Measuring Pressure In Warm Dense Tungsten Plasma Created In Plasma Filled Rod-Pinch Diodes

Pressure (or equivalently, energy density) measurements are crucial for determining, or testing models of, the equation of state (EOS) in warm, dense plasma. The plasma-filled rod pinch diode (PFRP)
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on the Gamble II generator creates tungsten plasma with parameters in the warm, dense regime: $\mathrm {T}\sim 30$ eV, $r \sim 0.7\mathrm {g} /$cm
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, $\mathrm {Z}\sim 18$ and $\mathrm {P}\sim 16$ Mb.
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The plasma is created by an intense $\sim $ MeV electron beam that forms at the tip of a 1-mm diameter tungsten rod tapered over 15 mm to a sharp point. The beam develops after an injected plasma conducts the generator current like a short circuit for 50 ns while the current increases to 600 kA, then the PFRP impedance increases and an $\sim $ MeV, 500 kA electron beam rapidly deposits energy at the end of the tapered rod. The energetic electrons that heat the tungsten-rod plasma also produce hard x-ray emission. The time-dependent axial and radial shapes of the x-ray distribution are diagnosed using an array of PIN diodes behind rolled edges. The x-ray distributions are assumed to match the mass distribution, an assumption to be tested using Monte-Carlo calculations. Using this assumption, the axial and radial x-ray distributions are converted to mass distributions, since the dimensions of the solid rod tip are known. The evolution of the mass distributions is determined by the internal pressure (and to a lesser extent by the external magnetic pressure). The radial distributions can be represented by Gaussian functions, and a self-similar equation of motion determines the pressure. The pressure calculated this way is many times greater than the kinetic pressure $(1 +\mathrm {Z})$ nkT. This could be the result of ionion repulsion in this unconventional plasma, in which the number of electrons in a Debye sphere is of order unity. Independent measurements of ionization (Z) and temperature imply the coulomb coupling factor is also much greater than one, supporting the importance of ion-ion coupling causing high internal pressure.