Low Frequency Modes in Inhomogeneous Magnetic Fields

Book chapter, 2012

We have now seen how some typical low frequency modes can be driven unstable by density, pressure or current gradients in simple geometries. A more accurate description of collective modes in magnetic confinement systems, in general, requires more detailed geometry effects as well as separate effects of density and temperature gradients [1–197]. In the present chapter we will aim at making the geometrical description more accurate, thus in most cases leading to eigenvalue problems for the modes concerned. We will also derive a more complete drift kinetic description, introduce the gyrokinetic equation and present an advanced fluid model. We will furthermore review briefly the fields of transport due to magnetic fluctuations and advanced fluid models.