Kinetic Description of Low Frequency Modes in Inhomogeneous Plasma

Book chapter, 2012

In the previous chapter we derived simple dispersion relations for some of the most dangerous low frequency instabilities using a fluid description. We will now show how this can be done by kinetic theory, [1–4], from the Vlasov equation in a simple slab geometry. We will start by using the method of integration along unperturbed orbits [1–5], which gives the most general result, i.e. including also modes with$$ \omega \geqslant {{\Omega }_{\rm{c}}} $$, full finite Larmor radius effects and wave particle resonances. We will, however, restrict attention to modes with$$ \omega<< {{\Omega }_{\rm{c}}} $$. We will show how wave-particle resonances may impede the free electron motion along the field lines, thus causing drift instability and how the lowest order finite Larmor radius (FLR) effect agrees with that obtained from the stress tensor in Chap. 2. After the more general treatment we will show how the wave-particle resonances can be described by a simpler drift-kinetic equation that does not contain FLR effects and how the lowest order FLR effect can be obtained by a simple orbit averaging.