Theory of generation of kinetic Alfvén waves by Non-conventional Global Alfvén Eigenmodes

Abstract

The process of radiation of kinetic Alfvén Waves (KAWs) by a non-conventional global Alfvén eigenmode (NGAE) or a reversed-shear Alfvén eigenmode (modes which exist above maxima of Alfvén continuum branches) is studied analytically and numerically. The Schrödinger equation describing a localized NGAE and emitted KAWs in the space of radial wave number is derived. Analytical expressions for the mode eigenfrequencies, the radiative damping rates and the wave amplitudes are obtained. The results obtained analytically are in agreement with those obtained numerically by means of two codes based on different methods. It is found that the amplitude of the radiated KAWs can be as large as the amplitude of the radiating mode, with the radiative damping rate being rather small.

Affinity and difference between energetic-ion-driven instabilities in 2D and 3D toroidal systems

“…This means that the KAWs generated by NGAEs/RSAEs result in damping of these modes (radiative damping, see section 3.6). The possibility of this process was mentioned for the first time in [51] and considered in detail in [56,57]. It turned out that the amplitude of the generated KAWs can be comparable to the amplitude of the NGAE/RSAE, despite a rather small damping rate of KAW (γ ∼ 10 −2 ω in examples considered in [57]).…”

“…The possibility of this process was mentioned for the first time in [51] and considered in detail in [56,57]. It turned out that the amplitude of the generated KAWs can be comparable to the amplitude of the NGAE/RSAE, despite a rather small damping rate of KAW (γ ∼ 10 −2 ω in examples considered in [57]). This surprising, at first sight, result (small radiative damping implies small energy flux) is explained by the fact that the radial component of the group velocity (v g ) of KAWs is very small, much less than the longitudinal one.…”

“…The radiative damping rate of TAEs strongly depends on the radial distributions of the plasma density and the safety factor (rotational transform), which determine the AC shape. NGAEs/RSAEs generate the KAWs above the AC [51,56,57], see section 3.1. Note that kinetic eigenmodes (such as KGAE, KTAE, KMAE) are intrinsically exempt from the radiative damping.…”

Transformations of kinetic Alfvén waves in toroidal plasmas

“…In particular, the modes associated with local maxima of the Alfvén continuum are known to exist in this frequency range in both stellarators (NGAE modes described in [5,16]) and tokamaks (EAE-RSAE and NAE-RSAE modes [17,18]). The radiative damping, which is inherent to these modes [19,20], results in the emission of KAWs. It follows from our results that these waves are transformed (at least, partly) when they pass the rational flux surfaces with q = (m±1/2)/n, where m and n are the poloidal and toroidal numbers of the wave, respectively.…”

“…The transformation may be of importance for diagnostics because it may change the mode numbers observed by external magnetic measurements. The amplitude of the KAWs radiated by an unstable mode may be comparable to the amplitude of the mode itself [20]. Therefore, it is not clear without studying the wave propagation at the plasma periphery what is better observed by external coils-the unstable Alfvén mode or the KAW radiated by the mode.…”