The variation in the magnetic field strength on a magnetic surface as a function of the magnetic angles is one of the most important properties of an equilibrium because it determines the trajectories of the charged particles. Even a small change in the field strength can produce a qualitative change in the trajectories. The perturbed magnetic field strength as a function of magnetic coordinates is derived for a given displacement ξ⃗ of the magnetic field lines. Ideal magnetohydrodynamics stability theory can be used to determine the field line displacement ξ⃗ of a perturbed plasma equilibria and, therefore, the perturbed field strength.
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Allen H. Boozer (2006) studied this question.
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