Determination of optimum proton pulse duration for triggering fast ignition in inertial confinement fusion

Two relatively simple analytic Models for investigation of fast ignition dynamics are developed, that are the subsonic and the supersonic models. On the basis of the subsonic model, which a pre-compressed fuel of density is heated by a subsonic thermal wave, the beam energy and the intensity required for ignition is closely related to proton range. Whereas, on the basis of supersonic model, for ranges shorter than 0.25 gr/cm2, the mentioned energy remains constant and the intensity decreases. For ranges larger than this value, not only energy but also the beam intensity will increase with the proton range. Considering that proton pulse duration depend on proton range implicitly, these results allow for the determination of an optimum proton pulse duration value, that we have obtained this value equal to 2.14×103 po-1 ps.