On the validity of the guiding-center approximation in the presence of strong magnetic gradients

Abstract

The motion of a charged particle in a nonuniform straight magnetic field with a uniform magnetic-field gradient is solved exactly in terms of elliptic functions. The connection between this problem and the guiding-center approximation is discussed. It is shown that, for this problem, the predictions of guiding-center theory agree very well with the orbit-averaged particle motion and hold well beyond the standard guiding-center limit $\epsilon \equiv \rho /L\ll 1$, where $\rho$ is the gyromotion length scale and $L$ is the magnetic-field gradient length scale.

5 pages, 5 figures, accepted for publication in Physics of Plasmas

References in corpus (3)

• Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
• Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
• Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry

Cited by in corpus (2)

• Faithful guiding-center orbits in an axisymmetric magnetic field
• On the validity of the guiding-center approximation in a magnetic dipole field