  We present an ion kinetic model describing the ignition and burn of the
deuterium-tritium fuel of inertial fusion targets. The analysis of the
underlying physical model enables us to develop efficient numerical methods to
simulate the creation, transport and collisional relaxation of fusion reaction
products (alpha-particles) at a kinetic level. A two-energy-scale approach
leads to a self-consistent modeling of the coupling between suprathermal
alpha-particles and the thermal bulk of the imploding plasma. This method
provides an accurate numerical treatment of energy deposition and transport
processes involving suprathermal particles. The numerical tools presented here
are validated against known analytical results. This enables us to investigate
the potential role of ion kinetic effects on the physics of ignition and
thermonuclear burn in inertial confinement fusion schemes.
