Classical billiards in magnetic fields
Open Access
- 21 June 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (9), 1361-1378
- https://doi.org/10.1088/0305-4470/18/9/019
Abstract
A particle moves in circular arcs with Larmor radius R between specular reflections at the smooth convex boundary of a planar region. The dynamics depends on the value of R in relation to the extreme curvature radii rho min and rho max and the radius R* of the largest circle that can be inscribed in the boundary. For Rminmax there are 'flyaway intervals' on the boundary for which glancing orbits are a powerful source of chaos in the map (on the phase cylinder) relating successive bounces; this type of chaos is a characteristic feature of magnetic billiards. For sufficiently large R the simplest closed orbits consist of two arcs associated with diameters of the boundary; their existence and stability can be determined. In several regimes where motion consists of short skips between nearby boundary points (including the strong-field case R to 0), an explicit adiabatic invariant can be found which gives an excellent approximation to the exact invariant curves in these regimes. Computations for a magnetic billiard with elliptic boundary illustrate the theory.Keywords
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