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

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.

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 s, 10 s, 100 s and 500 s from the

target blast. However, D and He shockwaves already reflect from the wall past the 10 s, 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.

Initial Velocities from BUCKY CodeBase 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.

Initial Pressures from BUCKY CodeBase pressure “30 mTorr” Base pressure 50 mTorr

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

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.

Thermal Regimes in The Chamber

•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”.

compressive heating and cooling by radiation

“free cooling”

1st bullet

2nd and 3rd bullet

Thermal Regimes in The Chamber Base pressure < 50 mTorr Base pressure = 50 mTorr

compressive heating and cooling by radiation

“free cooling”

•Cooling rates of Deuterium, Helium and Xenon at base pressures < 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).

He

Final Temperature Distributions at 100 ms

30 mTorr

50 mTorr

D Xe

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

[K]

Tmax

Tmax

3 mTorr

Final Temperatures of Chamber Gas at 100 ms

Base pressure < 50 mTorr Base pressure = 50 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.

3 mTorr

30 mTorr

30 mTorr

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.

He

Final Velocities at 100 ms

30 mTorr

50 mTorr

D Xe

•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.

[m/s]

3 mTorr

Acceleration of Target Due to Drag Force at 100 ms

Base pressure < 50 mTorr Base pressure = 50 mTorr

•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.

deflects target by 2mm (injection

speed = 500 m/s)

3 mTorr

28

30 mTorr

30 mTorr

Summary of Chamber Gas Pressures at 100 ms

Base pressure < 50 mTorr Base pressure = 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).

3 mTorr 50 mTorr

30 mTorr

Acceleration of Target Due to Pressure Gradients at 100 ms

Base pressure < 50 mTorr Base pressure 50 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.

3 mTorr30 mTorr

30 mTorr

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 doesn’t 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.

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.

Supporting Slides

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 doesn’t hit the wall.

•Except for Xenon, the temperatures are significantly above 1eV, therefore the background plasma effects are important.

Relative Importance of Viscosity and Thermal Conductivity

D He Xe

30 mTorr 75 85 85

50 mTorr 260 140 8600

D He Xe

30 mTorr 40 60 50

50 mTorr 140 100 4900

Reynolds Number Peclet 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.