The main idea of a plasma maser effect is to use plasma nonlinearities for wave amplification when there is no inverse particle population. This possibility occurs when the particle distribution is a homogeneous and in the presence of intense radiation (waves). The nature of the plasma maser is a transition amplification of waves when they are scattered by inhomogeneities produced by plasma nonlinearities. The plasma-maser effect is a new nonlinear plasma process overlooked in most descriptions of nonlinear plasma physics. The necessary condition for amplification (or a new nonlinear absorption) is either that the system is open (presence of external energy or particle sources) or that the inhomogeneity is sharp compared to the wavelength of the amplified (absorbed) wave. Only a slight anysotropy of the pump waves is sufficient for amplification to be present. In the case of smooth inhomogeneities and in the closed system there is an adiabatic invariant - conservation of number of quanta of the amplified (absorbed) waves. Thus, the previous nonlinear theory can be valid only in this adiabatic limit. But even in this limit the pump waves can produce space and momentum fluxes of the test (amplified or absorbed) waves, changing their distribution in configuration and wave-number space. These nonlinear fluxes can be comparable with other nonlinear fluxes. Special attention is paid to the interaction of resonant and nonresonant waves both in open and closed systems. The nonresonant waves in this treatment are the test (amplified or absorbed) waves and the resonant waves are the pump waves. This interaction can lead to the amplification of a high-phase-velocity nonresonant waves by low-phase-velocity resonant waves (an example is the amplification of electromagnetic waves by plasma waves). A characteristic feature of the plasma maser effect is the possibility of an interaction of waves with a great difference in wavelengths and frequencies. This effect competes with other nonlinear effects which allow the interaction of waves within a narrow frequency interval and do not usually provide an interaction of waves with a large change in frequency (usually the domain of wavenumbers and frequencies of the waves is regulated by the resonant wave conditions). The plasma maser can produce a large up-conversion or down-conversion in frequencies and is not restricted in frequency domain although the efficiency of up- or down-conversion decreases with increasing frequency difference. The plasma maser can be considered to be a nonlinear dissipative amplification or absorption.

1. Introduction.........................................................................................................................143

1.1. Statement of the problem..........................................................................................................143
1.2. The simplest qualitative model.................................................................................................147

2. Direct nonlinear interaction between nonresonant and resonant waves...........................................149

2.1. Nonlinear dielectric permittivity for longitudinal waves..........................................................149
2.2. Nonlinear dielectric permittivity for arbitrarily polarized waves............................................152
2.3. The additional polarization contribution...................................................................................154
2.4. The role of spontaneous processes..........................................................................................155
2.5. Perturbation of heating of resonant particles...........................................................................158
2.6. Interaction of nonresonant waves with regular resonant fields..............................................160

3. Interaction of waves in closed systems.....................................................................................162

3.1. Nonstationarity..........................................................................................................................335
3.2. Spontaneous processes............................................................................................................169
3.3. Spatial inhomogeneity...............................................................................................................170
3.4. Arbitrary modes of oscillations.................................................................................................173
3.5. Higher orders of perturbation theory........................................................................................174
3.6. Degenerate plasma...................................................................................................................175

4. Nonlinear interactions in open systems: external sources and dissipative instabilities.........................340

4.1. External sources and a possibility for up-conversion............................................................178
4.2. The amplification of Langmuir waves due to electron-ion collisions.....................................183
4.3. Regular sources.........................................................................................................................186
4.4. Hydrodynamical approach.........................................................................................................188

5. Wave interactions in a plasma with an external magnetic field........................................................191

6. Down-conversion.................................................................................................................192

7. The inverse plasma maser......................................................................................................195

7.1. The nonlinear collision integral.................................................................................................195
7.2. The stationary solution..............................................................................................................201
7.3. The evolution of an electron beam............................................................................................203

8. Some general aspects of the interaction. Conclusion....................................................................206
References.............................................................................................................................212

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