  We develop a conservative phase-space grid-adaptivity strategy for the
Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is
normalized to the thermal speed and shifted by the bulk-fluid velocity. The
configuration-space grid is moved according to a
mesh-motion-partial-differential equation (MMPDE), which equidistributes a
monitor function that is inversely proportional to the gradient-length scales
of the macroscopic plasma quantities. The grid adaptation ensures discrete
conservation of the collisional invariants (mass, momentum, and energy). The
conservative grid-adaptivity strategy provides an efficient scheme which
resolves important physical structures in the phase-space while controlling the
computational complexity at all times. We demonstrate the favorable features of
the proposed algorithm through a set of test cases of increasing complexity.
