  Relativistic fluid dynamics and the theory of relativistic detonation fronts
are used to estimate the space-time dynamics of the burning of the D-T fuel in
Laser driven pellet fusion experiments. The initial "High foot" heating of the
fuel makes the compressed target transparent to radiation, and then a rapid
ignition pulse can penetrate and heat up the whole target to supercritical
temperatures in a short time, so that most of the interior of the target
ignites almost simultaneously and instabilities will have no time to develop.
In these relativistic, radiation dominated processes both the interior,
time-like burning front and the surrounding space-like part of the front will
be stable against Rayleigh-Taylor instabilities. To achieve this rapid, volume
ignition the pulse heating up the target to supercritical temperature should
provide the required energy in less than ~ 10 ps.
