Compression of matter to superhigh densities by an accelerating heat wave

Abstract

A one-dimensional analytical model is presented for the compression of matter (e.g., thermonuclear fusion fuel to densities of more than 103 times the solid density) by an accelerating subsonic heat wave. The heat wave, driven possibly by the absorption of a temporally tailored laser pulse, launches a large number of successive weak shock waves which compress and heat the target quasiadiabatically in order to keep the energy expenditure at a minimum. The net power to drive this heat wave must have a stepwise increase in time approximated by W = 98ρ0c03K2/τ2, where K = Dfρf/D0ρ0 is the fraction of the initial target mass (of density ρ0 and thickness Df) which reaches the final state (of ρf and Df. The adiabaticondition sets the requirement that K should be much smaller than one. The time t is scaled as τ = 1 − t/t8, where t8 = D0/c0 and c0 is the initial sound speed. The sound speed in the compressed matter, from which pressure and density can be obtained using the adiabatic equations of state, will increase approximately as c0(K/τ)1/4. Half of the total driving energy is expended by the time tf[τf = (Df/D0) (ρ0/ρf)1/3], from which time the power has to be held constant at Wf = 98(ρf/ρ0)8/3ρ0c03 until time t8.