Stochastic Ion Heating Research Articles

Lower-hybrid-heating data on the Wega experiment revisited, using ion-stochastic-heating and electron-Landau-damping theories

Previously obtained data on the Wega tokamak by lower hybrid heating (f = 500 MHz; PHF = 130 kW) are re-visited in the light of recent theories on ion stochastic heating and quasi-linear electron Landau damping. It is possible, with the help of these theories, to correctly estimate the fast-ion mean energy, the HF power density coupled to the ions and that coupled to the electrons. The values of the parallel index of refraction, N‖, which are necessary to obtain a good quantitative agreement between experiment and theoretical estimates, are the same for ions and electrons, although higher than expected.

Stochastic ion heating by an electrostatic wave in a sheared magnetic field

Effects of the shear of the magnetic field on the stochastic acceleration of ions due to an electrostatic wave with a frequency in the lower-hybrid range are considered. An appropriate Hamiltonian formalism is used to analyze the equations of motion numerically and theoretically. The surface of section method is used to visualize the solutions and to compare these with the theoretical predictions. From this analysis it appears that there exists an upper adiabatic barrier for the stochastic region which seems to be responsible for the formation of a hot tail in the ion velocity distribution. In addition to lowering the threshold for the onset of stochasticity, the effect of shear is to shift the tail structure to lower values of the velocities. Consequently, these results might help to improve the efficiency of heating by external radiation in the lower-hybrid frequency range.

Stochastic ion heating by a lower hybrid wave: II

The motion of an ion in a coherent lower hybrid wave (characterized by ‖k∥‖<<‖k⊥‖ and ω≳≳Ωi) in a tokamak plasma is studied. For ions satisfying v⊥≳ω/k⊥, the Lorentz force law for the ions is reduced to a set of difference equations which give the Larmor radius and phase of an ion on one cyclotron orbit in terms of these quantities a cyclotron period earlier. These equations exhibit stochastic behavior when the wave amplitude exceeds a threshold. The stochasticity threshold is given a simple physical interpretation. In addition, the difference equations are used to derive a diffusion equation governing the heating of the ions above the stochasticity threshold. Far above the stochasticity threshold, ion Landau damping is recovered. By including the effects of collisions, the heating rate for the bulk ions is obtained.

Stochastic ion heating by a lower hybrid wave

The motion of an ion in a lower hybrid wave in a tokamak type plasma is studied. For ions with ν⊥≳ω/k⊥ the motion is stochastic for fields satisfying E/B0≳ (1/4)(Ωi/ω)1/3(ω/k⊥). Provided that the perpendicular phase velocity, ω/k⊥, can be slowed down to a few times the ion thermal speed, this stochastic ion motion may be an important mechanism by which injected rf power near the lower hybrid frequency can directly heat the ions.

Stochastic Ion Heating by a Perpendicularly Propagating Electrostatic Wave

The motion of an ion in the presence of a constant magnetic field and a perpendicularly propagating electrostatic wave with frequency several times the ion cyclotron frequency is shown to become stochastic for fields satisfying $\frac{E}{{B}_{0}}>\frac{1}{4}{(\frac{\ensuremath{\Omega}}{\ensuremath{\omega}})}^{\frac{1}{3}}(\frac{\ensuremath{\omega}}{k})$. This stochasticity condition is independent of how close $\ensuremath{\omega}$ is to a cyclotron harmonic. Applications of current interest in supplementary heating of plasmas with rf power near the lower-hybrid frequency are suggested.

Cross-Field-Current Driven Lower-Hybrid Instability and Stochastic Ion Heating

A suprathermal electron beam is injected parallel to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$ in a low-$\ensuremath{\beta}$ plasma. The sharp space-potential drop across the surface of the beam generates a strong cross-field current which in turn drives a modified two-stream instability at the lower hybrid frequency. Intense stochastic ion heating is observed with the onset of the instability, and the heating rate is found to be proportional to the wave energy.

Stochastic heating of electrons and ions in an isothermal plasma by hydrodynamic current instability

Turbulent heating of electrons and ions by a collisionless shock wave propagating in a plasma across the magnetic field is investigated. Plasma heating in isothermal plasma occurs as a result of the development of hydrodynamic current instabilities. Heating of plasma subject to hydrodynamic current instabilities is caused by a stochastic mechanism. The temperature variation of the plasma particles at the shock front as well as an estimate of the heating time are obtained. The estimates agree well with the known experimental data.

Stochastic heating of ions in a modulated electron beam-plasma system

A modulation of an electron beam density at frequencies lower than an ion cyclotron frequency enhanced the low frequency instability of broad band and heated plasma ions in a beam-plasma system. The heating of ions is explained by the stochastic process of a weakly turbulent plasma.

Stochastic Ion Heating Due to the Parametric Ion-Acoustic Decay Instability

We report intense stochastic ion heating comparable to the electron heating, proportional to the energy density of the fluctuating electric fields of the ion-acoustic component of the decay instability. The ion-temperature rise time is comparable to, but longer than, the instability growth time, and many orders of magnitude shorter than collisional relaxation times.

Stochastic Ion Heating by Ion-Acoustic Turbulence

Stochastic Ion Heating by Ion-Acoustic Turbulence

Stochastic heating of the ions and electrons of a turbulent plasma with transverse current

Evaluations are given of the level of turbulent pulsations in a plasma with current flowing perpendicular to the magnetic field, in which longitudinal oscillations are excited with characteristic frequencyRe ω ∼ Im ω ∼ min{ ωpi} ≫ ωHiIt is shown that in such a plasma it is possible to have an effective stochastic heating of ions and electrons resulting in an increase in the transverse ion temperature and longitudinal electron temperature.