聚变装置中边界等离子体的磁鞘层特性
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摘要
采用流体模型研究了聚变装置中边界等离子体的磁鞘层结构,考虑了离子磁化和离子热压强的作用,研究了磁场强度、磁场方向、等离子体密度、离子温度等对鞘层特性的影响,得到了离子温度效应下的壁面悬浮电势和等离子体磁鞘层的玻姆判据。
本文以氢离子及其同位素离子为例研究了各种参数下等离子体鞘层的特性。当磁场倾斜的角度增大时,壁面电势的绝对值也增大,鞘层厚度先减小后增大。在鞘边净电荷和离子密度出现了振荡,这是因为在强磁场的作用下离子做回旋运动,离子密度在鞘边出现了起伏。角度越大,振荡越剧烈；当磁场大小增加时,鞘层厚度会减小；当离子温度增加时,鞘层厚度会减小；当等离子体的密度增加时,鞘层厚度也会减小,这是与无磁化等离子体鞘层的性质是一致的。密度较低时,在鞘边离子密度和净电荷密度会出现一个峰值；当离子质量越大时,壁面电势的绝对值越大,鞘层厚度也越大。
由于聚变装置中边界等离子体的温度为十几到上百电子伏特,电子或离子与器壁相互作用会产生二次电子,因此本文又研究了二次电子发射对等离子体磁鞘层特性的影响。二次电子的发射使得壁面电势的绝对值和鞘层厚度都减小,二次电子发射系数越大,则壁面电势的绝对值和鞘层厚度越小。在考虑二次电子发射时,通过对磁场大小、磁场方向、不同等离子体等情况下对等离子体磁鞘层特性影响的研究,发现这时得到的结果与无二次电子发射时的结果是一致的。
通过对二次电子在鞘层内的密度分布研究,发现离子质量越大,鞘层内二次电子的密度越小,这是因为离子质量越大,壁面电势的绝对值越大,电子到达壁面的速度和能量越小,电子与壁面相互作用产生的二次电子越少；离子温度越高,鞘层内二次电子的密度越大,这是因为离子温度越高,壁面电势的绝对值越小,则电子到达壁面的速度和能量越大,因此电子与壁面相互作用产生的二次电子也越多。
The magnetic sheath structure of edge plasma in fusion device is investigated by using fluid dynamics method. Ion thermal pressure and ion magnetization are considered and the effects of the intensity of magnetic field, magnetic field direction, different plasma density and ion temperature on the character of plasma sheath are researched. And the suspended potential of the wall and the Bohm criterion of plasma magnetized sheath under the ion temperature effect are also deduced.
Take H ion and its isotope as an example, we do research on the character of plasma sheath under many parameters. We get that the absolute of wall potential increase when the magnetic field tilt angle increase, and sheath thickness decrease first and then increase. As angle increasing, the density of net charge and ion appear vibration for the ion gyromotion under the strong magnetic field.; When the intensity of magnetic field increases, the sheath thickness decreases.; When ion temperature is higher,the sheath thickness is lower; When the plasma density is higher, the sheath thickness is lower.The result is the same with the character of plasma sheath without magnetization. In lower plasma density, the density of ion and net charge appear peak value at the boundary of plasma sheath; When ion mass is higher, the absolute value of wall potential is higher, and the sheath thickness is higher.
Because the temperature of edge plasma in fusion device is more than ten to one hundred electron volt, the interaction between high energy electrons or ions and wall may creates secondary electrons, and the effects of secondary electrons to the character of plasma sheath are also researched. Secondary electrons emission makes that the absolute value of wall potential and sheath thickness decrease. The coefficient of secondary electrons is higher, and the absolute value of wall potential and sheath thickness are lower. On the considering of secondary electrons emission, through researching the effects of the intensity of magnetic field, magnetic field direction, different plasma density and ion temperature on the character of plasma sheath, we find that the results are the same with the condition of no secondary electrons emission.
Based on the research of secondary electrons density distribution in the sheath, we find that ion mass is higher and the density distribution of secondary electrons is lower. It's because that ion mass is higher, absolute of wall potential higher, the velocity and energy of electrons at the wall lower, and the secondary electrons produced by the interaction of electrons and wall are less.; Ion temperature is higher, and the density of secondary electrons is higher. It's because that ion temperature is higher, absolute of wall potential lower, the velocity and energy of electrons at the wall higher, and the secondary electrons produced by the interaction of electrons and wall are more.
本文以氢离子及其同位素离子为例研究了各种参数下等离子体鞘层的特性。当磁场倾斜的角度增大时,壁面电势的绝对值也增大,鞘层厚度先减小后增大。在鞘边净电荷和离子密度出现了振荡,这是因为在强磁场的作用下离子做回旋运动,离子密度在鞘边出现了起伏。角度越大,振荡越剧烈；当磁场大小增加时,鞘层厚度会减小；当离子温度增加时,鞘层厚度会减小；当等离子体的密度增加时,鞘层厚度也会减小,这是与无磁化等离子体鞘层的性质是一致的。密度较低时,在鞘边离子密度和净电荷密度会出现一个峰值；当离子质量越大时,壁面电势的绝对值越大,鞘层厚度也越大。
由于聚变装置中边界等离子体的温度为十几到上百电子伏特,电子或离子与器壁相互作用会产生二次电子,因此本文又研究了二次电子发射对等离子体磁鞘层特性的影响。二次电子的发射使得壁面电势的绝对值和鞘层厚度都减小,二次电子发射系数越大,则壁面电势的绝对值和鞘层厚度越小。在考虑二次电子发射时,通过对磁场大小、磁场方向、不同等离子体等情况下对等离子体磁鞘层特性影响的研究,发现这时得到的结果与无二次电子发射时的结果是一致的。
通过对二次电子在鞘层内的密度分布研究,发现离子质量越大,鞘层内二次电子的密度越小,这是因为离子质量越大,壁面电势的绝对值越大,电子到达壁面的速度和能量越小,电子与壁面相互作用产生的二次电子越少；离子温度越高,鞘层内二次电子的密度越大,这是因为离子温度越高,壁面电势的绝对值越小,则电子到达壁面的速度和能量越大,因此电子与壁面相互作用产生的二次电子也越多。
The magnetic sheath structure of edge plasma in fusion device is investigated by using fluid dynamics method. Ion thermal pressure and ion magnetization are considered and the effects of the intensity of magnetic field, magnetic field direction, different plasma density and ion temperature on the character of plasma sheath are researched. And the suspended potential of the wall and the Bohm criterion of plasma magnetized sheath under the ion temperature effect are also deduced.
Take H ion and its isotope as an example, we do research on the character of plasma sheath under many parameters. We get that the absolute of wall potential increase when the magnetic field tilt angle increase, and sheath thickness decrease first and then increase. As angle increasing, the density of net charge and ion appear vibration for the ion gyromotion under the strong magnetic field.; When the intensity of magnetic field increases, the sheath thickness decreases.; When ion temperature is higher,the sheath thickness is lower; When the plasma density is higher, the sheath thickness is lower.The result is the same with the character of plasma sheath without magnetization. In lower plasma density, the density of ion and net charge appear peak value at the boundary of plasma sheath; When ion mass is higher, the absolute value of wall potential is higher, and the sheath thickness is higher.
Because the temperature of edge plasma in fusion device is more than ten to one hundred electron volt, the interaction between high energy electrons or ions and wall may creates secondary electrons, and the effects of secondary electrons to the character of plasma sheath are also researched. Secondary electrons emission makes that the absolute value of wall potential and sheath thickness decrease. The coefficient of secondary electrons is higher, and the absolute value of wall potential and sheath thickness are lower. On the considering of secondary electrons emission, through researching the effects of the intensity of magnetic field, magnetic field direction, different plasma density and ion temperature on the character of plasma sheath, we find that the results are the same with the condition of no secondary electrons emission.
Based on the research of secondary electrons density distribution in the sheath, we find that ion mass is higher and the density distribution of secondary electrons is lower. It's because that ion mass is higher, absolute of wall potential higher, the velocity and energy of electrons at the wall lower, and the secondary electrons produced by the interaction of electrons and wall are less.; Ion temperature is higher, and the density of secondary electrons is higher. It's because that ion temperature is higher, absolute of wall potential lower, the velocity and energy of electrons at the wall higher, and the secondary electrons produced by the interaction of electrons and wall are more.
引文
[1]L. Tons and I. Langmuir. Oscillations in ionized Gases[J]. Phys. Rev.,1929, 33(2):195-210.
[2]邱励俭.聚变能及其应用[M].北京：科学出版社,2004.
[3]石秉仁.磁约束聚变原理与实践[M].北京：原子能出版社,1999.
[4]朱士尧.核聚变原理[M].合肥：中国科学技术大学出版社,1992.
[5]I. Langmuir, The interaction of Electron and positive ion Space Charges in Cathode Sheaths[J]. Phys. Rev.,1929,33(6):954-989.
[6]Self S A. Exact Solution of Collisionless Plasma-Sheath Equation [J]. Phys. Fluids, 1963,6(12):1762-1768.
[7]Emmert G A, Wieland R M, Mense A T, Davidson J N. Electric sheath and presheath in a collisionless, finite ion temperature plasma [J]. Phys. Fluids,1980,23(4): 803-812.
[8]Valentini H B. Bohm criterion for the collisional sheath [J]. Phys. Plasmas,1996, 3(4):1459-1461.
[9]戴忠玲,王友年,马腾才.射频等离子体鞘层动力学模型[J].物理学报,2001,50(12)：2398-2402.
[10]谷云鹏,马腾才.粒子束对玻姆鞘层判据的影响[J].物理学报,2003,52(5)：1196-1202.
[11]王道泳,马锦秀,李毅人,张文贵.等离子体中热阴极鞘层的结构[J].物理学报,2009,58(12)：8432-8439.
[12]Chodura R. Plasma-wall transition in an oblique magnetic field [J]. Phy. Fluids, 1982,25 (9):1628-1633.
[13]Valsaque F, Manfredi G. Numerical study of plasma-wall transition in an oblique magnetic field [J]. J. Nucl. Mat,2001,290-293:763-767.
[14]Ahedo E. Structure of the plasma-wall interaction in an oblique magnetic field [J]. Phys. Plasma,1997,4(12):4419-4430.
[15]Beilis I I, Keidar M. Sheath and presheath structure in the plasma-wall transition layer in an oblique magnetic field [J]. Phys. Plasmas,1998,5(5):1545-1553.
[16]Tskhakaya D D, Shukla P K, Eliasson B E, Kuhn S. Theory of the plasma sheath in a magnetic field parallel to the wall [J]. Phys. Plasma 2005,12(10).
[17]邹秀,刘惠平,谷秀娥.磁化等离子体的鞘层结构[J].物理学报,2008,57(8)：5111-5116.
[18]邹秀,籍延坤,邹滨雁.斜磁场中碰撞等离子体鞘层的玻姆判据[J].物理学报,2010,59(3)：1902-1906.
[19]邹秀,刘金远,于正汹,宫野,刘悦,王晓钢.磁场中等离子体鞘层的结构[J].物理学报,2004,53(10)：3409-3412.
[20]Bergman A. Two-dimensional particle simulation of Langmuir probe sheaths whith oblique magnetic field [J]. Phys. Plasma,1994,1(11):3598-3606.
[21]邹秀,邹滨雁,刘惠平.外加磁场对碰撞射频鞘层离子能量分布的影响[J].物理学报,2009 58(9)：6392-6396.
[22]Kim G H, Hershkowitz N, Diebold D A, Cho M H. Magnetic and collisional effects on presheaths [J]. Phys. Plasmas,1995,2(8):3222.
[23]Stangeby P C. The Bohm-Chodura plasma sheath criterion [J]. Phys. Plasma,1995, 2(3):702-706.
[24]王正汹,刘金远,邹秀,刘悦,王晓钢.尘埃等离子体鞘层的玻姆判据[J].物理学报,2004,53(3)：793-797.
[25]Singha B, Sarma A, Chutia J. Experimental observation of sheath and magnetic presheath over an oblique metallic plate in the presence of a magnetic field [J]. Phys. Plasmas,2002,9(2):683-690.
[26]G. D. Hobbs and J. A. Wesson. Heat flow through a Langmuir sheath in the presence of electron emission[J]. Plasma Phys,1967,9:85-87.
[27]P. C. Stangeby. The Bohm-chodura plasma sheath criterion. Physics of plasma[J]. 1995,2:702-706.
[28]R. N. Franklin, W.E.Han. The stability of the plasma-sheath with secondary emission[J]. Plasma Physics and controlled Fusion,1998,30:771-784.
[29]L. A.. Schwager, C.K. Birdsall. Collector and source sheaths of a finite ion temperature plasma[J]. Phys. FluidsB,1990,2(5):1057-1068.
[30]A.Bergman. Transport of edge-localizde mode energy in scrape-off layer in the presence of collisionless fast electrons[J]. Nucl. Fusion,2002,42:1162-1167.
[31]D. Tsknakaya, S. Kuhn. Influence of initial energy on the effective secondary electron emission coeffient in the presence of an oblique magnetic field[J]. Contrib. Plasma Phys,2000,40:484-490.
[2]邱励俭.聚变能及其应用[M].北京：科学出版社,2004.
[3]石秉仁.磁约束聚变原理与实践[M].北京：原子能出版社,1999.
[4]朱士尧.核聚变原理[M].合肥：中国科学技术大学出版社,1992.
[5]I. Langmuir, The interaction of Electron and positive ion Space Charges in Cathode Sheaths[J]. Phys. Rev.,1929,33(6):954-989.
[6]Self S A. Exact Solution of Collisionless Plasma-Sheath Equation [J]. Phys. Fluids, 1963,6(12):1762-1768.
[7]Emmert G A, Wieland R M, Mense A T, Davidson J N. Electric sheath and presheath in a collisionless, finite ion temperature plasma [J]. Phys. Fluids,1980,23(4): 803-812.
[8]Valentini H B. Bohm criterion for the collisional sheath [J]. Phys. Plasmas,1996, 3(4):1459-1461.
[9]戴忠玲,王友年,马腾才.射频等离子体鞘层动力学模型[J].物理学报,2001,50(12)：2398-2402.
[10]谷云鹏,马腾才.粒子束对玻姆鞘层判据的影响[J].物理学报,2003,52(5)：1196-1202.
[11]王道泳,马锦秀,李毅人,张文贵.等离子体中热阴极鞘层的结构[J].物理学报,2009,58(12)：8432-8439.
[12]Chodura R. Plasma-wall transition in an oblique magnetic field [J]. Phy. Fluids, 1982,25 (9):1628-1633.
[13]Valsaque F, Manfredi G. Numerical study of plasma-wall transition in an oblique magnetic field [J]. J. Nucl. Mat,2001,290-293:763-767.
[14]Ahedo E. Structure of the plasma-wall interaction in an oblique magnetic field [J]. Phys. Plasma,1997,4(12):4419-4430.
[15]Beilis I I, Keidar M. Sheath and presheath structure in the plasma-wall transition layer in an oblique magnetic field [J]. Phys. Plasmas,1998,5(5):1545-1553.
[16]Tskhakaya D D, Shukla P K, Eliasson B E, Kuhn S. Theory of the plasma sheath in a magnetic field parallel to the wall [J]. Phys. Plasma 2005,12(10).
[17]邹秀,刘惠平,谷秀娥.磁化等离子体的鞘层结构[J].物理学报,2008,57(8)：5111-5116.
[18]邹秀,籍延坤,邹滨雁.斜磁场中碰撞等离子体鞘层的玻姆判据[J].物理学报,2010,59(3)：1902-1906.
[19]邹秀,刘金远,于正汹,宫野,刘悦,王晓钢.磁场中等离子体鞘层的结构[J].物理学报,2004,53(10)：3409-3412.
[20]Bergman A. Two-dimensional particle simulation of Langmuir probe sheaths whith oblique magnetic field [J]. Phys. Plasma,1994,1(11):3598-3606.
[21]邹秀,邹滨雁,刘惠平.外加磁场对碰撞射频鞘层离子能量分布的影响[J].物理学报,2009 58(9)：6392-6396.
[22]Kim G H, Hershkowitz N, Diebold D A, Cho M H. Magnetic and collisional effects on presheaths [J]. Phys. Plasmas,1995,2(8):3222.
[23]Stangeby P C. The Bohm-Chodura plasma sheath criterion [J]. Phys. Plasma,1995, 2(3):702-706.
[24]王正汹,刘金远,邹秀,刘悦,王晓钢.尘埃等离子体鞘层的玻姆判据[J].物理学报,2004,53(3)：793-797.
[25]Singha B, Sarma A, Chutia J. Experimental observation of sheath and magnetic presheath over an oblique metallic plate in the presence of a magnetic field [J]. Phys. Plasmas,2002,9(2):683-690.
[26]G. D. Hobbs and J. A. Wesson. Heat flow through a Langmuir sheath in the presence of electron emission[J]. Plasma Phys,1967,9:85-87.
[27]P. C. Stangeby. The Bohm-chodura plasma sheath criterion. Physics of plasma[J]. 1995,2:702-706.
[28]R. N. Franklin, W.E.Han. The stability of the plasma-sheath with secondary emission[J]. Plasma Physics and controlled Fusion,1998,30:771-784.
[29]L. A.. Schwager, C.K. Birdsall. Collector and source sheaths of a finite ion temperature plasma[J]. Phys. FluidsB,1990,2(5):1057-1068.
[30]A.Bergman. Transport of edge-localizde mode energy in scrape-off layer in the presence of collisionless fast electrons[J]. Nucl. Fusion,2002,42:1162-1167.
[31]D. Tsknakaya, S. Kuhn. Influence of initial energy on the effective secondary electron emission coeffient in the presence of an oblique magnetic field[J]. Contrib. Plasma Phys,2000,40:484-490.