The nonstationary solution for temperature spatial distribution in a substance heated by fast ion stream and the contrast of temperature “Bragg-Peak”

An analytical solution describing the temperature space-time evolution in a substance heated by monoenergetic fast-ion bunch of an arbitrary duration is obtained. The temperature peak and coordinate of its position are determined in real conditions of ion stopping, when as a result of decrease in ion energy, on the one hand, and an increase in the substance temperature, on the other hand, the Bragg law of stopping power ceases to operate. The dependences of these characteristics on ion-bunch flux density and duration as well as on the initial ion energy are discussed in relation to the medical applications and inertial confinement fusion.