Stability regions of dissipative trapped-ion instability
Stability regions of dissipative trapped-ion instability
复制标题
耗散捕获离子不稳定性的稳定区域
DOI：
10.1088/0029-5515/12/1/001
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发表时间：
1972
期刊：
影响因子：
3.3
通讯作者：
D. P. Kostomarov
中科院分区：
文献类型：
--
作者：
M. Rosenbluth;D. Ross;D. P. Kostomarov
本文研究了轴对称环形约束系统中耗散囚禁离子模的稳定性条件，并对几种托卡马克装置的等离子体不稳定的温度和磁场范围进行了数值计算。将碰撞阻尼作为囚禁离子速度空间中的边界层问题来研究。Fokker-Planck方程用变分形式求解，变分形式的阶数为νiR/r <$ω <$2 π/τi，其中R/r为纵横比，νiR/r为有效碰撞频率，τi为反弹时间。发现相对阻尼率与（νiR/rω）1/2 [In（rω/νiR）1/2]−3/2而不是νiR/rω成正比。将该阻尼项与电子驱动项（与rω/Rνe成正比）和共振非俘获离子引起的朗道阻尼项进行了比较。温度梯度的存在被认为是不稳定的。当dT/dr=0时，朗道项提供相对强的阻尼，但当d ln T/d In n > 2/3时改变符号。在后一种情况下，它的结论是，离子碰撞是不足以稳定的模式下，建议的机器的典型操作条件。当d ln T/d In n > 1.75时，离子碰撞阻尼本身也向增长方向发展，模式不能稳定。
Conditions for the stability of the dissipative trapped ion mode in axisymmetric toroidal confinement systems are investigated, and the ranges of temperature and magnetic field for which the plasma is expected to be unstable are calculated numerically for several proposed Tokamaks. The collisional damping is studied as a boundary layer problem in the velocity space of the trapped ions. The Fokker-Planck equation is solved by means of a variational form with the ordering νiR/r ≪ ω ≪2π/τi, where R/r is the aspect ratio, νiR/r is the effective collision frequency, and τi is the bounce time. The relative damping rate is found to be proportional to (νiR/rω) 1/2 [In (rω/νiR)1/2]−3/2 rather than νiR/rω. This damping term is compared with the electron driving term, which is proportional to rω/Rνe, and with the Landau damping caused by resonant untrapped ions. The presence of a temperature gradient is found to be destabilizing. The Landau term provides relatively strong damping when dT/dr=0 but changes sign when d ln T/d In n > 2/3. In the latter case it is concluded that ion collisions are insufficient to stabilize the mode under typical operating conditions of the proposed machines. Finally, if d ln T/d In n > 1.75 the ion collisional damping itself changes to growth, and the mode cannot be stabilized.