X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations.

(Received 3 April 2003; publishe 14 April 2004) We have measured the x-ray power and energy radiated by a tungsten-wire-array z pinch as a function of the peak pinch current and the width of the anode-cathode gap at the base of the pinch. The measurements were performed at 13- and 19-MA currents and 1-, 2-, 3-, and 4-mm gaps. The wire material, number of wires, wire-array diameter, wire-array length, wire-array-electrode design, normalized-pinch-current time history, implosion time, and diagnostic package were held constant for the experiments. To keep the implosion time constant, the mass of the array was increased as I 2 (i.e., the diameter of each wire was increased as I), where I is the peak pinch current. At 19 MA, the mass of the 300-wire 20-mm-diam 10-mm-length array was 5.9 mg. For the configuration studied, we find that to eliminate the effects of gap closure on the radiated energy, the width of the gap must be increased approximately as I. For shots unaffected by gap closure, we find that the peak radiated x-ray power P r I 1 . 2 4 ′ 0 . 1 8 , the total radiated x-ray energy E r I 1 . 7 3 ′ 0 . 1 8 , the x-ray-power rise time τ r I 0 . 3 9 ′ 0 . 3 4 , and the x-ray-power pulse width τ w I 0 . 4 5 ′ 0 . 1 7 . Calculations performed with a time-dependent model of an optically thick pinch at stagnation demonstrate that the internal energy and radiative opacity of the pinch are not responsible for the observed subquadratic power scaling. Heuristic wire-ablation arguments suggest that quadratic power scaling will be achieved if the implosion time τ i is scaled as I - 1 / 3 . The measured 1σ shot-to-shot fluctuations in P r , E r , τ r , τ w , and τ i are approximately 12%, 9%, 26%, 9%, and 2%, respectively, assuming that the fluctuations are independent of 1. These variations are for one-half of the pinch. If the half observed radiates in a manner that is statistically independent of the other half, the variations are a factor of 2 1 / 2 less for the entire pinch. We calculate the effect that shot-to-shot fluctuations of a single pinch would have on the shot-success probability of the double-pinch inertial-confinement-fusion driver proposed by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. We find that on a given shot, the probability that two independent pinches would radiate the same peak power to within a factor of I ′ α (where 0≤α<<1) is equal to erf(α/2σ), where σ is the 1σ fractional variation of the peak power radiated by a single pinch. Assuming α must be ≤7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, a must be <3% for the shot-success probability to be ≥90%. The observed (12/2 1 / 2 )%=8.5% fluctuation in P r would provide adequate symmetry on 44% of the shots. We propose that three-dimensional radiative-magnetohydrodynamic simulations be performed to quantify the sensitivity of the x-ray emission to various initial conditions, and to determine whether an imploding z pinch is a spatiotemporal chaotic system.