Microstability in tokamaks with low magnetic shear

The stability of drift waves in configurations with low magnetic shear, s, including the case with a minimum in the safety factor, q(min), which is a situation relevant to the formation of internal transport barriers, is analysed. First the small s limit of the ballooning representation is shown to, indeed, coincide with the result of a shear free calculation. Then, the limitations associated with using the ballooning transformation at low shear are discussed. Radially extended ballooning modes can be considered to result from the toroidal coupling of 'modelets' (each of which can contain a number of poloidal harmonics) centred on adjacent resonant surfaces. In a region of low magnetic shear, a modelet situated on a particular resonant surface does not extend to the adjacent surface and therefore the coupling of these is weak and the ballooning theory fails. An alternative approach based on a recurrence relation between modelets is used to analyse these situations with small s. This is then applied to electron drift waves and ion temperature gradient modes as examples. These studies show that for sufficiently long wavelengths, radially extended ballooning modes cannot exist close to a point of zero magnetic shear; however, independent modelets can still exist at resonant surfaces near q(min). The criteria on the wavelength for this situation to prevail are presented. The example of electron drift waves centred on q(min) is analysed and it is found that, even for this 'slab-like' electron drift wave, damping from an outgoing wave can be entirely suppressed.