Kramers escape rate for a charged particle in a magnetic field

Universität Bielefeld, Fakultät für Physik - 33615 Bielefeld, Germany

Received: 21 November 2006
Accepted: 11 December 2006

Abstract

We determine and discuss the escape rate of a charged particle from a metastable state in the presence of Lorentz forces due to a time-independent magnetic field. Compared to the case without magnetic field, there is one specific direction along which a magnetic field does not modify the rate at all, independently of its absolute value. Along any other direction, the magnetic field always leads to a reduction of the escape rate. The reduction depends non-uniformly on the orientation of the field and for strong magnetic fields a critical cone is identified where the rate behaves fundamentally different depending on whether the field lies inside or outside the cone. Though the exponentially leading Arrhenius-factor is completely independent of the magnetic field, the rate suppression via the pre-exponential factor can become arbitrarily strong for specific directions of the sufficiently large magnetic field. In the most general case of an inhomogeneous magnetic field, only its value in the activated state (saddle point of the potential) is of relevance for the escape rate.