What is being attempted is a variation of the ICF principle or Inertial confinement fusion reaction. The issue with this process is uncontrolled plasma expansion of the fuel and capsule during firing. The challenges with ICF or Inertial confinement fusion reactors is that at the time of the laser firing, you have incredible rapid expansion of the fuel and the capsule. I am sure that the engineers and scientists have worked out the mathematics for fuel temperature and the confinement time of the reaction. At any rate the links below talk more on fusion reactors and starting them with lasers.