Energetics of a long-implosion-time, 12-cm-diameter argon-gas-puff Z pinch at 6.5 MA

Abstract

We carry out an energy-inventory analysis for a 12-cm-diameter, argon gas-puff shot on the Saturn generator. From the measured pinch inductance time history, we infer the average radius of the pinch current, r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ind</inf> , and the total work done on the pinch, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</inf> , both as functions of time. The kinetic energy as a function of time, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KE</inf> , is inferred from r <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ind</inf> and the measured initial mass distribution, assuming all of the mass is accreted as in a snowplow. The results show that early in the implosion, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</inf> ≈ E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KE</inf> . However, when the pinch begins to radiate significantly, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">KE</inf> begins to decrease while E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</inf> continues to increase. The increase in coupled energy goes into plasma internal energy, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">int</inf> , i.e., ionization and thermal energies of the z-pinch plasma, and total radiation, E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rad</inf> . During the time of K-shell emission, the significant (∼ 150-kJ) increase in E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</inf> is reflected in approximately the same increase in E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rad</inf> . There is agreement between E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">int</inf> at the time of peak K-shell emission inferred from E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coupled</inf> and measurements of E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rad</inf> , and E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">int</inf> inferred from independent spectroscopic measurements combined with an atomic-physics model.