Ichiro Kawakami

Expansion and Thermalization of Plasma in a Non-Uniform Magnetic Channel

Theoretical investigations of the unsteady motion of plasma in a magnetic channel are made on the basis of the hydromagnetic theory of an ideal fluid. A set of one dimensional equations on which the investigations are made is derived in the near-axis approximation from three dimensional equations. Using these equations dynamical expansion of an initially uniform plasma at rest contained in a region of strong magnetic field into a region of weaker field, and shock thermalization of the expanding plasma on colliding with a rigid wall (or with another flow in the opposite direction) or being decelerated by a magnetic barrier are investigated. Analyses are made both analytically and numerically.

Perturbation Approach to Nonlinear Vlasov Equation

A new perturbation theory based on a canonical transformation for solving the Vlasov equation is developed. The theory is designed to cope with time secularities. The method is based on the transformation of orginal system to the new system where the particle is in free motion, that is, the transformed Vlasov equation is of free streaming. Practical calculation is systematic but restricted to the second order approximation in the expansion parameter (wave potential energy/particle kinetic energy). The result is used to obtain Fokker-Planck type equation, and a velocity space diffusion coefficient is obtained.

Axial Behaviors and Confinement of the Plasma in the Mirror Field Theta Pinch

The mechanism of the end loss and the axial behaviors of a mirror θ-pinch plasma are studied. For this purpose, both the mirror and the straight field configurations are used at the first half cycle controlling the reverse bias field. The end loss in the mirror field is found to be decided by the axial motion, which is caused by the axial pressure gradient of the plasma due to the axially inhomogeneous magnetic field. The e -folding time of the decaying plasma at the midplane agrees well with the result of the numerical calculations on the basis of non-steady M.H.D. equations. The relation between the confinement time and the initial conditions of produced plasma is discussed.

Perturbation Approach to Nonlinear Vlasov Equation. III. Stationary Nonlinear Oscillation

One-dimensional stationary nonlinear electrostatic waves which are periodic in space are investigated by use of the perturbation method. The distribution functions are derived. For these functions, some conditions under which there exists periodic waves are derived.

Gravitational Instability in a Plasma in a Magnetic Field I. Ideal Magnetohydrodynamics

The instability of a plasma supported under gravity by a magnetic field is reconsidered using the magnetohydrodynamic equations of a perfectly conducting fluid. It is shown that the wave number ( k ) of physically important perturbations is limited to k a ≃1 by a finite thickness ( a ) of the plasma-vacuum boundary surface, and the instability growth rate is given by ≃( g / a ) 1/2 . There are some experimental supports for this result in the theta-pinch data. It is also pointed out how the interchange picture of the instability for a low β case will be generalized in a high β case, where β=(plasma pressure)/(magnetic pressure).

Finite element method with optimal nodal velocity

Abstract The finite element method FEMALE [15] is outlined. Accuracy is much improved when the velocity of a finite element is equal to that of a local nonlinear wave. In this paper we give a proof of the improvement of accuracy for the discretized equations. The need for node annihilation is discussed for a hyperbolic system of equations and a restructuring algorithm of finite elements is proposed.

The Drift of a Theta Pinch Plasma Due to the Asymmetry of Magnetic Field

The effects of the 1 % local magnetic field asymmetry on the confinement of a low \(\dot{B}\)(\(\cong 10^{8}\) Gauss/sec) theta pinch plasma were studied by means of high-speed photograph. The plasma drifts radially toward the region where the strength of the magnetic field is minimum. The mean drift velocity is several ×10 5 cm/sec. It decreases appreciably as the field strength at the instant of the crowbar loweres less than 0.5 of the maximum in a half-cycle. The outward acceleration in the early stage was found to be \begin{aligned} \alpha{=}\frac{2k(T_{e}+T_{i})}{m_{i}a\beta}\left(\frac{b}{B_{0}}\right), \end{aligned} by the magnetohydrodynamic model where b / B 0 is the degree of the field asymmetry and a is the radius of the plasma column. The dependences of the observed drift velocity on the time of the crowbar and on the initial pressure are explained according to the above formula. The 1 % local field asymmetry gives a serious limitation On containment of a high-temperature plasma.

GRAVITATIONAL INSTABILITY IN A PLASMA IN A MAGNETIC FIELD. II. PARTICLE PICTURE FOR COLLISIONAL DAMPING IN A WEAKLY IONIZED PLASMA

The instability of a plane boundary of Plasma supported under gravity by a magnetic field is investigated in the first order orbit theory taking into account the collisions between charged and neutral particles, where the collision frequency is assumed to be small as compared with the Larmor frequency. It is demonstrated that the instability growth rate may be suppressed by collisions of ions with neutral particles, and the physical mechanism of the stabilization is the “discharge” of surface charges as a result of the collisional drift motion of ions which takes place across the magnetic field in the direction of the produced electric field. The results are applied to the slow theta-pinch experiments in order to understand the observation of no Rayleigh-Taylor instabilities in the contraction stage of the slow theta-pinch.