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Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial fielda)
a)Paper JI2 6, Bull. Am. Phys. Soc. 54, 136 (2009).
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1.R. B. Spielman, C. Deeney, G. A. Chandler, M. R. Douglas, D. L. Fehl, M. K. Matzen, D. H. McDaniel, T. J. Nash, J. L. Porter, T. W. L. Sanford, J. F. Seamen, W. A. Stygar, K. W. Struve, S. P. Breeze, J. S. McGurn, J. A. Torres, D. M. Zagar, T. L. Gilliland, D. O. Jobe, J. L. McKenney, R. C. Mock, M. Vargas, T. Wagoner, and D. L. Peterson, Phys. Plasmas 5, 2105 (1998).
2.R. A. Vesey, M. C. Herrmann, R. W. Lemke, M. P. Desjarlais, M. E. Cuneo, W. A. Stygar, G. R. Bennett, R. B. Campbell, P. J. Christenson, T. A. Mehlhorn, and S. A. Slutz, Phys. Plasmas 14, 056302 (2007).
3.R. Landshoff, Phys. Rev. 76, 904 (1949).
4.J. Nuckolls, L. Wood, A. Thiessen, and G. Zimmerman, Nature (London) 239, 139 (1972).
5.M. M. Widner, 1980 (personal communication).
6.M. M. Widner, C. J. Chang, A. V. Farnsworth, Jr., R. J. Leeper, T. S. Prevender, L. Baker, and J. N. Olsen, Bull. Am. Phys. Soc. 22, 1139 (1977).
7.M. A. Sweeney and A. V. Farnsworth, Jr., Nucl. Fusion 21, 41 (1981).
8.I. R. Lindemuth and R. C. Kirkpatrick, Nucl. Fusion 23, 263 (1983).
9.R. C. Kirkpatrick, I. R. Lindemuth, and M. S. Ward, Nucl. Fusion 27, 201 (1994).
10.R. E. Siemon, I. R. Lindemuth, and K. F. Schoenberg, Comments Plasma Phys. Controlled Fusion 18, 363 (1999).
11.R. D. Jones and W. C. Mead, Nucl. Fusion 26, 127 (1986).
12.T. A. Mehlhorn, B. B. Cipiti, C. L. Olson, and G. E. Rochau, Fusion Eng. Des. 83, 948 (2008).
13.D. C. Barnes, Comments Plasma Phys. Controlled Fusion 18, 71 (1997).
14.Y. B. Khariton, Usp. Fiziol. Nauk 120, 706 (1976)
14.Y. B. Khariton, [Sov. Phys. Usp. 19, 1032 (1976)].
15.I. R. Lindemuth, E. E. Reinovsky, R. E. Chrien, J. M. Christian, C. A. Ekdahl, J. H. Goforth, R. C. Haight, G. Idzorek, N. S. King, R. C. Kirkpatrick, R. E. Larson, G. L. Morgan, B. W. Olinger, H. Oona, R. T. Sheehey, J. S. Shlachter, R. C. Smith, L. R. Veeser, B. J. Warthen, S. M. Younger, V. K. Chernyshev, V. N. Mokhov, A. N. Demin, Y. N. Dolin, S. F. Garanin, V. A. Ivanov, V. P. Korchagin, O. D. Mikhailov, I. V. Morozov, S. V. Pak, E. S. Pavlovskii, N. Y. Seleznev, A. N. Skobelev, G. I. Volkov, and V. A. Yakubov, Phys. Rev. Lett. 75, 1953 (1995).
16.K. F. Schoenberg and R. E. Siemon, “Magnetized target fusion, a proof of principle research proposal,” Report No. LA-UR-98-2413, 1998.
17.M. Tuszewski, Nucl. Fusion 28, 2033 (1988).
18.T. Intrator, M. Taccetti, D. A. Clark, J. H. Degnan, D. Gale, S. Coffey, J. Garcia, P. Rodriguez, W. Sommars, B. Marshall, F. Wysocki, R. Siemon, R. Faehl, K. Forman, R. Bartlett, T. Cavazos, R. J. Faehl, M. H. Frese, D. Fulton, J. C. Gueits, T. W. Hussey, R. Kirkpatrick, G. F. Kiuttu, F. M. Lehr, J. D. Letterio, I. Lindemuth, W. McCullough, R. Moses, R. E. Peterkin, R. E. Reinovsky, N. F. Roderick, E. L. Ruden, K. F. Schoenberg, D. Scudder, J. Shlachter, and G. A. Wurden, Nucl. Fusion 42, 211 (2002).
19.T. Intrator, S. Y. Zhang, J. H. Degnan, I. Furno, C. Grabowski, S. C. Hsu, E. L. Ruden, P. G. Sanchez, J. M. Taccetti, M. Tuszewski, W. J. Waganaar, and G. A. Wurden, Phys. Plasmas 11, 2580 (2004).
20.A. J. Kemp, M. Basko, and J. Meyer-ter-Vehn, Nucl. Instrum. Methods Phys. Res. A 464, 192 (2001).
21.O. V. Gotchev, N. W. Jang, J. P. Knauer, M. D. Barbero, R. Betti, C. K. Li, and R. D. Petrasso, J. Fusion Energy 27, 25 (2008).
22.D. D. Ryutov, Fusion Sci. Technol. 56, 1489 (2009).
23.Y. B. Zel’dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, New York, 1966), pp. 4552.
24.G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), p. 198.
25.J. Lindl, Phys. Plasmas 2, 3933 (1995).
26.S. A. Slutz, M. R. Douglas, J. S. Lash, R. A. Vesey, G. A. Chandler, T. J. Nash, and M. S. Derzon, Phys. Plasmas 8, 1673 (2001).
27.A. R. Miles, Phys. Plasmas 16, 032702 (2009).
28.J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen, and L. J. Suter, Phys. Plasmas 11, 339 (2004).
29.S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1, p. 205.
30.S. Atzeni and J. Meyer-Ter-Vehn, The Physics of Inertial Fusion (Clarendon, Oxford, 2004).
31.R. M. White, D. A. Resler, and G. M. Hale, “FENDL/C-2.0. Charged-particle reaction data library for fusion applications,” summary documentation by A. B. Pashchenko and H. Wienke, IAEA Report No. IAEA-NDS-177, 1997.
32.M. M. Basko, A. J. Kemp, and J. Meyer-ter-Vehn, Nucl. Fusion 40, 59 (2000).
33.D. Ryutov, Phys. Plasmas 9, 4085 (2002).
34.G. B. Zimmerman and W. B. Kruer, Comments Plasma Phys. Controlled Fusion 2, 51 (1975).
35.S. A. Slutz, D. B. Seidel, and R. S. Coats, J. Appl. Phys. 59, 11 (1986).
View: Figures


Image of FIG. 1.

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FIG. 1.

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.

Image of FIG. 2.

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FIG. 2.

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 B-field effects and classical magnetic conductivity inhibition, (2) -transport including B-field effects and Bohm magnetic conductivity inhibition, (3) transport ignoring B-field effects and classical magnetic conductivity inhibition, and (4) transport including B-field effects and conductivity ignoring B-field.

Image of FIG. 3.

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FIG. 3.

Current profiles generated by the Z machine, for two Marx bank charging voltages (kilovolts), are plotted as a function of time.

Image of FIG. 4.

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FIG. 4.

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.

Image of FIG. 5.

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FIG. 5.

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.

Image of FIG. 6.

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FIG. 6.

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).

Image of FIG. 7.

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FIG. 7.

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.

Image of FIG. 8.

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FIG. 8.

(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.

Image of FIG. 9.

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FIG. 9.

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 1D-simulated yield.

Image of FIG. 10.

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FIG. 10.

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.

Image of FIG. 11.

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FIG. 11.

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.

Image of FIG. 12.

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FIG. 12.

Plasma temperatures as calculated from an analytic solution for laser heating, at several times, are plotted as a function of axial distance.

Image of FIG. 13.

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FIG. 13.

(a) Schematic of the geometry for Lasnex simulations of laser heating of the fuel. Contour plots of the plasma temperature (b) , (c) , and (d)

Image of FIG. 14.

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FIG. 14.

Lasnex simulated laser-heated plasma temperatures at two times are plotted as a function of axial distance.

Image of FIG. 15.

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FIG. 15.

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.

Image of FIG. 16.

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FIG. 16.

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 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 pulsed-power-driven implosions of cylindrical metal liners onto magnetized and preheated (100–500 eV) deuterium-tritium (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 Z-Beamlet laser. The magneto-Rayleigh-Taylor (MRT) instability poses the greatest threat to this approach to fusion. Two-dimensional 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 Z-Beamlet 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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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial fielda)