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The high confinement mode (H-mode) is a preferred operation mode of tokamak devices in the future, but the burst of edge localized mode (ELM) will sharply increase the heat load deposited on the divertor target, raising the target temperature rapidly and strengthening surface thermionic emission. In this paper, a one-dimensional fluid model is used to simulate the influence of thermionic emission on the characteristics of the magnetized sheath. The results show that the amplitude of float potential and the electric field strength both decrease under the action of thermionic emission. Plenty of thermionic emission electrons leave the target, resulting in a region with negative charge density near the target plate, and the magnetized sheath is divided into two parts: ion sheath and electron sheath. In the electron sheath, with the rise of the target surface temperature, electrons accumulated in front of the target also increase, the potential distribution is non-monotonic, and a “virtual cathode” structure appears. The reverse electric field formed near the target will confine the thermionic emission electrons leaving the target and slow down the ion movement, leading to a decrease of the ion energy deposited on the target. With the increase of the angle between the magnetic field and the target normal, the potential of the magnetized sheath and the proportion of the thickness of the electron sheath in the magnetized sheath both increase. The virtual cathode potential decreases, the temperature of the target required to form the virtual cathode rises.
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Keywords:
- magnetized sheath /
- thermionic emission /
- virtual cathode
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图 1 模拟区域示意图
Figure 1. Schematic diagram of the simulation region.
图 2 离子速度
$ V $ 、离子密度$ {N_{\text{i}}} $ 及电子密度$ {N_{\text{e}}} $ 的空间分布Figure 2. Spatial distribution of ion velocity V, ion density
$ {N_{\text{i}}} $ and electron density$ {N_{\text{e}}} $ .
图 3 电势
$ \phi $ 、电场$ E $ 的空间分布Figure 3. Spatial distribution of electric potential
$ \phi $ and electric field E.
图 4 不同靶板温度时靶板处的电势
$ {\phi _{{\text{sw}}}} $ 和热电子发射流JsFigure 4. Electric potential at the wall
$ {\phi _{{\text{sw}}}} $ and thermionic emission flux$ {J_{\text{s}}} $ at different target temperatures.
图 5 不同靶板温度
$ {T_{\text{s}}} $ 下 (a)电势$ \phi $ 和(b)电场${{E}}$ 分布Figure 5. Distribution of (a) electric potential
$ \phi $ and (b) electric field$ {{E}} $ in the full region at different target temperatures.
图 6 不同靶板温度
$ {T_{\text{s}}} $ 下 (a)净电荷密度$ \rho $ 和(b)热发射电子密度$ {N_{\text{s}}} $ 分布Figure 6. Distribution of (a) net charge density
$ \rho $ and (b) thermionic emission electron density$ {N_{\text{s}}} $ in the full region at different target temperatures.
图 7 靶板温度
$ {T_{\text{s}}} $ = 2950 K时, 磁化鞘层(a)电势$ \phi $ 和(b)电场$ E $ 分布Figure 7. When target temperature
$ {T_{\text{s}}} $ = 2950 K, distribution of (a) electric potential$ \phi $ and (b) electric field E in the magnetized sheath .
图 8 靶板温度
$ {T_{\text{s}}} $ = 2950 K时, 磁化鞘层(a)净电荷密度$ \rho $ 和(b)热发射电子密度$ {N_{\text{s}}} $ 分布Figure 8. When target temperature
$ {T_{\text{s}}} $ = 2950 K, distribution of (a) net charge density$ \rho $ and (b) thermionic emission electron density$ {N_{\text{s}}} $ in the magnetized sheath.
图 9 不同磁场角度
$ \theta $ 下, 电子鞘中电势$ \phi $ 分布Figure 9. Distribution of electric potential
$ \phi $ in electron sheath at different magnetic field angles$ \theta $ .
图 10 磁场角度
$ \theta $ = 80°时, 不同靶板温度下磁化鞘层(a)电势$ \phi $ 和(b)电场$ E $ 分布Figure 10. When the magnetic field angle
$ \theta $ = 80°, distribution of (a) electric potential$ \phi $ and (b) electric field$ E $ in the magnetized sheath at different target temperatures. -
[1] Burkart W 2005 Nucl. Fusion. 45 E01
Google Scholar
[2] Wagner F, Becker G, Behringer K, Campbell D, Eberhagen A, Engelhardt W, Fussmann G, Gehre O, Gernhardt J, Gierke G, Haas G, Huang M, Karger F, Keilhacker M, Klüber O, Kornherr M, Lackner K, Lisitano G, Lister G G, Mayer H M, Meisel D, MIiller 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 1408
Google Scholar
[3] ASDEX team 1989 Nucl. Fusion 29 1959
Google Scholar
[4] Hobbs G D, Wesson J A 1967 Plasma Phys. 9 85
Google Scholar
[5] Takamura S, Ohno N, Ye M Y, Kuwabara T 2004 Contrib. Plasma Phys. 44 126
Google Scholar
[6] Gyergyek T, Kovačič J 2013 Contrib. Plasma Phys. 53 189
Google Scholar
[7] Tierno S P, Donoso J M, Domenech-Garret J L, Conde L 2016 Phys. Plasmas 23 013503
Google Scholar
[8] Li S H, Li J Q 2021 Vacuum 192 110496
Google Scholar
[9] Snipes J A, Hubbard A E, Garnier D T, Golovato S N, Granetz R S, Greenwald M, Hutchinson I H, Irby J, LaBombard B, Marmar E S, Niemczewski A, O’Shea P J, Porkolab M, Stek P, Takase Y, Terry J L, Watterson R, Wolfe S M 1996 Plasma Phys. Control. Fusion 38 1127
Google Scholar
[10] Campbell D J, the JET team 1997 Plasma Phys. Control. Fusion 39 A285
Google Scholar
[11] Maingi R, Bell M G, Bell R E, Bush C E, Fredrickson E D, Gates D A, Kaye S M, Kugel H W, LeBlanc B P, Menard J E, Mueller D, Sabbagh S A, Stutman D, Taylor G, Johnson D W, Kaita R, Maqueda R J, Ono M, Paoletti F, Paul S F, Peng Y K M, Roquemore A L, Skinner C H, Soukhanovskii V A, Synakowski E J 2002 Phys. Rev. Lett. 88 035003
Google Scholar
[12] Burrell K H, Austin M E, Brennan D P, DeBoo J C, Doyle E J, Gohil P, Greenfield C M, Groebner R J, Lao L L, Luce T C, Makowski M A, McKee G R, Moyer R A, Osborne T H, Porkolab M, Rhodes T L, Rost J C, Schaffer M J, Stallard B W, Strait E J, Wade M R, Wang G, Watkins J G, West W P, Zeng L 2002 Plasma Phys. Control. Fusion 44 A253
Google Scholar
[13] Duan X R, Dong J Q, Yan L W, Ding X T, Yang Q W, Rao J, Liu D Q, Xuan W M, Chen L Y, Li X D, Lei G J, Cao J Y, Cao Z, Song X M, Huang Y, Liu Y, Mao W C, Wang Q M, Cui Z Y, Ji X Q, Li B, Li G S, Li H J, Luo C W, Wang Y Q, Yao L H, Yao L Y, Zhang J H, Zhou J, Zhou Y, Liu Y, HL-2 A team 2010 Nucl. Fusion 50 095011
Google Scholar
[14] Komm M, Ratynskaia S, Tolias P, Cavalier J, Dejarnac R, Gunn J P, Podolnik A 2017 Plasma Phys. Control. Fusion 59 094002
Google Scholar
[15] 邹秀, 刘惠平, 谷秀娥 2008 物理学报 57 5111
Google Scholar
Zou X, Liu H P, Gu X E 2008 Acta. Phys. Sin. 57 5111
Google Scholar
[16] 邹秀, 籍延坤, 邹滨雁 2010 物理学报 59 1902
Google Scholar
Zou X, Ji Y K, Zou B Y 2010 Acta. Phys. Sin. 59 1902
Google Scholar
[17] 邱明辉, 刘惠平, 邹秀 2012 物理学报 61 155204
Google Scholar
Qiu M H, Liu H P, Zou X 2012 Acta. Phys. Sin. 61 155204
Google Scholar
[18] Gyergyek T, Kovačič J 2015 Phys. Plasmas 22 093511
Google Scholar
[19] Sharma G, Adhikari S, Moulick R, Kausik S S, Saikia B K 2020 Phys. Scr. 95 035605
Google Scholar
[20] 陈龙, 孙少娟, 姜博瑞, 段萍, 安宇豪, 杨叶慧 2021 物理学报 70 245201
Google Scholar
Chen L, Sun S J, Jiang B R, Duan P, An Y H, Yang Y H 2021 Acta. Phys. Sin. 70 245201
Google Scholar
[21] Liu J Y, Wang F, Sun J Z 2011 Phys. Plasmas 18 013506
Google Scholar
[22] Herring C, Nichols M H 1949 Rev. Mod. Phys. 21 185
Google Scholar
[23] 赵晓云, 刘金远, 段萍, 李世刚 2012 真空科学与技术学报 32 279
Google Scholar
Zhao X Y, Liu J Y, Duan P, Li S G 2012 Chin. J. Vacuum Sci. Technol. 32 279
Google Scholar
[24] Michaelson H B 1977 J. Appl. Phys. 48 4729
Google Scholar
[25] Sternberg N, Poggie J 2004 IEEE Trans. Plasma Sci. 32 2217
Google Scholar
[26] Bohdansky J 1983 Nucl. Instruments Methods Phys. Res. 2 587
[27] Hu W P, Sang C F, Sun Z Y, Wang D Z 2016 Fusion Eng. Des. 109 330
Google Scholar
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