Compression of matter to superhigh densities by an accelerating heat wave

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 $\mathrm{W\hspace{0.17em}=\hspace{0.17em}}\frac{9}{8}{\rho }_0{c}_0^3{K}^2{\mathrm{/\tau }}^2$ , where ${\mathrm{K\hspace{0.17em}=\hspace{0.17em}D}}_f{\rho }_f{\mathrm{/D}}_0{\rho }_0$ is the fraction of the initial target mass (of density ${\rho }_0$ and thickness $D_f$ ) which reaches the final state (of ${\rho }_f$ and $D_f$ . The adiabatic ondition sets the requirement that $K$ should be much smaller than one. The time $t$ is scaled as ${\text{τ\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}−\hspace{0.17em}t/t}}_8$ , where $t_8{\mathrm{\hspace{0.17em}=\hspace{0.17em}D}}_0{\mathrm{/c}}_0$ and $c_0$ 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 $c_0{\mathrm{(K/\tau )}}^{\text{1/4}}$ . Half of the total driving energy is expended by the time $t_f{\mathrm{[\tau }}_f{\mathrm{\hspace{0.17em}=\hspace{0.17em}(D}}_f{\mathrm{/D}}_0{\mathrm{)\hspace{0.17em}(\rho }}_0{\mathrm{/\rho }}_f{)}^{\text{1/3}}]$ , from which time the power has to be held constant at $W_f\mathrm{\hspace{0.17em}=\hspace{0.17em}}\frac{9}{8}{\mathrm{(\rho }}_f{\mathrm{/\rho }}_0{)}^{\text{8/3}}{\rho }_0{c}_0^3$ until time $t_8$ .