-
中国首台准环对称仿星器(CFQS)是目前世界上唯一在建的准环对称仿星器. 本文利用回旋弗拉索夫代码GKV开展了CFQS中离子温度梯度模(ITG)的模拟研究. 在静电绝热条件下, 模拟的结果给出了CFQS中纯的ITG与密度梯度和温度梯度间的依赖关系. ITG的激发存在温度梯度阈值, 此温度梯度阈值受到密度梯度的影响. ITG的增长率不仅与密度梯度的绝对值相关, 还取决于密度梯度的正负, 负密度梯度对ITG具有强的抑制作用. 非绝热的模拟结果表明, 捕获电子对ITG具有去稳作用, 电子温度梯度也对ITG具有去稳作用. 当考虑电磁条件时, 有限的等离子体比压会抑制ITG, 导致ITG向阿尔芬离子温度梯度模/动理学气球模(AITG/ KBM)的转化. 当密度和温度梯度都较大时, KBM的最大增长率与密度梯度和温度梯度近似成线性关系.
-
关键词:
- 中国首台准环对称仿星器 /
- 离子温度梯度模 /
- 等离子体比压 /
- 动理学气球模
The Chinese First Quasi-axisymmetric Stellarator (CFQS) is now the only quasi-axisymmetric stellarator under construction in the world. In this work, ion temperature gradient (ITG) mode in CFQS is studied by using gyrokinetic Vlasov code GKV. The basic characteristics of the eletrtostatic ITG are separately given under the adiabatic condition and the non-adiabatic condition. There is a critical temperature gradient for ITG. The growth rate of ITG is proportional to the temperature gradient. Furthermore, the growth rate depends on not only the absolute value of density gradient, but also the plus or minus sign of the density gradient. The negative density gradient can strongly suppress the ITG. The kinetic electron can destabilize the ITG and the electron temperature gradient can also destabilize the ITG. For electromagnetic condition, the ITG modes can be suppressed by the finite plasma beta, and then a transition from ITG to Alfvenic ion temperature gradient mode/kinetic ballooning mode (AITG/KBM) comes into being. The maximum growth rate of KBM is linearly proportional to density gradient and temperature gradient when both gradients are large.-
Keywords:
- Chinese First Quasi-axisymmetric Stellarator /
- ion temperature gradient mode /
- plasma beta /
- kinetic ballooning mode
[1] Xu Y 2016 Matter Radiat. Extremes 1 192
Google Scholar
[2] Ho D D M 1987 Phys. Fluids 30 442
Google Scholar
[3] Boozer A H 1995 Plasma Phys. Controlled Fusion 37 A103
Google Scholar
[4] Subbotin A A, Mikhailov M I, Shafranov V D, Isaev M Yu, Nührenberg C, Nührenberg J, Zille R, Nemov V V, Kasilov SV, Kalyuzhnyj V N 2006 Nucl. Fusion 46 921
Google Scholar
[5] Garabedian P 1996 Phys. Plasmas 3 2483
Google Scholar
[6] Shimizu A, Liu H F, Isobe M, Okamura S, Nishimura S, Suzuki C, Xu Y, Zhang X, Liu B, Huang J, Wang X Q, Liu H, Tang C J, CFQS team 2018 Plasma Fusion Res. 13 3403123
Google Scholar
[7] Zarnstorff M C, Berry L A, Brooks A, Fredrickson1 E, Fu G Y, Hirshman S, Hudson, Ku L P, Lazarus E, Mikkelsen D, Monticello D, Neilson G H, Pomphrey N, Reiman A, Spong D, Strickler D, Boozer A, Cooper W A, Goldston R, Hatcher R, Isaev M, Kessel C, Ewandowski J L, Lyon J F, Merkel P, Mynick H, Nelson B E, Nuehrenberg C, Redi M, Reiersen W, Rutherford P, Sanchez R, Schmidt J, White R B 2001 Plasma Phys. Controlled Fusion 43 A237
Google Scholar
[8] Okamura S, Matsuoka K, Nishimura S, Isobe M, Nomura I, Suzuki C, Shimizu A, Murakami S, Nakajima N, Yokoyama M 2001 Nucl. Fusion 41 1865
Google Scholar
[9] Liu H F, Shimizu A, Isobe M, Okamura S, Nishimura S, Suzuki C, Xu Y, Zhang X, Liu B, Huang J, Wang X Q, Liu H, Tang C J, Yin D P, Wan Y, CFQS team 2018 Plasma Fusion Res. 13 3405067
Google Scholar
[10] Isobe M, Shimizu A, Liu H F, Liu H, Xiong G Z, Yin D P, Ogawa K, Yoshimura Y, Nakata M, Kinoshita S, Okamura S, tang C J, Xu Y, CFQS Team 2019 Plasma Fusion Res. 14 3402074
Google Scholar
[11] Liu H F, Shimizu A, Xu Y, Okamura S, Kinoshita S, Isobe M, Li Y B, Xiong G Z, Wang X Q, Huang J, Cheng J, Liu H, Zhang X, Yin D P, Wang Y, Murase T, Nakagawa S, Tang C J 2021 Nucl. Fusion 61 016014
Google Scholar
[12] Wang X Q, Xu Y, Shimizu A, Isobe M, Okamura S, Todo Y, Wang H, Liu H F, Huang J, Zhang X, Liu H, Cheng J, Tang C J, CFQS team 2021 Nucl. Fusion 61 036021
Google Scholar
[13] Horton W 1999 Rev. Mod. Phys. 71 735
Google Scholar
[14] Watanabe T H, Sugama H 2006 Nucl. Fusion 46 24
Google Scholar
[15] Nakata M, Nunami M, Sugama H 2017 Phys. Rev. Lett. 118 165002
Google Scholar
[16] Antonsen T M, Lane B 1980 Phys. Fluids 23 1205
Google Scholar
[17] Nakata M, Honda M, Yoshida M, Urano H, Nunami M, Maeyama S, Watanabe T H, Sugama H 2016 Nucl. Fusion 56 086010
Google Scholar
[18] Beer M A, Cowley S C, Hammett G W 1995 Phys. Plasmas 2 2687
Google Scholar
[19] Romanelli M, Bourdelle C, Dorland W 2004 Phys. Plasmas 11 3845
Google Scholar
[20] Du H R, Jhang H, Hahm T S, Dong J Q, Wang Z X 2017 Phys. Plasmas 24 122501
Google Scholar
[21] 沈勇, 董家齐, 徐红兵 2018 物理学报 67 195203
Google Scholar
Shen Y, Dong J Q, Xu H B 2018 Acta Phys. Sin. 67 195203
Google Scholar
[22] Baumgaertel J A, Hammett G W, Mikkelsen D R, Nunami M, Xanthopoulos P 2012 Phys. Plasmas 19 122306
Google Scholar
[23] Dominguez R R, Waltz R E 1988 Phys. Fluids 31 3147
Google Scholar
[24] Nunami M, Watanabe T H, Sugama H, Tanaka K 2011 Plasma Fusion Res. 6 1403001
Google Scholar
[25] Alcusón J A, Xanthopoulos P, Plunk G G, Helander P, Wilms F, Turkin Y, Stechow A von, Grulke O 2020 Plasma Phys. Controlled Fusion 62 035005
Google Scholar
[26] 罗一鸣, 王占辉, 陈佳乐, 吴雪科, 付彩龙, 何小雪, 刘亮, 杨曾辰, 李永高, 高金明, 杜华荣, 昆仑集成模拟设计组 2022 物理学报 71 075201
Google Scholar
Luo Y M, Wang Z H, Chen J L, Wu X K, Fu C L, He X X, Liu L, Yang Z C, Li Y G, Gao J M, Du H R, Kulun Integrated Simulation and Design Group 2022 Acta Phys. Sin. 71 075201
Google Scholar
[27] Mahmood M A, Rafiq T, Persson M, Weiland J 2009 Phys. Plasmas 16 022503
Google Scholar
[28] Dong J Q, Mahajan S M, Horton W 1997 Phys. Plasmas 4 755
Google Scholar
[29] Peeters A G, Angioni C, Apostoliceanu M, Jenko F, Ryter F, the ASDEX Upgrade team 2005 Phys. Plasmas 12 022505
Google Scholar
[30] Sandberg I, Isliker H, Pavlenko V P 2007 Phys. Plasmas 14 092504
Google Scholar
[31] Qi L, Kwon J, Hahm T S, Jo G 2016 Phys. Plasmas 23 062513
Google Scholar
[32] Malinov P, Zonca F 2005 J. Plasma Phys. 71 301
Google Scholar
[33] Kim J Y, Han H S 2017 Phys. Plasmas 24 072501
Google Scholar
[34] Pueschel M J, Jenko F 2010 Phys. Plasmas 17 062307
Google Scholar
[35] Xie H S, Lu Z X, Li B 2018 Phys. Plasmas 25 072106
Google Scholar
[36] Aleynikova K, Zocco A 2017 Phys. Plasmas 24 092106
Google Scholar
[37] Turnbull A D, Strait E J, Heidbrink W W, Chu M S, Duong H H, Greene J M, Lao L L, Taylor T S, Thompson S J 1993 Phys. Fluids B 5 2546
Google Scholar
[38] Dong J, Chen L, Zonca F 1999 Nucl. Fusion 39 1041
Google Scholar
[39] 谢华生 2015 博士学位论文 (杭州: 浙江大学)
Xie H S 2015 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
[40] Aleynikova K, Zocco1 A, Xanthopoulos1 P, Helander1 P, Nührenberg C 2018 J. Plasma Phys. 84 745840602
Google Scholar
-
图 1 不同密度梯度和温度梯度下绝热ITG的增长率波数谱 (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ Fig. 1. Growth rate spectra of ITG for different density gradients and temperature gradients: (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ .
图 2 不同密度梯度和温度梯度下绝热ITG的频率波数谱 (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ Fig. 2. Real frequency spectra of ITG for different density gradients and temperature gradients: (a)
$ {R}_{0}/{L}_{n}=-2 $ ; (b)$ {R}_{0}/{L}_{n}=2 $ ; (c)$ {R}_{0}/{L}_{n}=8 $ .
图 3 绝热ITG的最大增长率与密度梯度和温度梯度的关系
Fig. 3. Relationship of the maximum growth rate of adiabatic ITG to
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{T} $ .
图 4 考虑捕获电子效应后ITG的增长率(a)和频率(b)波数谱, 其中
$ {R}_{0}/{L}_{n}=2 $ , 电子温度梯度标长和离子温度梯度标长相等, 即$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ Fig. 4. Growth rate (a) and real frequency spectra (b) of kinetic ITG for
$ {R}_{0}/{L}_{n}=2 $ . Here,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ .
图 5 考虑捕获电子效应后ITG/TE-ITG最大增长率与密度梯度和温度梯度的关系, 其中
$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}} $ Fig. 5. Contour map of the maximum growth rate of kinetic ITG/TE-ITG mode vs.
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{T} $ . Here,${R}_{0}/ {L}_{{T}_{\mathrm{e}}} $ $ ={R}_{0}/{L}_{{T}_{\mathrm{i}}}$ .
图 6 考虑捕获电子效应后ITG的增长率(a)和频率波数谱(b), 其中
$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 6. Growth rate (a) and real frequency spectra (b) of kinetic ITG for
$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ .
图 7 考虑捕获电子效应后ITG最大增长率与密度梯度和离子温度梯度的关系, 其中
$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 7. Contour map of the maximum growth rate of kinetic ITG vs.
$ {R}_{0}/{L}_{n} $ and$ {R}_{0}/{L}_{{T}_{\mathrm{i}}} $ . Here,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ .
图 8 当波数
$ {k}_{y}{\rho }_{\mathrm{i}}=1.0 $ 时增长率(a)与频率(b)随比压的变化(其中,$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}={R}_{0}/{L}_{{T}_{\mathrm{i}}}=8 $ ), 图(a)中的箭头是从ITG转变为KBM的转变点Fig. 8. Growth rates (a) and real frequencies (b) vs.
$ \beta $ for$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{i}}}={R}_{0}/{{L}}_{{{T}}_{\mathrm{e}}}=8 $ at$ {k}_{y}{\rho }_{\mathrm{i}}=1.0 $ . The arrow is plotted in panel (a) to point the transition point from ITG to KBM.
图 9 取
$\beta =1{\text{%}}$ 时, KBM的增长率(a)和频率(b)波数谱, 其中$ {R}_{0}/{L}_{n}=2 $ ,$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ Fig. 9. Growth rate (a) and real frequency spectra (b) of KBM for
$ {R}_{0}/{L}_{n}=2 $ and$ {R}_{0}/{L}_{{T}_{\mathrm{e}}}=8 $ . Here,$\beta =1{\text{%}}$ . -
[1] Xu Y 2016 Matter Radiat. Extremes 1 192
Google Scholar
[2] Ho D D M 1987 Phys. Fluids 30 442
Google Scholar
[3] Boozer A H 1995 Plasma Phys. Controlled Fusion 37 A103
Google Scholar
[4] Subbotin A A, Mikhailov M I, Shafranov V D, Isaev M Yu, Nührenberg C, Nührenberg J, Zille R, Nemov V V, Kasilov SV, Kalyuzhnyj V N 2006 Nucl. Fusion 46 921
Google Scholar
[5] Garabedian P 1996 Phys. Plasmas 3 2483
Google Scholar
[6] Shimizu A, Liu H F, Isobe M, Okamura S, Nishimura S, Suzuki C, Xu Y, Zhang X, Liu B, Huang J, Wang X Q, Liu H, Tang C J, CFQS team 2018 Plasma Fusion Res. 13 3403123
Google Scholar
[7] Zarnstorff M C, Berry L A, Brooks A, Fredrickson1 E, Fu G Y, Hirshman S, Hudson, Ku L P, Lazarus E, Mikkelsen D, Monticello D, Neilson G H, Pomphrey N, Reiman A, Spong D, Strickler D, Boozer A, Cooper W A, Goldston R, Hatcher R, Isaev M, Kessel C, Ewandowski J L, Lyon J F, Merkel P, Mynick H, Nelson B E, Nuehrenberg C, Redi M, Reiersen W, Rutherford P, Sanchez R, Schmidt J, White R B 2001 Plasma Phys. Controlled Fusion 43 A237
Google Scholar
[8] Okamura S, Matsuoka K, Nishimura S, Isobe M, Nomura I, Suzuki C, Shimizu A, Murakami S, Nakajima N, Yokoyama M 2001 Nucl. Fusion 41 1865
Google Scholar
[9] Liu H F, Shimizu A, Isobe M, Okamura S, Nishimura S, Suzuki C, Xu Y, Zhang X, Liu B, Huang J, Wang X Q, Liu H, Tang C J, Yin D P, Wan Y, CFQS team 2018 Plasma Fusion Res. 13 3405067
Google Scholar
[10] Isobe M, Shimizu A, Liu H F, Liu H, Xiong G Z, Yin D P, Ogawa K, Yoshimura Y, Nakata M, Kinoshita S, Okamura S, tang C J, Xu Y, CFQS Team 2019 Plasma Fusion Res. 14 3402074
Google Scholar
[11] Liu H F, Shimizu A, Xu Y, Okamura S, Kinoshita S, Isobe M, Li Y B, Xiong G Z, Wang X Q, Huang J, Cheng J, Liu H, Zhang X, Yin D P, Wang Y, Murase T, Nakagawa S, Tang C J 2021 Nucl. Fusion 61 016014
Google Scholar
[12] Wang X Q, Xu Y, Shimizu A, Isobe M, Okamura S, Todo Y, Wang H, Liu H F, Huang J, Zhang X, Liu H, Cheng J, Tang C J, CFQS team 2021 Nucl. Fusion 61 036021
Google Scholar
[13] Horton W 1999 Rev. Mod. Phys. 71 735
Google Scholar
[14] Watanabe T H, Sugama H 2006 Nucl. Fusion 46 24
Google Scholar
[15] Nakata M, Nunami M, Sugama H 2017 Phys. Rev. Lett. 118 165002
Google Scholar
[16] Antonsen T M, Lane B 1980 Phys. Fluids 23 1205
Google Scholar
[17] Nakata M, Honda M, Yoshida M, Urano H, Nunami M, Maeyama S, Watanabe T H, Sugama H 2016 Nucl. Fusion 56 086010
Google Scholar
[18] Beer M A, Cowley S C, Hammett G W 1995 Phys. Plasmas 2 2687
Google Scholar
[19] Romanelli M, Bourdelle C, Dorland W 2004 Phys. Plasmas 11 3845
Google Scholar
[20] Du H R, Jhang H, Hahm T S, Dong J Q, Wang Z X 2017 Phys. Plasmas 24 122501
Google Scholar
[21] 沈勇, 董家齐, 徐红兵 2018 物理学报 67 195203
Google Scholar
Shen Y, Dong J Q, Xu H B 2018 Acta Phys. Sin. 67 195203
Google Scholar
[22] Baumgaertel J A, Hammett G W, Mikkelsen D R, Nunami M, Xanthopoulos P 2012 Phys. Plasmas 19 122306
Google Scholar
[23] Dominguez R R, Waltz R E 1988 Phys. Fluids 31 3147
Google Scholar
[24] Nunami M, Watanabe T H, Sugama H, Tanaka K 2011 Plasma Fusion Res. 6 1403001
Google Scholar
[25] Alcusón J A, Xanthopoulos P, Plunk G G, Helander P, Wilms F, Turkin Y, Stechow A von, Grulke O 2020 Plasma Phys. Controlled Fusion 62 035005
Google Scholar
[26] 罗一鸣, 王占辉, 陈佳乐, 吴雪科, 付彩龙, 何小雪, 刘亮, 杨曾辰, 李永高, 高金明, 杜华荣, 昆仑集成模拟设计组 2022 物理学报 71 075201
Google Scholar
Luo Y M, Wang Z H, Chen J L, Wu X K, Fu C L, He X X, Liu L, Yang Z C, Li Y G, Gao J M, Du H R, Kulun Integrated Simulation and Design Group 2022 Acta Phys. Sin. 71 075201
Google Scholar
[27] Mahmood M A, Rafiq T, Persson M, Weiland J 2009 Phys. Plasmas 16 022503
Google Scholar
[28] Dong J Q, Mahajan S M, Horton W 1997 Phys. Plasmas 4 755
Google Scholar
[29] Peeters A G, Angioni C, Apostoliceanu M, Jenko F, Ryter F, the ASDEX Upgrade team 2005 Phys. Plasmas 12 022505
Google Scholar
[30] Sandberg I, Isliker H, Pavlenko V P 2007 Phys. Plasmas 14 092504
Google Scholar
[31] Qi L, Kwon J, Hahm T S, Jo G 2016 Phys. Plasmas 23 062513
Google Scholar
[32] Malinov P, Zonca F 2005 J. Plasma Phys. 71 301
Google Scholar
[33] Kim J Y, Han H S 2017 Phys. Plasmas 24 072501
Google Scholar
[34] Pueschel M J, Jenko F 2010 Phys. Plasmas 17 062307
Google Scholar
[35] Xie H S, Lu Z X, Li B 2018 Phys. Plasmas 25 072106
Google Scholar
[36] Aleynikova K, Zocco A 2017 Phys. Plasmas 24 092106
Google Scholar
[37] Turnbull A D, Strait E J, Heidbrink W W, Chu M S, Duong H H, Greene J M, Lao L L, Taylor T S, Thompson S J 1993 Phys. Fluids B 5 2546
Google Scholar
[38] Dong J, Chen L, Zonca F 1999 Nucl. Fusion 39 1041
Google Scholar
[39] 谢华生 2015 博士学位论文 (杭州: 浙江大学)
Xie H S 2015 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese)
[40] Aleynikova K, Zocco1 A, Xanthopoulos1 P, Helander1 P, Nührenberg C 2018 J. Plasma Phys. 84 745840602
Google Scholar
-
[1] 侯玉梅, 陈伟, 邹云鹏, 于利明, 石中兵, 段旭如. HL-2A装置高能量离子驱动的比压阿尔芬本征模的扫频行为. 物理学报, 2023, 72(21): 215211. doi: 10.7498/aps.72.20230726 [2] 周利娜, 胡汉卿, 刘钺强, 段萍, 陈龙, 张瀚予. 等离子体对共振磁扰动的流体和动理学响应的模拟研究. 物理学报, 2023, 72(7): 075202. doi: 10.7498/aps.72.20222196 [3] 苏祥, 王先驱, 符添, 许宇鸿. CFQS准环对称仿星器低 $\boldsymbol \beta$ 等离子体中三维磁岛的抑制机制. 物理学报, 2023, 72(21): 215205. doi: 10.7498/aps.72.20230546[4] 陈凝飞, 魏广宇, 仇志勇. 径向电场对离子温度梯度模稳定性的影响. 物理学报, 2023, 72(21): 215217. doi: 10.7498/aps.72.20230798 [5] 肖士妍, 贾大功, 聂安然, 余辉, 吉喆, 张红霞, 刘铁根. 开放式多通道多芯少模光纤表面等离子体共振生物传感器. 物理学报, 2020, 69(13): 137802. doi: 10.7498/aps.69.20200353 [6] 沈勇, 董家齐, 徐红兵. 托卡马克离子温度梯度湍流输运同位素定标修正中杂质的影响. 物理学报, 2018, 67(19): 195203. doi: 10.7498/aps.67.20180703 [7] 谢会乔, 谭熠, 刘阳青, 王文浩, 高喆. 中国联合球形托卡马克氦放电等离子体的碰撞辐射模型及其在谱线比法诊断的应用. 物理学报, 2014, 63(12): 125203. doi: 10.7498/aps.63.125203 [8] 邹长林, 叶文华, 卢新培. 一维动理学数值模拟激光与等离子体的相互作用. 物理学报, 2014, 63(8): 085207. doi: 10.7498/aps.63.085207 [9] 陆赫林, 陈忠勇, 李跃勋, 杨恺. 磁场剪切对离子温度梯度模带状流产生的影响. 物理学报, 2011, 60(8): 085202. doi: 10.7498/aps.60.085202 [10] 陆赫林, 王顺金. 离子温度梯度模湍流的带状流最小自由度模型. 物理学报, 2009, 58(1): 354-362. doi: 10.7498/aps.58.354 [11] 简广德, 董家齐. 环形等离子体中电子温度梯度不稳定性的粒子模拟. 物理学报, 2003, 52(7): 1656-1662. doi: 10.7498/aps.52.1656 [12] 黄朝松, 李钧. 等离子体交换不稳定性的模耦合理论. 物理学报, 1992, 41(5): 783-791. doi: 10.7498/aps.41.783 [13] 张澄, 邓晓华, 霍裕平. 输运与撕裂模相互作用下等离子体的时空结构. 物理学报, 1990, 39(10): 1573-1582. doi: 10.7498/aps.39.1573 [14] 汪茂泉. 流动等离子体对托卡马克中撕裂模的影响. 物理学报, 1986, 35(9): 1227-1232. doi: 10.7498/aps.35.1227 [15] 潘传红, 丁厚昌, 吴灵桥. 耗散气球模动力理论. 物理学报, 1986, 35(11): 1411-1425. doi: 10.7498/aps.35.1411 [16] 董家齐. 有磁辫等离子体的双撕裂模研究. 物理学报, 1984, 33(10): 1341-1349. doi: 10.7498/aps.33.1341 [17] 顾永年. 小环径比锐边界等离子体的扭曲模不稳定性. 物理学报, 1984, 33(4): 554-560. doi: 10.7498/aps.33.554 [18] 石秉仁. 环流器等离子体高n气球模的第二稳定区. 物理学报, 1983, 32(11): 1398-1406. doi: 10.7498/aps.32.1398 [19] 郭世宠, 沈解伍, 陈骝, 蔡诗东. 离子温度梯度不稳定性的解析理论. 物理学报, 1982, 31(1): 17-29. doi: 10.7498/aps.31.17 [20] 石秉仁. 高比压环流器等离子体位形的稳定性. 物理学报, 1982, 31(10): 1308-1316. doi: 10.7498/aps.31.1308
下载:
计量
- 文章访问数: 5701
- PDF下载量: 89
- 被引次数: 0
