SPARTAN Chamber Dynamics Code

1
SPARTAN Chamber Dynamics Code

• Zoran Dragojlovic and Farrokh Najmabadi
• University of California in San Diego
• HAPL Meeting, June 20-21, 2005, Lawrence
  Livermore National Laboratory

2
Motivation/Thesis

• Motivation
• To understand the chamber condition with
  different fill gases and pressures at 100 ms. The
  emphasis is on Deuterium and Helium as they will
  always exist in the chamber.
• To explore the impact of gas temperature on
  target survival.
• To explore the deflection of target during
  injection by velocity drag and pressure gradient.
• Thesis
• Xenon was chosen as fill gas because it easily
  absorbs and re-radiates the energy released by
  the target.
• Deuterium and Helium absorb less energy. They
  should be cooler and thus have less impact on a
  target.

3
The Cases Studied

• Chamber gases
• Deuterium
• Helium
• Xenon
• Base pressures
• 30 mTorr
• 50 mTorr
• BUCKY data were received from G. Moses in January
  2005.
• We requested the states at 1 ms, 10 ms, 100 ms
  and 500 ms from the target blast. However, D and
  He shockwaves already reflect from the wall past
  the 10 ms, which renders some of the BUCKY cases
  useless because we have multidimensional
  geometry.
• We should have asked for chamber states at
  certain position of the shock front instead of
  specifying the times.

4
Initial Velocities from BUCKY Code
Base pressure 30 mTorr
Base pressure 50 mTorr

• For SPARTAN runs, the best initial condition is
  when the shock fronts are at the same, small
  distance from the wall.
• Deuterium has a much higher velocity than Xenon,
  due to its lower mass. At 50 mTorr, the peak
  velocity of Xenon is 2.6 km/s, while the peak
  velocity of Deuterium is 60 km/s.

5
Initial Pressures from BUCKY Code
Base pressure 30 mTorr
Base pressure 50 mTorr

• Xenon at 30 mTorr case is actually at 3 mTorr.

6
Motivation/Thesis

• Motivation
• To understand the chamber condition with
  different fill gases and pressures at 100 ms. The
  emphasis is on Deuterium and Helium as they will
  always exist in the chamber.
• To explore the impact of gas temperature on
  target survival.
• To explore the deflection of target during
  injection by velocity drag and pressure gradient.
• Thesis
• Xenon was chosen as fill gas because it easily
  absorbs and re-radiates the energy released by
  the target.
• Deuterium and Helium absorb less energy. They
  should be cooler and thus have less impact on a
  target.

7
Thermal Regimes in The Chamber
compressive heating and cooling by radiation
free cooling
1st bullet
2nd and 3rd bullet

• The initial temperatures are different because
  the initial conditions are taken at different
  times.
• Heating due to shockwave compression and
  subsequent cooling by radiation govern the
  chamber temperatures in the first millisecond.
• The exponentially decaying parts of the curves
  correspond to free cooling.

8
Thermal Regimes in The Chamber
Base pressure lt 50 mTorr
Base pressure 50 mTorr
compressive heating and cooling by radiation
free cooling

• Cooling rates of Deuterium, Helium and Xenon at
  base pressures lt 50 mTorr directly correspond to
  their thermal diffusivities (D 26 m2/s, He 18
  m2/s, Xe 16 m2/s).
• Xenon at 50 mTorr is much hotter than Deuterium
  or Helium, due to its slow cooling rate (thermal
  diffusivity of 1.2 m2/s).

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Final Temperature Distributions at 100 ms
K
50 mTorr
Tmax
He
D
Xe
3 mTorr
30 mTorr
Tmax

• Deuterium almost reaches the wall temperature.
  The difference between the contour lines is 20K.

10
Final Temperatures of Chamber Gas at 100 ms
Base pressure lt 50 mTorr
Base pressure 50 mTorr
3 mTorr
30 mTorr
30 mTorr

• Deuterium at both base pressures has a nearly
  uniform temperature, within 30-40 K from the
  equilibrium with the wall.
• Average temperature of the Helium is within 200 K
  from the wall temperature, only the central hot
  region stands out.
• Xenon is the most extreme case, with a highly
  non-uniform temperature field and far from
  equilibrium with the wall. Even at 3 mTorr, the
  peak temperature did not drop below 3000 K.

11
Motivation/Thesis

• Motivation
• To understand the chamber condition with
  different fill gases and pressures at 100 ms. The
  emphasis is on Deuterium and Helium as they will
  always exist in the chamber.
• To explore the impact of gas temperature on
  target survival.
• To explore the deflection of target during
  injection by velocity drag and pressure gradient.
• Thesis
• Xenon was chosen as fill gas because it easily
  absorbs and re-radiates the energy released by
  the target.
• Deuterium and Helium absorb less energy. They
  should be cooler and thus have less impact on a
  target.

12
Final Velocities at 100 ms
m/s
50 mTorr
D
He
Xe
3 mTorr
30 mTorr

• The initial velocity of Deuterium was much higher
  than Xenon, due to the low mass of Deuterium.
  Final velocity of Deuterium is similar to that of
  Xenon, due to the lower final temperature of
  Deuterium.
• Xenon at 50 mTorr shows turbulence note the
  smoky features. The Reynolds number for this
  case is 8,600. For all the other cases, the Re
  100.

13
Acceleration of Target Due to Drag Force at 100 ms
Base pressure lt 50 mTorr
Base pressure 50 mTorr
deflects target by 2mm (injection speed 500 m/s)
3 mTorr
30 mTorr
30 mTorr
28

• Accelerations are based on velocity field in the
  chamber (excluding beam lines), gas viscosity,
  target diameter of 4 mm and target mass of 4.8
  milligrams.
• Drag force depends on gas velocity and viscosity.
  Acceleration of target by Deuterium is smaller
  than that of Xenon because the viscosity of Xenon
  is 5 times higher than viscosity of Deuterium.

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Summary of Chamber Gas Pressures at 100 ms
Base pressure lt 50 mTorr
Base pressure 50 mTorr
30 mTorr
3 mTorr
50 mTorr

• Only Deuterium returns to within several pascals
  from the base pressure, 100 ms after the target
  ignition.
• Chamber gas pressures of Deuterium and Helium gas
  are nearly uniform (min ave max), while Xenon
  at base pressure 50 mTorr is highly non-uniform
  (max/min 3).

15
Acceleration of Target Due to Pressure Gradients
at 100 ms
Base pressure lt 50 mTorr
Base pressure 50 mTorr
30 mTorr
3 mTorr
30 mTorr

• Accelerations are based on the pressure gradients
  in the chamber (excluding beam lines), target
  diameter of 4 mm and target mass of 4.8
  milligrams.
• The acceleration of target due to pressure
  gradients is negligible compared to the
  acceleration caused by drag force.

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Conclusions

• Deuterium and Helium show excellent features at
  the two base pressures considered
• They both achieve thermal equilibrium with the
  wall within the 100 ms. Deuterium is considerably
  better here than Helium.
• They both feature a laminar flow that doesnt
  heavily impact the target.
• Xenon at 50 mTorr is the most extreme case in the
  following sense
• It never gets close to the thermal equilibrium
  with the wall, within the 100 ms.
• it shows the largest impact on the target, due to
  the high gas temperature and high drag force.

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Future Work

• Physics
• Redo the calculations with the correct initial
  conditions (shock front at small distance from
  the wall, Xenon at 30 mTorr).
• Include cases with Tritium gas.
• Explore what happens at lower base pressures,
  such as 10 mTorr.
• Algorithm Development
• We have implemented implicit radiation source
  term calculation in our present algorithm.
• Planning to add multi-species capability and
  incorporate the aerosol model in SPARTAN.

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Supporting Slides
19
Initial Temperatures from BUCKY Code
Base pressure 30 mTorr
Base pressure 50 mTorr

• The temperature profiles were taken at different
  times for different gases, based on the
  requirement that the shock wave doesnt hit the
  wall.
• Except for Xenon, the temperatures are
  significantly above 1eV, therefore the background
  plasma effects are important.

20
Relative Importance of Viscosity and Thermal
Conductivity
Peclet Number
Reynolds Number

• According to Reynolds number, all cases are
  laminar, except for Xenon at 50 mTorr, which is
  in turbulent flow regime.
• Peclet Number indicates that temperature
  distribution in the chamber is controlled by the
  flow and not the thermal conduction. This is
  especially true for Xe at 50 mTorr and explains
  the good mixing in temperature field.
• Both numbers increase with base pressure.