  A knowledge of the particle escape time from the acceleration regions of many
space and astrophysical sources is of critical importance in the analysis of
emission signatures produced by these particles and in the determination of the
acceleration and transport mechanisms at work. This paper addresses this
general problem, in particular in solar flares, where in addition to scattering
by turbulence, the magnetic field convergence from the acceleration region
towards its boundaries also influences the particle escape. We test an
(approximate) analytic relation between escape and scattering times, and the
field convergence rate, based on the work of Malyshkin and Kulsrud (2001),
valid for both strong and weak diffusion limits and isotropic pitch angle
distribution of the injected particles, with a numerical model of particle
transport. To this end, a kinetic Fokker-Planck transport model of particles is
solved with a stochastic differential equation scheme assuming different
initial pitch angle distributions. This approach enables further insights into
the phase-space dynamics of the transport process, which would otherwise not be
accessible. We find that in general the numerical results agree well with the
analytic equation for the isotropic case, however, there are significant
differences weak diffusion regime for non-isotopic cases, especially for
distributions beamed along the magnetic field lines. The results are important
in the interpretation of observations of energetic particles in solar flares,
and other similar space and astrophysical acceleration sites and for the
determination of acceleration-transport coefficients, commonly used in
Fokker-Planck type kinetic equations.
