  Multi-epoch observations with ACS on HST provide a unique and comprehensive
probe of stellar dynamics within NGC 6397. We are able to confront analytic
models of the globular cluster with the observed stellar proper motions. The
measured proper motions probe well along the main sequence from 0.8 to below
0.1 M$_\odot$ as well as white dwarfs younger than one gigayear. The observed
field lies just beyond the half-light radius where standard models of globular
cluster dynamics (e.g. based on a lowered Maxwellian phase-space distribution)
make very robust predictions for the stellar proper motions as a function of
mass. The observed proper motions show no evidence for anisotropy in the
velocity distribution; furthermore, the observations agree in detail with a
straightforward model of the stellar distribution function. We do not find any
evidence that the young white dwarfs have received a natal kick in
contradiction with earlier results. Using the observed proper motions of the
main-sequence stars, we obtain a kinematic estimate of the distance to NGC 6397
of $2.2^{+0.5}_{-0.7}$ kpc and a mass of the cluster of $1.1 \pm 0.1 \times
10^5 \mathrm{M}_\odot$ at the photometric distance of 2.53 kpc. One of the
main-sequence stars appears to travel on a trajectory that will escape the
cluster, yielding an estimate of the evaporation timescale, over which the
number of stars in the cluster decreases by a factor of e, of about 3 Gyr. The
proper motions of the youngest white dwarfs appear to resemble those of the
most massive main-sequence stars, providing the first direct constraint on the
relaxation time of the stars in a globular cluster of greater than or about 0.7
Gyr.
