Dynamic Response of Ionized Gas in IFE Chamber

1
Dynamic Response of Ionized Gas in IFE Chamber

• Zoran Dragojlovic and Farrokh Najmabadi
• Department of Electrical Computer Engineering
  and Center for Energy
• Research, University of California in San Diego

2
Outline

• Overview of the previous results.
• The present algorithm.
• Effects of background plasma
• Impact of free electrons on thermal conductivity
  and viscosity.
• Radiation.
• Discussion and future plans.

3
Overview of the Previous Results

• 2D effects are important. Number and
  configuration of beam channels have an influence
  on the distribution of eddies in the chamber,
  which affects the heat transfer.
• Viscosity and thermal conductivity of neutral gas
  should not be neglected.
• Dynamic loads on the final optics and chamber
  walls are negligible (Structural analysis of
  chamber walls demonstrated by Ghoniem, December
  2002).

4
The Present Algorithm

• Navier-Stokes equations with state dependent
  transport properties.
• Arbitrary domain boundary implemented on a
  Cartesian grid.
• Discrete conservative update
• Time-explicit Godunov method for advection
• Two-stage Runge-Kutta update for diffusion.
• Conservation on partial cells enforced by local
  redistribution scheme.
• Adaptive mesh refinement algorithm implemented
  with the conservative update described above.
• Second order convergence achieved both at the
  boundary and inside the fluid domain as
  documented by a journal publication (Journal of
  Computational Physics).
• Grid indexing space is handled by BoxLib, a
  library of C classes and structures which
  enables parallel computation. Initial test runs
  were successfully made with help from Marcus Day,
  Lawrence Berkeley Lab.

5
Impact of Background Plasma

• Coronal equilibrium in the chamber gas assumed.
• Electron density, ion density and radiated power
  per unit volume are uniquely determined by the
  density and temperature of the gas.
• Coronal equilibrium parameters calculated by
  IONMIX and provided by Jiankui Yuan, University
  of Wisconsin.
• Electron thermal conductivity kelectron and
  electron viscosity melectron obtained from NRL
  plasma formulary (2002).
• Neutral gas diffusive terms calculated by empiric
  formula (Sutherland law).
• Resulting conductivity and viscosity obtained by
  hybrid law

• Span of values in the IFE Chamber Model

r \kg/m3 T K kneutral W/(mK) kelectron W/(mK) mneutral Ns/m2 melectron Ns/m2 P W/m3
min 3.84 10-4 973.16 0.025 0.004 9.25 10-5 1.73 10-8 1.33 106
max 77 10-4 4.5 105 0.437 1.14 105 0.0016 597.48 2.71 1012
6
Test Cases

1. Neutral gas, point of departure.
2. Electron conductivity neutral gas.
3. Electron viscosity neutral gas.
4. Combined electron conductivity and viscosity
   neutral gas.
5. Radiation sink neutral gas.
6. Electron diffusivity terms radiation sink
   neutral gas.

7
Properties Compared Case to Case

• Evolution of Gas Energy from 0-100 ms
• Internal
• Kinetic
• Total.
• Chamber State at 100 ms
• Temperature
• Particle Velocity.

8
Evolution of Gas Energy

1. Neutral Gas
2. Electron Conductivity Neutral Gas
3. Electron Viscosity Neutral Gas
4. Electron Conductivity Electron Viscosity
   Neutral Gas

9
Evolution of Gas Energy

1. Neutral Gas
2. Electron Conductivity Neutral Gas
3. Electron Viscosity Neutral Gas
4. Electron Conductivity Electron Viscosity
   Neutral Gas
5. Radiation Neutral Gas
6. Electron Diffusivity Terms Radiation Neutral
   Gas

10
Temperature at 100 ms
Neutral Gas
Electron Conductivity Neutral Gas
Electron Viscosity Neutral Gas
Tmin 973.16 K

• Tmax 2.23 104K
• Tave 1.06 104K

Tmax 1.43 104K Tave 0.93 104K
Tmax 2.56 104K Tave 1.12 104K
Electron Diffusivity Terms Neutral Gas
Radiation Neutral Gas
Electron Diffusivity Terms Radiation Neutral
Gas
Tmax 1.63 104K Tave 1.00 104K
Tmax 0.44 104K Tave 0.22 104K
Tmax 0.42 104K Tave 0.22 104K
11
Velocity at 100 ms
Electron Diffusivity Terms Neutral Gas
Electron Diffusivity Terms Radiation Neutral
Gas
Vmax m/s Vaverage m/s
Neutral Gas 319.38 93.76
Electron Conductivity Neutral Gas 298.82 91.82
Electron Viscosity Neutral Gas 263.05 78.90
Vmax m/s Vaverage m/s
Electron Diffusivity Terms Neutral Gas 260.15 82.55
Radiation Neutral Gas 288.91 81.88
Electron Diffusivity Terms Radiation Neutral Gas 252.65 79.56
12
Conclusions

• Effects of background plasma on IFE chamber gas
  evolution were taken into account by assuming a
  coronal equilibrium in the chamber and including
  electron thermal conductivity, electron viscosity
  and radiation power loss into Navier-Stokes
  equations.
• Electron thermal conductivity and electron
  viscosity did not make a large impact on chamber
  state evolution.
• Radiation heat sink made a large reduction of
  internal energy (temperature) of the chamber.
  Most of the energy loss (50) occurred within
  the first 10 ms. The internal energy remained
  nearly constant after that.
• Radiation heat sink changed the flow pattern and
  kinetic energy profile but did not significantly
  reduce the velocities in the chamber.

13
Future Plans

• Governing equations in cylindrical coordinate
  system.
• Completed the algorithm for regular grid domain.
• In progress
• Adaptation of embedded boundary (partial cells,
  redistribution, etc.) to cylindrical equations.
• Modification of AMR to synchronize grid levels in
  cylindrical geometry.
• Multi-species code to include various chamber
  constituents, such as those originating from the
  target, material ablated from the wall, etc.
  First version to include Xe, He, D, T.
• Gain access to a parallel computer and provide
  higher accuracy of solution.