1. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher1 PFRP MHD NRL Symposium on Recent Advances in Plasma Physics June 10-12, 2007 The Plasma-Filled Rod Pinch: a Pulsed-Power HED Plasma Radiographic Source D. Mosher, B.V. Weber, and J.W. Schumer Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA * Work supported by the U.S. Office of Naval Research, Sandia National Laboratories, and AWE Aldermaston, UK

2. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher2 PFRP MHD NRL Background NRL has a long-term program to develop intense, mm-diam bremsstrahlung radiography sources driven by 100-ns, 1- to 6-MV, TW-level pulsed-power generators Our star performer is the plasma-filled rod pinch (PFRP), a sub-mm source concentrating a 0.5-MA, MeV electron beam onto the tip of a 1-mm-diam, tapered tungsten rod 1 Tungsten plasma expansion during the x-ray pulse limits the source brightness Understanding the dynamics of the high-energy-density tungsten plasma will help to improve this promising radiography source W plasma expansion was studied with holographic interferometry 2 These measurements and radiation imaging are compared with the results of simple, self-similar modeling of the plasma expansion Model predictions of the expansion and radiation patterns agree with measurements and indicate peak thermal energy densities of about 2 MJ/cc, corresponding to > 10 Mbar peak pressure 1 B.V. Weber, et al., Phys. Plas. 11, 2916-2927(2004). 2 D.M. Ponce, D. Phipps, D.D. Hinshelwood, and B.V Weber, Proc. 14 th Inter. Pulsed Power Conf.

3. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher3 PFRP MHD NRL PFRP operation on Gamble II 1-mm-diam rod tapered to a point over 1- to 1.5-cm length Voltage before x-rays due to d(LI)/dt of the run-down phase About 40% of the 30-kJ diode energy is deposited as electrons in the tip Plasma conducts current Gap opens, MeV electrons deposited at tip Tip explodes, anode plasma expands Anode

4. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher4 PFRP MHD NRL X-Ray Radiography 101: Edge Spread x z y x-y view at IP on line of sight tungsten rolled edge x-ray source image plate (IP) ESF y dose on IP Edge Spread Function Y 0 -Y 0Y

5. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher5 PFRP MHD NRL X-Ray Radiography 101: Edge Spread x z y x-y view at IP on line of sight tungsten rolled edge x-ray source image plate Y 0 -Y ESF dose on IP -Y0Y y

6. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher6 PFRP MHD NRL X-Ray Radiography 101: Edge Spread x z y x-y view at IP on line of sight tungsten rolled edge x-ray source image plate Y 0 -Y ESF dose on IP -Y0Y y

7. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher7 PFRP MHD NRL X-Ray Radiography 101: Line Spread LSF(y)dy is a measure of x-ray energy emitted in a thin strip along x Source radial distribution: Point Spread Function PSF(r) PSF recovered from LSF by Abel inversion x z y x-ray source PSF(r) ESF LSF dose on IP Line Spread Function y x-y view

8. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher8 PFRP MHD NRL The plasma filled rod pinch diode on GAMBLE II has a line spread with two distinct length scales 0.4-mm FWHM characteristic of conical-rod-tip emission Few-mm "wings" associated with tungsten plasma expansion during the x-ray pulse X-ray pinhole images and interferometry show plasma expansion at the rod tip Use hydro-expansion model to confirm the wing feature cathode Line Spread for 1-mm-Diam Tapered W Rod Interferogram and Rod Shadow at the End of the X-Ray Pulse

9. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher9 PFRP MHD NRL The axial line spread measures the x-ray intensity emitted along the rod The axial line spread is a measure of electron-beam heating vs z Beam heating near the rod tip has a FWHM of about 4 mm This axial heating profile is used in the model to drive tungsten- plasma expansion Hydro-expansion model predictions are compared to – 2D, time-dependent interferometry – the measured time-integrated LSF Agreement with these measurements will indicate that the tungsten plasma parameters are reasonable and in the HED regime x z y image plate rolled edge pinhole image

10. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher10 PFRP MHD NRL A self-similar expansion model is used to estimate the line spread of the PFRP Tungsten mass in length L of the conical tip is distributed in a cylinder The axial LSF suggests L in the 3- to 5-mm range P h (t) = 0.4I diode V diode /L Black-body radiation with emissivity  from radius R(t) Tungsten equation of state from SESAME 3 – E int = 1.5(1+Z)NkT + ionization – E th = 1.5(1+Z)NkT  0.4E int – max pressure = 0.67E th /  R 2 (t) (r) is the PSF from which the model line spread is calculated Self-Similar Cylindrical Expansion (per cm length of plasma) 3 NTIS Doc. DE94-011699, J. D. Johnson, ‘‘SESAME Data Base’’

11. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher11 PFRP MHD NRL heating kinetic internal radiation Self-Similar Expansion of the Rod Tip  = 0.1, L = 3.5 mm Energy PartitionExpansion History E th /  R 2 (MJ/cc) R (mm) T(eV)/10 Z/3 P h (10 11 W/cm)

12. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher12 PFRP MHD NRL Self-similar hydro expansion reproduces the PFRP line spread Predicted line spreads are nearly independent of emissivity Best fit to data for L = 3 - 4 mm, agrees with axial line spread PSF from Model for L = 3.5 mm Line Spreads from Experiment and Model for L = 3 and 4 mm

13. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher13 PFRP MHD NRL The self-similar expansion model can be generalized to one-dimensional axial variations 1 N(z) =  R rod (z) 2  W /m W P h (z,t) from axial line spread Add return-current ohmic heating to the energy balance – I z ~ axial edge spread – Spitzer resistivity Expansion Model Variations with z 1 B.V. Weber, et al., Phys. Plas. 11, 2916-2927(2004). JeJe IzIz return current t = 40 ns z 0

14. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher14 PFRP MHD NRL Fringe count determines experimental electron density n eS (z,t) at the schlieren boundary R exS (z,t) Axial-expansion equations provide the self-similar expansion radius R(z,t) Determine theoretical schlieren boundary R thS (z,t) from Schlieren boundary can be calculated from axial hydro and compared to experiment mm n eS at R exS R thS Interferogram and Rod Shadow at 110 ns Axial-cylindrical modeling reproduces expansion Analysis valid for dR/dz < 1 Does not predict spherical expansion at z < 2 mm from tip

15. Pulsed Power Physics Branch, Plasma Physics Division D. Mosher15 PFRP MHD NRL Conclusions For the tapered-rod PFRP on Gamble II, intense beam heating of the low-mass rod tip produces rapid tungsten-plasma expansion leading to extended wings in the line spread Measured Schlieren images and line-spread distributions compare well with self-similar hydrodynamic modeling of rod-plasma expansion Model predictions indicate peak thermal energy densities of about 2 MJ/cc, corresponding to > 10 Mbar peak pressure When axial variations are taken into account, higher energy density is predicted very close to the rod tip early in the expansion, though the assumption of 2D-cylindrical expansion breaks down Future plans include 2-D MHD and PIC simulations of the PFRP Challenges for future work include – rod return-current-heating effects during the run-down phase – the role of adsorbed gases in the rod – following the run-down/plasma-opening transition – beam- and plasma-current distributions in the expanding rod plasma – geometries that reduce the wings in the line spread