Theoretical Interpretation of Alfvén Cascades in Tokamaks with NonmonotonicqProfiles

Abstract

Alfvén spectra in a reversed-shear tokamak plasma with a population of energetic ions exhibit a quasiperiodic pattern of primarily upward frequency sweeping (Alfvén cascade). Presented here is an explanation for such asymmetric sweeping behavior which involves finding a new energetic particle mode localized around the point of zero magnetic shear.The presence of energetic particles in a plasma can alter its behavior from that predicted by conventional magnetohydrodynamics (MHD) theory in two ways. First these particles can perturbatively destabilize a basic MHD mode. Alternatively, a sufficient number of these particles can nonperturbatively alter the very structure of the MHD modes. This latter behavior is relevant to certain shear Alfvénic perturbations often called energetic particle modes (EPM) [1][2][3]. In addition, in recent years there has been a great deal of interest in plasmas with reversed magnetic shear profiles, where transport and MHD stability properties have been shown to improve [4,5]. It is important for fusion experiments in shear reversed fields to understand the collective properties associated with energetic particles. Experiments in JT-60U [6] and JET [7] have investigated reversed shear regimes and have produced energetic particles with ion cyclotron heating (ICRH) [8]. Alfvén modes emerge in these experiments but their spectrum is often puzzling. This paper presents an example of how a purely MHD description is incompatible with the data while a description which accounts for the nonperturbative energetic particle response explains a large part of the data. The interpretation suggests a sensitive method to experimentally determine q min (the minimum safety factor) in reversed magnetic shear tokamaks.The JET experiments exhibit upward frequency sweeping phenomena, named Alfvén wave cascades (ACs) [9] (see Fig. 1a). Each cascade consists of several modes with different toroidal mode numbers and different frequencies.The toroidal mode numbers vary from n 1 to n 6. The frequency starts from 20 40 kHz and increases up to 100 120 kHz which is the toroidal Alfvén eigenmode (TAE) gap frequency. Similar data were obtained some time ago on JT-60U [6]. In both the JET and JT-60U data, the modes with higher toroidal mode numbers exhibit a more rapid frequency sweeping, and the higher n modes re-occur more often than the lower n modes. It is striking that downward frequency sweeping either does not appear, or appears only rarely. In both JET and JT-60U experiments, the minimum value of q decreases in time and a population of energetic ions is created by ICRH heating.ACs resemble the global Alfvén eigenmode [10,11], whose frequency is close to the local value of the Alfvén wave frequency at the zero shear point in minor radius, r r 0 , i.e., 2pf AC ഠ v A ͑r 0 ͒ ϵ jk k ͑r 0 ͒jV A ͑r 0 ͒, where V A is Alfvén velocity and k k is the wave-vector component along the equilibrium magnetic field B 0 . To avoid strong damping, the frequency f AC needs to be somewhat larger than v A ͑r 0 ͒ if v A ͑r͒ has a maxi...

NBI-driven Alfvénic modes at ASDEX Upgrade

“…the determination of plasma parameters via the frequency evolution of these modes has to be examined. Recently, reversed shear Alfvén eigenmodes (RSAE) [5] attracted a lot of attention. Due to advances in both the experimental measurements and the code simulation capabilities, refined information about their 2d mode structures [6,7] and transition to TAEs [8] could be obtained.…”

Nonlocal energetic particle mode in a JT-60U plasma

“…12 and 13) and similar to the EPM which is predicted for ICRF heated plasma with reversed magnetic shear. 14,15 However, it was shown numerically that the reversed-shear-induced Alfvén eigenmode, 16 which has properties similar to the global Alfvén eigenmode, 17 can exist in reversed shear plasmas. It was demonstrated that MHD theory can explain frequency chirping behavior of so-called Alfvén cascades observed in reversed shear plasmas.…”

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“…In RS tokamak plasmas, characteristic energetic-iondriven modes called RSAEs or Alfvén cascade modes are observed [23][24][25][26][27][28][29][30][31]. Moreover, a GAM having an n = 0 mode structure is sometimes excited by energetic ions [32,33].…”