Charged particle motion near a linear magnetic null

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Abstract
Charged particle motion near the null of a two‐dimensional magnetic field is studied. Specifically, the magnetic field is given by the vector potential A=ẑψ0[(y/a)2+(εx/a)2], in which ψ0,a, and ε are constants with ε parameterizing the ellipticity of the flux surfaces. Conservation of canonical z momentum pz reduces the number of nontrivial degrees of freedom to two. Scaling reduces the number of parameters in the system to two, ε and σ (the sign of pz ). Analytical and numerical methods are used to study the nature of orbits. The results are expressed conveniently in terms of ε and Q≡(2mE)1/2/pz. When ε is unity, the additional symmetry implies integrability. When ε is less than unity (the case ε>1 is trivially related) three regimes are found: (1) For ‖Q‖≫1 particle orbits are regular, (2) for ε3/2≲‖Q‖≲1 most particle orbits are stochastic, and (3) for ‖Q‖≪ε3/2 particle orbits are regular, with the third invariant being the magnetic moment.

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