General relationships between wave amplification and particle diffusion in a magnetoplasma

The general conditions for wave generation (γ > 0) or wave absorption (γ < 0) by a given distribution of energetic particles are discussed in the case of electromagnetic waves propagating along the dc magnetic field. It is shown that the nature of the interaction (γ > 0 or γ < 0) can be easily determined by considering the relative position of three curves in the υ ∥ , υ ⊥ plane (where υ ∥ and υ ⊥ are the parallel and perpendicular velocity of the particle): the isodensity curve, the constant energy curve, and the diffusion curve. For ‘regular’ distribution functions (i.e., distributions which are concave around the origin and for which there are less particles of high energy than particles of low energy) a necessary and sufficient condition for positive growth rate is that the third curve be situated within the area delineated by the other two curves. This geometrical formalism is extended to other kinds of distributions (field‐aligned beams or ring distributions). It is also applied to wave‐particle interactions in multicomponent plasmas. The conclusions which we arrive at are in agreement with previous findings. The analytical demonstration of this geometrical property is given. It is linked with the fact that the equations which govern the wave amplification and the particle diffusion involve the same operator, which is the derivative of the distribution function taken along the diffusion curve. The origin of this property lies in the special form of the Boltzmann‐Vlasov equation.