The rich nonlinear phenomena that occur in plasmas are reviewed in a systematic way. The foundations of turbulence theory (both weak and strong) and experiments performed in the past decade to verify such theories are presented. The aim is to emphasize those experiments that demonstrate clearly the validity (or failure) of some of the theories. In particular, we discuss experiments that demonstrate the validity and/or limits of weak turbulence theory, strong turbulence theory, parametric instabilities, echoes, trapping of particles in large-amplitude waves, and electrostatic ion acoustic shocks. We present concluding remarks in each section regarding the present status of each of these phenomenon.

Nonlinear wave effects in laboratory plasmas: A comparison between theory and experiment

Anomalous Absorption of Electromagnetic Energy through Parametrically Induced Lower-Hybrid Turbulence

The stability of ion Bernstein waves (frequency ω, wave number ) in a plasma with two ion species pumped by a magneto-acoustic wave (ωp, p) which propagates perpendicularly to the static magnetic field is studied. The background plasma is assumed to be infinite, homogeneous and collision-free. If ωp > |ω| is properly chosen, ion Bernstein waves become unstable (decay instability, non-linear Landau instability) at rather low values of the pump electric field amplitude |D|. The instability is excited by the relative drift motion of different species induced by the pump wave. Assuming |⋅(a−b)|1 (a = displacement for particles of species a, a = e, 1, 2) the general non-linear dispersion relation is approximately solved in a deuterium-tritium plasma for two different : In case A (=⊥ ∥ p) only the relative ion motion d⋅t comes into play; this gives rise to decay instabilities which are only present in plasmas with two ion species. The instabilities of case B(k⊥ ⊥ kp, kz ≠ 0) caused mainly by the relative electron-ion drift motion are similar to those in plasmas with only one ion species. For given |p| the growth rates in both cases are equal in order of magnitude (for low values of ωp, case A is slightly more favourable); however, in case A the theory is valid up to considerably higher values of |p|. Some effects depending substantially on the presence of two ion species are discussed in detail.

http://iopscience.iop.org/0029-5515/14/5/008/pdf/0029-5515_14_5_008.pdf

Parametric excitation of ion Bernstein waves in a plasma with two ion species

A survey of parametric instabilities in plasma, and associated particle heating, is presented. A brief summary of linear theory is given. The physical mechanism of decay instability, the purely growing mode (oscillating two-stream instability) and soliton and density cavity formation is presented. Effects of density gradients are discussed. Possible nonlinear saturation mechanisms are pointed out. Experimental evidence for the existence of parametric instabilities in both unmagnetized and magnetized plasmas is reviewed in some detail. Experimental observation of plasma heating associated with the presence of parametric instabilities is demonstrated by a number of examples. Possible application of these phenomena to heating of pellets by lasers and heating of magnetically confined fusion plasmas by high power microwave sources is discussed.

/pdf/high-frequency-parametric-wave-phenomena-and-plasma-heating-4axvu5xtlc.pdf

High frequency parametric wave phenomena and plasma heating: A review

An integral equation which generalizes the dispersion relation for electrostatic plasma modes with wave numbers in the presence of a large-scale magnetoacoustic (pump) oscillation is derived. This calculation is accurate to all orders in the parameter where is the amplitude of the particle displacement induced by the pump wave. Expanding in the latter parameter, we obtain a second-order differential equation including three-wave processes, non-linear frequency shifts and nonlinear Landau damping. The electromagnetic wave may disintegrate into two Bernstein waves (three-wave interaction) if the appropriate resonance condition (between the real parts of the frequencies) can be satisfied approximately. However, a Bernstein wave can still be excited when the resonance condition is not fulfilled. In the latter case, instability arises through inverse non-linear Landau damping, and the non-linear dispersion relation can be approximated, to a high degree of accuracy, by a three-by-three matrix. In the former case, the dispersion relation reduces, to a good approximation, to the standard two-by-two matrix only if the linear decrements of both electrostatic waves are sufficiently small; otherwise, the three-wave process identifies with the non-linear Landau instability calculated in the appropriate limit (of matching between the real parts of the frequencies). The relative importance of resonant and off-resonant coupling of the pump wave to the plasma is discussed.

Excitation of electrostatic plasma turbulence by a magneto-acoustic wave

The possibility of heating a Tokamak plasma with the help of a compression wave induced in the plasma by a wave guide system is considered. The frequency of the wave is a high harmonic of the ion cyclotron frequency. Plasma heating cannot occur through linear resonant mechanisms. Heating due to the non-linear amplification of ion Bernstein modes is studied, taking into account the existence of the magnetic surfaces and the non-uniformity of the static field. The value of the wave field which is necessary to obtain effective plasma heating is calculated.

https://iopscience.iop.org/article/10.1088/0032-1028/15/8/004/pdf

Non-linear heating in a Tokamak plasma

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Non-linear heating in a Tokamak plasma