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Time evolution for different geometrical configurations of charged particles in a time-varying magnetic field

Published online by Cambridge University Press:  13 March 2009

S. Bouquet ,
L. Cairó  and
M. R. Feix
S. Bouquet
Affiliation:
PMMS/CNRS, 45071 Orleans Cedex 2
L. Cairó
Affiliation:
PMMS/CNRS, 45071 Orleans Cedex 2
M. R. Feix
Affiliation:
PMMS/CNRS, 45071 Orleans Cedex 2
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Abstract

Through rescaling and obtaining invariant equations, we study the expansion of charged particles immersed in a time-varying magnetic field B(t) = B0(1+Ωt)–β. We develop the theory for a configuration of point particles confined in a plane with an initial cylindrical symmetric configuration. It is found that the system expands according to (1+Ωt)2β/3 for β ≤ 1 and it is conjectured that in a properly rescaled space and time, it reaches asymptotically an inhomogeneous (in space) Brillouin flow with rigid rotation at half the cyclotron frequency (ω = ½ωc). Particular attention is given to the ‘pivot’ case β = 1. It is shown then that the radius of the rescaled configuration is now dependent on the ratio Ω/ωc, and grows indefinitely with time for Ω/> 3.2–3/2;. Numerical experiments are presented which confirm these theoretical predictions and conjectures. Finally, the properties of this system are compared with those of single-particle and ‘rod’ electrostatic models.

Type
Research Article
Information
Journal of Plasma Physics , Volume 34 , Issue 1 , August 1985 , pp. 127 - 141
Copyright
Copyright © Cambridge University Press 1985

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References

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