In tokamak the parallel divergence of the parallel current is non-zero due to the time variation of the vorticity. This has an interesting connection with the axial anomaly usually invoked in baryogenesis. In two-dimensions (good approximation for the plasma in strong magnetic field) the field of vorticity can be seen as a discrete set of positive and negative elementary vortices, of fixed...

Relativistic effects in astrophysical objects and fusion plasmas do not necessarily require extremely high temperatures and energies. They appear to be non-negligible even for electron temperatures $T_e$ of the order of tens of keV, i.e. when $T_e\ll m_ec^2$. Relativistic effects in transport physics appear due to macroscopic features of the relativistic thermodynamic equilibrium given by the...

While the curse of high dimensionality associated with the Fokker-Planck equation can be resolved by Monte Carlo solution to the underlying stochastic process, the distribution of discretization points for the resulting random walk-based method follows the evolution of the target distribution function, leading to the weight-spreading phenomenon in the $\delta f$ method, and therefore increase...

In order to achieve sustainable confinement in fusion plasmas, it is crucial to understand and mitigate all transport mechanisms. In recent years observations show that there is a strong evidence that the overall transport of heat and particles is to a large part caused by intermittency (or bursty events) related to coherent structures. In this work a novel approach where a global heat flux...

The pedestal, and transport barriers in general, play an important role in tokamak performance and thus it is desirable to find a comprehensive model for these regions. In transport barriers, the applicability of standard neoclassical theory is limited because of sharp gradients of temperature, density, and radial electric field. We have developed a new neoclassical approach that sets the...

We provide a gyrofluid model of a collisionless and magnetized plasma, valid for finite βe, finite parallel magnetic perturbations and electron finite Larmor radius effects. This model is used to study the linear and non-linear evolution of magnetic reconection and magnetic islands. Gyrofluid models provide an effective tool, complementary to kinetic models, for studying such effects.

To understand plasma behaviour in the scrape-off layer (SOL), we need to know the boundary conditions for the plasma and electromagnetic fields near a divertor. At the boundary, in the direction perpendicular to the wall, there are four length scales of interest. These are the Debye length $\lambda_D$, the ion gyroradius $\rho_i$, the projection of the collisional mean free path in the...

The transport of particles and energy from the core plasma in a divertor tokamak to the reactor walls, via the scrape-off layer (SOL), occurs largely parallel to the magnetic field lines. Experimental evidence and theoretical considerations suggest that a fluid approach to modelling this transport may miss some important behaviour. In particular, temperatures at the target may be modified by...

Particle-in-cell (PIC) codes are one of the workhorses for numerically exploring plasma dynamics across a vast parameter space. While explicit discretizations of PIC systems allow for a straightforward time integration, stability requirements set strict limitations on both the maximal time-step and maximal grid spacing. Implicit PIC methods on the other hand put laxer restrictions on the...

Drift-reduced plasma fluid models are commonly used to model the edge-SOL region of L-mode discharges in tokamaks. It is often observed that electrostatic simulations of plasma turbulence are restricted to a very small explicit timestep, or the implicit timestep is very poorly conditioned. The origins of this restriction can be traced to the properties of the linear waves supported by the...

Numerical codes for electromagnetic wave propagation in fusion plasmas are mainly based on frequency-domain asymptotic methods, which provide a fast solution and are thus valuable for experiment design and control applications. However, in several cases of practical interest (like O-X-B mode conversion, mm-diagnostics) these tools run close to their limits of validity and should be compared to...

Wave-particle interactions are ubiquitous in space and laboratory plasma systems and have been the subject of intense research interest for many decades. From a theoretical point of view, the nonlinear motion of a charged particle with an electrostatic wave has been one of the basic paradigms of complex and chaotic Hamiltonian dynamics. However, although single particle dynamics have been...

The assumption of a small relative deviation from background f_0 under the delta-f scheme often used to simulate the plasma core will not be valid when simulating the plasma edge, characterized by low density and temperature and strong gradients. In order to retain the noise reduction benefit of the delta-f scheme as compared to the full-f approach, a study of a transition scheme by means of a...

The development of the EU-DEMO reactor is at the pre-conceptual design phase. At this stage, close attention is paid to the heating mix necessary to fulfill all the plasma requirements: breakdown, ramp-up, L-H transition, burn control, NTM stabilization, sawteeth pacing, radiative instability control and ramp-down. Integrated modeling is an effective tool to compare the impact of dominant...

The MHD dynamo effect is an intrinsic and fundamental feature of reversed-field pinch (RFP) plasmas. It plays an important role in the tokamak as well (commonly as referred to as the "flux pumping" mechanism) in particular for the hybrid scenario with central safety factor close to one. In this contribution, we review results based on the above-mentioned nonlinear 3D MHD theory and...