Abstract:

In general, the energy distribution of energetic particles is bump-on-tail when both the neutral beam injection and electron/ion cyclotron resonant heating are used in tokamak plasma experiment. It is easier to induce instability for energy distribution profile with positive energy gradient regions existing such as the bump-on-tail. Therefore, a new dispersion function is introduced in dispersion relation due to bump-on-tail of the energy distribution. The calculation method of the new dispersion function is studied. T results show that the real and imaginary parts of dispersion functions are odd and even functions respectively. There are 2 to 4 extremes for real parts of the dispersion function and the positions of the extremes are dependent on Δ , the gradient of the energy distribution, whereas there are 1 to 3 extremes for imaginary parts and the positions of these extremes are independent of Δ . Both the real and imaginary parts of the dispersion function go to zero when the arguments of Z_t go to infinity. The calculated values agree very well with those given in dispersion function table when the bump-on-tail distribution goes to Maxwellian distribution.

Key words: Energetic particles, Bump-on-tail, Dispersion function

摘要：

当同时使用离子(或电子)回旋及中性束注入方式加热等离子体时，高能量粒子的能量分布函数一般应为尾部隆起(简称尾隆)分布。这种具有正能量梯度区域的分布函数更容易激发不稳定性，同时由于分布函数尾部隆起，在色散关系中引入了新的色散函数。主要研究了这种新色散函数的计算方法，结果表明：色散函数实部是关于原点对称的奇函数；而虚部则是关于纵轴对称的偶函数。色散函数的实部有2~4 个极值点且极值点的位置与尾隆分布函数的能量梯度Δ 有关、虚部有1~3 个极值点但极值点位置与Δ 无关。当其宗量趋于无穷大时，色散函数的值趋于零。当尾隆分布趋近于麦克斯韦分布时，用该方法计算的结果与色散函数表中给出的结果非常吻合。

关键词: 高能量粒子, 尾隆分布, 色散函数