# Presentation: 349369

## 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 **

## 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**

- 1B.V. Weber, et al., Phys. Plas. **11**, 2916-2927(2004).
- 2D.M. Ponce, D. Phipps, D.D. Hinshelwood, and B.V Weber, Proc. 14th Inter. Pulsed Power Conf.

## 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

## X-Ray Radiography 101: Edge Spread

**x-y view at IP**
**on line of sight **

**tungsten**
**rolled**
**edge**

**x-ray**
**source**

**image**
**plate**
**(IP)**

**Edge Spread Function**

**Y**

**0**

**-Y**

**-Y**

**0**

**Y**

## X-Ray Radiography 101: Edge Spread

**x-y view at IP**
**on line of sight**

**tungsten**
**rolled**
**edge**

**x-ray**
**source**

**image**
**plate**

**Y**

**0**

**-Y**

## X-Ray Radiography 101: Edge Spread

**x-y view at IP**
**on line of sight**

**tungsten**
**rolled**
**edge**

**x-ray**
**source**

**image**
**plate**

**Y**

**0**

**-Y**

## 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-ray**
**source**
**PSF(r)**

**x-y view **

## 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**

## 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**

**image plate**

**pinhole image**

## 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**
- Eint = 1.5(1+Z)NkT + ionization
- Eth = 1.5(1+Z)NkT   0.4Eint
- max pressure = 0.67Eth/R2(t)
**<P****br****>(r) is the PSF from which the model line spread is calculated**

**Self-Similar Cylindrical Expansion****(per cm length of plasma)**

- 3NTIS Doc. DE94-011699, J. D. Johnson, ‘‘SESAME Data Base’’** **

## Self-Similar Expansion of the Rod Tip = 0.1, L = 3.5 mm

**Self-Similar Expansion of the Rod Tip******** = 0.1, L = 3.5 mm**

**Energy Partition**

**Expansion History**

## Self-similar hydro expansion reproduces the PFRP line spread

**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**

## The self-similar expansion model can be generalized to one-dimensional axial variations1 

**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**
- Iz ~ axial edge spread
- Spitzer resistivity

**Expansion Model Variations with z**

- 1B.V. Weber, et al., Phys. Plas. **11**, 2916-2927(2004).

## Fringe count determines experimental electron density neS(z,t) at the schlieren boundary RexS(z,t)
Axial-expansion equations provide the self-similar expansion radius R(z,t)
Determine theoretical schlieren boundary RthS(z,t) from

**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**

**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**

## 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