1 THERMAL LOADING OF A DIRECT DRIVE TARGET IN RAREFIED GAS B. R. Christensen, A. R. Raffray, and M. S. Tillack Mechanical and Aerospace Engineering Department and Center for Energy Research, University of California, San Diego, La Jolla, CA , Presented at the 16th ANS TOFE Madison, WI September 14-16, 2004

2 The Cryogenic Direct-Drive Target will be Subjected to Challenging Conditions when Injected into an IFE Chamber IFE Chamber (R~6 m) Example Protective Gas: ~10 21 m -3 Xe at 1000 – 4000K, q’’ condensation ~ 1-10 W/cm 2 Chamber wall ~ 1000–1500 K, q’’ rad = 0.2 – 1.2 W/cm 2 Target Injection (~400 m/s) Target Implosion Point

3 Introduction For each fusion micro explosion (~ 10 Hz), ions and heat loads threaten to damage the reactor wall and driver optics. A background gas, such as Xe, could reduce the damage on the wall from ion and heat loading. The thermal loading of a target (radiation from the chamber wall and convection from the protective gas) may threaten the symmetry, smoothness, or uniformity requirements placed on a target. The radiation loading is simply calculated using the Stefan-Boltzman law (0.2 – 1.2 W/cm 2 ). The convective loading is computed using DS2V, a commercial DSMC program. -The DSMC method is used due to the high Knudsen number (Kn = 0.4 – 40) for a target in a low density (n= 3x10 19 – 3x10 21 m -3 ) protective gas.

4 Modeling Target Injection Using DS2V Temperature Field Around a Direct Drive Target -Xe flowing at 400 m/s in the positive x-dir K stream temperature x10 21 m -3 stream density. -Sticking coefficient = 0. - Target surface temperature = 18 K. Assumptions Axially symmetric flow. Target is stationary, Xe stream velocity = 400 m/s. Target surface temp. = 18 K = constant. Sticking coefficient = 0 or 1, Accommodation coefficient = 1 Target doesn’t rotate.

5 The Number Flux at the Target Surface Decreases with Increasing Sticking Coefficient (sigma) when the Stream Density is High The number flux is a strong function of stream temperature and position on the target surface. Kinetic theory and DS2V show good agreement. High Density Stream, n = 3.22x10 21 m -3

6 For a High Density Stream the Heat Flux Decreases with a Decreasing in Sticking Coefficient The heat flux is decreased when sigma = 0 due to the influence of low temperature reflected particles interacting with the incoming stream (see the first viewgraph). For the low density cases there is less interaction between reflected and incoming particles. The rapid change in heat flux with position suggests that the average maximum heat flux could be reduced by rotating the target. High Density Stream, n = 3.22x10 21 m -3

7 The Influence of the Sticking Coefficient (  ) and the Accommodation Coefficient (  ) on the Maximum Heat Flux Leading Edge). Parameters: 400 m/s injection into 3.22x10 21 m -3 and 4000 K. (Max. heat flux (with  = 1 and  =1) = 27 W/cm 2. In general, reducing a causes the heat flux to reduce more rapidly with . Note that the heat flux decreases when  =1 for  < 0.8. If there were no interactions between reflected and incoming particles the normalized heat flux would be unity for all .

8 A Summary of the Expected Heat Flux the Leading Edge) as a Function of Chamber Conditions All heat flux values are reported in W/cm 2.

9 The Effect of the Injection Velocity, Xe Density, and  on the Maximum Incident Heat Flux the leading edge) When  = 1 the relationship between the heat flux and the Xe density is linear for each injection velocity. It is apparent that the shielding effect occurs over the density and velocity range studied, and is a stronger effect as the density is increased.

10 Maximizing the Protective Gas Density DS2V is used to predict heat flux as a function of protective gas density and injection velocity. An integrated thermomechanical model is used to predict the response of a target to an imposed heat flux. The maximum allowable heat flux for a given time of flight is obtained. Coupling the data from DS2V and the integrated thermomechanical model, the maximum protective gas density for a given injection velocity is obtained.

11 For a Basic Target, There is an Optimum Injection Velocity when  = 1.  (sticking coefficient) = 1  (sticking coefficient) = 0

12 For an Insulated Target, a High Injection Velocity Significantly Increases the Maximum Allowable Gas Density 100 mm, 10% dense insulator,  (sticking coefficient) = 1

13 Summary The heat flux caused by the interaction of the target with the protective chamber gas can be modeled using DS2V (a commercial DSMC program). The sticking (condensation) coefficient and the accommodation coefficient affect the heat flux at the target surface. Experimental determination of the sticking (condensation) coefficient and accommodation coefficient are needed. There may be an optimum injection velocity that allows for the maximum amount of protective gas.