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Abstract
The radial convergence required to reach fusion conditions is considerably higher for cylindrical than for spherical implosions since the volume is proportional to versus , respectively. Fuel magnetization and preheat significantly lowers the required radial convergence enabling cylindrical implosions to become an attractive path toward generating fusion conditions. Numerical simulations are presented indicating that significant fusion yields may be obtained by pulsedpowerdriven implosions of cylindrical metal liners onto magnetized and preheated (100–500 eV) deuteriumtritium (DT) fuel. Yields exceeding 100 kJ could be possible on Z at 25 MA, while yields exceeding 50 MJ could be possible with a more advanced pulsed power machine delivering 60 MA. These implosions occur on a much shorter time scale than previously proposed implosions, about 100 ns as compared to about for magnetic target fusion(MTF) [I. R. Lindemuth and R. C. Kirkpatrick, Nucl. Fusion23, 263 (1983)]. Consequently the optimal initial fuel density (1–5 mg/cc) is considerably higher than for MTF. Thus the final fuel density is high enough to axially trap most of the particles for cylinders of approximately 1 cm in length with a purely axial magnetic field, i.e., no closed field configuration is required for ignition. According to the simulations, an initial axial magnetic field is partially frozen into the highly conducting preheated fuel and is compressed to more than 100 MG. This final field is strong enough to inhibit both electron thermal conduction and the escape of particles in the radial direction. Analytical and numerical calculations indicate that the DT can be heated to 200–500 eV with 5–10 kJ of green laser light, which could be provided by the ZBeamlet laser. The magnetoRayleighTaylor (MRT) instability poses the greatest threat to this approach to fusion. Twodimensional Lasnex simulations indicate that the liner walls must have a substantial initial thickness (10–20% of the radius) so that they maintain integrity throughout the implosion. The Z and ZBeamlet experiments are now being planned to test the various components of this concept, e.g., the laser heating of the fuel and the robustness of liner implosions to the MRT instability.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the National Nuclear Security Administration of the United States Department of Energy under Contract No. DEAC0494AL85000.
I. INTRODUCTION
II. IGNITION AND GAIN REQUIREMENTS
A. Implosion physics and preheat requirements
B. Fusion selfheating
C. Inertial confinement and gain
III. NUMERICAL SIMULATIONS AND YIELD SCALING
IV. FUEL PREHEAT
V. LINER MAGNETIZATION
VI. CONCLUSIONS
Key Topics
 Magnetic fields
 52.0
 Inertial confinement
 21.0
 Fusion fuels
 19.0
 Beryllium
 14.0
 Thermal conductivity
 14.0
Figures
Schematic of the MagLIF concept (a) overall geometry including field coils, electrodes, and laser entrance path and (b) a blowup of the liner with preheated and magnetized fuel before implosion.
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Schematic of the MagLIF concept (a) overall geometry including field coils, electrodes, and laser entrance path and (b) a blowup of the liner with preheated and magnetized fuel before implosion.
Magnetized fuel ignition space contours are plotted as a function of fuel areal density and the ratio of the cylinder radius over the cyclotron radius of a fusion particle with its initial energy as calculated with the following assumptions, (1) transport including Bfield effects and classical magnetic conductivity inhibition, (2) transport including Bfield effects and Bohm magnetic conductivity inhibition, (3) transport ignoring Bfield effects and classical magnetic conductivity inhibition, and (4) transport including Bfield effects and conductivity ignoring Bfield.
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Magnetized fuel ignition space contours are plotted as a function of fuel areal density and the ratio of the cylinder radius over the cyclotron radius of a fusion particle with its initial energy as calculated with the following assumptions, (1) transport including Bfield effects and classical magnetic conductivity inhibition, (2) transport including Bfield effects and Bohm magnetic conductivity inhibition, (3) transport ignoring Bfield effects and classical magnetic conductivity inhibition, and (4) transport including Bfield effects and conductivity ignoring Bfield.
Current profiles generated by the Z machine, for two Marx bank charging voltages (kilovolts), are plotted as a function of time.
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Current profiles generated by the Z machine, for two Marx bank charging voltages (kilovolts), are plotted as a function of time.
Several normalized parameters are plotted as a function of time. The results are from a Lasnex simulation of a beryllium liner with an aspect ratio of 6, an initial magnetic field of 30 T, an initial fuel density of 3 mg/cc, and an initial fuel temperature of 250 eV. The yield was about 500 kJ for a 0.5 cm long liner.
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Several normalized parameters are plotted as a function of time. The results are from a Lasnex simulation of a beryllium liner with an aspect ratio of 6, an initial magnetic field of 30 T, an initial fuel density of 3 mg/cc, and an initial fuel temperature of 250 eV. The yield was about 500 kJ for a 0.5 cm long liner.
Normalized parameters simulated by Lasnex are plotted as a function of normalized radius. The solid lines are with the Nernst term included. The simulation parameters were the same as Fig. 4.
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Normalized parameters simulated by Lasnex are plotted as a function of normalized radius. The solid lines are with the Nernst term included. The simulation parameters were the same as Fig. 4.
The yields from 1D Lasnex simulations of beryllium liners with aspect ratio 6 with a peak current drive of 30 MA are plotted as a function of the initial preheat temperature in (a). The corresponding initial fuel densities to obtain the convergence ratios of each curve are plotted in (b).
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The yields from 1D Lasnex simulations of beryllium liners with aspect ratio 6 with a peak current drive of 30 MA are plotted as a function of the initial preheat temperature in (a). The corresponding initial fuel densities to obtain the convergence ratios of each curve are plotted in (b).
1D yield as a function of initial magnetic field for a beryllium liner with an aspect and a peak current drive of 30 MA is plotted as a function of initial magnetic field strength.
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1D yield as a function of initial magnetic field for a beryllium liner with an aspect and a peak current drive of 30 MA is plotted as a function of initial magnetic field strength.
(a) 1D yields are plotted as a function of maximum drive current both with (solid) and without heating (dashed). (b) The ratio of the fusion yield over the energy absorbed in the liner (solid) and the ratio of the maximum fuel temperature with heating over the maximum temperature without heating (dashed) are plotted as a function of current. These results are for liners with aspect ratio 6, convergence ratio 20, an initial magnetic field of 30 T, fuel preheat temperature of 250 eV, and initial fuel density 2–5 mg/cc.
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(a) 1D yields are plotted as a function of maximum drive current both with (solid) and without heating (dashed). (b) The ratio of the fusion yield over the energy absorbed in the liner (solid) and the ratio of the maximum fuel temperature with heating over the maximum temperature without heating (dashed) are plotted as a function of current. These results are for liners with aspect ratio 6, convergence ratio 20, an initial magnetic field of 30 T, fuel preheat temperature of 250 eV, and initial fuel density 2–5 mg/cc.
2D Lasnex simulations of a beryllium liner at (a) near stagnation (enlarged), (b) near stagnation, (c) midway, and (d) at the start of the current pulse. The liner has an initial aspect ratio 6 with a 60 nm surface roughness. The yield was approximately 86% of 1Dsimulated yield.
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2D Lasnex simulations of a beryllium liner at (a) near stagnation (enlarged), (b) near stagnation, (c) midway, and (d) at the start of the current pulse. The liner has an initial aspect ratio 6 with a 60 nm surface roughness. The yield was approximately 86% of 1Dsimulated yield.
The simulated 1D and 2D yields are plotted as a function of initial liner aspect ratio. These results are for liners with convergence ratios of 20, an initial magnetic field of 30 T, fuel preheat temperature of about 250 eV, and an initial fuel density 3 mg/cc.
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The simulated 1D and 2D yields are plotted as a function of initial liner aspect ratio. These results are for liners with convergence ratios of 20, an initial magnetic field of 30 T, fuel preheat temperature of about 250 eV, and an initial fuel density 3 mg/cc.
Yields are plotted as a function of the mass fraction of beryllium initially mixed into the fuel. The yield is normalized to the yield with pure DT.
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Yields are plotted as a function of the mass fraction of beryllium initially mixed into the fuel. The yield is normalized to the yield with pure DT.
Plasma temperatures as calculated from an analytic solution for laser heating, at several times, are plotted as a function of axial distance.
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Plasma temperatures as calculated from an analytic solution for laser heating, at several times, are plotted as a function of axial distance.
(a) Schematic of the geometry for Lasnex simulations of laser heating of the fuel. Contour plots of the plasma temperature (b) , (c) , and (d)
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(a) Schematic of the geometry for Lasnex simulations of laser heating of the fuel. Contour plots of the plasma temperature (b) , (c) , and (d)
Lasnex simulated laserheated plasma temperatures at two times are plotted as a function of axial distance.
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Lasnex simulated laserheated plasma temperatures at two times are plotted as a function of axial distance.
Contours of the fusion yield for magnetized liners (colors) are plotted as a function of the laser beam radius and the fuel preheat temperature. The black lines are curves of the required preheat energy in kilojoules. The results are for a beryllium liner with and . The initial magnetic field was 30 T and the convergence ratios are fixed at 25 by adjusting the fuel density.
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Contours of the fusion yield for magnetized liners (colors) are plotted as a function of the laser beam radius and the fuel preheat temperature. The black lines are curves of the required preheat energy in kilojoules. The results are for a beryllium liner with and . The initial magnetic field was 30 T and the convergence ratios are fixed at 25 by adjusting the fuel density.
The fraction of the initial fuel mass remaining at stagnation as a function of the liner length: (1) 2D numerical simulation with open end, (2) analytic result for open end, (3) analytic result for , and (4) analytic result for .
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The fraction of the initial fuel mass remaining at stagnation as a function of the liner length: (1) 2D numerical simulation with open end, (2) analytic result for open end, (3) analytic result for , and (4) analytic result for .
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Abstract
The radial convergence required to reach fusion conditions is considerably higher for cylindrical than for spherical implosions since the volume is proportional to versus , respectively. Fuel magnetization and preheat significantly lowers the required radial convergence enabling cylindrical implosions to become an attractive path toward generating fusion conditions. Numerical simulations are presented indicating that significant fusion yields may be obtained by pulsedpowerdriven implosions of cylindrical metal liners onto magnetized and preheated (100–500 eV) deuteriumtritium (DT) fuel. Yields exceeding 100 kJ could be possible on Z at 25 MA, while yields exceeding 50 MJ could be possible with a more advanced pulsed power machine delivering 60 MA. These implosions occur on a much shorter time scale than previously proposed implosions, about 100 ns as compared to about for magnetic target fusion(MTF) [I. R. Lindemuth and R. C. Kirkpatrick, Nucl. Fusion23, 263 (1983)]. Consequently the optimal initial fuel density (1–5 mg/cc) is considerably higher than for MTF. Thus the final fuel density is high enough to axially trap most of the particles for cylinders of approximately 1 cm in length with a purely axial magnetic field, i.e., no closed field configuration is required for ignition. According to the simulations, an initial axial magnetic field is partially frozen into the highly conducting preheated fuel and is compressed to more than 100 MG. This final field is strong enough to inhibit both electron thermal conduction and the escape of particles in the radial direction. Analytical and numerical calculations indicate that the DT can be heated to 200–500 eV with 5–10 kJ of green laser light, which could be provided by the ZBeamlet laser. The magnetoRayleighTaylor (MRT) instability poses the greatest threat to this approach to fusion. Twodimensional Lasnex simulations indicate that the liner walls must have a substantial initial thickness (10–20% of the radius) so that they maintain integrity throughout the implosion. The Z and ZBeamlet experiments are now being planned to test the various components of this concept, e.g., the laser heating of the fuel and the robustness of liner implosions to the MRT instability.
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