Wire Arrays
A majority of the laboratory research effort is focused on wire array z-pinch physics. During the last years, we have shown that wire-array Z-pinch experiments, including on Z at 20 MA, proceed via four distinct phases: plasma initiation by current driven wire explosion, ablation from stationary dense wire cores and redistribution of the array mass by global-field-driven flow of the ablation plasma, snowplow-like implosion of the redistributed mass, and stagnation of the imploding plasma on axis, at which time an intense x-ray pulse is generated. The optical streak camera image shown below illustrates the four phases of wire-array z-pinch dynamics identified above, except that the initiation phase, which takes place close to the beginning of the streak, does not emit enough light to be visible in the streak.
In addition to standard cylindrical wire array loads, several novel configurations have been investigated experimentally, including nested, radial and conical arrays and X-pinches, because they enable detailed measurements of particular aspects of z-pinch physics and extend the available range of plasma parameters and applications. We begin with a discussion of the four phases of cylindrical wire-arrays.
Initiation
At early times, the flow of current through the wires increases their temperature and resistance, melts them and then partially vaporizes and ionizes them, resulting in the formation of coronal plasmas around the wires. The voltage across the wire then abruptly collapses as the current transfers to the coronal plasma and continues to rise. By measuring the load current and voltage, the energy deposited in the wires prior to plasma formation has been measured in both single wire experiments and wire-arrays. For most wires, the wire cores are only partially vaporized, which is consistent with radiographic images showing a foam-like mixture of liquid and vapor states. The energy deposited in the wire cores and their subsequent size has been shown to be sensitive to the wire – electrode contacts and to the polarity and geometry of the electric field. When the current transfers to the coronal plasmas around the wires, the ablation phase is initiated.
Ablation
Since the majority of the current is flowing in the coronal plasma, little force is applied directly to the wire cores, and so they remain stationary. Plasma is ablated from the wire cores by radiation and heat conduction and is driven by the jxB force (j is the current density and B the array magnetic field) towards the array axis, filling the interior of the array. This process is shown in the 150 ps laser image, including “precursor” plasma buildup on axis.
The ablation process is reasonably well described by a rocket model, which argues that the ablation rate is proportional to the JxB force divided by the flow (“ablation”) velocity. Analysis of wire-array z-pinch experiments from 1-20MA has shown that the velocity remains essentially the same despite the huge difference in the driving force. However, the ablation velocity is sensitive to the gap between wires in the array. The wire ablation rate is important in determining the radial distribution of mass at the start of implosion and the sensitivity to magneto-Rayleigh-Taylor (R-T) instabilities. The ablated plasma radial profile converges to an equilibrium that arises as a result of the nature of the MHD equations in cylindrical geometry.
While the above data characterizes the average ablation of the wires, it is clear that the ablated plasma has a strong axial modulation. The corresponding modulation of the ablation rate has been observed in all wire array configurations and provides a seed perturbation for Rayleigh-Taylor instabilities during the implosion phase. Variations in wavelength and amplitude have been characterized experimentally. In recent COBRA experiments, up to five X-pinches emitting x-ray bursts between 70 and 170 ns after the start of the current pulse were used to image W wire arrays. Three such radiographs from one pulse are shown below.
These radiographs are being used to evaluate quantitatively the temporal and spatial evolution of the ablation plasma, including the axial modulations, in individual pulses. High-resolution 3D MHD simulations are now showing axial modulations that are similar to the observed modulations, suggesting that an MHD instability mode is responsible. Joint experiments with Sandia scientists using chemically etched wires showed that variations in initial wire diameter do not remove the “natural” wavelength of this modulation, but allow introduction of controlled perturbations. The results of these experiments were used to benchmark Sandia’s ALEGRA and the laboratory’s GORGON MHD codes. The only configuration tested so far that eliminates this modulation is the helical wire array, in which the introduction of the axial magnetic field associated with the helical current path appears to lock the modulation wavelength to the period of the helices.
Implosion
This phase of wire-array dynamics begins when ~50% of the initial wire material has been ablated. As plasma is swept up by the implosion “snowplow,” the variation of the ablation rate along the wires provides a large-amplitude seed perturbation for the R-T instability and also results in a fraction of the initial array mass being left behind (as “trailing mass”) by the implosion. The growth of the instability in the implosion surface and evolution of the trailing mass can be seen in the series of XUV images from COBRA shown below.
Our investigations showing the importance of the trailing mass are now accepted by the Z-pinch community. he plasma filling the interior of the array is accreted by the implosion surface giving rise to “snowplow” radiation which can be used to tailor the foot of the radiation pulse. laboratory experiments have shown how further control over radiation pulse shaping can be achieved using nested wire arrays in the current transfer mode. Methods to increase the duration of the radiation pulse using zippered implosions in conical wire arrays have also been explored.
Stagnation
The assembly of the imploding plasma on axis leads directly to the first high intensity x-ray pulse, the part of the x-ray output that is important for ICF. Detailed analysis of gated XUV images has shown that the temporal spread in the stagnation of different parts of the plasma structure onto the axis can be directly correlated with the x-ray rise-time. The helical instability visible in the post-stagnation frames like the last one in the above figure may be responsible for the late-time breakup of the z-pinch.
Very careful spectroscopic measurements of gas-puff z-pinches by our Weizmann Institute partner show that the implosion kinetic energy was adequate to explain the radiation pulse. However, in wire-array z-pinches, this may not be so. For example, in experiments with wire arrays in which the current through the stagnated plasma column was held constant but the implosion kinetic energy was changed by a factor of two, the X-ray power was observed to be unchanged. There remains uncertainty over what fraction of the x-ray pulse is generated by the kinetic energy of the implosion versus other mechanisms that might convert magnetic energy into electron thermal energy and radiation, such as turbulence, Ohmic heating or MHD instabilities.