Could anyone explain why the D+T inside the pellet is in two distinct regions? And why the center is a lot less dense than the outside region? I have been trying to find answers online but i cant seem to find a explanation.
Could anyone explain why the D+T inside the pellet is in two distinct regions?
I assume you mean why is it in both vapor form (in the center) and solid (ice) form (layered in the shell). This is coupled to your second question regarding the lower density in the center.
The general idea underlying ICF is to set up a hot-spot in the center of the compressed pellet that propagates outward and consumes fuel around it. The design of the capsule allows for this to occur more readily.
So, as the fuel pellet is compressed, the goal is to create a hot-spot in the center with a temperature of several kilo-electron-volts. This causes fusion reactions to occur in the center of the capsule, producing fusion reaction products. For the case of D-T, one of these products is an alpha particle. If a sufficiently large number of alpha particles are produced, and if the surrounding compressed DT (the hot spot) is dense enough, the alpha particles will stop within the hot spot on the inside of the DT ice shell, sustaining the hot spot and thereby rapidly heating a layer of the surrounding ice up to fusion conditions. This in turn produces more alpha particles, which go on to do the same thing. So a "burn wave" is setup in this way.
The density of the compressed DT vapor (the hot spot) must be sufficiently large to stop alpha particles. The density of the DT ice, however, must be much larger - large enough for inertial confinement to be effective. Starting off in a solid state (ice) helps, and the ice is further compressed as the target converges (shockwaves launched into the ice cause compression). This explains why the ice layer is referred to as the fuel and why it must be dense.
As for the center of the pellet, it is much harder to reach the high temperatures required for ignition at the center of the pellet if it were completely filled with ice. The spherical convergence of the shell contributes to heating at the center of the pellet and this would be impossible for a solid sphere of ice, for instance.
As the pellet is compressed, it undergoes many stages. At first, the ablation causes inward acceleration of the shell (the DT ice). The acceleration phase ends, and the shell then coasts for a while, after which it decelerates and stagnates. Stagnation occurs because of the increase in pressure (accompanied by a large increase in temperature) of the relatively lower density vapor inside the shell. Once the pressure applied by the inward shell equals that of the hot-spot, stagnation occurs, and if the temperature is high enough, the burn wave is set up. This explains the two distinct regions after compression.
Note that all of this happens much faster than the time it takes the mass to dissemble due to inertia - so the fuel (ice) literally has no time to move on its own accord (to fall apart, for instance).
EDIT: The Laboratory for Laser Energetic (University of Rochester) has a 60-beam system (OMEGA) that conducts ICF experiments. They also host a summer school where practitioners from the field explain a lot of introductory and advanced ICF concepts. You can find slides from those lectures here:
The 3-part slides by Betti will help with a lot of these questions.