Laser-accelerated proton beam for fast ignition considering formation factor of a cloud and penetrability in P11B reaction

•The stopping power and range of protons in P11B fuel are determined.•The contribution of bonus energy in P11B fuel by laser-accelerated proton beams is calculated.•The formation factor of a cloud and penetrability in P11B reaction are estimated.

In this work proton beam is proposed in fast ignition of P11B fuel considering uniform density equal to 300 g cm−3. The total stopping power and range of protons are estimated by introducing the stopping power contribution of electrons and ions as a function of initial energy and temperature in the fuel. Also bonus energy and total deposition energy due to the additional fusion reactions are calculated. The bonus energy and total deposited energy are remarkable at smaller beam energy and higher electron temperature. Also this article show that the cross section of P11B fusion reaction is increased by increasing the penetrability of nuclei through the Coulomb barrier. In this approach, an intense laser field of more than 100 PW is required to distort the Coulomb barrier to obtain enough penetrability. We have calculated the penetrability of nuclei and the formation factor using available relations.