  The probability per unit time for a thermally activated Brownian particle to
escape over a potential well is in general well-described by Kramers theory.
Kramers showed that the escape time decreases exponentially with increasing
barrier height. The dynamics slow down when the particle is charged and
subjected to a Lorentz force due to an external magnetic field. This is evident
via a rescaling of the diffusion coefficient entering as a prefactor in the
Kramers escape rate without any impact on the barrier-height-dependent
exponent. Here we show that the barrier height can be effectively changed when
the charged particle is subjected to an external vortex flow. While the
external vortex alone does not affect the mean escape time of the particle,
when combined with a magnetic field it effectively pushes the fluctuating
particle either radially outside or inside depending on its sign relative to
that of the magnetic field. In particular, the effective potential over which
the particle escapes can be changed to a flat, a stable, and an unstable
potential by tuning the signs and magnitudes of the external vortex and the
applied magnetic field. Notably, the last case corresponds to enhanced escape
dynamics.
