Excitation of the beta-induced Alfvén eigenmode by a plasma flow around the magnetic island

Abstract

It is well known that the rotation of a magnetic island in the reference frame of plasma guiding centers generates parallel electron current outside the island, which is induced by the geodesic curvature of a magnetic field (Smolyakov et al 2007 Phys. Rev. Lett. 99 055002). It is shown in the present work that the surface part of this current located at the island separatrix can drive a pair of counter-propagating, tearing-parity, beta-induced Alfvén eigenmodes, which have the same helicity as that of the magnetic island and form a standing wave in the island frame. These Alfvénic modes can accompany tearing activity in tokamak discharges without energetic particles.

Observation of tungsten impurities induced 2/1 snake fluctuations and their interactions with discrete double BAE pairs on EAST

“…The fine splittings around each pair of BAEs (presumably for the same |m| and |n|) as shown in figure 7(a) may be attributed to the fine structure of the BAE gaps for the same |m| and |n|. In [51] it has been shown that the pure MHD toroidal Alfvénic (TA) continuum spectra can be described by the differ ential equation (26) with respect to θ for circular flux surfaces, which is a Mathieu equation whose cosine 'potential' reflects the periodic change of the magnetic field strength on each flux surface in toroidal geometry. It is well-known that this equation admits infinite pair of distinct eigen-frequencies and infinite sets of TA gaps delineated by them.…”

“…Furthermore, the novel island-induced Alfvén eigenmodes were identified on a reversed field pinch [20], and the multi-pairs of BAEs have also been observed on LHD [21] during the excitation of strong interchange modes. Several theoretical models have been developed aiming at explaining those phenomena [14,[22][23][24][25][26].…”

“…We note that the relation f B2 − f B1 = 2f tm for the conventional BAE pair has been interpreted [13] as the Doppler effect of the rotation of the magnetic island for pure tearing mode with frequency f tm . Some linear mechanisms for excitating the BAE quartet may play a role, such as the inverse Landau damping due to the poloidal gradient of the ion distribution [22] or the electron flow [26] for the magnetic island modified equilibrium. Furthermore, there exist the bifurcation structures that adjoin the frequencies 2f tm and 3f tm that are measured by edge magnetic pickup probes as shown in (d), which could also be one of the outcomes that are generated by the asymmetry of the STM inside the annulus around 0.3 < ρ < 0.7.…”

“…How do the global structures of BAEs emerge? Marchenko et al [22,26] have demonstrated that a radial differential equation for the amplitude (excluding the propagating factor of BAE) of the perturbed scalar potential of the principal harmonic can be derived from the quasi-neutrality condition ∂ jr /∂r + ∇ j 0, where j is the perturbed parallel current, jr is the total radial component of the perturbed current consisting of the polarization current, the gradient B and curvature drift currents for both electron and ion. In this eigenmode equation, the more complete BA continuum (local) dispersion function (comparing to equation ( 1)) that includes finite shear Alfvén frequency for non-vanishing parallel wave vector k ≡ (m − nq)/(qR) in the case of circular equilibrium flux surfaces, i.e.…”

“…This implies that when considering the radially standing wave solutions to the corre sponding radial eigen-mode equation, there should be at least two distinct constant frequencies with relatively large gap between them. On the other hand, it has been shown [4,26] that the radial differential equations of the BAEs have one 'ground state' with lower eigenfrequency as well as a tower of 'excited states' with relatively higher eigenfrequencies and more radial nodes. These effects can be responsible for the splitting of one BAE pair into two frequency bands with relatively large gap between them, as shown in figure 7(a).…”