  We present a numerical algorithm that enables a phase-space adaptive Eulerian
Vlasov-Fokker-Planck (VFP) simulation of an inertial confinement fusion (ICF)
capsule implosion. The approach relies on extending a recent mass, momentum,
and energy conserving phase-space moving-mesh adaptivity strategy to spherical
geometry. In configuration space, we employ a mesh motion partial differential
equation (MMPDE) strategy while, in velocity space, the mesh is
expanded/contracted and shifted with the plasma's evolving temperature and
drift velocity. The mesh motion is dealt with by transforming the underlying
VFP equations into a computational (logical) coordinate, with the resulting
inertial terms carefully discretized to ensure conservation. To deal with the
spatial and temporally varying dynamics in a spherically imploding system, we
have developed a novel nonlinear stabilization strategy for MMPDE in the
configuration space. The strategy relies on a nonlinear optimization procedure
that optimizes between mesh quality and the volumetric rate change of the mesh
to ensure both accuracy and stability of the solution. Implosions of ICF
capsules are driven by several boundary conditions: 1) an elastic moving wall
boundary; 2) a time-dependent Maxwellian Dirichlet boundary; and 3) a
pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian
boundary driver is new to our knowledge. The implementation of our strategy is
verified through a set of test problems, including the Guderley and Van-Dyke
implosion problems --the first-ever reported using a Vlasov-Fokker-Planck
model.
