Modeling Studies of Photoionization Experiments Driven by Z-Pinch X-rays

Nathan Shupe

ADVISOR: Professor David Cohen

Outline

I. X-ray Binaries

II. Photoionized vs. Coronal Plasmas

III. Z Accelerator

IV. Gas Cell Experiments

V. Scope of the Thesis

INTRO

VI. Viewfactor Simulation

VII. Hydrodynamic Simulation

VIII.Spectral Synthesis

IX. Scaling Studies

X. Conclusions

MODELING

X-ray Binaries

• Photoionized plasmas are characteristic of some of the brightest x-ray sources in the sky, including black hole and neutron star binaries.

X-ray creation in an x-ray binary

(1) Compact object gravitationally captures some wind material from nearby star.

(2) Gravitational potential energy converted to thermal kinetic energy in the inner accretion disk. High energy x-rays are produced.

(3) These x-rays photoionize the nearby cool circumstellar gas. Giant Star Accretion Disk

Compact Object

Photoionized vs. Coronal• Collisions drive ionizations in coronal plasmas. Collisions and

photoionizations drive ionizations in photoionized plasmas.

• Photoionized plasmas are said to be overionized relative to their electron temperature because they can achieve the same degree of ionization with fewer collisional ionizations (i.e. lower electron temperature).

• The ionization parameter,

determines the degree of photoionization (or overionization) of a plasma.

• In coronal plasmas, ionization is balanced by dielectronic recombination. In photoionized plasmas, ionization is balanced by radiative recombination and cascade following recombination.

2,

e

L

n r

Z-machine

• The load in the machine is a cylindrical array of several hundred tungsten wires.

• A 20 MA current is applied to the load over a pulse of 100 ns.

• The current and magnetic field produce a J x B force directed toward the z-axis. This causes the wire array to pinch toward the z-axis.

• Kinetic energy of pinch is converted to thermal energy when it stagnates on the z-axis. Produces 200 TW of x-ray power over 100 ns (1.9 MJ of energy)

(b)

Wire array

Gas Cell Experiments• A series of gas cell shots have been conducted on the Z-machine.

• Gas in the cell Photoionized plasma in x-ray binary system.

• Pinch X-ray emitting inner shell of accretion disk.

Face-on, top, and pinch views of the experimental setup, with the spectroscopic lines of sight shown in red and blue.

• Experiments have used neon of density nion ~ 1018 cm-3 observed in absorption with a time integrated spectrometer.

Scope of Thesis

(1) Use simulation codes to model a gas cell shot that has already been conducted (shot Z543) to validate the simulation procedure.

(2) Use the same modeling procedure to design new gas cell experiments.

(3) Use modeling procedure to synthesize new diagnostics of the photoionized plasma (time dependent absorption and emission spectra).

Modeling Big Picture

• Modeling procedure has three main steps, each one building off of the previous step.

(1) Compute incident flux on face of gas cell.

(2) Use hydrodynamic code to compute the temperature and density distributions.

(3) Synthesize time-resolved absorption spectra.

VisRad

Helios

Spect3D

Step 1: Viewfactor Simulation• The objects in the setup are included, as well as albedos (how shiny or

reflective the object is) and the time-dependent power and radius of the pinch (both measured in actual experiment).

Radius vs. time Power vs. time

VisRad Workspace

Gas Cell Pinch

Gas Cell

Viewfactor Simulation

Pinch, Current Return Can, Anode Insert

Step 2: Hydrodynamics Simulation

• The time-dependent flux (from step 1) on the face of the gas cell and opacity and equation of state (EOS) models for the gas cell materials are inputs for the hydro simulation.

• Using the 1-D Lagrangian code Helios, a non-LTE hydrodynamics simulation is run, and the time-dependent temperature and density distributions are computed.

Temperature and Density DistributionsTemperature vs. Position

Temperature vs. Time vs. Position

Density vs. Position

Power vs. Time

Step 3: Spectral Synthesis

• The temperature and density distributions (from step 1), the incident flux on the face of the gas cell (from step 2), and the atomic level structure and transition rates are inputs for the spectral synthesizer.

• So far we have only done absorption spectra (with the pinch as the backlighter), but we will model the emission spectra for these plasmas.

Absorption Spectra for Shot Z543

Spect3D synthesized spectrum (red) matched to the measured time-integrated absorption spectrum from Shot Z543 (black). Resolution: E/dE = 800.

Scaling Studies

• Lower density gas fill to boost the ionization parameter.

• Different gas cell window properties (thickness, composition), gas cell positions, and gas cell fills.

• Detailed diagnostics: time-dependent absorption and emission spectra.

Conclusions

• Validated our procedure as an effective method for modeling the experiment.

• Planning future experiments using scaling studies.

• Modeling more detailed diagnostics (time-resolved absorption and emission spectra) for future experiments.

• Testing, validation, and improvement of codes in modeling gas cell experiments works toward using these codes to model astrophysical sources.

Appendix

Where is the photoionized plasma?• X-rays emitted by the accretion disk photoionize the nearby cool circumstellar gas

(predominantly wind material).

• Radiation is emitted from this photoionized plasma in the form of radiative recombination continua and recombination cascades.

A high-resolution x-ray spectrum of the ionized stellar wind of Vela X-1 during eclipse captured with the HETGS on the Chandra Observatory. The radiative recombination continua are labeled in red. Figure from Schulz et al., ApJ, 564, L22 (2002).

Photoionized vs. Coronal• In coronal plasmas, ionization is primarily balanced by dielectronic

recombination (excess electron energy excites additional ionic electron).

• In photoionized plasmas, ionization is primarly balanced by radiative recombination (excess electron energy is radiated away) and cascade following recombination.

Iron model emission rate spectra for a (a) photoionized plasma and a (b) coronal plasma. Notice that despite identical electron densities for the plasmas, the spectra are markedly different. Figures taken from Liedahl et al. Ap.J., 350, L37 (1990).

(a) (b)

Ionization Parameter• A typical value for ionization parameter in a cosmic x-ray

photoionized nebula is on the order of several hundred.

• An ionization parameter of ~5 is typical of our gas cell experiments (because of high gas cell fill density).

Contours of constant ionization parameter (logarithmic) for the HMXRB Vela X-1. Figure taken from Sako et al. Ap.J., 525, 921 (1999).

Z Accelerator

Z accelerator banking its pulse forming switches before a shot.

Z Accelerator

• The most powerful source of x-rays on Earth.

• Produces 200 TW of x-ray power for an order 100 ns pulse which amounts to a total of 1.9 MJ for the entire pulse.

• Most efficient x-ray source on Earth.

• Converts 10% of its input energy into output radiant x-ray energy.

How does it work?

• Converts electrical energy at low powers and long timescales to high powers and short timescales.

(1) Slowly charges in parallel capacitors lining the rim of the accelerator.

(2) Once fully charged, capacitors slowly (µs) discharge in series to a cylindrical pulse-forming line (PFL).

(3) Once charged to capacity, the PFL rapidly (ns) discharges into the Z-pinch load.

Z-pinch X-rays• X-rays are produced by the pinch when the pinch plasma

stagnates on the z-axis.

• The magnitude of the J x B force is large given the large current, so the implosion velocity is also large, of order 108 cm s-1.

• High kinetic energy is converted to thermal energy when the pinch stagnates on the z-axis, and a large flux of x-rays are produced.

• Multi-wire system gives you the ability to increase the x-ray energy output without increasing the voltage or power of the machine.

Viewfactor Simulation Output• VisRad outputs the time-dependent flux incident on the face of the gas cell.

Time-dependent flux at the center (blue square) of the face of the gas cell.

Note that the peak incident flux coincides with the peak pinch emission at 100 ns.

Also note that the incident spectrum at 104 ns has a high energy shoulder when compared to the spectrum at 96 ns since the pinch emission temperature (due to a smaller pinch radius) is higher at later times following the peak than it was before the peak.