Ad-hoc continuum damping

The resonance absorption trick [19] has been used to regularize the MHD singularity when a global wavefield is formed in the presence of Alfvén resonances; the so-called continuum damping of AEs has first been computed numerically [26,27], implemented in the LION and CASTOR codes and solved analytically [28,29] for radially localized modes. Using two cold resistive fluids for validation purposes, we repeated such calculations with the PENN code in Ref.[8] by writing the current perturbation along the magnetic field as

$$j_\Vert = -\frac{i\omega}{4\pi} \left\{\frac{\omega_p^2}{\... ...\quad \rightarrow \quad -\frac{\omega_p^2}{4\pi\nu_e} E_\Vert$$ (5)

where the term $\omega(\omega +i\nu_e)$ in the denominator is first replaced by $i\omega\nu_e$ to reduce the 4th order equation in $k_\perp$ down to 2nd order (neglecting the electron inertia in the momentum balance) before taking the collisionless limit $\nu_e \rightarrow 0$. The large continuum damping $\vert\gamma/\omega\vert\ge 0.01$ obtained suggested first that only gap modes (having no intersection with the shear-Alfvén continuum) can be observed in actual plasmas. Serious contradictions have been found since both within theory [21] and the experiments [30,31]; weakly damped modes have been measured with large fields in the neighborhood of Alfvén resonances with continuum damping rates exceeding the damping from mode conversion and the measurements by more than an order of magnitude [30]. Such arguments show that the continuum damping of global AEs is misleading and that shear-Alfvén continuum plots such as Fig.1 are of little value to predict the damping and even the existence of AEs.