Generalization of Suydam's criterion

For low-shear systems Suydam's criterion is generalized to include stability against localized quasikink instabilities. In the obtained criterion, containing pressure gradient, shear, and a term responsible for the quasikink, the shear enters in a completely different way than in an earlier derived criterion by Shafranov. The reason for the discrepancy is pointed out. The present criterion is more restrictive than Suydam's criterion if m is below a certain critical value depending on the shear. The special case of a force-free field having a pitch extremum is separately treated. Several limitations of the use of local criteria are indicated.