In normal MHD theory, the eigen frequency of toroidal Alfven eigenmodes (TAEs) is only determined by the Alfven speed, which is a function of the plasma density but the temperature. I was wondering, if there is any correction to the eigen frequency by the change of electron/ion temperature using the kinetic theory of plasma.
Considering the finite Larmor radius effect (kinetic correction) to the eigen frequency of AEs. The formula is given in the paper of R.R. Mett [1]. This is a rather small correction. Overall, the real eigenmode frequency of TAE is determined by the fluid contribution in deltaW_MHD.
[1] METT R R, MAHAJAN S M. Kinetic theory of toroidicity-induced alfvén eigenmodes[J]. Physics of fluids. B, Plasma physics, 1992, 4(9):2885-2893.
Just change the dielectric tensor components using any toroidal kinetic theory model (it means to including finite Larmor radius corrections and finite electron inertia), mainly the components XX, XZ, ZX, ZZ (have to write them i na toroidal system of course!) components! In my list o papers you can find those calculations!
Altair de Assis Thank you for the answer. But in the papers of R.R Mett [1], K. Stasiewicz [2] and the thesis of S. D. Pinches [3], the calculations of kinetic correction to the eigenmode frequency are actually given as:
omega^2=k_parallel^2 V_A^2 (1+(3/4+Te/Ti)(k_perp^2 rho_i^2))
Where V_A is Alfven speed, rho_i is ion Larmor radius. Maybe you can check about that.
[1] R. R. Mett and S. M. Mahajan, “Kinetic theory of toroidicity-induced Alfvén eigenmodes,” Phys. Fluids B, vol. 4, no. 9, pp. 2885–2893, 1992.
[2] K. Stasiewicz, “Finite Larmor Radius Effects in the Magnetosonic Pulse,” Phys. Fluids, vol. 12, no. 12, p. 2580, 2004.
[3] S. D. PINCHES, Nonlinear interaction of fast particles with Alfven waves in tokamaks[D]. Nottingham, UK: University of Nottingham, 1996: 14,19.
Dear Nan,
Related to: omega^2=k_parallel^2 V_A^2 (1+(3/4+Te/Ti)(k_perp^2 rho_i^2))
Where V_A is Alfven speed, rho_i is ion Larmor radius. Maybe you can check about that.
You are correct, in part, this is only valid for finite but small ion Larmor radius.
The general expression derived earlier by VD Shafranov has no aproximation to the ion Larmor radius (Rev. of Plasma Physics Vol. 3), but later Akira Hasegawa and others derived your expression considering finite but small ion Larmor radius!
In toroidal geometry the Alfven wave dispersion relation is much more complicated!
Finite pressure do not influence on the toroidal Alfven eigenfrequence (unless finite Larmor radius effects are taken into account). However, the pressure can sufficiently change the poloidal Alfven eigenfrequence. See
D. Yu. Klimushkin, Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure, Ann. Gephys., V.16, # 3, p.303-321, 1998.
Klimushkin D. Yu., and Mager P. N. (2015), The Alfvén mode gyrokinetic equation in finite-pressure magnetospheric plasma, J. Geophys. Res. Space Physics, 120, P. 4465–4474, doi: 10.1002/2015JA021045.
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