磁流体径向本征函数的演化规律

Evolution of Radial Eigenfunction in Magnetohydrodynamic

应用傅里叶变换,将线性化的理想磁流体方程组转化为一个关于径向本征函数的二阶常微分方程。通过求解此方程,数值模拟了角向模数m=2时,圆柱磁流体径向本征函数在不同热压强时随波数和增长率的演化规律。数值模拟结果表明径向本征函数对波长的变化比较敏感,在短波模式有一定波动,长波时不受增长率的影响。此结果有利于加深对高角向模数不稳定性的理解,同时也验证了半解析方法解决磁流体问题的有效性和简洁性。

Herein,we reported the semi-analytical simulation of the behavior of cylindrical magnetic fluid.First,Fourier transformation turns the linearized ideal magnetohydrodynamic（MHD） equations into 2 nd-order ordinary differential equation of radial eigenfunction. Next,with the poloidal mode number m = 2,the evolution of the radial eigenfunction in cylindrical MHD with the wave-number and growth-rate at different thermal pressures p0 was evaluated by numerically solving the transformed equation. The simulated results show that the thermal pressure and wave-number strongly affect the radial eigenfunction. For example,when p0= 0,the radial eigenfunction depends strongly on the wave-number and weakly on the growth-rate,fluctuating in short wavelength; when p0= 0. 01,it is sensitive to the wave-number and growth-rate in short wavelength mode; when p0= f（r）,it markedly fluctuates in short wavelength mode,though its maximum corresponds to long wavelength mode.