Trapped Particle Effects Research Articles

Linear amplitude oscillation of a whistler wave excited by high power microwaves

Large-amplitude whistler waves launched from an open-waveguide antenna are found to exhibit amplitude oscillation as if due to trapped-particle effects. However, the possibility of such nonlinear effects has been excluded by propagation measurements of the small-amplitude test wave. Two-dimensional ray tracing has revealed that the amplitude oscillation observed along lines of force is closely related to snakelike motions of whistlers in an inhomogeneous plasma. The ray trajectory is calculated in a simple geometry, and the results are in good agreement with the experimental observations.

SOLITONS, ENVELOPE SOLITONS IN COLLISIONLESS PLASMAS

A review is given to extensive development of theoretical, computational and experimental studies of nonlinear wave propagation in collisionless plasmas. Firstly, the historical experiment of Ikezi et a/. is discussed in comparison with theoretical analysis based on the Kortewegde Vries equation. Systematic discrepancy between the observation and the theoretical prediction suggests that it is necessary to examine such as higher order mode coupling effect and contribution of trapped particles. Secondly, effects of the nonlinear Landau damping on the envelope soliton of ion plasma wave is discussed on the basis of theoretical study of Ichikawa-Taniuti, experimental observation of Watanabe and numerical analysis of Yajin~a et al. Finally, a new type of evolution equation derived for the Alfven wave is examined in some detail. The rigorous solution obtained for this mode represents a new kind of envelope soliton, in which both of its phase and amplitude are subject to modulation of comparable spatial extension. In conclusion, the emphasis will be placed on the fact that much more intensive experimental researches are expected to be done, since the powerful methods to disentangle various nonlinear evolution equations are now available for theoretical approach.

On the effect of trapped particles in the regime of cyclotron resonance

The motion of particles in a finite amplitude wave, propagating obliquely to the homogeneous magnetostatic field is discussed. As follows from simple integral properties, in the neighbourhood of Doppler-shifted cyclotron resonance similar trapping effects appear as in a plasma without magnetostatic field. Consequences of this trapping are discussed, in particular, the possibility of a strong absorption of the wave, and the origin of stochastic instabilities caused by the perturbation of an effective trapping potential and leading to the acceleration of particles.

Effect of trapped particles in an electrostatic wave on the whistler mode

It is shown that there exists a new series of resonances due to the interaction between a whistler propagating along an ambient magnetic field and the particles which are trapped in a large amplitude electrostatic wave. These resonances seem to produce sideband growths of the whistler.

Effects of neutral injection heating upon toroidal equilibria

Effects of neutral beam injection upon the equilibrium of a toroidal plasma are considered. The distribution function of energetic ions produced by the beam in the plasma is calculated for injection both parallel and perpendicular to the magnetic field taking account of effects due to the toroidal geometry. The effect of trapped particles on the current induced in the plasma by such a beam is calculated, together with the associated cross-field diffusion. Loss mechanisms for the momentum deposited in the plasma by the neutral beam are considered. Ripples in the toroidal magnetic field strength are particularly efficient at destroying toroidal momentum and lead to flow velocities much less than the sound speed for typical injection parameters.

Collisional resistivity in low aspect ratio tori

The electrical conductivity of a toroidal plasma in the long mean free path limit is evaluated for finite values of the aspect ratio by using physical arguments on the effect of trapped particles.

Steady-state solutions of the neo-classical transport equations

The neo-classical transport equations of Rosenbluth, Hazeltine and Hinton have been solved for steady-state conditions in which the trapped-particle pinch effect balances the particle diffusion. By using the banana-regime coefficients at all radii (this introduces only small errors for steady-state solutions) and the simplest possible boundary conditions, the solutions for a given aspect ratio are found to depend on the single parameter , where a is the minor tube radius and ωpi the ion plasma frequency for the central density. The results indicate (i) a permanent skin current at intermediate values of α2, (ii) the importance of the trapped-particle Ettingshausen effect, (iii) the relative unimportance in the steady state of trapped-particle effects on the current and (iv) almost constant . Item (iv) agrees with the T-3 experimental results and the numerical values show no large anomaly in the electron thermal conductivity other than that caused by the increased collision frequency which is indicated by the observed average electrical conductivity .

Applicability of quasi-linear theory for dynamical plasmas

Validity of quasi-linear theory as an initial value problem is shown to depend on sufficient localization of the disturbance, which condition prevents saturation due to trapped particle effect.

Effect of Trapped Particles on the Drift-Cyclotron Instability in a Multipole

The effect of trapped particles on the drift-cyclotron instability in a multipole machine has been considered. Dispersion equations have been obtained for this instability in a nonuniform collisionless plasma using a simplified approach which takes into consideration the magnetic field strength and curvature variation along field lines. The results show the existence of a branch of oscillations with frequency $|\ensuremath{\omega}|\ensuremath{\sim}{\ensuremath{\Omega}}_{0}\ensuremath{-}k{\overline{v}}_{g}\ensuremath{-}{\overline{\ensuremath{\omega}}}_{b}$, where ${\ensuremath{\Omega}}_{0}$, ${\overline{v}}_{g}$, and ${\overline{\ensuremath{\omega}}}_{b}$ are the average gyrofrequency, the drift velocity due to magnetic field gradient, and the ion bounce frequency, respectively, with $k$ being the wave vector transverse to the magnetic field. This may explain the discrepancy between the experimentally observed frequency and the theoretical value obtained previously. This branch of the oscillation also shows a larger growth rate.

Effects of Electron Emission on Electrostatic Probes at Arbitrary Pressures

A systematic investigation of the effects on probe response caused by electrons emitted with a half-Maxwellian distribution is performed. In the absence of collisions a theory for spherical and cylindrical probes in a plasma of infinite extent is formulated, based on orbit calculations. A simple method is developed which greatly facilitates the solution of the space-charge-limited emission problem. The structure of the resulting double sheath is analyzed in detail. Effects of trapped particles are found to be unimportant under practical situations. Solutions of current-voltage characteristics and space-charge-limited current are presented for the case of thermionic emission. Theories in the transitional and continuum regimes for a spherical probe in a weakly ionized gas are formulated by the moment method. For a dense plasma with a free fall sheath the emission is usually both space charge and diffusion limited.

Effect of Trapped Particles on Nonaxially Symmetric Toroidal Equilibria

The effect of trapped particles on nonaxially symmetric toroidal plasma equilibria in the guiding-center limit is treated by means of the stellarator expansion. A few particles, trapped in the mirrors associated with the small-amplitude helical field, can induce an electrostatic field in a manner analogous to that which appears in the familiar treatment of nonlinear electrostatic oscillations in a one-dimensional plasma. These trapped particles directly affect the component of the current along the field and hence the final magnetic field configuration. Thus, they modify the diffusion across magnetic flux surfaces when small resistivity is introduced.

Drift Instabilities in General Magnetic Field Configurations

A theory of low-frequency drift (universal) instabilities in a nonuniform collisionless plasma is developed for general magnetic field configurations including trapped particle effects, rather than the plane geometry which has previously received most attention. A type of energy principle shows that the special equilibrium distribution F(∈, μ), of interest in minimum-B mirror configurations, is absolutely stable to these modes provided ∂F/∂∈ < 0 together with a second condition on ∂F/∂μ. For equilibrium distributions not of this special form, in particular for a Maxwell distribution with a density gradient, the case of axisymmetric toroidal configurations with closed poloidal field lines is considered in detail. Three unstable drift modes are found, a flute-like mode, a drift-ballooning mode local to the region of unfavorable curvature, and a drift-universal mode. Stability criteria and growth rates for the modes are given. The equations also describe a recently discussed low-frequency trapped-particle instability.