STABILIZATION OF THE UNSTABLE EQUILIBRIA OF CHARGES BY INTENSE MAGNETIC-FIELDS

The problem of stabilizing unstable (by Earnshaw's theorem) equilibria of a free charge in an electrostatic field by adding a steady magneti c field is considered. The additional Lorentz force that thereby arise s has a gyroscopic form. An example of the possibility of stabilizatio n in a rigorous relativistic formulation of the problem is given. Crit eria for the stabilization of unstable equilibria of linearized system s are obtained. The conditions for charge stability in intense magneti c fields are investigated and estimates of the stabilization probabili ty are given. Some multidimensional analogues of these results are pre sented. In particular, the problem of gyroscopic stabilization when th e matrix of the gyroscopic forces is degenerate is considered. Some ex tremal criteria of the stability of the equilibrium positions are give n. (C) 1997 Elsevier Science Ltd. All rights reserved.