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 co
mpressed 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.
Fluid dynamical models preceded the first heavy ion accelerator experiments, and led to the main trend of this research since then. In recent years fluid dynamical processes became a dominant direction of research in high energy heavy ion reactions.
The Quark-gluon Plasma formed in these reactions has low viscosity, which leads to significant fluctuations and turbulent instabilities. One has to study and separate these two effects, but this is not done yet in a systematic way. Here we present a few selected points of the early developments, the most interesting collective flow instabilities, their origins, their possible ways of detection and separation form random fluctuations arising from different origins, among these the most studied is the randomness of the initial configuration in the transverse plane.
The dynamical development of collective flow is studied in a (3+1)D fluid dynamical model, with globally symmetric, peripheral initial conditions, which take into account the shear flow caused by the forward motion on the projectile side and the back
ward motion on the target side. While at $sqrt{s_{NN}} = 2.76A$,TeV semi-peripheral Pb+Pb collisions the earlier predicted rotation effect is visible, at more peripheral collisions, with high resolution and low numerical viscosity the initial development of a Kelvin-Helmholtz instability is observed, which alters the flow pattern considerably. This effect provides a precision tool for studying the low viscosity of Quark-gluon Plasma.
