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 (ICE) offers a unique promise as a diagnostic of the fusion born alpha-particle population in magnetically confined plasmas. Pioneering observations from JET and TFTR found that ICE intensity P_{ICE} scales approximately linearly with the measured neutron flux from fusion reactions, and with the inferred concentration, n_{α}/n_{i}, of fusion born alpha particles confined within the plasma. We present fully nonlinear self-consistent kinetic simulations that reproduce this scaling for the first time. This resolves a long-standing question in the physics of fusion alpha-particle confinement and stability in magnetic confinement fusion plasmas. It confirms the magnetoacoustic cyclotron instability as the likely emission mechanism and greatly strengthens the basis for diagnostic exploitation of ICE in future burning plasmas.

Fast particle-driven waves in the ion cyclotron frequency range (ion cyclotron emission or ICE) have provided a valuable diagnostic of confined and escaping fast ions in many tokamaks. This is a passive, non-invasive diagnostic that would be compatible with the high radiation environment of deuterium-tritium plasmas in ITER, and could provide important information on fusion -particles and beam ions in that device. In JET, ICE from confined fusion products scaled linearly with fusion reaction rate over six orders of magnitude and provided evidence that -particle confinement was close to classical. In TFTR, ICE was observed from super-Alfvénic -particles in the plasma edge. The intensity of beam-driven ICE in DIII-D is more strongly correlated with drops in neutron rate during fishbone excitation than signals from more direct beam ion loss diagnostics. In ASDEX Upgrade ICE is produced by both super-Alfvénic DD fusion products and sub-Alfvénic deuterium beam ions. The magnetoacoustic cyclotron instability (MCI), driven by the resonant interaction of population-inverted energetic ions with fast Alfvén waves, provides a credible explanation for ICE. One-dimensional particle-in-cell (PIC) and hybrid simulations have been used to explore the nonlinear stage of the MCI, thereby providing a more exact comparison with measured ICE spectra and opening the prospect of exploiting ICE more fully as a fast ion diagnostic. For realistic values of fast ion concentration, nonlinearly saturated ICE spectra in these simulations closely resemble measured spectra. The PIC/hybrid approach should soon make it possible to simulate the nonlinear physics of ICE in full toroidal geometry. Emission has been observed at a wide range of poloidal angles, so there is flexibility in the location of ICE detectors. Such a detector could be implemented in ITER by installing a small toroidallyorientated loop near the plasma edge or by adding a detection capability to the ICRH antennae.

The dynamics of RE (runaway electrons) in fusion plasmas span a wide range of temporal scales, from the fast gyro-motion, ∼10−11 s, to the observational time scales, ∼10−2→1 s. To cope with this scale separation, RE are usually studied within the bounce-average or the guiding center approximations. Although these approximations have yielded valuable insights, a study with predictive capabilities of RE in fusion plasmas calls for the incorporation of full orbit effects in configuration space in the presence of three-dimensional magnetic fields. We present numerical results on this problem using the Kinetic Orbit Runaway electrons Code that follows relativistic electrons in general electric and magnetic fields under the full Lorentz force, collisions, and radiation losses. At relativistic energies, the main energy loss is due to radiation damping, which we incorporate using the Landau-Lifshitz formulation of the Abraham-Lorentz-Dirac force. The main focus is on full orbit effects on synchrotron radiation. It is shown that even in the absence of magnetic field stochasticty, neglecting orbit dynamics can introduce significant errors in the computation of the total radiated power and the synchrotron spectra. The statistics of collisionless (i.e., full orbit induced) pitch angle dispersion, and its key role played on synchrotron radiation, are studied in detail. Numerical results are also presented on the pitch angle dependence of the spatial confinement of RE and on full orbit effects on the competition of electric field acceleration and radiation damping. Finally, full orbit calculations are used to explore the limitations of gyro-averaging in the relativistic regime. To explore the practical impact of the results, DIII-D and ITER-like parameters are used in the simulations.