In many real physical and astrophysical situations, an external magnetic field is present. The magnetic field results in a variety of specific plasma modes and leads to an anisotropic distribution of plasma oscillations. The present review reflects the present state of the theory of modulational interactions in magnetized plasmas. Modulational interactions are considered on the basis of a simple and universal approach using new methods developed for the description of the modulational effects in arbitrary media. This approach enables us to visualize the physical processes occuring in plasmas in the presence of modulational interactions. Emphasis is given to the role of modulational interactions in the processes of particle acceleration, generation of current drive, physical phenomena in the Earth's magnetosphere and in active geophysical and space experiments. The influence of boundary conditions and plasma inhomogeneity is considered in detail. These effects can essentially change the dispersion properties of plasma modes, and their influence can be even more significant than effects of plasma anisotropy (caused by the external magnetic field) or thermal corrections to the dielectric permittivity tensor. Modulational interaction is the most important nonlinear process for waves excited as a result of the lower-hybrid drift; in particular, the modulational interaction determines the saturation mechanism for this instability which in turn enables us to obtain the effective collision frequency and to estimate the width of the Earth's magnetopause region. The theory of modulational interactions is presented for the explanation of magnetic structures, particle spectra, and the electric field amplitude observed in active geophysical experiments.

1. Introduction.........................................................................................................................330

2. General nonlinear formalism...................................................................................................333

3. General nonlinear equation for lower-hybrid waves....................................................................335

3.1. Linear LH waves........................................................................................................................335
3.2. Third--order responses............................................................................................................336

4. Modulational instability of monochromatic LH wave....................................................................340

4.1. Equation for modulational instability.........................................................................................340
4.2. Instability rates...........................................................................................................................341
4.3. Comparison with other nonlinear processes.............................................................................345

5. LH solitons.........................................................................................................................347

5.1. Effective third--order response................................................................................................347
5.2. Envelope solitons........................................................................................................................351
5.3. Solitons in the case of transverse virtual fields........................................................................354

6. Modulational instability and LH wave-particle interactions............................................................................................................................356

6.1. Modulational instability and LH plasma heating......................................................................357
6.2. Modulational instability and LH current drive..........................................................................358
6.3. Particle acceleration...................................................................................................................363

7. Modulational interactions in bounded plasmas............................................................................364

7.1. Linear dispersion relationships.................................................................................................364
7.2. Nonlinear equations for slowly varying amplitudes of potential.............................................366
7.3. Instability of monochromatic pump wave. Solitary solutions..................................................368
7.4. Soliton acceleration in inhomogeneous magnetic field.............................................................371
7.5. Solitons in inverse dispersion media.........................................................................................371

8. Modulational instability of LH drift waves.................................................................................374

8.1. Basic relationships.....................................................................................................................374
8.2. Linear solutions..........................................................................................................................376
8.3. Nonlinear responses..................................................................................................................378
8.4. Instability of monochromatic pump wave..................................................................................379

9. Macroscopic consequencies of modulational interactions in plasma of the Earth's magnetosphere.......385

9.1. Effective collision frequency.......................................................................................................385
9.2. Modulational instability and reconnection of magnetic field lines in the magnetopause........388

10. Modulational interactions and active experiments......................................................................390

10.1. Major observational data on the AMPTE barium release.....................................................390
10.2. Hydrodynamical LH drift instability.........................................................................................392
10.3. Modulational instability of waves excited due to hydrodynamical LH drift instability.........394

11. Conclusions........................................................................................................................399
Acknowledgements..................................................................................................................400
References.............................................................................................................................400

Return to Chapters in Books and Major Reviews Page

S.Vladimirov@Physics.usyd.edu.au

Return to my Home Page