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Particle Confinement and Adiabatic Invariance
B. V. Chirikov
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 145-156
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2398233
Page Count: 12
You can always find the topics here!Topics: Particle resonance, Chaos theory, Magnetism, Magnetic fields, Magnets, Fine structure, Mathematical problems, Libration, Particle motion, Particle diffusion
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The general problem of adiabatic invariance is discussed by using, as an example, the particle motion in a mirror magnetic trap. A new, resonant, adiabaticity parameter is introduced, which allows the reduction of the axisymmetric problem to the standard map, and which provides a sharp estimate for the chaos (instability) border in magnetic traps. Peculiarities of the particle diffusion out of the trap, due to the presence of the chaos border, are considered. The mechanism of slow Arnol'd diffusion in a non-axisymmetric field is explained, and some rough estimates are given, including the impact of weak noise (gas scattering).
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1987 Royal Society