A model for ablated-plasma distribution and width for wire-array Z-pinch implosions
- Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1194 (United States)
A one-dimensional radial magnetohydrodynamic model of the plasma ablated from a multi-MA wire-array Z pinch is developed. The model is used to compute the mass weighted-density width {delta} of the plasma at the end of the ablation phase. The wire-array cores are represented as a prescribed source of plasma injection. The plasma, beyond a thin boundary layer, is approximated as a perfect conductor experiencing only magnetic forces and negligible pressure gradients. Assuming that the current driving the Z-pinch implosion increases linearly with time t during the ablation phase, and that the mass-ablation rate varies as t{sup {nu}}, it is shown that the density width {delta} is a function of the dimensionless parameter {lambda}=u{sub a}(t{sub a})t{sub a}/r{sub 0}, where u{sub a} is the ablation velocity, t{sub a} is the total ablation time, and r{sub 0} is the initial wire-array radius. The velocity u{sub a} is defined such that its product with the mass-ablation rate equals the magnetic force at r{sub 0}, which is assumed to be the mass injection point. A solution is obtained for the plasma flow in semianalytical form when the current is an exponential function of time, and u{sub a} is constant. The ablated plasma density width {delta} obtained under these two sets of conditions is compared. In addition, assuming that the plasma sheath at stagnation is proportional to the width {delta}, scaling relationships for the peak x-ray power radiated when the pinch stagnates on axis are suggested.
- OSTI ID:
- 20787374
- Journal Information:
- Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 6 Vol. 13; ISSN PHPAEN; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ABLATION
BOUNDARY LAYERS
DISTRIBUTION
ELECTRIC CURRENTS
EXPLODING WIRES
IMPLOSIONS
LINEAR Z PINCH DEVICES
LONGITUDINAL PINCH
MAGNETOHYDRODYNAMICS
MATHEMATICAL SOLUTIONS
PLASMA
PLASMA DENSITY
PLASMA SHEATH
PRESSURE GRADIENTS
RADIATION TRANSPORT
TIME DEPENDENCE
X-RAY SOURCES