Theory of the rippling instability in toroidal devices

The theory of the rippling instability is developed for axisymmetric toroidal plasmas including ion viscosity and parallel electron heat conduction, but assuming that the growth rate is small compared to the wave angular frequency omega 0 =(1+1.71 eta e ) omega e *. omega e * is the electron diamagnetic frequency and eta e identical to (dlnT e /dr)/(dlnN/dr). Three (in)stability regions must be considered, viz. (c i /$R omega 0 ) 2 <0.12 where toroidal effects are negligible and the plasma is stable; 0.12<(c i /R omega 0 ) 2 <0.26 q 2 where the magnetic curvature destabilizes the mode; and 0.26 q 2 <(c i /R omega 0 ) 2 where the plasma is stable again. (The numerical values are given for eta e = eta i =2 and T e =T i , not heat conduction or viscosity.) Parallel electron heat conduction is stabilizing; ion viscosity broadens or narrows the instability domain, according to the value of the parameter omega i * 0,i /P i . Under certain conditions, an important up-down asymmetry of the density fluctuation spectrum may arise.