1 - Basic equations

Summary

Approximations

In view of the applications of our theory to the conditions of the Earth's magnetosphere the following assumptions are made:

1. The plasma is assumed to be homogeneous in the sense that its actual inhomogeneity does not influence its dispersion characteristics, instability or damping at any particular point, although in general these characteristics can change from one point to another. For low-amplitude waves this assumption is valid when the wavelength is well below the characteristic scale length of plasma inhomogeneity, a condition which is satisfied for whistlermode waves propagating in most areas of the magnetosphere (except in the lower ionosphere). For finite amplitude waves the condition for plasma homogeneity depends on wave amplitude, but the discussion of these effects is beyond the scope of the book (see e.g. Karpman, 1974).

2. The plasma is assumed to be collisionless in the sense that we neglect the contribution of Coulomb collisions between charged particles as well as collisions between charged and neutral particles leading to charge exchange. More rigorously this assumption can be written as: where q_α is the particle's charge (index α indicates the type of particle: α = e for electrons, α = p for protons; 〈r₁₂〉 is the average distance between particles; T_α is the particles' temperature in energy units.

The physical meaning of (1.1) is obvious: the average energy of interaction between charged particles is well below their average kinetic energy.