Abstract
This paper extends the velocity dependent Krook (VDK) model, developed at NRL over the last 4 years, to two dimensions and presents a variety of calculations. One dimensional spherical calculations presented here investigate shock ignition. Comparing VDK calculations to a flux limit calculation shows that the laser profile has to be retuned and some gain is sacrificed due to preheat of the fuel. However, preheat is by no means a show stopper for laser fusion. The recent foil acceleration experiments at the University of Rochester Laboratory for Laser Energetics are modeled with twodimensional simulations. The radial loss is very important to consider in modeling the foil acceleration. Once this is done, the VDK model gives the best agreement with the experiment.
This work was supported by NNSA and ONR. We would like to especially thank Valeri Goncharov and Philippe Nicolai. Valeri Goncharov collaborated with us in the early phase of this work and is a coauthor of Ref. 1, as we are of Ref. 7. Philippe Nicolai aided us greatly in understanding Ref. 8.
I. INTRODUCTION
II. THEORY
III. ONE DIMENSIONAL CALCULATIONS: SPHERICAL SHOCK IGNITION
IV. INTERPRETATION OF THE URLLE ACCELERATED FOIL EXPERIMENT
Key Topics
 Irradiance
 17.0
 Thermal models
 7.0
 Laser fusion
 6.0
 Collision theories
 4.0
 Limiters
 4.0
Figures
This is taken from a plot of electron density and temperature at a particular time in the laser implosion of a spherical target. The arrows show the mean free path for points with an energy of ten times the temperature. Clearly, there is an important nonlocal component to the electron thermal transport.
This is taken from a plot of electron density and temperature at a particular time in the laser implosion of a spherical target. The arrows show the mean free path for points with an energy of ten times the temperature. Clearly, there is an important nonlocal component to the electron thermal transport.
(a) A plot of fuel mass averaged alpha for two calculations of the performance of a shock ignition target. Red is a calculation with f = 0.075, black is the VDK model. Note the evidence of preheat in the higher alpha of the latter. (b) A plot of the laser power for optimized shock ignition targets for a f = 0.075 and VDK model for transport. Note the four arrows. They are the times of shock breakout, start of the main pulse, start of the ignition pulse, and time of maximum ρR for the flux limited calculation. For the VDK calculation, these times are about a nanosecond earlier.
(a) A plot of fuel mass averaged alpha for two calculations of the performance of a shock ignition target. Red is a calculation with f = 0.075, black is the VDK model. Note the evidence of preheat in the higher alpha of the latter. (b) A plot of the laser power for optimized shock ignition targets for a f = 0.075 and VDK model for transport. Note the four arrows. They are the times of shock breakout, start of the main pulse, start of the ignition pulse, and time of maximum ρR for the flux limited calculation. For the VDK calculation, these times are about a nanosecond earlier.
Four plots showing the alpha as a function of mass at the four times indicated, for the f = 0.075 and VDK calculation. Note the unmistakable evidence of preheat in the VDK calculation.
Four plots showing the alpha as a function of mass at the four times indicated, for the f = 0.075 and VDK calculation. Note the unmistakable evidence of preheat in the VDK calculation.
Shape of the accelerated foil as calculated via FAST2D, to be compared with Fig. 1(b) of Ref. 14.
Shape of the accelerated foil as calculated via FAST2D, to be compared with Fig. 1(b) of Ref. 14.
Position of the center of the foil as a function of time for a FAST 2D calculation of the foil acceleration using a VDK model for thermal transport where the laser irradiance is 9 × 10^{14 }W/cm^{2}. Solid curve is the dense model, dashed is the sparse model. Note they are virtually identical, indicating that the nonlocal transport is principally axial.
Position of the center of the foil as a function of time for a FAST 2D calculation of the foil acceleration using a VDK model for thermal transport where the laser irradiance is 9 × 10^{14 }W/cm^{2}. Solid curve is the dense model, dashed is the sparse model. Note they are virtually identical, indicating that the nonlocal transport is principally axial.
Position of the center of the foil for the acceleration by laser irradiance of 6 × 10^{14 }W/cm^{2}. The top dashed curve is the VDK model for electron thermal conduction in a one dimensional calculation. The three curves below are two dimensional calculations using three models of electron thermal transport, Spitzer, VDK, and f = 0.06. Notice that any of these agree better than the one dimensional calculation, indicating the importance of transverse effects in their experiment. However, it is the VDK curve in two dimensions, which agrees best. The inset is the temporal profile of the laser flux used in the calculation.
Position of the center of the foil for the acceleration by laser irradiance of 6 × 10^{14 }W/cm^{2}. The top dashed curve is the VDK model for electron thermal conduction in a one dimensional calculation. The three curves below are two dimensional calculations using three models of electron thermal transport, Spitzer, VDK, and f = 0.06. Notice that any of these agree better than the one dimensional calculation, indicating the importance of transverse effects in their experiment. However, it is the VDK curve in two dimensions, which agrees best. The inset is the temporal profile of the laser flux used in the calculation.
Two dimensional calculations using the 3 transport models, at each irradiance. None show perfect agreement, but the VDK model is the best. What is interesting is that this figure shows that the three curves move away from one another as the irradiance increases, indicating that nonlocal transport becomes more important at higher irradiances.
Two dimensional calculations using the 3 transport models, at each irradiance. None show perfect agreement, but the VDK model is the best. What is interesting is that this figure shows that the three curves move away from one another as the irradiance increases, indicating that nonlocal transport becomes more important at higher irradiances.
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