Typical data from outer array diameter, total mass, 2:1 mass and radius ratio, tall, nested stainless steel arrays on Z. (a) Load current (black) and MITL current (green) are just under , implosion time is near , total x-ray power (red) is with yield, -shell x-ray power (blue) is with yield, both have FWHM near . (b) Space- and time-integrated -shell spectrum shows line emission from Fe and other stainless steel constituents. (c) Gated image near peak x rays shows final pinch radius .
Measured radiated outputs from 2:1 mass and radius ratio, tall, implosion time, nested stainless steel Z pinches as a function of initial outer array diameter. Total yield (red diamonds) and -shell yield (blue circles) measured through a tall aperture both drop for the largest array sizes. Estimated -shell yield per the scaling model of Sec. V B is shown (blue dotted line). Adapted from C. A. Coverdale et al., Physics of Plasmas 15, 023107 (2008) (Ref. 10) Copyright 2008, American Institute of Physics.
Gated pinhole pictures of the Z-pinch viewed at 12° from the horizontal within of peak x-ray power for stainless steel wire array shots with (a) , and (b) initial outer diameter. Disruption at the cathode end occurs prior to peak x-ray power and is of greater axial extent for larger initial diameter loads. PCD aperture configuration as used in Fig. 2 is indicated.
Radiography of -diameter, 104-wire, stainless steel wire arrays using the ZBL radiation source and bent crystal imaging: (a) expanded wire cores at (load current at ) from Z shot 1084, (b) wire ablation and core break-up at from Z1085, and (c) the start of the magnetic Rayleigh–Taylor unstable implosion at from Z1309.
(a) Optical streak showing the start of implosion of the edge of the Z1085 outer wire array agrees with the effective current radius (solid black curve) from the circuit inductance analysis. (b) A least-squares fit of the 0D calculated implosion trajectory (solid red curve) to the experimental effective current radius (solid black curve) gives with a factor of 2 error. The thin shell implosion trajectory calculated with no ablation (dashed blue curve) is shown for comparison. The position of the wire cores in the radiograph of Fig. 4(b) is indicated (green).
(a) radiograph of ablating wire plasma from Fig. 4(b). (b) Lineout of the radiograph, averaging over axial structure (solid black line). Vertical gray bars indicate the regions where transmission through the ablated plasma can be viewed unobstructed by the wire cores. Comparison with transmission curves calculated using SPECT3D for rocket-model ablated plasma profiles with various ablation velocities indicates the best fit is for . (c) View along the -axis of plasma profile used with SPECT3D analysis. Ablated plasma is confined to the azimuthal positions of the wires, and radial density profile is determined by the rocket model ( in this plot).
PROPACEOS opacity model for stainless steel used with SPECT3D radiography simulation. (a) Opacity vs photon energy plotted for various densities at temperature shows little dependence on density in the -shell continuum region where radiography is performed. (b) Opacity vs temperature at photon energy shows little density and temperature dependence for the ablated plasma.
(a) 0D-calculated implosion trajectories for a standard outer diameter, 2:1 mass and radius ratio stainless steel wire array with (dotted) and without (solid) including a rocket ablation model (, ). The ablated mass is swept up at large radius and has no effect on the final implosion. The AOABL code allows for transparency of the inner array with 25% momentum transfer as the outer material passes through in both cases shown. (b) Whether or not ablation is included has little effect on the calculated coupled energy (the total kinetic energy of both arrays in this model).
(a) Total radiated x-ray power from shot Z1084. The time difference between the two peaks observed is interpreted as the delay between the outer and inner arrays stagnating on axis. (b) For this load with a relatively small, massive inner array, transparency of the inner array to the imploding outer material can easily produce such a time delay in 0D calculations. Trajectories of the outer (red) and inner (blue) arrays are shown in a completely transparent calculation , in contrast to a calculation where the two arrays stick and implode together (dashed green curve, ). (c) The 0D calculated time delay (solid) compared to the measured delay (dotted) indicates momentum transfer in the experiment.
(a) Total, and (b) -shell x-ray power for shot Z1084 (red dashed curve) where implosion of outer and inner arrays was not simultaneous, and Z1308 (solid blue curve) which was designed for more nearly simultaneous implosion.
Space- and time-integrated spectrum shows smaller Fe line ratio for shot Z1084 (red dashed curve) where implosion of outer and inner arrays was not simultaneous than for Z1308 (solid blue curve) which was designed for more nearly simultaneous implosion.
(a) Contours of calculated Fe line ratio, and (b) contours of calculated -shell power (TW/cm) vs electron temperature and Fe ion density for a diameter stainless steel plasma column.
Radiated peak power (a) and yield (b) as a function of nested array initial radius ratio for the shots of Table I. Total x-ray outputs are shown with red diamonds, while -shell x-ray outputs are shown with blue circles. Hollow points indicate loads that were not designed for simultaneous implosion of the outer and inner wire arrays.
The scaling model indicates that -shell yield should be proportional to for stainless steel loads on Z. Data from the shots of Table I are shown as blue circles, and diameter single array shots Z89, 121, and 122 are shown as green triangles. Hollow circles indicate nested loads that were not designed for simultaneous implosion of the outer and inner wire arrays. is estimated through 0D calculation for all shots.
(a) Calculated 0D implosion trajectory for triple nested shot Z1747, with approximate timing of outer/middle, outer/inner, and middle/inner array interactions indicated. (b) Linear scale and (c) log scale total x-ray power pulses from Z1747 (solid red curve), 978 (a “standard” 2:1 load; dashed green curve) and 1308 (4:1 radius ratio; dotted blue curve). Triple nesting increases the peak power and decreases the FWHM by 30%.
Thin-shell 0D implosion calculations carried out over initial total mass and radius parameter space to estimate (a) implosion time, (b) peak load current, and (c) -coupled energy for nested stainless steel wire arrays on the refurbished Z machine ( Marx charge). Per the -shell yield scaling model of Ref. 32, the parameters (d) [Eq. (2)], (e) [Eq. (8)], and (f) [Eq. (9)] are calculated.
Using thin-shell 0D implosion calculations as in Fig. 16, the stainless steel -shell yield [Eq. (7)] on the refurbished Z machine is estimated over mass-radius parameter space for Marx charge voltages of (a) , (b) , and (c) .
Configuration of double-nested stainless steel wire arrays discussed in this work. All were tall with a anode-cathode power feed gap, and had identical outer wire arrays ( array diameter, , 104 wires, wire diameter). The shot labeled “standard” represents a 2:1 mass and radius ratio configuration that was fielded times on Z and which we consider as a baseline for comparison with other variants.
Results of spectroscopic analysis for selected shots from Table I, which lists load diameters and masses. Shot Z978 is a “standard” nested array. A delay between the outer and inner array implosions was seen for Z1084, and the analysis indicates worse compression at stagnation. Z1308 and Z1386 were designed for nearly simultaneous implosion of outer and inner arrays. 30% systematic error in power and yield is not accounted for.
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