先进磁镜装置中径向电场对高能粒子的约束性能研究
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摘要
本文运用Boris算法对紧凑型聚变反应装置(compact fusion reactor, CFR)中高能a粒子的运动轨道进行了数值模拟,分析了高能a粒子在不同径向电场作用下运动轨道的差异性;探究了不同径向电场对CFR装置中不同位置处a粒子约束性能的影响.研究结果表明,当正、负径向电场强度达到一定临界值时,都能够使高能a粒子很好地约束在CFR装置内部,但不同位置处径向电场强度临界值与a粒子初始条件有关.
The radial electric field Er in a magnetic confined machine, such as the compact fusion reactor(CFR), the field-reserved configuration(FRC), and the tokamak, plays an essential role in affecting the confinement properties of the high energy particles. The parallel velocities of the high energy particles will be accelerated or decelerated by applying a radial electric field, which could change the loss rate of the high energy particles in the magnetic confined machines. Unlike the fourth-order Runge-Kutta method RK4, the recently-developed Boris method can strictly preserve energy conservation of the high energy particles in the case without radial electric field. The orbit of high energy a particle in compact fusion reactor(CFR) is simulated by solving the equations of motion numerically with the Boris Algorithm. The effect of radial electric field on the orbit of the high energy a particle is investigated and the confinement of plasma in different radial electric fields in the CFR machine is studied in the present paper. By changing the strength of the radical electric field and the particles' radical locations in the middle plane of the CFR configuration, the confinement property of the high energy a particle is studied. The numerical results indicate that both the positive radial electric field and negative electric field can significantly affect the confinement of the high energy a particle. When the radial electric field is increased to a threshold, the high energy a particle could be confined in the central region of the CFR machine for a long enough time. The threshold of the radial electric field depends on the initial parameters of the confined particle. Systematic investigations of the radical electronic field effect will conduce to greatly improving the performance of the designed CFR machines.
The radial electric field Er in a magnetic confined machine, such as the compact fusion reactor(CFR), the field-reserved configuration(FRC), and the tokamak, plays an essential role in affecting the confinement properties of the high energy particles. The parallel velocities of the high energy particles will be accelerated or decelerated by applying a radial electric field, which could change the loss rate of the high energy particles in the magnetic confined machines. Unlike the fourth-order Runge-Kutta method RK4, the recently-developed Boris method can strictly preserve energy conservation of the high energy particles in the case without radial electric field. The orbit of high energy a particle in compact fusion reactor(CFR) is simulated by solving the equations of motion numerically with the Boris Algorithm. The effect of radial electric field on the orbit of the high energy a particle is investigated and the confinement of plasma in different radial electric fields in the CFR machine is studied in the present paper. By changing the strength of the radical electric field and the particles' radical locations in the middle plane of the CFR configuration, the confinement property of the high energy a particle is studied. The numerical results indicate that both the positive radial electric field and negative electric field can significantly affect the confinement of the high energy a particle. When the radial electric field is increased to a threshold, the high energy a particle could be confined in the central region of the CFR machine for a long enough time. The threshold of the radial electric field depends on the initial parameters of the confined particle. Systematic investigations of the radical electronic field effect will conduce to greatly improving the performance of the designed CFR machines.
引文
[1]Dolan T J,Brotankova J,Cadwallader L C,Costley A E,Ivanov D P,Manheimer W,Merola M,Moir R W,Neumann M J,Parrish A,Waganer L M 2013 Magnetic Fusion Technology(New York:Springer)pp23-68
[2]Baylor L R,Combs S K,Foust C R,Jernigan T C,Meitner SJ,Parks P B,Caughman J B,Fehling D T,Maruyama S,Qualls A L,Rasmussen D A,Thomas C E 2009 Nucl.Fusion49 085013
[3]Sun X,Liu M,Xie J L,Yu Y,Lin M N,Zhang Q 2014 J.Univ.Sci.Technol.China 44 374(in Chinese)[孙玄,刘明,谢锦林,余羿,林木楠,张情2014中国科学技术大学学报44 374]
[4]Bodin H A B,Newton A A 2011 Nucl.Fusion 20 1255
[5]Steinhauer L C 2011 Phys.Plasmas 18 070501
[6]Tuszewski M,Smirnov A,Thompson M C,Korepanov S,Akhmetov T,Ivanov A,Voskoboynikov R,Schmitz L,Barnes D,Binderbauer M W,Brown R,Bui D Q,Clary R,Conroy KD,Deng B H,Dettrick S A,Douglass J D,Garate E,Glass FJ,Gota H,Guo H Y,Gupta D,Gupta S,Kinley J S,Knapp K,Longman A,Hollins M,Li X L,Luo Y,Mendoza R,Mok Y,Necas A,Primavera S,Ruskov E,Schroeder J H,Sevier L,Sibley A,Song Y,Sun X,Trask E,Van Drie A D,Walters JK,Wyman M D,Team T A E 2012 Phys.Rev.Lett.108255008
[7]Binderbauer M W,Tajima T,Steinhauer L C,Garate E,Tuszewski M,Schmitz L,Guo H Y,Smirnov A,Gota H,Barnes D,Deng B H,Thompson M C,Trask E,Yang X,Putvinski S,Rostoker N,Andow R,Aefsky S,Bolte N,Bui DQ,Ceccherini F,Clary R,Cheung A H,Conroy K D,Dettrick S A,Douglass J D,Feng P,Galeotti L,Giammanco F,Granstedt E,Gupta D,Gupta S,Ivanov A A,Kinley J S,Knapp K,Korepanov S,Hollins M,Magee R,Mendoza R,Mok Y,Necas A,Primavera S,Onofri M,Osin D,Rath N,Roche T,Romero J,Schroeder J H,Sevier L,Sibley A,Song Y,Van Drie A D,Walters J K,Waggoner W,Yushmanov P,Zhai K 2015 Phys.Plasmas 22 056110
[8]Forsen H K 1988 J.Fusion Energy 7 269
[9]Park J,Krall N A,Sieck P E,Offermann D T,Skillicorn M,Sanchez A,Davis K,Alderson E,Lapenta G 2015 Phys.Rev.X 5 021024
[10]Carr M,Khachan J 2010 Phys.Plasmas 17 052510
[11]Cornish S,Gummersall D,Carr M,Khachan J 2014 Phys.Plasmas 21 092502
[12]Miley G H,Murali S K 2014 Inertial Electrostatic Confinement(IEC)Fusion(New York:Springer)pp1-400
[13]Hoffman A L,Guo H Y,Miller K E,Milroy R D 2005 Nucl.Fusion 45 176
[14]McGuire T J 2014 US Patent 201414242999
[15]Lockheed Martin Compact Fusion Reactor Concept,Confinement Model and T4B Experiment(PDF).Lockheed Martin Corporation.2016.Archived from the original(PDF)on December 25,2017.Retrieved 25 December2017(https://en.wikipedia.org/wiki/Lockheed_Martin_Comp act_Fusion_Reactor)
[16]Zhu L M,Liu H F,Wang X Q 2016 Phys.Scr.91 095604
[17]Wagner F,Becker G,Behringer K,Campbell D,Eberhagen A,Engelhardt W,Fussmann G,Gehre O,Gernhardt J,Gierke G v,Haas G,Huang M,Karger F,Keilhacker M,Klüber O,Kornherr M,Lackner K,Lisitano G,Lister G G,Mayer H M,Meisel D,Müller E R,Murmann H,Niedermeyer H,Poschenrieder W,Rapp H,R?hr H,Schneider F,Siller G,Speth E,St?bler A,Steuer K H,Venus G,Vollmer O,YüZ1982 Phys.Rev.Lett.49 1408
[18]Taylor R J,Brown M L,Fried B D,Grote H,Liberati J R,Morales G J,Pribyl P,Darrow D,Ono M 1989 Phys.Rev.Lett.63 2365
[19]Shaing K C,Crume Jr E C,1989 Phys.Rev.Lett.63 2369
[20]Van Oost G 2006 Fusion Sci.Technol.49 327
[21]Groebner R J,Burrell K H,Seraydarian 1990 Phys.Rev.Lett.64 3015
[22]Gorman J G 1966 Phys.Fluids 9 2504
[23]Itoh K,Itoh S I 1996 Plasma Phys.Controlled Fusion 38 1
[24]Silva C,Figueiredo H,Cabral J A C,Gonáalves B,Nedzelsky I,Varandas C A F 2004 Plasma Phys.Controlled Fusion 46163
[25]Sun Y,Chen Z P,Zhu T Z,et al.2014 Plasma Phys.Controlled Fusion 56 015001
[26]Zhang Q,Shi P Y,Liu M,Lin M N,Sun X 2015 Fusion Sci.Technol.68 50
[27]Zhang J,Luo J R,Wang S J 2006 Acta Phys.Sin.55 1077(in Chinese)[张杰,罗家融,王少杰2006物理学报55 1077]
[28]Xu X L,Zhao X M,Wang Z T,Tang C J 2012 Acta Phys.Sin.61 185201(in Chinese)[徐欣亮,赵小明,王中天,唐昌建2012物理学报61 185201]
[29]Mou M L,Liu Y,Wang Z T,Chen S Y,Tang C J 2014 Acta Phys.Sin.63 165201(in Chinese)[牟茂淋,刘宇,王中天,陈少永,唐昌建2014物理学报63 165201]
[30]Zhang L 2009 Ph.D.Dissertation(Beijing:Tsinghua University)(in Chinese)[张良2009博士学位论文(北京:清华大学)]
[31]Qin H,Zhang S X,Xiao J Y,Liu J,Sun Y J,Tang W M2013 Phys.Plasmas 20 084503
[32]Delzanno G L,Camporeale E 2013 J.Comput.Phys.253 259
[33]Kuley A,Wang Z X,Lin Z,Wessel F 2013 Phys.Plasmas 20102515
[34]Wei X S,Xiao Y,Kuley A,Lin Z 2015 Phys.Plasmas 22092502
[35]Winkel M,Speck R,Ruprecht D 2015 J.Comput.Phys.295456
[36]He Y,Sun Y,Liu J,Qin H 2015 J.Comput.Phys.281 135
[37]Freidberg J P 2007 Plasma Physics and Fusion Energy(Cambridge:Cambridge University Press)pp149-160
[2]Baylor L R,Combs S K,Foust C R,Jernigan T C,Meitner SJ,Parks P B,Caughman J B,Fehling D T,Maruyama S,Qualls A L,Rasmussen D A,Thomas C E 2009 Nucl.Fusion49 085013
[3]Sun X,Liu M,Xie J L,Yu Y,Lin M N,Zhang Q 2014 J.Univ.Sci.Technol.China 44 374(in Chinese)[孙玄,刘明,谢锦林,余羿,林木楠,张情2014中国科学技术大学学报44 374]
[4]Bodin H A B,Newton A A 2011 Nucl.Fusion 20 1255
[5]Steinhauer L C 2011 Phys.Plasmas 18 070501
[6]Tuszewski M,Smirnov A,Thompson M C,Korepanov S,Akhmetov T,Ivanov A,Voskoboynikov R,Schmitz L,Barnes D,Binderbauer M W,Brown R,Bui D Q,Clary R,Conroy KD,Deng B H,Dettrick S A,Douglass J D,Garate E,Glass FJ,Gota H,Guo H Y,Gupta D,Gupta S,Kinley J S,Knapp K,Longman A,Hollins M,Li X L,Luo Y,Mendoza R,Mok Y,Necas A,Primavera S,Ruskov E,Schroeder J H,Sevier L,Sibley A,Song Y,Sun X,Trask E,Van Drie A D,Walters JK,Wyman M D,Team T A E 2012 Phys.Rev.Lett.108255008
[7]Binderbauer M W,Tajima T,Steinhauer L C,Garate E,Tuszewski M,Schmitz L,Guo H Y,Smirnov A,Gota H,Barnes D,Deng B H,Thompson M C,Trask E,Yang X,Putvinski S,Rostoker N,Andow R,Aefsky S,Bolte N,Bui DQ,Ceccherini F,Clary R,Cheung A H,Conroy K D,Dettrick S A,Douglass J D,Feng P,Galeotti L,Giammanco F,Granstedt E,Gupta D,Gupta S,Ivanov A A,Kinley J S,Knapp K,Korepanov S,Hollins M,Magee R,Mendoza R,Mok Y,Necas A,Primavera S,Onofri M,Osin D,Rath N,Roche T,Romero J,Schroeder J H,Sevier L,Sibley A,Song Y,Van Drie A D,Walters J K,Waggoner W,Yushmanov P,Zhai K 2015 Phys.Plasmas 22 056110
[8]Forsen H K 1988 J.Fusion Energy 7 269
[9]Park J,Krall N A,Sieck P E,Offermann D T,Skillicorn M,Sanchez A,Davis K,Alderson E,Lapenta G 2015 Phys.Rev.X 5 021024
[10]Carr M,Khachan J 2010 Phys.Plasmas 17 052510
[11]Cornish S,Gummersall D,Carr M,Khachan J 2014 Phys.Plasmas 21 092502
[12]Miley G H,Murali S K 2014 Inertial Electrostatic Confinement(IEC)Fusion(New York:Springer)pp1-400
[13]Hoffman A L,Guo H Y,Miller K E,Milroy R D 2005 Nucl.Fusion 45 176
[14]McGuire T J 2014 US Patent 201414242999
[15]Lockheed Martin Compact Fusion Reactor Concept,Confinement Model and T4B Experiment(PDF).Lockheed Martin Corporation.2016.Archived from the original(PDF)on December 25,2017.Retrieved 25 December2017(https://en.wikipedia.org/wiki/Lockheed_Martin_Comp act_Fusion_Reactor)
[16]Zhu L M,Liu H F,Wang X Q 2016 Phys.Scr.91 095604
[17]Wagner F,Becker G,Behringer K,Campbell D,Eberhagen A,Engelhardt W,Fussmann G,Gehre O,Gernhardt J,Gierke G v,Haas G,Huang M,Karger F,Keilhacker M,Klüber O,Kornherr M,Lackner K,Lisitano G,Lister G G,Mayer H M,Meisel D,Müller E R,Murmann H,Niedermeyer H,Poschenrieder W,Rapp H,R?hr H,Schneider F,Siller G,Speth E,St?bler A,Steuer K H,Venus G,Vollmer O,YüZ1982 Phys.Rev.Lett.49 1408
[18]Taylor R J,Brown M L,Fried B D,Grote H,Liberati J R,Morales G J,Pribyl P,Darrow D,Ono M 1989 Phys.Rev.Lett.63 2365
[19]Shaing K C,Crume Jr E C,1989 Phys.Rev.Lett.63 2369
[20]Van Oost G 2006 Fusion Sci.Technol.49 327
[21]Groebner R J,Burrell K H,Seraydarian 1990 Phys.Rev.Lett.64 3015
[22]Gorman J G 1966 Phys.Fluids 9 2504
[23]Itoh K,Itoh S I 1996 Plasma Phys.Controlled Fusion 38 1
[24]Silva C,Figueiredo H,Cabral J A C,Gonáalves B,Nedzelsky I,Varandas C A F 2004 Plasma Phys.Controlled Fusion 46163
[25]Sun Y,Chen Z P,Zhu T Z,et al.2014 Plasma Phys.Controlled Fusion 56 015001
[26]Zhang Q,Shi P Y,Liu M,Lin M N,Sun X 2015 Fusion Sci.Technol.68 50
[27]Zhang J,Luo J R,Wang S J 2006 Acta Phys.Sin.55 1077(in Chinese)[张杰,罗家融,王少杰2006物理学报55 1077]
[28]Xu X L,Zhao X M,Wang Z T,Tang C J 2012 Acta Phys.Sin.61 185201(in Chinese)[徐欣亮,赵小明,王中天,唐昌建2012物理学报61 185201]
[29]Mou M L,Liu Y,Wang Z T,Chen S Y,Tang C J 2014 Acta Phys.Sin.63 165201(in Chinese)[牟茂淋,刘宇,王中天,陈少永,唐昌建2014物理学报63 165201]
[30]Zhang L 2009 Ph.D.Dissertation(Beijing:Tsinghua University)(in Chinese)[张良2009博士学位论文(北京:清华大学)]
[31]Qin H,Zhang S X,Xiao J Y,Liu J,Sun Y J,Tang W M2013 Phys.Plasmas 20 084503
[32]Delzanno G L,Camporeale E 2013 J.Comput.Phys.253 259
[33]Kuley A,Wang Z X,Lin Z,Wessel F 2013 Phys.Plasmas 20102515
[34]Wei X S,Xiao Y,Kuley A,Lin Z 2015 Phys.Plasmas 22092502
[35]Winkel M,Speck R,Ruprecht D 2015 J.Comput.Phys.295456
[36]He Y,Sun Y,Liu J,Qin H 2015 J.Comput.Phys.281 135
[37]Freidberg J P 2007 Plasma Physics and Fusion Energy(Cambridge:Cambridge University Press)pp149-160