmetrical form for plasmas in a magnetic field. For a two-component fully ionized gas where the electrons make many free gyrations interference between electrical and thermal conductions vanish. When the mean gyration radius r g of the electrons is shorter than the Debye length l D , the diagonal elements of tensors of the electric conductivity and diffusion coefficient perpendicular to the magnetic field are proportional to \begin{aligned} \ln(kTl_{D}/Ze^{2})+(3/4)[\ln(l_{D}/r_{g})]^{2}, \end{aligned} where Z e and - e are the charges of an ion and electron respectively.

Virial Coefficients and Intermolecular Potential for Small Nonspherical Molecules

It has been proved that for a special model of nonspherical intermolecular potential the nonspherical correction to the virial coefficients is equivalent to the quantum correction. The second and third virial coefficients of hydrogen has been investigated by use of this model, and the intermolecular potential has been determined, which can be compared with the result of quantum-mechanical calculations. The model has also been applied to the second virial coefficient between argon and hydrogen.

Trapping of Charged Particles by a Travelling Wave with Increasing Phase Velocity

The number of charged particles which are trapped by an accelerated wave in a plasma is calculated on the basis of a simple model. It is assumed that particles move adiabatically in travelling mirr...