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A perturbation theory analogous to that of quasi-linear theory is developed to treat the behavior of magnetic surfaces, in particular to estimate their stability against field irregularities. The method exploits the similarity between the Vlasov equation and the Liouville equation for field lines. We find that a very important role is played by field resonances, that isolated resonances have a limited effect, extended over a finite width which we estimate, but as soon as resonances overlap, a very rapid destruction of flux surfaces may be expected.
Rosenbluth et al. (Thu,) studied this question.