Magnetic-island formation and destruction in a levitron

Abstract

The effect of non-axisymmetric perturbations on the magnetic surfaces of a levitron is investigated. A Hamiltonian theory is developed for predicting the formation of both primary and secondary magnetic islands for the main resonances. Numerical calculations are made for a range of levitron parameters and compared with results of the Hamiltonian theory. Good agreement is obtained both for island width and for local rotational transform of the islands. A simple criterion for island destruction and the consequent stochasticity of the field lines agrees well with numerical results. A ring tilt of 0.5 degree is found to destroy the magnetic surfaces in the neighbourhood of the main resonances (i = π, 2π).

Field-line stochasticity in a Tokamak with an Ergodic Magnetic Limiter

“…!ster ~pp!ier! to v a r i o~~s problems involving plasma confinement schemes: Tokamaks (Hamzeh, 1974), Stellarators (Filonenko et al, 1967), Levitrons (Freis et al, 1973) and Compact Tori (Viana, 1995), among others.…”

Hamiltonian description of toroidal magnetic fields in vacuum

“…Freis et al 25 considered such a model as the basis of a Hamiltonian description of an axisymmetric levitron device. Their analysis, however, differs from the present one in that only first-order toroidal effects were incorporated into the field-line Hamiltonian.…”

Magnetic field line mappings for a tokamak with ergodic limiters

“…This case will be called the square-pulse map (SPM). Another possible form for f(z) is a periodic sequence of delta function pulses (10) the latter form being its Fourier expansion, where the period is the tokamak length 2nR,. The map so obtained will be called the impulsive excitation map (IEM).…”