Fundamentals of Plasma Physics

8.6 Drift waves 251

cylindrical

magnetized

plasma

typical particle orbit

typicalfield line

radial

density

profile

z

r

Figure 8.3: Cylindrical magnetized plasma with radial density gradient

Drift waves will be examined using three progressively more realisticpoints of view.
These are:

1. A collisionless two-fluid model where ions are assumed to be cold and electrons are
   assumed to be hot. This model establishes existence of the mode and provides a
   derivation for the intrinsic frequency, but provides no information regarding stability.


2. A collisional two-fluid model which shows thatcollisionsdestabilize drift waves.


3. A Vlasov model including both finite ion temperature and net axial current. This
   model shows that both Landau damping and axial currents destabilize driftwaves.
   Drift waves involve physically distinctive ion and electron motions, three-dimensional
   geometry, magnetized warm plasma effects, pressure gradients, collisionality, and Landau
   damping/instability. Drift waves are often of practical importance because they are so eas-
   ily driven unstable. While real plasmas have geometry resembling Fig.8.3,the cylindrical
   geometry will now be replaced by Cartesian geometry to make the analysismore straight-
   forward.
   Using Cartesian geometry, the equilibrium magnetic field is assumed tobe in thez
   direction and the new feature, an exponential density gradient in thexdirection, represents
   the pressure gradient. Thexdirection thus corresponds to therdirection of cylindrical
   geometry, and theydirection corresponds to theθdirection. Theyandzdirections, but not
   thexdirection, are ignorable coordinates, and so the governing equations may beFourier-
   transformed in theyandzdirections, but not in thexdirection.