Helicon waves in a non-uniform plasma

The dispersion relation for helicon waves in a cold plasma of radially varying density has been reduced to compact form, and the radial eigenmodes have been computed for different density profiles. The results show a marked asymmetry between the left- and right-hand circulariy polarized modes: the m = -1 (left) mode has a centrally peaked wave intensity and resonates with a much higher central density than the m = +1 mode. Positive feedback is therefore possible, leading to nonlinear channelling of the discharge. At a radius where the density falls to a certain value, a singularity arises in the coefficients of the wave equation; care must be taken in integrating through this point. This singularity has no physical significance. The marked difference between the m = +1 and -1 modes in a non-uniform plasma is caused by a difference in sign of the electron drift along the density gradient. Energy deposition is peaked near the radius of the peak in B(z). so that broad, uniform density profiles can be obtained by using the m = +1 mode and narrow, dense columns by using the m = -1 mode. These results explain many features observed by various groups over the past two years.