Parametric decay of magneto-acoustic oscillations in a cylindrical plasma

Abstract

Parametric decay of magneto-acoustic oscillations in a cylindrical plasma column is considered, including the Hall effect and the effects of finite resistivity. Growth rates for axisymmetric modes in decay instabilities are derived and applied to the problems of parametric excitation of Alfvén waves and supplementary heating of plasmas. It is shown that both the slow (ion cyclotron) and fast (compressional) modes may be parametrically excited. The threshold &litudes for nonlinear dissipation of pump field energy are calculated and briefly discussed.

The Excitation of Ion-acoustic Waves by a Magnetic Pump in Cylindrical Geometry

“…a shear Alfven wave, and the density perturbation resonates with the ion-acoustic mode. The resonance condition Wo = w+wA is approximately satisfied and the parametric decay instability results, as has been discussed by Elfimov and Nekrasov (1973) for cylindrical geometry and Cramer (1977) for slab geometry. The forced wave a1(w+) is non-resonant, provided that we do not have w ~ WA' and may be neglected.…”

“…( Cramer and Sy 1979), so that the equation describing the excited Alfven wave is gained by taking the curl of equation (4) and eliminating v by means of (3): (7) Since the pump wave providing the coupling has no spatial variation in the z direction, all the excited wave fields may be assumed to have the same wavenumber kz = k. Then the z, 8 and time variation of V z is written as exp(i kz + i m8 -i Wi t) and that of jz as exp(i kz + i m8 --i W 2 t).…”

“…The analysis proceeds by considering an interaction between single radial modes (as in Cramer and Sy 1979) so that in equation (9) only the nth radial mode of jz appears on the RHS. The values of ken and ken' are determined by the boundary conditions: in the case of the metal-wall bounded plasma, Eo and Ez vanish at the wall.…”

“…Some experimental evidence of the role of ion-acoustic waves parametrically excited by a magnetic pump has been obtained by Demirkhanov et al (1977) who attributed the observed ion heating to either ion Landau damping (collisionless case) or ion viscous damping (collisional case) of ion-acoustic waves.…”

“…The decay instability of the magnetic pump to ail ion-acoustic plus an Alfven wave has been considered by Elfimov and Nekrasov (1973) (cylindrical geometry) and Cramer (1977) (slab geometry), who found a growth rate proportional to {ri.…”