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先进磁镜装置中径向电场对高能粒子的约束性能研究

石黎铭 吴雪科 万迪 李会东 樊群超 王中天 冯灏 王占辉 马杰

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先进磁镜装置中径向电场对高能粒子的约束性能研究

石黎铭, 吴雪科, 万迪, 李会东, 樊群超, 王中天, 冯灏, 王占辉, 马杰

Effects of radial electric field on confinement of high energy particles in advanced fusion mirror reactor

Shi Li-Ming, Wu Xue-Ke, Wan Di, Li Hui-Dong, Fan Qun-Chao, Wang Zhong-Tian, Feng Hao, Wang Zhan-Hui, Ma Jie
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  • 本文运用Boris算法对紧凑型聚变反应装置(compact fusion reactor, CFR)中高能α粒子的运动轨道进行了数值模拟, 分析了高能α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α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α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α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 α 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 α 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 α 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 α particle. When the radial electric field is increased to a threshold, the high energy α 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.
      通信作者: 李会东, huidongli@mail.xhu.edu.cn ; 樊群超, fanqunchao@mail.xhu.edu.cn
    • 基金项目: 国家自然科学基金青年基金(批准号: 11605143)、 四川省杰出青年学术与技术带头人支持计划(批准号: 2019JDJQ0050, 2019JDJQ0051)、 国家自然科学基金(批准号: 11575055)、西华大学高性能科学计算重点实验室开放课题(批准号: szjj2017-011, szjj2017-012)和量子光学与光量子国家重点实验室(批准号: KF201811)资助的课题.
      Corresponding author: Li Hui-Dong, huidongli@mail.xhu.edu.cn ; Fan Qun-Chao, fanqunchao@mail.xhu.edu.cn
    • Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11605143), the Sichuan Provincial Foundation for Distinguished Young Leaders of Disciplines in Science and Technology, China (Grant Nos. 2019JDJQ0050, 2019JDJQ0051), the National Natural Science Foundation of China (Grant No. 11575055), the Open Program of Key Laboratory of High Performance Scientific Computing of Xihua University, China (Grant Nos. szjj2017-011, szjj2017-012), and the State Key Laboratory of Quantum Optics and Quantum Optics Devices, China (Grant No. KF201811).
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    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

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    Carr M, Khachan J 2010 Phys. Plasmas 17 052510Google Scholar

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    Cornish S, Gummersall D, Carr M, Khachan J 2014 Phys. Plasmas 21 092502Google Scholar

    [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 176Google Scholar

    [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 December 2017(https://en.wikipedia.org/wiki/Lockheed_Martin_Compact_Fusion_Reactor)

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    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, Röhr H, Schneider F, Siller G, Speth E, Stäbler A, Steuer K H, Venus G, Vollmer O, Yü Z 1982 Phys. Rev. Lett. 49 1408Google Scholar

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    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 2365Google Scholar

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    Shaing K C, Crume Jr E C, 1989 Phys. Rev. Lett. 63 2369Google Scholar

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    Van Oost G 2006 Fusion Sci. Technol. 49 327

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    Groebner R J, Burrell K H, Seraydarian 1990 Phys. Rev. Lett. 64 3015Google Scholar

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    Gorman J G 1966 Phys. Fluids 9 2504Google Scholar

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    Itoh K, Itoh S I 1996 Plasma Phys. Controlled Fusion 38 1Google Scholar

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    Silva C, Figueiredo H, Cabral J A C, GonÁalves B, Nedzelsky I, Varandas C A F 2004 Plasma Phys. Controlled Fusion 46 163Google Scholar

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    Sun Y, Chen Z P, Zhu T Z, et al. 2014 Plasma Phys. Controlled Fusion 56 015001Google Scholar

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    Zhang Q, Shi P Y, Liu M, Lin M N, Sun X 2015 Fusion Sci. Technol. 68 50Google Scholar

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    张杰, 罗家融, 王少杰 2006 物理学报 55 1077Google Scholar

    Zhang J, Luo J R, Wang S J 2006 Acta Phys. Sin. 55 1077Google Scholar

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    徐欣亮, 赵小明, 王中天, 唐昌建 2012 物理学报 61 185201Google Scholar

    Xu X L, Zhao X M, Wang Z T, Tang C J 2012 Acta Phys. Sin. 61 185201Google Scholar

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    牟茂淋, 刘宇, 王中天, 陈少永, 唐昌建 2014 物理学报 63 165201Google Scholar

    Mou M L, Liu Y, Wang Z T, Chen S Y, Tang C J 2014 Acta Phys. Sin. 63 165201Google Scholar

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    张良 2009 博士学位论文 (北京:清华大学)

    Zhang L 2009 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)

    [31]

    Qin H, Zhang S X, Xiao J Y, Liu J, Sun Y J, Tang W M 2013 Phys. Plasmas 20 084503Google Scholar

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    Delzanno G L, Camporeale E 2013 J. Comput. Phys. 253 259Google Scholar

    [33]

    Kuley A, Wang Z X, Lin Z, Wessel F 2013 Phys. Plasmas 20 102515Google Scholar

    [34]

    Wei X S, Xiao Y, Kuley A, Lin Z 2015 Phys. Plasmas 22 092502Google Scholar

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    Winkel M, Speck R, Ruprecht D 2015 J. Comput. Phys. 295 456Google Scholar

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    He Y, Sun Y, Liu J, Qin H 2015 J. Comput. Phys. 281 135Google Scholar

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    Freidberg J P 2007 Plasma Physics and Fusion Energy (Cambridge: Cambridge University Press) pp149–160

  • 图 1  Lockheed Martin紧凑型聚变反应磁镜装置 (a)构造; (b)等离子体分布

    Fig. 1.  (a) The structure of CFR machine; (b) plasma distribution in CFR (https://en.wikipedia.org/wiki/Lockheed_Martin_Compact_Fusion_Reactor)

    图 2  CFR装置中R-Z平面上的磁场位形

    Fig. 2.  The magnetic flux of the R-Z plane in the CFR machine

    图 3  Boris 算法和RK4算法模拟下第一个漂移周期和最后一个漂移周期的轨道(模拟时间1200 μs) (a) Boris 算法; (b) RK4算法

    Fig. 3.  Orbits of the first and the last drift motion periods by the Boris algorithm and the RK4 algorithm (simulation time is 1200 μs): (a) The Boris algorithm; (b) the RK4 algorithm

    图 4  Boris算法和RK4算法数相对能量误差随时间变化对比

    Fig. 4.  Comparison of the relative energy errors between Boris method and RK4 method

    图 5  (a) CFR粒子轨道; (b)粒子轨道在X-Y截面的投影; (c)粒子轨道在R-Z截面的投影

    Fig. 5.  (a) The orbit of particles in CFR; (b) the projection of the particle orbital in the X-Y plane; (c) the projection of the particle orbital in the R-Z plane

    图 6  CFR中α粒子损失轨道

    Fig. 6.  The lost orbits of theαparticles in CFR

    图 7  粒子约束时间随着正向电场强度的变化

    Fig. 7.  The particle confinement time changes with the intensity of the positive electric field

    图 8  初始位置${r_0}/a = 0.3$处α粒子在不同正向径向电场作用下的运动轨迹

    Fig. 8.  The orbits of α particle under the different positive radial electric fields at ${r_0}/a = 0.3$

    图 9  粒子约束时间随着负向径向电场强度的变化

    Fig. 9.  The variations of particle confinement time with the intensity of the negative radial electric field

    图 10  初始位置${r_0}/a = 0.3$处α粒子在不同负向径向电场作用下的轨道

    Fig. 10.  The orbits of α particle under the different negative radial electric fields at${r_0}/a = 0.3$

    图 11  不同径向电场作用下的α粒子损失率

    Fig. 11.  The loss rates of the α particles with different radial electric fields

    表 1  CFR装置线圈参数

    Table 1.  Main parameters of coils in CFR.

    参数中心线圈内部线圈封装线圈1封装线圈2磁镜线圈
    轴向位置Z/m0 ± 0.4 ± 0.7 ± 1 ± 1.25
    半径R/m0.70.250.70.50.3
    电流I/MA–4.37–1–1–10
    下载: 导出CSV
  • [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 S J, Parks P B, Caughman J B, Fehling D T, Maruyama S, Qualls A L, Rasmussen D A, Thomas C E 2009 Nucl. Fusion 49 085013Google Scholar

    [3]

    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 374Google Scholar

    Sun X, Liu M, Xie J L, Yu Y, Lin M N, Zhang Q 2014 J. Univ. Sci. Technol. China 44 374Google Scholar

    [4]

    Bodin H A B, Newton A A 2011 Nucl. Fusion 20 1255

    [5]

    Steinhauer L C 2011 Phys. Plasmas 18 070501Google Scholar

    [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 K D, Deng B H, Dettrick S A, Douglass J D, Garate E, Glass F J, 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 J K, Wyman M D, Team T A E 2012 Phys. Rev. Lett. 108 255008Google Scholar

    [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 D Q, 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 056110Google Scholar

    [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 052510Google Scholar

    [11]

    Cornish S, Gummersall D, Carr M, Khachan J 2014 Phys. Plasmas 21 092502Google Scholar

    [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 176Google Scholar

    [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 December 2017(https://en.wikipedia.org/wiki/Lockheed_Martin_Compact_Fusion_Reactor)

    [16]

    Zhu L M, Liu H F, Wang X Q 2016 Phys. Scr. 91 095604Google Scholar

    [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, Röhr H, Schneider F, Siller G, Speth E, Stäbler A, Steuer K H, Venus G, Vollmer O, Yü Z 1982 Phys. Rev. Lett. 49 1408Google Scholar

    [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 2365Google Scholar

    [19]

    Shaing K C, Crume Jr E C, 1989 Phys. Rev. Lett. 63 2369Google Scholar

    [20]

    Van Oost G 2006 Fusion Sci. Technol. 49 327

    [21]

    Groebner R J, Burrell K H, Seraydarian 1990 Phys. Rev. Lett. 64 3015Google Scholar

    [22]

    Gorman J G 1966 Phys. Fluids 9 2504Google Scholar

    [23]

    Itoh K, Itoh S I 1996 Plasma Phys. Controlled Fusion 38 1Google Scholar

    [24]

    Silva C, Figueiredo H, Cabral J A C, GonÁalves B, Nedzelsky I, Varandas C A F 2004 Plasma Phys. Controlled Fusion 46 163Google Scholar

    [25]

    Sun Y, Chen Z P, Zhu T Z, et al. 2014 Plasma Phys. Controlled Fusion 56 015001Google Scholar

    [26]

    Zhang Q, Shi P Y, Liu M, Lin M N, Sun X 2015 Fusion Sci. Technol. 68 50Google Scholar

    [27]

    张杰, 罗家融, 王少杰 2006 物理学报 55 1077Google Scholar

    Zhang J, Luo J R, Wang S J 2006 Acta Phys. Sin. 55 1077Google Scholar

    [28]

    徐欣亮, 赵小明, 王中天, 唐昌建 2012 物理学报 61 185201Google Scholar

    Xu X L, Zhao X M, Wang Z T, Tang C J 2012 Acta Phys. Sin. 61 185201Google Scholar

    [29]

    牟茂淋, 刘宇, 王中天, 陈少永, 唐昌建 2014 物理学报 63 165201Google Scholar

    Mou M L, Liu Y, Wang Z T, Chen S Y, Tang C J 2014 Acta Phys. Sin. 63 165201Google Scholar

    [30]

    张良 2009 博士学位论文 (北京:清华大学)

    Zhang L 2009 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)

    [31]

    Qin H, Zhang S X, Xiao J Y, Liu J, Sun Y J, Tang W M 2013 Phys. Plasmas 20 084503Google Scholar

    [32]

    Delzanno G L, Camporeale E 2013 J. Comput. Phys. 253 259Google Scholar

    [33]

    Kuley A, Wang Z X, Lin Z, Wessel F 2013 Phys. Plasmas 20 102515Google Scholar

    [34]

    Wei X S, Xiao Y, Kuley A, Lin Z 2015 Phys. Plasmas 22 092502Google Scholar

    [35]

    Winkel M, Speck R, Ruprecht D 2015 J. Comput. Phys. 295 456Google Scholar

    [36]

    He Y, Sun Y, Liu J, Qin H 2015 J. Comput. Phys. 281 135Google Scholar

    [37]

    Freidberg J P 2007 Plasma Physics and Fusion Energy (Cambridge: Cambridge University Press) pp149–160

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出版历程
  • 收稿日期:  2018-11-07
  • 修回日期:  2019-03-12
  • 上网日期:  2019-05-01
  • 刊出日期:  2019-05-20

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