The modulational instability development of Langmuir and electromagnetic waves is reviewed in highly collisional plasmas where the characteristic frequency of the modulated perturbations is much less than the effective electron collision frequency. All calculations are based on Braginskii's system of hydrodynamic equations in collision--dominated plasmas and use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. It is demonstrated that the modulational instability for the situation considered is mostly determined by collisional effects (differential Joule heating nonlinearity), in contrast to the wellknown modulational instability in collisionless plasmas (where ponderomotive force nonlinearity dominates). Rates and thresholds of the instabilities are found in various limits. Coupled nonlinear Langmuir and sound waves are presented. Theory taking into account combined effect of the differential Joule heating, ponderomotive force and relativistic electron mass variation on the instability of electromagnetic waves is presented. Effects of magnetic fields are briefly discussed.

1. Introduction.........................................................................................................................161

2. General nonlinear formalism...................................................................................................162

3. Basic equations....................................................................................................................164

4. Linear perturbations in collisional plasmas.................................................................................164

4.1. Low-frequency solutions.........................................................................................................164
4.2. Low-frequency dielectric permittivity.....................................................................................165
4.3. High-frequency solutions........................................................................................................166

5. Effective third-order plasma response.....................................................................................167

5.1. Responses of second-order in wave field...............................................................................167
5.2. Responses of third-order in wave field...................................................................................169

6. Instability of Langmuir wave...................................................................................................170

6.1. Evolution equations..................................................................................................................170
6.2. Instability rates.........................................................................................................................171

7. Coupled Langmuir and nonlinear sound waves............................................................................173

7.1. Equation for wave fields............................................................................................................173
7.2. Quasi-stationary solution........................................................................................................174

8. Instabilities of electromagnetic waves.....................................................................................175

8.1. Instabilities in highly collisional underdense plasmas............................................................175
8.2. Combined effect of Joule heating, ponderomotive force, and relativistic nonlinearities.........176
8.3. Effects of magnetic field.............................................................................................................177

9. Conclusions.........................................................................................................................178
Acknowledgements..................................................................................................................179
References............................................................................................................................179

Return to Chapters in Books and Major Reviews Page

S.Vladimirov@Physics.usyd.edu.au

Return to my Home Page