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
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.
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).
The Present Algorithm
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•
•
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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.
Impact of Background Plasma
•
•
•
•
•
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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:
k  kneutral  kelectron
m  m neutral  melectron
• 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
Test Cases
1.
2.
3.
4.
Neutral gas, point of departure.
Electron conductivity + neutral gas.
Electron viscosity + neutral gas.
Combined electron conductivity and
viscosity + neutral gas.
5. Radiation sink + neutral gas.
6. Electron diffusivity terms + radiation sink
+ neutral gas.
Properties Compared Case to
Case
• Evolution of Gas Energy from 0-100 ms:
– Internal;
– Kinetic;
– Total.
• Chamber State at 100 ms:
– Temperature;
– Particle Velocity.
Evolution of Gas Energy
1.
2.
3.
4.
Neutral Gas
Electron Conductivity + Neutral Gas
Electron Viscosity + Neutral Gas
Electron Conductivity + Electron
Viscosity + Neutral Gas
Evolution of Gas Energy
1.
2.
3.
4.
5.
6.
Neutral Gas
Electron Conductivity + Neutral Gas
Electron Viscosity + Neutral Gas
Electron Conductivity + Electron
Viscosity + Neutral Gas
Radiation + Neutral Gas
Electron Diffusivity Terms +
Radiation + Neutral Gas
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
Electron Diffusivity Terms +
Neutral Gas
Tmax = 1.63 104K
Tave = 1.00 104K
Tmax = 1.43 104K
Tave = 0.93 104K
Radiation + Neutral
Gas
Tmax = 0.44 104K
Tave = 0.22 104K
Tmax = 2.56 104K
Tave = 1.12 104K
Electron Diffusivity Terms +
Radiation + Neutral Gas
Tmax = 0.42 104K
Tave = 0.22 104K
Velocity at 100 ms
Electron Diffusivity Terms + Neutral
Gas
|V|max [m/s]
|V|average
[m/s]
Electron Diffusivity Terms +
Radiation + Neutral Gas
|V|max [m/s]
|V|average [m/s]
260.15
82.55
Neutral Gas
319.38
93.76
Electron Diffusivity Terms
+ Neutral Gas
Electron Conductivity +
Neutral Gas
298.82
91.82
Radiation + Neutral Gas
288.91
81.88
252.65
79.56
Electron Viscosity +
Neutral Gas
263.05
78.90
Electron Diffusivity Terms
+ Radiation + Neutral Gas
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.
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.