This research complements the large national and international research program, based on wire array Z-pinches, by conducting an in-depth investigation of radial foil geometries.  By changing the type of material and the geometry of the experimental setup, it is possible to vary the different parameters governing the dynamics of high energy density plasmas in thin radial foil configurations.  We are investigating how plasma dynamics (radiation, magnetically threaded flows and shocks) changes with foil material and electrode geometry.  Particular attention is given to the measurement of magnetic fields and plasma velocity fields.  The information collected can be used to maximize radiation yield, to understand the physics of magnetically threaded astrophysical jets, to mitigate magneto-hydrodynamics instabilities and to validate the theoretical models used in computational codes.

While foils have been extensively used in cylindrical geometries, thermal and striation instabilities were found very strong and the overall foil mass too large to be optimally driven by actual pulsed-power generators. Historically, replacing cylindrical foils by a series of vertical wires was more successful as the Rayleigh-Taylor (RT) instability subsided.  Another major disadvantage of cylindrical foil configurations comes from striation, as the current does not only travel along the vertical direction but also azimuthally.  As a result, current channels can twist and deviate from a vertical path, degrading the quality of the implosion and reducing the radiation yield.

On the other hand, radial foil arrays have two major advantages.  First the current is forced to run towards the axis.  Hence the current density becomes very large at the center of the foil.  Consequently, moderate generators can explode radial foils since the mass density of the foil is not as limiting a parameter as in cylindrical geometries.  The other important characteristic comes from the radial geometry.  Since the current path is radial, any twisted current channel at the edge of the foil has to straighten to go through the inner (axial) electrode.  This phenomenon is extremely important since it favors current symmetry. Despite such advantages, radial foil physics is still largely unexplored.The experimental setup is described in the following cartoon.

Formation

The major difference in plasma formation between wire arrays and foils is ablation.  Foils do not go through such a physical process.  At best, ablation mainly occurs at the top of the central electrode.  As a result, there is no or little material in front of the plasma flow.  Despite these large density gradients, no RT instabilities were visible in the formation phase despite strong density gradients.  This phenomenon requires investigation to understand the reason why radial foils behave differently from wire arrays.  A possible explanation comes from the lack of coronal plasma at the foil edge.  Consequently, the wavenumber of the instabilities thriving in the corona is relatively small which reduces the growth rate of the RT instability.

Ejection

The initial phase is rapidly followed by an ejection phase where a plasma jet shoots from the central electrode (cathode).  This jet develops from compression due to pinch forces.  The dynamics is consistent with the 0-D model across the whole cathode. 

Bubble

The ejection phase leads to the formation of a magnetic bubble which expands rapidly.  As the bubble grows and the current lines stretch, another plasma ejection start on the cathode and the process repeats.  Since the newly born bubble is less resistive than the previous instance, the current redistributes in the vicinity of the smaller bubble and the large bubble decays away.  Several bubble events are observed during a single shot. As the bubble open, the top of the bubble becomes a projectile with ballistic velocities of 400 km/s. This projectile was capture by the streak camera.

Radiation

Radiation yield is a major parameter that one should maximize when producing high energy density plasmas.  As in wire arrays (cylindrical or radial), the pinch formed by the JxB force produces X-rays.  The figure above shows the X-ray radiations produced by a radial foil using different filters. At the moment, wire arrays produce larger X-ray yields than radial foils. However they have been tuned over many years of experimental research.  Radial foil physics is still is its infancy and radiation yield has not been optimized yet.  The proposed work will focus on understanding and optimizing such configuration for maximum radiation throughput.