一维Fokker-Planck方程的有限体积法求解及其在中性束注入加热中的应用

One-dimensional Fokker-Planck Equation Solving by Finite Volume Method and Its Application in Neutral Beam Injection Heating

采用有限体积法数值求解一维Fokker-Planck方程,通过模拟电子自碰撞过程进行程序校验。研究表明,有限体积法能高效求解Fokker-Planck方程,能确保分布函数的非负性和粒子数密度守恒,同时计算程序能有效克服传统求解方法中出现的分布函数对麦克斯韦分布的过冲现象。模拟了HL-2A装置在中性束注入加热等离子体过程中,离子分布函数和温度随时间的演化情况。结果表明,随着中性束的注入,离子分布函数出现非麦克斯韦化,离子温度迅速增加后稳定;计算结果和实验结果符合较好。进一步讨论束能量和功率的影响,随束能量和功率的增加,等离子体离子温度均升高,离子温度随束能量的增加升高的幅值较大,而随束功率的增加升高的幅值较小。

The one‐dimensional Fokker‐Planck equation was solved by finite volume method .The reliability of program was verified by simulation of electron self‐collision . T he results show that the numerical scheme assures positive distribution function and particle number conservation .It is an effective method of solution for Fokker‐Planck equation .And the overshoot of the Maxwell distribution that arouse from Fokker‐Planck equation solving by traditional numerical method was eliminated .Furthermore ,＆amp;nbsp;the evolutions of ion distribution function and temperature were simulated in neutral beam injection heating on the HL‐2A .The results show that the ion distribution func‐tion tends to non‐Maxwell distribution as the neutral beam injects ,and the ion tempera‐ture rises rapidly and then reaches stability .The effects of beam power and energy on the ion temperature were investigated ,and the results show that the ion temperature increases with the beam power and energy .The change is more obvious by increasing beam energy than power .