Yoshinosuke Terashima

Stochastic model of electron-cyclotron heating in a magnetic mirror

A heating mechanism of electron plasmas by high-power microwaves in a magnetic mirror is investigated theoretically, with reference to experiments in a device named TP-M. The heating is assumed to be due to a microwave mode propagating perpendicular to the magnetic field since higher harmonic resonances, the main features of the experiments, exist. The heating mechanism can be interpreted in terms of a stochastic process, a random walk in velocity space.It is confirmed numerically that localized resonance zones of finite width exist, the electrons are effectively heated only in the resonance zones, and that the presence of a randomization process of the relative phase relation between the wave and the electron gyration is essential for the heating process. On the basis of the numerical analysis, the heating process is treated analytically. The electrons are assumed to pass the resonance zones repeatedly in the course of oscillatory motions between turning points, and the relative phase relation is assumed to be random at each passage through the resonance zone. The heating rate is calculated and found to agree with the experimental value. The causes of phase randomization, the effects of the loss cone and the observed saturation of electron temperature are also discussed.

A Scaling Law for High Density Tokamaks and Its Application to J.I.P.P. T-II Device

A scaling law for high density and high current tokamaks is presented on the basis of the nonlocal theory of electrostatic current-driven drift instability in both collisionless and collisional regimes with the assumption of quasilinear saturation level. It is shown that the energy confinement time scales as (tau_{E}{propto}nq(a)/sqrt{T_{e}}) ( n , T e and q ( a ) are the averaged density, electron temperature and the safety factor at the plasma edge.) in relatively lower density region and (tau_{E}{propto}B/sqrt{n}) ( B is the toroidal magnetic field) in higher density region where a combined effect of the electron collisions and of a plasma current works. Trapped particle effects are assumed to be negligible and no magnetic fluctuation is considered. A test experiment of the scaling law on the J.I.I.P.T-II device where both tokamak operation and the operation with superposition of helical fields are possible is proposed.

Nonlinear heat and particle transport due to collisional drift waves

A nonlinear analysis of collisional drift instability is developed in a slab model based on the two fluid equations, where inhomogeneities in electron and ion temperatures and unperturbed current are included in addition to ion inertia, finite ion gyroradius, and viscosity. A systematic expansion is introduced by taking e=‖κ‖l as a smallness parameter, where κ is the degree of density gradient and l is the linear scale of the slab along the density gradient. The nonlinear development of the drift wave near marginal stability is studied on the basis of the model equations. A new feature, hard excitation, has been found, which is due to the effects of the nonlinear frequency shift and the electron temperature gradient. The saturation amplitude is calculated, and the expressions for wave‐associated particle and heat fluxes are obtained. A comparison of the expressions with the experimental results of a stellerator device is also made.

Numerical Study on Drift and Alfven Waves in a Current-Carrying Plasma

A set of coupled eigenmode equations for drift and Alfven modes in a current-carrying stab plasma with magnetic shear is studied numerically. The modes with odd-φ and even- A // parity are investigated where φ and A // are the electrostatic potential and the parallel component of the vector potential of the perturbations, respectively. The shear Alfven mode of this parity is marginally stable for the high β value, and the drift mode of this parity is more stable than that with even-φ and odd- A // parity. Electron-ion collisions are found to stabilize both the modes. The current can not make both the shear Alfven mode and the drift mode unstable. The former remains marginally stable and may contribute to the anomalous transport.

Numerical Analysis of Nonlinear Collisional Drift Instability

Nonlinear evolution of collisional drift wave instability is studied numerically. The model equations of quasilinear type are used which describe the modification of background density and the amplitude of unstable drift wave. Their solutions are classified according to the value of a parameter η which is proportional to the ratio of ion viscous damping to linear growth rate γ L . In the vicinity of marginal stability the unstable drift waves are shown to be saturated by flattening of the background density. As η decreases further we first obtain periodic and latter aperiodic solutions. The wave associated diffusion coefficient is obtained numerically as a function of η and found to be much less than the usual estimate γ L / k ⊥ 2 .

Particle Trajectories in Cross-Field Acceleration by an Electrostatic Wave Transverse to Uniform Magnetic Field

Particle trajectories in the wave frame are expressed in an integral form which elucidates the roles of the applied electrostatic wave field and of the induced V p × B field. Both the non-relativistic and relativistic cases are treated. In each case, the energy integral is shown to exist and a criterion for transition from trapping to detrapping is obtained, and thereby the optimum value of energy gain is deduced. It is shown that, when the E × B velocity, υ E , due to the wave field in the wave frame is less than the light speed, the Lorents factor of an accelerated particle, γ(υ), is almost limited by γ c =(1-υ E 2 / c 2 ) -1/2 , while for υ E > c , γ(υ) possibly increases linearly with time.

An Energy Integral and Variational Principle for Plasma Kinetic Modes

An energy principle is extended to include kinetic processes, finite gyroradius effects and wave-particle interactions, in electromagnetic instabilities in a toroidal plasma. The present arguments are based on the energy integrals which are derived from the eigenmode equations for electromagnetic perturbations. First, the finite gyroradius effects are included in the energy integral and it is shown that this integral can be used for determining the eigenmode by minimizing the excess energy of the perturbed state. The generalized stability conditions for kink-like mode and ballooning mode are obtained by use of this improved energy principle. For the case where wave-particle interaction is important, the energy integral becomes a rate equation of energy exchange, and a variational form can independently be constructed for the mode analysis.