Rotation shear and drift wave stability
The stability of short wave-length drift instabilities in toroidally confined plasma is conventionally analysed using the ballooning transformation. This reduces the two-dimensional stability problem to the solution of two consecutive one-dimensional equations. The first, the lowest order in n (n is the toroidal mode number), equation produces a local eigenvalue that is a function of radius, x, due to profile variation and also has a periodic dependence on a parameter k, representing a radial wave-number. Usually one finds that profile variation defines a radial position where the growth rate is a maximum. In next order one finds that this position determines the mode’s radial location and that the parameter k is such as to maximise the growth rate.