SUNIST单粒子模拟系统开发及应用研究
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摘要
单粒子运动研究对于理解环形等离子体物理有重要意义。通常采用的导心方法由于简化了回旋运动,而在某些条件下(例如具有大尺度的回旋运动或者回旋轨道被破坏时)的应用受到限制。论文采用洛伦兹模拟方法开发了环形等离子体单粒子模拟系统,研究了SUNIST球形托卡马克中的单粒子运动,并为SUNIST上的阿尔芬波电流驱动研究提供了运行参数空间的参考。
在粒子运动的洛伦兹模拟中,时间步长直接影响到计算的准确性和效率,但以往的研究都是通过经验选定合适的步长。论文通过对Boris算法和Runge-Kutta算法的比较,发现Boris算法在环形位形下并不是一个高效的选择,而且以往使用的Boris算法时间步长选择标准在复杂磁场中将导致错误的运动轨道。论文给出了一种通用的时间步长选择方法。以单粒子运动程序为基础,论文开发了一套具有良好管理性能和用户界面的单粒子模拟系统。
论文研究了SUNIST典型放电条件下的氢离子运动轨道。研究发现,如果不考虑波纹度的影响,SUNIST粒子运动具有和传统托卡马克下相似的特点。这是因为SUNIST较低的电流(< 50 KA)造成极向场即使在弱场侧仍远小于环向场,而且较低的温度(< 100 eV)使得轨道效应不明显。但是,如果电流提高至150 kA,粒子将出现瘦香蕉轨道和局部捕获轨道。另外, SUNIST紧凑的设计导致其具有高达±20%的环向场波纹度。考虑波纹度的影响,磁矩不再是一个绝热不变量,导致弱场侧复杂的粒子运动轨道。不过,在目前的参数下,波纹度造成的离子损失并不严重。但当温度提高到1keV时,离子约束变差,轨道损失增加,而SUNIST高的波纹度导致的随机波纹扩散进一步加剧了离子损失。
阿尔芬波电流驱动是SUNIST即将开展的探索性实验。论文对SUNIST中的捕获电子比例和回弹频率进行了模拟研究,并和标准模型磁场下的解析结果进行了对比。研究发现,在设计的阿尔芬波共振位置处电子捕获比例非常高,有可能研究阿尔芬波电流驱动中的捕获电子效应。通过比较回弹频率和有效碰撞频率的相对大小,论文给出了SUNIST装置中捕获电子有效存在的运行参数区间,为未来的阿尔芬波电流驱动实验提供了有价值的参考。
Single particle motion has an important role in understanding toroidal plasma physics. The guiding center method, where the gyro-motion is averaged, is not valid in some cases, for example, when the gyro-radius is large enough or when the orbit of gyro-motion is distorted. In this dissertation, a single particle simulation system was developed by employing the Lorentz method. Using this code, the behavior of single particle motion in the SUNIST spherical tokamak is investigated and, especially, results are applied to analyze the experimental conditions for Alfven wave current driving in the SUNIST.
Computation methods are considered throughout in the dissertation. In particle simulation by the Lorentz method, time step is a very important parameter to be chosen, which concerns the validity as well as the efficiency of computation. However, in previous codes, the time steps are chosen empirically. Boris method and Runge-Kutta method are compared both in the slab and toroidal geometry and it is found that Boris method is not a good choice in simulating toroidal plasma. Moreover, the criterion of time step for Boris method obtained previously leads to wrong orbits in complicated fields. Finally, a general method of choosing the time step is given in the dissertation. Based on the single particle code programmed, a comprehensive simulation system is developed which provides effective database management and a friendly interface.
Employing the code, the single particle motion of hydrogen ion is investigated for the SUNIST. At typical discharge parameters, regardless of the ripple of the toroidal field, particle orbits have similar behaviors as in conventional tokamaks, and, therefore, can be approximately described by analytical results from the guiding center method in the standard model magnetic field. It is partially because the poloidal field is less than the toroidal field even outside the torus due to relative low plasma current (<50 kA) in typical discharge at SUNIST, and partially because the plasma temperature is so low (< 100 eV) that the finite orbit effect is not significant. If the plasma current increases to 150 kA, magnetic islands will appear in the low field side and then thin banana orbits and local trapped orbits will appear as well as known in other spherical tokamaks. Another notable point is that there is a large ripple (±20%) of the toroidal field in the low field side of the SUNIST due to its compact design. Due to the ripple effect, magnetic moment is not a good adiabatic invariant any longer. The ripple results in some complex orbits of particle, such as ripple-trapped-particles which are limited in very small toroidal range. The ripple of the field also induces the enhancement of ion loss, although ion ripple loss at the SUNIST is not serious at current discharge parameters (ion temperature < 100 eV). However, when ion temperature increases to 1 keV, ion orbit loss become substantial and the stochastic ripple banana diffusion enhances the ion loss dramatically.
Alfven wave current drive experiment is scheduled at the SUNIST. The ratio of trapped electrons and their bounce frequency are simulated at experimental parameters. The simulation results are compared to the analytical results from the guiding center method in the standard model magnetic field as well. It is found that, at the expected Alfven resonance layer, the trapped ratio of electrons is very high, so it might be a good platform to investigate the role of trapped electrons in Alfven wave current drive. By comparing the average bounce frequency to the effective collision frequency, the regime where electrons are effectively trapped and not distorted by collisions is identified, which is determined by plasma parameters such as density, temperature and plasma current. These results provide scenarios for the Alfven wave current drive experiment at the SUNIST.
在粒子运动的洛伦兹模拟中,时间步长直接影响到计算的准确性和效率,但以往的研究都是通过经验选定合适的步长。论文通过对Boris算法和Runge-Kutta算法的比较,发现Boris算法在环形位形下并不是一个高效的选择,而且以往使用的Boris算法时间步长选择标准在复杂磁场中将导致错误的运动轨道。论文给出了一种通用的时间步长选择方法。以单粒子运动程序为基础,论文开发了一套具有良好管理性能和用户界面的单粒子模拟系统。
论文研究了SUNIST典型放电条件下的氢离子运动轨道。研究发现,如果不考虑波纹度的影响,SUNIST粒子运动具有和传统托卡马克下相似的特点。这是因为SUNIST较低的电流(< 50 KA)造成极向场即使在弱场侧仍远小于环向场,而且较低的温度(< 100 eV)使得轨道效应不明显。但是,如果电流提高至150 kA,粒子将出现瘦香蕉轨道和局部捕获轨道。另外, SUNIST紧凑的设计导致其具有高达±20%的环向场波纹度。考虑波纹度的影响,磁矩不再是一个绝热不变量,导致弱场侧复杂的粒子运动轨道。不过,在目前的参数下,波纹度造成的离子损失并不严重。但当温度提高到1keV时,离子约束变差,轨道损失增加,而SUNIST高的波纹度导致的随机波纹扩散进一步加剧了离子损失。
阿尔芬波电流驱动是SUNIST即将开展的探索性实验。论文对SUNIST中的捕获电子比例和回弹频率进行了模拟研究,并和标准模型磁场下的解析结果进行了对比。研究发现,在设计的阿尔芬波共振位置处电子捕获比例非常高,有可能研究阿尔芬波电流驱动中的捕获电子效应。通过比较回弹频率和有效碰撞频率的相对大小,论文给出了SUNIST装置中捕获电子有效存在的运行参数区间,为未来的阿尔芬波电流驱动实验提供了有价值的参考。
Single particle motion has an important role in understanding toroidal plasma physics. The guiding center method, where the gyro-motion is averaged, is not valid in some cases, for example, when the gyro-radius is large enough or when the orbit of gyro-motion is distorted. In this dissertation, a single particle simulation system was developed by employing the Lorentz method. Using this code, the behavior of single particle motion in the SUNIST spherical tokamak is investigated and, especially, results are applied to analyze the experimental conditions for Alfven wave current driving in the SUNIST.
Computation methods are considered throughout in the dissertation. In particle simulation by the Lorentz method, time step is a very important parameter to be chosen, which concerns the validity as well as the efficiency of computation. However, in previous codes, the time steps are chosen empirically. Boris method and Runge-Kutta method are compared both in the slab and toroidal geometry and it is found that Boris method is not a good choice in simulating toroidal plasma. Moreover, the criterion of time step for Boris method obtained previously leads to wrong orbits in complicated fields. Finally, a general method of choosing the time step is given in the dissertation. Based on the single particle code programmed, a comprehensive simulation system is developed which provides effective database management and a friendly interface.
Employing the code, the single particle motion of hydrogen ion is investigated for the SUNIST. At typical discharge parameters, regardless of the ripple of the toroidal field, particle orbits have similar behaviors as in conventional tokamaks, and, therefore, can be approximately described by analytical results from the guiding center method in the standard model magnetic field. It is partially because the poloidal field is less than the toroidal field even outside the torus due to relative low plasma current (<50 kA) in typical discharge at SUNIST, and partially because the plasma temperature is so low (< 100 eV) that the finite orbit effect is not significant. If the plasma current increases to 150 kA, magnetic islands will appear in the low field side and then thin banana orbits and local trapped orbits will appear as well as known in other spherical tokamaks. Another notable point is that there is a large ripple (±20%) of the toroidal field in the low field side of the SUNIST due to its compact design. Due to the ripple effect, magnetic moment is not a good adiabatic invariant any longer. The ripple results in some complex orbits of particle, such as ripple-trapped-particles which are limited in very small toroidal range. The ripple of the field also induces the enhancement of ion loss, although ion ripple loss at the SUNIST is not serious at current discharge parameters (ion temperature < 100 eV). However, when ion temperature increases to 1 keV, ion orbit loss become substantial and the stochastic ripple banana diffusion enhances the ion loss dramatically.
Alfven wave current drive experiment is scheduled at the SUNIST. The ratio of trapped electrons and their bounce frequency are simulated at experimental parameters. The simulation results are compared to the analytical results from the guiding center method in the standard model magnetic field as well. It is found that, at the expected Alfven resonance layer, the trapped ratio of electrons is very high, so it might be a good platform to investigate the role of trapped electrons in Alfven wave current drive. By comparing the average bounce frequency to the effective collision frequency, the regime where electrons are effectively trapped and not distorted by collisions is identified, which is determined by plasma parameters such as density, temperature and plasma current. These results provide scenarios for the Alfven wave current drive experiment at the SUNIST.
引文
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