Mode conversion

Is the fundamental process through which power can be linearly transferred between two waves if their phase velocities somewhere match. First described by Hasegawa & Chen in the presence of an Alfvén resonance, it can be understood locally in Fig.2 in terms of a bi-quadratic dispersion relation of the form $ak_\perp^4 +bk_\perp^2 +c=0$, where a fast (long fluid scalelength) wave coalesces with a slow (short kinetic scalelength) wave $k^2_{\perp,\mathrm{fast}}\approx k^2_{\perp,\mathrm{slow}}$ in the neighborhood of the resonance. The efficiency of the power transfer depends on the wavefield amplitude and the spatial extension over which the characteristic length and phase of both waves match; a correct evaluation therefore requires solving a 4th order equation, which, for the kinetic-Alfvén wave, amounts to keeping the FLR correction term of $\mathcal{O}(k_\perp^2\rho_i^2)$ in (eq.1).

  

Figure 2: Mode conversion in the neighborhood of an Alfvén resonance.

Several ``ad-hoc'' models have been proposed to approximate this conversion from the 2nd order (shear Alfvén) fluid MHD equation of the form $ek_\perp^2+f=0$, which becomes singular as $e\rightarrow 0$ at the resonance. Continuum damping [18,19] calculates the residual absorption of the singularity directly from the MHD model in the limit of an infinitesimal dissipation. The trick describes the correct amount of mode converted power in an unbounded domain [20], but we recently showed in Ref.[21] that it dramatically fails when global effects alter the amplitude and the phase of the fluid wavefield. Complex resistivity resolves the singularity of the MHD equations by adding an ad-hoc 4th order term, without consistently keeping the $\mathcal{O}(k_\perp^2\rho_i^2)$ corrections characteristic of the kinetic-Alfvén wave. The mode conversion efficiency calculated in this manner has never been validated even in 1D against a gyrokinetic calculation, but the inconsistent treatment of the dispersion in the neighborhood of fluid resonances is likely to suffer from the same short commings as the continuum damping.

It is finally important to note that mode conversion is not only possible in the neighborhood of fluid resonances and neither does it take place exclusively to the kinetic Alfvén wave: mode conversion can in principle occur anywhere in the plasma where the spatial scale of a fast (fluid, MHD) wave and a slow (drift, surface quasi-electrostatic, kinetic Alfvén, energetic particle) wave match.