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Global simulations of electromagnetic turbulence, collisionless tearing modes, and Alfven Eigenmodes in the presence of fast particles are carried out using the gyrokinetic particle-in-cell codes ORB5 (E. Lanti et al, Comp. Phys. Comm., ${\bf 251}$, 107072 (2020)) and EUTERPE (V. Kornilov et al, Phys. Plasmas, ${\bf 11}$, 3196 (2004)) in tokamak and stellarator geometries. Computational feasibility of simulating such complex coupled systems is demonstrated.

The excitation of toroidicity induced Alfv{\'e}n eigenmodes (TAEs) using prescribed external electromagnetic perturbations (hereafter ``antenna") acting on a confined toroidal plasma as well as its nonlinear couplings to other modes in the system is studied. The antenna is described by an electrostatic potential resembling the target TAE mode structure along with its corresponding parallel electromagnetic potential computed from Ohm's law. Numerically stable long-time linear simulations are achieved by integrating the antenna within the framework of a mixed representation and pullback scheme [A. Mishchenko, et al., Comput. Phys. Commun. \textbf{238} (2019) 194]. By decomposing the plasma electromagnetic potential into symplectic and Hamiltonian parts and using Ohm's law, the destabilizing contribution of the potential gradient parallel to the magnetic field is canceled in the equations of motion. Besides evaluating the frequencies as well as growth/damping rates of excited modes compared to referenced TAEs, we study the interaction of antenna-driven modes with fast particles and indicate their margins of instability. Furthermore, we show first nonlinear simulations in the presence of a TAE-like antenna exciting other TAE modes, as well as Global Alfv\'en Eigenmodes (GAE) having different toroidal wave numbers from that of the antenna.

Electromagnetic turbulence is addressed in tokamak and stellarator plasmas with the global gyrokinetic particle-in-cell codes ORB5 [E. Lanti et al, Comp. Phys. Comm, vol. 251, 107072 (2020)] and EUTERPE [V. Kornilov et al, Phys. Plasmas, vol. 11, 3196 (2004)]. The large-aspect-ratio tokamak, down-scaled ITER, and Wendelstein 7-X geometries are considered. The main goal is to increase the plasma beta, the machine size, the ion-to-electron mass ratio, as well as to include realistic-geometry features in such simulations. The associated numerical requirements and the computational cost for the cases on computer systems with massive GPU deployments are investigated. These are necessary steps to enable electromagnetic turbulence simulations in future reactor plasmas.

The pullback scheme is implemented in the global gyrokinetic particle-in-cell code ORB5 [S. Jolliet et al, Comp. Phys. Comm., 177, 409 (2007)] to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfven Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise.

The gyrokinetic stability of electron-positron plasmas contaminated by ion (proton) admixture is studied in slab geometry. The appropriate dispersion relation is derived and solved. The ion-temperature-gradient driven instability, the electron-temperature-gradient driven instability, the universal mode, and the shear Alfven wave are considered. The contaminated plasma remains stable if the contamination degree is below some threshold, and it is found that the shear Alfven wave can be present in a contaminated plasma in cases where it is absent without ion contamination.

Due to their capability to reduce turbulent transport in magnetized plasmas, understanding the dynamics of zonal flows is an important problem in the fusion programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric tokamaks, it is known that studying the linear and collisionless relaxation of zonal flow perturbations gives valuable information and physical insight. Recently, the problem has been investigated in stellarators and it has been found that in these devices the relaxation process exhibits a characteristic feature: a damped oscillation. The frequency of this oscillation might be a relevant parameter in the regulation of turbulent transport, and therefore its efficient and accurate calculation is important. Although an analytical expression can be derived for the frequency, its numerical evaluation is not simple and has not been exploited systematically so far. Here, a numerical method for its evaluation is considered, and the results are compared with those obtained by calculating the frequency from gyrokinetic simulations. This "semianalytical" approach for the determination of the zonal-flow frequency reveals accurate and faster than the one based on gyrokinetic simulations., Comment: 30 pages, 14 figures

The linear dynamics of Alfven modes in tokamaks is investigated here by means of the global gyrokinetic particle-in-cell code NEMORB. The model equations are shown and the local shear Alfven wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfven Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is described. In particular, a phase-shift in the poloidal angle is found to be present for modes whose frequency touches the continuum, whereas a radial symmetry is found to be characteristic of modes in the continuum gap., Comment: Submitted to "Physics of Plasmas"

In ideal MHD, shear Alfv\'{e}n eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfv\'{e}n continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfv\'{e}n eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD code CKA . In this paper we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7X and H1-NF stellarator cases. To the authors' knowledge these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7X and H1-NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics., Comment: 23 pages, 12 colour figures

In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the GENE and EUTERPE codes. Calculations of the residual value in stellarators are provided for much shorter wavelengths than previously available in the literature. Electrons must be treated kinetically in stellarators because, unlike in tokamaks, kinetic electrons modify the residual value even at long wavelengths. This effect, that had already been predicted theoretically, is confirmed by gyrokinetic simulations., Comment: 31 pages, 15 figures

It is shown that a considerable improvement in the global gyrokinetic electromagnetic simulations can be achieved by a slight modification of the simulation scheme. The new scheme is verified, simulating a Toroidal Alfv\'en Eigenmode in tokamak geometry at low perpendicular mode numbers, the so-called "MHD limit". Also, an electromagnetic drift mode has been successfully simulated in a stellarator., Comment: Paper submitted for publication

Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly in the case of the toroidicity-induced shear Alfv\'en eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used., Comment: 19 pages, 9 figures