Kinetic Alfvén eigenmodes at ASDEX Upgrade

Abstract

Abstract. On the way to a comprehensive understanding of the properties of a burning plasma the physics of super-thermal particles due to external heating and fusion reactions plays a key role. Especially Alfvén and Alfvén-acoustic type instabilities are predicted to strongly interact with the fast particle population and to contribute critically to the radial redistribution of the energetic ions. This paper focuses on the comparison of the kinetic dispersion relation for BAEs/GAMs [1] with numerical results obtained by the gyrokinetic eigenvalue code LIGKA [2] and experimental findings at ASDEX Upgrade. It is shown that thermal ions with a finite perpendicular energy (circulating and trapped) modify the dispersion relation significantly for low frequencies. The resulting frequency down-shift together with shaping and diamagnetic effects is crucial to explain the mode frequency as measured at ASDEX Upgrade stressing the importance of a kinetic description for frequencies comparable to the thermal ion transit frequency. In the second part the BAE frequency behaviour during a sawtooth-cycle is investigated and the possibility of an accurate q-profile determination via kinetic Alfvén spectroscopy is discussed.

NBI-driven Alfvénic modes at ASDEX Upgrade

“…Both the solution with and without trapped background ions are plotted. As shown previously [31,18], trapped particles cause a downshift of the local spectrum. The minimum in the continuum is caused by the geodesic coupling.…”

“…In this frequency range, the background ions start to influence not only the damping rate but also the mode frequency. The lower the frequency, the more important is also the influence of trapped background ions [18,31]. In this paper no attempt to model the non-linear phase of the mode evolution is made.…”

“…In this paper, the linear gyrokinetic code LIGKA [23,18] is employed to describe the linear properties and to compare with the experiment. Since the equations had to be extended with respect to previous formulations [35] due to the inclusion of the NBI drive, a review of the equations is carried out here.…”

“…The relevant dispersion relation was re-derived [18] for the gyrokinetic model [35] underlying the eigenvalue code LIGKA. As can be seen in equations 2 and 3, the integration over velocity space is carried out completely numerically, and therefore it is possible to include a rather general distribution function for the EPs.…”

“…Finally, also the non-linear interaction with other Alfvénic instabilities, such as TAEs has been investigated [10]. In this paper, we aim to describe and model another, closely connected Alfvénic mode in the same frequency regime as the RSAE, the beam-driven beta induced Alfvén eigenmode (BAE) [11,12,13,16,17,18,19]. Although a lot of literature is available for BAE modes they have so far not been investigated in the current ramp-up phase of a tokamak discharge.…”