Theoretical z-pinch scaling relations for thermonuclear-fusion experiments
- Sandia National Laboratories, Albuquerque, New Mexico 87185-1196 (United States)
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 ({approx}0.4 GJ/shot) and inertial-fusion-energy ({approx}3 GJ/shot) research. We find that ({delta}{sub a}/{delta}{sub RT}){proportional_to}(m/l){sup 1/4}(R{gamma}){sup -1/2}, where {delta}{sub a} is the imploding-sheath thickness of a wire-ablation-dominated pinch, {delta}{sub RT} is the sheath thickness of a Rayleigh-Taylor-dominated pinch, m is the total wire-array mass, l 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/l, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power P{sub r}{proportional_to}(I/{tau}{sub i}){sup 3/2}Rl{phi}{gamma}, where I is the peak pinch current, {tau}{sub 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}{sub i}{<=}169 ns, 10 mm{<=}R{<=}20 mm, 10 mm{<=}l{<=}20 mm, and 2.0 mg/cm{<=}m/l{<=}7.3 mg/cm. Assuming an ablation-dominated pinch and that Rl{phi}{gamma} is held constant, we find that the x-ray-power efficiency {eta}{sub x}{identical_to}P{sub r}/P{sub a} of a coupled pinch-accelerator system is proportional to ({tau}{sub i}P{sub r}{sup 7/9}){sup -1}, where P{sub a} is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of P{sub r} are proportional to {tau}{sub i}, and the requisite accelerator energy E{sub a} is proportional to {tau}{sub i}{sup 2}. 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}{sub 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}{sub i}{sup 0.36} and {tau}{sub i}{sup 1.36}, 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}{sub i}. We also find that increasing the anode-cathode gap of the pinch from 2 to 4 mm increases the requisite values of P{sub a} and E{sub a} by as much as a factor of 2.
- OSTI ID:
- 20706326
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 72; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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