The extremely high temperatures needed to trigger nuclear fusion are proposed to be generated by laser irradiating a spherical pellet of deuterium and tritium fuel of diameter $D_p=1\mathrm{.}9mm.$

$($a$)$ Determine the maximum fuel temperature that can be achieved by irradiating the pellet with $200$ lasers, each producing a power of $P=500W.$ The pellet has an absorptivity $=0\mathrm{.}3$ and emissivity $=0\mathrm{.}8.$

$($b$)$ The pellet is placed inside a cylindrical enclosure. Two laser entrance holes are located at either end of the enclosure and have a diameter of $D_{\text{L}\text{E}\text{H}}=2\mathrm{.}2mm.$ Determine the maximum temperature that can be generated within the enclosure.

Determine the maximum fuel temperature that can be achieved in part $($a$),$ in $K.T_{\text{m}\text{a}\text{x}}=$

Determine the maximum fuel temperature that can be achieved in part $($b$),$ in $K.T_{\text{m}\text{a}\text{x}}=,K$