Energy spectrum of particles accelerated near a singular magnetic field line

An analysis is made of the distinctive properties of charged-particle motion near a singular line of force, along which the electric field strength is different from zero. In a plane perpendicular to this line of force the magnetic field has a hyperbolic structure. The particle acceleration process consists of a direct acceleration by the electric field in the nonadiabatic region along the singular line, followed by betatron acceleration in the drift region. The energy spectra are exponential in form at high energies. In the nonrelativistic limit the characteristic energy of the accelerated particles is determined solely by the particle charge, by the electric field strength, and by the scale of inhomogeneity of the magnetic field