14.4 Assignments 427
Show that the steady-state solution to this equation has the form (Fisch1978)
FT∼exp
−
∫w
dw
(2+Z)w
(
w^3 D ̄QL+
3
4
)
SketchFTfor the cases where (i)D ̄QL>> 1 over a certain range of velocities
(i.e., where wave spectrum is resonant with particles) and (ii)D ̄QL<< 1 .How
could this be used to drive a toroidal current in a tokamak? Using the appro-
priate form ofDQLshow that the normalized quasilinear diffusion for resonant
particles is
D ̄QL(w)=^8 π
(^2) E(ωr/v,t)
wmeω^2 pelnΛ
.
If the wave is electrostatic then show that
E(ωr/v,t)∼k|φ|^2
wherekis the wavenumber of the waves resonantly interacting with the particles
so that
D ̄QL(w)∼^8 π
(^2) k|φ| 2
mewω^2 pelnΛ
.
What sort of waves would be most efficient at driving current, large or smallk?
Would this current drive work best in high or low density plasmas?