Critical Value Ec Research Articles

Ion-cyclotron resonance heating in a strongly inhomogeneous magnetic field

Single particle ion-cyclotron resonance heating in a strongly inhomogeneous magnetic field with constant scale length κ−1 is studied for a uniform rf field. Because the ion-cyclotron frequency is energy dependent, ions get out of resonance, exhibiting superadiabatic response with no time-averaged energy gain. However, the anharmonicity of the motion results in resonances at multiple energy values, and for rf field amplitudes above a critical value Ec, these resonances overlap, resulting in stochastic heating. Explicit analytic expressions are given for the particle orbits and for Ec as a function of energy and rf frequency.

Effects of the fast wave on the drift-cyclotron loss-cone mode

Particle orbits in the presence of the fast wave fields are calculated. It is found that the resonant interaction of ions with the wave can be neglected at ω0 = 2ωci, provided that the wave electric field strength is less than a critical value Ec( = 4k∥T/e). The dominant effect on the dispersion relation of the drift‐cyclotron loss‐cone mode is thus found to be due to the nonresonant effects of the wave on electrons and ions. It is found that a fast wave with ω0 = 2ωci destabilizes the mode. For ω0<2ωci, fast waves can stabilize the mode for certain values of the plasma β, which is calculated numerically.

On the Nonlinear Kinetics in A Weakly Turbulent Plasma

The nonlipear kinetics of waves in a weakly turbulent classical plasma is investigated from a quantum mecnanical viewpoint. It is shown that the lowest order nonlinear effects in the long wave length region arise not only from the Compton scattering of plasmons by electrons, which is the only process previously considered, but also from the absorption and emission of plasmons accompanied by a collision between two electrons. The latter has an effect to smooth out the spectral distribution of the waves, while the former (the Compton scattering, process) exhibits two distinct effects depending on the magnitude of the total wave energy E; for E smaller than a certain critical value EC the Compton scattering process smooths out the wave distribution, while for E greater than EC the wave energy is directed towards the longest wave length region. The value of EC is roughly estimated to be four times the thermal level.

Run-aways im Neutralgas

The motion of electrons as determined by the field acceleration and the elastic and inelastic collisions with the gas atoms is calculated from the BOLTZMANN equation. We derive the average velocity and the scattering ellipsoid as a function of time. For particles starting from rest there exists always a critical electric field Ec depending on pressure and temperature. Below this critical value electrons approach the stationary drift process. Above the critical value the electrons do not reach a stationary state, they “run away”. For a finite initial velocity ν0 and a field below the critical value Ec the particles are either accelerated to drift, or decelerated to drift, or “run away”, depending on the value ν0. From a calculation of the scattering parameters we find for E &gt; Ec a focussing effect in the velocity space which increases with field strength. Also the relaxation time for the drift process and the stopping power for electron beams can be calculated. Applications to the glow discharge are discussed.