Electrostatic stability of electron-positron plasmas in dipole geometry

The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the zero-Debye-length case, the stability diagram is found to exhibit singular behavior. However, when the Debye length is non-zero, a fluid mode appears, which resolves the observed singularity, and also demonstrates that both the temperature and density gradients can drive instability. It is concluded that a finite Debye length is necessary to determine the stability boundaries in parameter space. Landau damping is investigated at scales sufficiently smaller than the Debye length, where instability is absent

Generalized universal instability: Transient linear amplification and subcritical turbulence

In this work we numerically demonstrate both significant transient (i.e. non-modal) linear amplification and sustained nonlinear turbulence in a kinetic plasma system with no unstable eigenmodes. The particular system considered is an electrostatic plasma slab with magnetic shear, kinetic electrons and ions, weak collisions, and a density gradient, but with no temperature gradient. In contrast to hydrodynamic examples of non-modal growth and subcritical turbulence, here there is no sheared flow in the equilibrium. Significant transient linear amplification is found when the magnetic shear and collisionality are weak. It is also demonstrated that nonlinear turbulence can be sustained if initialized at sufficient amplitude. We prove these two phenomena are related: when sustained turbulence occurs without unstable eigenmodes, states that are typical of the turbulence must yield transient linear amplification of the gyrokinetic free energy

Kuramoto model with coupling through an external medium

Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations. We conclude by discussing the relationship of the model to other variations of the Kuramoto model including the Kuramoto model with a bimodal frequency distribution and the Millennium Bridge problem.Comment: 9 pages, 3 figure

The zonal-flow residual does not tend to zero in the limit of small mirror ratio

The intensity of the turbulence in tokamaks and stellarators depends on its ability to excite and sustain zonal flows. Insight into this physics may be gained by studying the ''residual'', i.e. the late-time linear response of the system to an initial perturbation. We investigate this zonal-flow residual in the limit of a small magnetic mirror ratio, where we find that the typical quadratic approximation to RH (Rosenbluth & Hinton, 1998) breaks down. Barely passing particles are in this limit central in determining the resulting level of the residual, which we estimate analytically. The role played by the population with large orbit width provides valuable physical insight into the response of the residual beyond this limit. Applying this result to tokamak, quasi-symmetric and quasi-isodynamic equilibria, using a near-axis approximation, we identify the effect to be more relevant (although small) in the core of quasi-axisymmetric fields, where the residual is smallest. The analysis in the paper also clarifies the relationship between the residual and the geodesic acoustic mode, whose typical theoretical set-ups are similar.Comment: Associated Zenodo repository 10.5281/zenodo.1280569

Constructing precisely quasi-isodynamic magnetic fields

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their bootstrap currents, particle confinement, and available energy for trapped-electron driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.Comment: 25 pages, 10 figure

Quasi-isodynamic stellarators with low turbulence as fusion reactor candidates

The stellarator is a type of fusion energy device that - if properly designed - could provide clean, safe, and abundant energy to the grid. To generate this energy, a stellarator must keep a hot mixture of charged particles (known as a plasma) sufficiently confined by using a fully shaped magnetic field. If this is achieved, the heat from fusion reactions within the plasma can be harvested as energy. We present a novel method for designing reactor-relevant stellarator magnetic fields, which combine several key physical properties. These include plasma stability, excellent confinement of the fast moving particles generated by fusion reactions, and reduction of the turbulence that is known to limit the performance of the most advanced stellarator experiment in the world, Wendelstein 7-X.Comment: 11 pages, 15 figure

Predicting the Dimits shift through reduced mode tertiary instability analysis in a strongly driven gyrokinetic fluid limit

The tertiary instability is believed to be important for governing magnetised plasma turbulence under conditions of strong zonal flow generation, near marginal stability. In this work, we investigate its role for a collisionless strongly driven fluid model, self-consistently derived as a limit of gyrokinetics. It is found that a region of absolute stability above the linear threshold exists, beyond which significant nonlinear transport rapidly develops. Characteristically, this range exhibits a complex pattern of transient zonal evolution before a stable profile can arise. Nevertheless, the Dimits transition itself is found to coincide with a tertiary instability threshold, so long as linear effects are included. Through a simple and readily extendable procedure, tracing its origin to St-Onge (J. Plasma Phys., vol. 83, issue 05, 2017, 905830504), the stabilising effect of the typical zonal profile can be approximated, and the accompanying reduced mode estimate is found to be in good agreement with nonlinear simulations.</jats:p