Quantumlike theory for the nonadiabatic behavior of charged particles in inhomogeneous magnetic fields

Abstract

A new derivation is given of the set of Schrödinger-like equations for the nonadiabatic behavior of an ensemble of charged particles in inhomogeneous magnetic fields, starting from the Liouville equation for the ensemble. The nonadiabatic loss of charged particles from magnetic-mirror traps thus appears in the nature of quantum tunneling of the adiabatic potential with the initial value of the first action invariant playing the role of ħ . The equations also predict one-dimensional interference-like effects in periodic magnetic fields. Different equations of the set describe different modes of the nonadiabatic behavior of a "pure" ensemble prepared with δ-function distributions for the controllable (in the sense used by Khinchin) integrals of motion of the system. A new concept of "ensemble modes," as distinct from the collective modes, is thus introduced. These ensemble modes have indeed been observed as manifested through the recently observed multiplicity of lifetimes in the nonadiabatic decay.