Linear and nonlinear physics of the magnetoacoustic cyclotron instability of fusion-born ions in relation to ion cyclotron emission

Abstract

The magnetoacoustic cyclotron instability (MCI) probably underlies observations of ion cyclotron emission (ICE) from energetic ion populations in tokamak plasmas, including fusion-born alpha-particles in JET and TFTR [Dendy et al., Nucl. Fusion 35, 1733 (1995)]. ICE is a potential diagnostic for lost alpha-particles in ITER; furthermore, the MCI is representative of a class of collective instabilities, which may result in the partial channelling of the free energy of energetic ions into radiation, and away from collisional heating of the plasma. Deep understanding of the MCI is thus of substantial practical interest for fusion, and the hybrid approximation for the plasma, where ions are treated as particles and electrons as a neutralising massless fluid, offers an attractive way forward. The hybrid simulations presented here access MCI physics that arises on timescales longer than can be addressed by fully kinetic particle-in-cell simulations and by analytical linear theory, which the present simulations largely corroborate. Our results go further than previous studies by entering into the nonlinear stage of the MCI, which shows novel features. These include stronger drive at low cyclotron harmonics, the re-energisation of the alpha-particle population, self-modulation of the phase shift between the electrostatic and electromagnetic components, and coupling between low and high frequency modes of the excited electromagnetic field. V

Ion cyclotron emission from fusion-born ions in large tokamak plasmas: a brief review from JET and TFTR to ITER

“…These PIC simulations modelled fully kinetic ions and electrons, together with the self-consistent electric and magnetic fields, for plasma parameters aligned to relevant JET conditions. The results [23] strengthened the link to ICE observations, and this was reinforced by subsequent simulations of the MCI over even longer physical time durations [24] using a code implementing the hybrid approximation [25], where ions are treated as particles and electrons as a neutralising massless fluid. These simulations [23,24] corroborate predictions from linear analytical theory where applicable and, by extending previous studies deep into the nonlinear regime of the MCI [24], confirm that the MCI underlies the ICE observations from energetic ions in large magnetically confined plasmas.…”

“…Fig.1, reproduced with permission from Ref. [24]. Experimental ICE spectra compared with linear analytical growth rates for the MCI and with computed wave intensities obtained from fully nonlinear MCI simulations using the hybrid model.…”

“…[24]. This combines three elements: observational ICE spectra from a JET deuterium-tritium plasma; calculations of linear analytical growth rates for the MCI using corresponding parameter values; and the results of self-consistent nonlinear kinetic simulation using a hybrid model and exploiting contemporary high performance computation.…”

“…Electron physics is modelled in terms of a charge-neutralising fluid. The magnetic field is updated using Faraday's law, and the electric field is updated using the electron fluid momentum equation in the limit of zero electron inertia [24,25]. Like PIC models [22,23], hybrid models fully resolve ion kinetics, and thus include (unlike gyrokinetic models) the full orbit gyromotion of the ions.…”

“…The hybrid simulations [24] of the MCI and ICE were preceded chronologically by 1D3V PIC simulations [23], in which electrons are treated fully kinetically as well as ions, and the correct physical mass ratio for protons and electrons m p /m e = 1836 was used. The PIC approach has the advantage of maximum physical fidelity, and a corresponding disadvantage in that it is computationally expensive, such that the evolution of the MCI can be followed only for about five gyro-periods of the alpha-particles.…”