Non-equilibrium ignition criterion for magnetized deuterium–tritium fuel
|
摘要
In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions.Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature(T_e, T_i), areal density(q R), and seed magnetic field-dependent free parameters of B/q, mB, and BR. For B/ρ < 10~6 G cm~3 g~(-1),mB < 4 × 10~4 G cm g~(-1), and BR <3 × 10~5 G cm, the minimum fuel areal density exceeds between ρR >0.002 g cm~(-2), ρR> 0.25 g cm~(-2), and ρR > 0.02 g cm~(-2),respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥(6.13–4.64) × 10~5 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.
In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions.Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature(T_e, T_i), areal density(q R), and seed magnetic field-dependent free parameters of B/q, mB, and BR. For B/ρ < 10~6 G cm~3 g~(-1),mB < 4 × 10~4 G cm g~(-1), and BR <3 × 10~5 G cm, the minimum fuel areal density exceeds between ρR >0.002 g cm~(-2), ρR> 0.25 g cm~(-2), and ρR > 0.02 g cm~(-2),respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥(6.13–4.64) × 10~5 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.
In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions.Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature(T_e, T_i), areal density(q R), and seed magnetic field-dependent free parameters of B/q, mB, and BR. For B/ρ < 10~6 G cm~3 g~(-1),mB < 4 × 10~4 G cm g~(-1), and BR <3 × 10~5 G cm, the minimum fuel areal density exceeds between ρR >0.002 g cm~(-2), ρR> 0.25 g cm~(-2), and ρR > 0.02 g cm~(-2),respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥(6.13–4.64) × 10~5 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.
引文
1.R.C.Kirkpatrick,I.R.Lindemuth,M.S.Ward,Magnetized target fusion:an overview.Fusion Technol.27(3),201-214(1995).https://doi.org/10.13182/FST95-A30382
2.C.Yamanaka,Inertial confinement fusion:the quest for ignition and energy gain using indirect drive.Nucl.Fusion 39,825(1999).https://doi.org/10.1088/0029-5515/39/6/702
3.S.Atzeni,J.Meyer-ter-Vehn,The Physics of Inertial Fusion:BeamPlasma Interaction,Hydrodynamics,Hot Dense Matter(Oxford University Press,New York,2004),pp.35-39
4.R.C.Kirkpatrick,HEDP and new directions for fusion energy.High Energy Density Phys.6,207-209(2010).https://doi.org/10.1016/j.hedp.2010.01.017
5.I.R.Lindemuth,An extended study of the ignition design space of magnetized target fusion.Phys.Plasmas 24,055602(2017).https://doi.org/10.1063/1.4977538
6.I.R.Lindemuth,R.E.Siemon,The fundamental parameter space of controlled thermonuclear fusion.Am.J.Phys.77,407-416(2009).https://doi.org/10.1119/1.3096646
7.M.Sweeney,A.Farnsworth Jr.,High-gain,low-intensity ICFtargets for a charged-particle beam fusion driver.Nucl.Fusion21,41(1981).https://doi.org/10.1088/0029-5515/21/1/004
8.I.Lindemuth,R.Kirkpatrick,Parameter space for magnetized fuel targets in inertial confinement fusion.Nucl.Fusion 23,263(1983).https://doi.org/10.1088/0029-5515/23/3/001
9.I.Lindemuth,R.Reinovsky,R.Chrien,et al.,Joint US/Russian plasma formation experiments for magnetic compression/magnetized target fusion(MAGO/MTF),in Digest of Technical Papers.Tenth IEEE International Pulsed Power Conference,Albuquerque,NM,USA,vol.1(1995),pp.601-606.https://doi.org/10.1109/ppc.1995.596738
10.A.B.Sefkow,S.Slutz,J.Koning et al.,Design of magnetized liner inertial fusion experiments using the Z facility.Phys.Plasmas 21,072711(2014).https://doi.org/10.1063/1.4890298
11.K.Hahn,G.A.Chandler,C.L.Ruiz et al.,Fusion-neutron measurements for magnetized liner inertial fusion experiments on the Z accelerator.J.Phys:Conf.Ser.717,012020(2016).https://doi.org/10.1088/1742-6596/717/1/012020
12.A.Kemp,M.Basko,J.Meyer-ter-Vehn,Magnetized cylindrical targets for heavy ion fusion.Nucl.Instrum.Methods Phys.Res.Sect.A 464,192-195(2001).https://doi.org/10.1016/s0168-9002(01)00032-8
13.D.Kilcrease,R.Kirkpatrick,Magnetized fuel inertial confinement fusion.Nucl.Fusion 28,1465(1988).https://doi.org/10.1088/0029-5515/28/8/015
14.A.J.Kemp,M.M.Basko,J.Meyer-ter-Vehn,Implosion and ignition of magnetized cylindrical targets driven by heavy-ion beams.Nucl.Fusion 43,16(2002).https://doi.org/10.1088/0029-5515/43/1/302
15.I.R.Lindemuth,The ignition design space of magnetized target fusion.Phys.Plasmas 22,122712(2015).https://doi.org/10.1063/1.4937371
16.R.Ramis,J.Meyer-Ter-Vehn,On thermonuclear burn propagation in a pre-compressed cylindrical DT target ignited by a heavy ion beam pulse.Laser Part.Beams 32,41-47(2014).https://doi.org/10.1017/S0263034613000839
17.M.Basko,M.Churazov,A.Aksenov,Prospects of heavy ion fusion in cylindrical geometry.Laser Part.Beams 20,411-414(2002).https://doi.org/10.1017/S0263034602203080
18.M.Widner,J.Chang,A.Farnsworth et al.,Neutron-production from relativistic electron-beam targets.in Bulletin of the American Physical Society,American Institute of Physics Circulation and Fulfillment Division,500 Sunnyside Blvd,Woodbury,NY11797-2999(1977),pp.1139-1139.https://doi.org/10.1111/j.1749-6632.1975.tb00096.x
19.R.Jones,W.Mead,The physics of burn in magnetized deuterium-tritium plasmas:spherical geometry.Nucl.Fusion 26,127(1986).https://doi.org/10.1088/0029-5515/26/2/001
20.S.A.Slutz,R.A.Vesey,High-gain magnetized inertial fusion.Phys.Rev.Lett.108,025003(2012).https://doi.org/10.1103/PhysRevLett.108.025003
21.P.Schmit,P.Knapp,S.Hansen et al.,Understanding fuel magnetization and mix using secondary nuclear reactions in magnetoinertial fusion.Phys.Rev.Lett.113(15),155004(2014).https://doi.org/10.1103/PhysRevLett.113.155004
22.K.Schoenberg,R.Siemon,Magnetized target fusion,in A Proofof-Principle Research Proposal(Los Alamos National Lab,NM,US,1998).https://doi.org/10.2172/763201
23.G.A.Wurden,S.C.Hsu,T.P.Intrator et al.,Magneto-inertial fusion.J.Fusion Energy 35,69-77(2016).https://doi.org/10.1007/s10894-015-0038-x
24.S.C.Hsu,S.J.Langendorf,Magnetized plasma target for plasmajet-driven magneto-inertial fusion.J.Fusion Energy 38,182-198(2018).https://doi.org/10.1007/s10894-018-0168-z
25.J.Davies,R.Betti,P.Y.Chang et al.,The importance of electrothermal terms in Ohm’s law for magnetized spherical implosions.Phys.Plasmas 22,112703(2015).https://doi.org/10.1088/0029-5515/43/1/302
26.M.Basko,Magnetized implosions driven by intense ion beams.Phys.Plasmas 7,4579-4589(2000).https://doi.org/10.1063/1.1312182
27.M.Basko,J.Maruhn,T.Schlegel,Hydrodynamic instability of shells accelerated by direct ion beam heating.Phys.Plasmas 9,1348-1356(2002).https://doi.org/10.1063/1.1462634
28.A.Kemp,M.Basko,J.Meyer-ter-Vehn,Ignition conditions for magnetically insulated tamped ICF targets in cylindrical geometry.Nucl.Fusion 41,235(2001).https://doi.org/10.1088/0029-5515/41/2/311
29.A.J.Kemp,Magnetized Cylindrical Implosions Driven by Heavy ion Beams.Ph.D.Thesis,Technische Universita¨t Mu¨nchen(2001)
30.T.Intrator,S.Y.Zhang,J.H.Degnan et al.,A high density field reversed configuration(FRC)target for magnetized target fusion:first internal profile measurements of a high density FRC.Phys.Plasmas 11,2580-2585(2004).https://doi.org/10.1063/1.1689666
31.I.Lindemuth,R.Kirkpatrick,The promise of magnetized fuel:inertial confinement fusion with existing driver technology.Atomkernenerg/Kerntech 45,9-13(1984)
32.M.Basko,A.Kemp,J.Meyer-ter-Vehn,Ignition conditions for magnetized target fusion in cylindrical geometry.Nucl.Fusion40,59(2000).https://doi.org/10.1088/0029-5515/41/2/311
33.M.Temporal,A.Piriz,N.Grandjouan et al.,Numerical analysis of a multilayered cylindrical target compression driven by a rotating intense heavy ion beam.Laser Part.Beams 21,609-614(2003).https://doi.org/10.1017/S0263034603214208
34.O.V.Gotchev,N.W.Jang,J.P.Knauer et al.,Magneto-inertial approach to direct-drive laser fusion.J.Fusion Energy 27,25-31(2008).https://doi.org/10.1007/s10894-007-9112-3
35.S.Eliezer,Z.Henis,N.Nissim et al.,Introducing a two temperature plasma ignition in inertial confined targets under the effect of relativistic shock waves:the case of DT and p B 11.Laser Part.Beams 33,577-589(2015).https://doi.org/10.1017/S0263034615000701
36.Z.Fan,J.Liu,B.Liu et al.,Ignition conditions relaxation for central hot-spot ignition with an ion-electron non-equilibrium model.Phys.Plasmas 23,010703(2016).https://doi.org/10.1063/1.4940315
37.Z.Fan,Y.Liu,B.Liu et al.,Non-equilibrium between ions and electrons inside hot spots from National Ignition Facility experiments.Matter Radiat.Extremes 2,3-8(2017).https://doi.org/10.1016/j.mre.2016.11.003
38.J.W.Li,L.Chang,Y.S.Li et al.,Transition from equilibrium ignition to non-equilibrium burn for ICF capsules surrounded by a high-Z pusher.Nucl.Fusion 51,063005(2011).https://doi.org/10.1088/0029-5515/51/6/063005
39.Z.Fan,X.He,J.Liu et al.,A wedged-peak-pulse design with medium fuel adiabat for indirect-drive fusion.Phys.Plasmas 21,100705(2014).https://doi.org/10.1063/1.4898682
40.F.F.Chen,S.E.Von Goeler,Introduction to Plasma Physics and Controlled Fusion Volume 1:Plasma Physics(Springer,Berlin,1983),pp.6-7
41.S.Braginskii,Transport Processes in a Plasma,Consultants Bureau(New York,1965),pp.215-249
42.C.Cereceda,C.Deutsch,M.De Peretti et al.,Kinetic theory of alpha particles production in a dense and strongly magnetized plasma.Phys.Plasmas 7,4515-4533(2000).https://doi.org/10.1063/1.1308564
43.H.-S.Bosch,G.Hale,Improved formulas for fusion cross-sections and thermal reactivities.Nucl.Fusion 32,611(1992).https://doi.org/10.1088/0029-5515/32/4/I07
44.B.Zohuri,Inertial Confinement Fusion Driven Thermonuclear Energy(Springer,Cham,2017),pp.146-147
45.W.A.Fowler,G.R.Caughlan,B.A.Zimmerman,Thermonuclear reaction rates.Ann.Rev.Astron.Astrophys.5,525-570(1967).https://doi.org/10.1146/annurev.aa.05.090167.002521
46.R.Betti,A.Christopherson,B.Spears et al.,Alpha heating and burning plasmas in inertial confinement fusion.Phys.Rev.Lett.114,255003(2015).https://doi.org/10.1088/1742-6596/717/1/012007
47.M.C.Hermann,M.E.Cuneo,D.B.Sinars et al.,Magnetically driven implosions for inertial confinement fusion at Sandia National Laboratories.IEEE Trans.Plasma Sci.40,3222-3245(2012).https://doi.org/10.1109/tps.2012.2223488
48.M.Basko.Inertial confinement fusion with magnetized fuel in cylindrical targets,in Rep.EURCEA-FC 1645,CEA Cadarache(1998)
2.C.Yamanaka,Inertial confinement fusion:the quest for ignition and energy gain using indirect drive.Nucl.Fusion 39,825(1999).https://doi.org/10.1088/0029-5515/39/6/702
3.S.Atzeni,J.Meyer-ter-Vehn,The Physics of Inertial Fusion:BeamPlasma Interaction,Hydrodynamics,Hot Dense Matter(Oxford University Press,New York,2004),pp.35-39
4.R.C.Kirkpatrick,HEDP and new directions for fusion energy.High Energy Density Phys.6,207-209(2010).https://doi.org/10.1016/j.hedp.2010.01.017
5.I.R.Lindemuth,An extended study of the ignition design space of magnetized target fusion.Phys.Plasmas 24,055602(2017).https://doi.org/10.1063/1.4977538
6.I.R.Lindemuth,R.E.Siemon,The fundamental parameter space of controlled thermonuclear fusion.Am.J.Phys.77,407-416(2009).https://doi.org/10.1119/1.3096646
7.M.Sweeney,A.Farnsworth Jr.,High-gain,low-intensity ICFtargets for a charged-particle beam fusion driver.Nucl.Fusion21,41(1981).https://doi.org/10.1088/0029-5515/21/1/004
8.I.Lindemuth,R.Kirkpatrick,Parameter space for magnetized fuel targets in inertial confinement fusion.Nucl.Fusion 23,263(1983).https://doi.org/10.1088/0029-5515/23/3/001
9.I.Lindemuth,R.Reinovsky,R.Chrien,et al.,Joint US/Russian plasma formation experiments for magnetic compression/magnetized target fusion(MAGO/MTF),in Digest of Technical Papers.Tenth IEEE International Pulsed Power Conference,Albuquerque,NM,USA,vol.1(1995),pp.601-606.https://doi.org/10.1109/ppc.1995.596738
10.A.B.Sefkow,S.Slutz,J.Koning et al.,Design of magnetized liner inertial fusion experiments using the Z facility.Phys.Plasmas 21,072711(2014).https://doi.org/10.1063/1.4890298
11.K.Hahn,G.A.Chandler,C.L.Ruiz et al.,Fusion-neutron measurements for magnetized liner inertial fusion experiments on the Z accelerator.J.Phys:Conf.Ser.717,012020(2016).https://doi.org/10.1088/1742-6596/717/1/012020
12.A.Kemp,M.Basko,J.Meyer-ter-Vehn,Magnetized cylindrical targets for heavy ion fusion.Nucl.Instrum.Methods Phys.Res.Sect.A 464,192-195(2001).https://doi.org/10.1016/s0168-9002(01)00032-8
13.D.Kilcrease,R.Kirkpatrick,Magnetized fuel inertial confinement fusion.Nucl.Fusion 28,1465(1988).https://doi.org/10.1088/0029-5515/28/8/015
14.A.J.Kemp,M.M.Basko,J.Meyer-ter-Vehn,Implosion and ignition of magnetized cylindrical targets driven by heavy-ion beams.Nucl.Fusion 43,16(2002).https://doi.org/10.1088/0029-5515/43/1/302
15.I.R.Lindemuth,The ignition design space of magnetized target fusion.Phys.Plasmas 22,122712(2015).https://doi.org/10.1063/1.4937371
16.R.Ramis,J.Meyer-Ter-Vehn,On thermonuclear burn propagation in a pre-compressed cylindrical DT target ignited by a heavy ion beam pulse.Laser Part.Beams 32,41-47(2014).https://doi.org/10.1017/S0263034613000839
17.M.Basko,M.Churazov,A.Aksenov,Prospects of heavy ion fusion in cylindrical geometry.Laser Part.Beams 20,411-414(2002).https://doi.org/10.1017/S0263034602203080
18.M.Widner,J.Chang,A.Farnsworth et al.,Neutron-production from relativistic electron-beam targets.in Bulletin of the American Physical Society,American Institute of Physics Circulation and Fulfillment Division,500 Sunnyside Blvd,Woodbury,NY11797-2999(1977),pp.1139-1139.https://doi.org/10.1111/j.1749-6632.1975.tb00096.x
19.R.Jones,W.Mead,The physics of burn in magnetized deuterium-tritium plasmas:spherical geometry.Nucl.Fusion 26,127(1986).https://doi.org/10.1088/0029-5515/26/2/001
20.S.A.Slutz,R.A.Vesey,High-gain magnetized inertial fusion.Phys.Rev.Lett.108,025003(2012).https://doi.org/10.1103/PhysRevLett.108.025003
21.P.Schmit,P.Knapp,S.Hansen et al.,Understanding fuel magnetization and mix using secondary nuclear reactions in magnetoinertial fusion.Phys.Rev.Lett.113(15),155004(2014).https://doi.org/10.1103/PhysRevLett.113.155004
22.K.Schoenberg,R.Siemon,Magnetized target fusion,in A Proofof-Principle Research Proposal(Los Alamos National Lab,NM,US,1998).https://doi.org/10.2172/763201
23.G.A.Wurden,S.C.Hsu,T.P.Intrator et al.,Magneto-inertial fusion.J.Fusion Energy 35,69-77(2016).https://doi.org/10.1007/s10894-015-0038-x
24.S.C.Hsu,S.J.Langendorf,Magnetized plasma target for plasmajet-driven magneto-inertial fusion.J.Fusion Energy 38,182-198(2018).https://doi.org/10.1007/s10894-018-0168-z
25.J.Davies,R.Betti,P.Y.Chang et al.,The importance of electrothermal terms in Ohm’s law for magnetized spherical implosions.Phys.Plasmas 22,112703(2015).https://doi.org/10.1088/0029-5515/43/1/302
26.M.Basko,Magnetized implosions driven by intense ion beams.Phys.Plasmas 7,4579-4589(2000).https://doi.org/10.1063/1.1312182
27.M.Basko,J.Maruhn,T.Schlegel,Hydrodynamic instability of shells accelerated by direct ion beam heating.Phys.Plasmas 9,1348-1356(2002).https://doi.org/10.1063/1.1462634
28.A.Kemp,M.Basko,J.Meyer-ter-Vehn,Ignition conditions for magnetically insulated tamped ICF targets in cylindrical geometry.Nucl.Fusion 41,235(2001).https://doi.org/10.1088/0029-5515/41/2/311
29.A.J.Kemp,Magnetized Cylindrical Implosions Driven by Heavy ion Beams.Ph.D.Thesis,Technische Universita¨t Mu¨nchen(2001)
30.T.Intrator,S.Y.Zhang,J.H.Degnan et al.,A high density field reversed configuration(FRC)target for magnetized target fusion:first internal profile measurements of a high density FRC.Phys.Plasmas 11,2580-2585(2004).https://doi.org/10.1063/1.1689666
31.I.Lindemuth,R.Kirkpatrick,The promise of magnetized fuel:inertial confinement fusion with existing driver technology.Atomkernenerg/Kerntech 45,9-13(1984)
32.M.Basko,A.Kemp,J.Meyer-ter-Vehn,Ignition conditions for magnetized target fusion in cylindrical geometry.Nucl.Fusion40,59(2000).https://doi.org/10.1088/0029-5515/41/2/311
33.M.Temporal,A.Piriz,N.Grandjouan et al.,Numerical analysis of a multilayered cylindrical target compression driven by a rotating intense heavy ion beam.Laser Part.Beams 21,609-614(2003).https://doi.org/10.1017/S0263034603214208
34.O.V.Gotchev,N.W.Jang,J.P.Knauer et al.,Magneto-inertial approach to direct-drive laser fusion.J.Fusion Energy 27,25-31(2008).https://doi.org/10.1007/s10894-007-9112-3
35.S.Eliezer,Z.Henis,N.Nissim et al.,Introducing a two temperature plasma ignition in inertial confined targets under the effect of relativistic shock waves:the case of DT and p B 11.Laser Part.Beams 33,577-589(2015).https://doi.org/10.1017/S0263034615000701
36.Z.Fan,J.Liu,B.Liu et al.,Ignition conditions relaxation for central hot-spot ignition with an ion-electron non-equilibrium model.Phys.Plasmas 23,010703(2016).https://doi.org/10.1063/1.4940315
37.Z.Fan,Y.Liu,B.Liu et al.,Non-equilibrium between ions and electrons inside hot spots from National Ignition Facility experiments.Matter Radiat.Extremes 2,3-8(2017).https://doi.org/10.1016/j.mre.2016.11.003
38.J.W.Li,L.Chang,Y.S.Li et al.,Transition from equilibrium ignition to non-equilibrium burn for ICF capsules surrounded by a high-Z pusher.Nucl.Fusion 51,063005(2011).https://doi.org/10.1088/0029-5515/51/6/063005
39.Z.Fan,X.He,J.Liu et al.,A wedged-peak-pulse design with medium fuel adiabat for indirect-drive fusion.Phys.Plasmas 21,100705(2014).https://doi.org/10.1063/1.4898682
40.F.F.Chen,S.E.Von Goeler,Introduction to Plasma Physics and Controlled Fusion Volume 1:Plasma Physics(Springer,Berlin,1983),pp.6-7
41.S.Braginskii,Transport Processes in a Plasma,Consultants Bureau(New York,1965),pp.215-249
42.C.Cereceda,C.Deutsch,M.De Peretti et al.,Kinetic theory of alpha particles production in a dense and strongly magnetized plasma.Phys.Plasmas 7,4515-4533(2000).https://doi.org/10.1063/1.1308564
43.H.-S.Bosch,G.Hale,Improved formulas for fusion cross-sections and thermal reactivities.Nucl.Fusion 32,611(1992).https://doi.org/10.1088/0029-5515/32/4/I07
44.B.Zohuri,Inertial Confinement Fusion Driven Thermonuclear Energy(Springer,Cham,2017),pp.146-147
45.W.A.Fowler,G.R.Caughlan,B.A.Zimmerman,Thermonuclear reaction rates.Ann.Rev.Astron.Astrophys.5,525-570(1967).https://doi.org/10.1146/annurev.aa.05.090167.002521
46.R.Betti,A.Christopherson,B.Spears et al.,Alpha heating and burning plasmas in inertial confinement fusion.Phys.Rev.Lett.114,255003(2015).https://doi.org/10.1088/1742-6596/717/1/012007
47.M.C.Hermann,M.E.Cuneo,D.B.Sinars et al.,Magnetically driven implosions for inertial confinement fusion at Sandia National Laboratories.IEEE Trans.Plasma Sci.40,3222-3245(2012).https://doi.org/10.1109/tps.2012.2223488
48.M.Basko.Inertial confinement fusion with magnetized fuel in cylindrical targets,in Rep.EURCEA-FC 1645,CEA Cadarache(1998)