We have developed wire-array z-pinch scaling relations for plasma-physics and inertial-confinement-fusion (ICF) experiments. The relations can be applied to the design of z-pinch accelerators for high-fusion-yield (similar to 0.4 GJ/shot) and inertial-fusion-energy (similar to 3 GJ/shot) research. We find that (delta(a)/delta(RT))proportional to(m/center dot)(1/4)(R Gamma)(-1/2), where delta(a) is the imploding-sheath thickness of a wire-ablation-dominated pinch, delta(RT) is the sheath thickness of a Rayleigh-Taylor-dominated pinch, m is the total wire-array mass, center dot is the axial length of the array, R is the initial array radius, and Gamma is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product R Gamma is held constant the sheath thickness is, at sufficiently large values of m/center dot, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power P-r proportional to(I/tau(i))R-3/2 center dot Phi Gamma, where I is the peak pinch current, tau(i) is the pinch implosion time, and Phi is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when 13 MA <= I <= 20 MA, 93 ns <=tau(i)<= 169 ns, 10 mm <= R <= 20 mm, 10 mm <=center dot <= 20 mm, and 2.0 mg/cm <= m/center dot <= 7.3 mg/cm. Assuming an ablation-dominated pinch and that R center dot Phi Gamma is held constant, we find that the x-ray-power efficiency eta(x)equivalent to P-r/P-a of a coupled pinch-accelerator system is proportional to (tau P-i(r)7/9)(-1), where P-a is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of P-r are proportional to tau(i), and the requisite accelerator energy E-a is proportional to tau(2)(i). These results suggest that the performance of an ablation-dominated pinch, and the efficiency of a coupled pinch-accelerator system, can be improved substantially by decreasing the implosion time tau(i). For an accelerator coupled to a double-pinch-driven hohlraum that drives the implosion of an ICF fuel capsule, we find that the accelerator power and energy required to achieve high-yield fusion scale as tau(0.36)(i) and tau(1.36)(i), respectively. Thus the accelerator requirements decrease as the implosion time is decreased. However, the x-ray-power and thermonuclear-yield efficiencies of such a coupled system increase with tau(i). We also find that increasing the anode-cathode gap of the pinch from 2 to 4 mm increases the requisite values of P-a and E-a by as much as a factor of 2.

Theoretical z -pinch scaling relations for thermonuclear-fusion experiments