扭转Alfvén波共振的数学描述

提出完备正交函数基(OFSE)展开方法,求解冕环中无耗散扭转Alfvn波。每个基函数对应冕环中每根磁力线的一个固有角频率ω_n,当冕环足点驱动频率等于磁力线的固有频率时,Alfvn波将在这根磁力线处发生共振。采用OFSE方法求解了双足点驱动时冕环Alfvn波的时变演化问题,给出了时变解析解的新形式,其中包含共振项,从共振项可以发现,在共振角频率为ω的共振磁力线附近,在时间t为π/ω的整数倍时,出现δ型间断;在t为π/(2ω)的奇数倍时,出现1/x间断。共振磁力线振幅随时间线性增加,增加的斜率正比于Alfvn波速,反比于冕环长度,与驱动频率无关。

MATHEMATICAL DESCRIPTION OF TORSIONAL ALFVEN WAVE RESONANCE IN CORONAL LOOP

A method called complete Orthogonal Function Series Expansion (OFSE) in Hilbert space is proposed to solve the non-dissipative torsional Alfven wave in coronal loops. Every base function corresponds to an intrinsic angular frequency wn of every magnetic field line in coronal loops. Torsional Alfven wave resonance of a magnetic field line in coronal loops comes out when the driven angular frequency equals to its intrinsic angular frequency. With the method, we present a new form of Torsional Alfven wave evolution solution with two-footpoint driven boundary condition. There exists a resonant term in the solution, from which it could be found that: near the resonant place with an angular frequency w,a discontinuity profile appears at times t equal to the multiples of n/w and a 1/x discontinuity profile appears at times t equal to the odd multiples of n/(2w). It is also found that the wave amplitude at resonant place increases linearly with time and the slope is proportional to Alfven wave speed, inverse proportional to loop length and independent of driven frequency.