Simulating the nonlinear interaction of relativistic electrons and tokamak plasma instabilities: Implementation and validation of a fluid model.

For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to self-consistently describe the nonlinear coupled evolution of runaway electrons (REs) and plasma instabilities during disruptions. In this model, the runaway electrons are considered as a separate fluid species in which the initial seed is generated through the Dreicer source, which eventually grows by the avalanche mechanism (further relevant source mechanisms can easily be added). Advection of the runaway electrons is considered primarily along field lines, but also taking into account the E×B drift. The model is implemented in the nonlinear magnetohydrodynamic (MHD) code jorek based on Bezier finite elements, with current coupling to the thermal plasma. Benchmarking of the code with the one-dimensional runaway electron code go is done using an artificial thermal quench on a circular plasma. As a first demonstration, the code is applied to the problem of an axisymmetric cold vertical displacement event in an ITER plasma, revealing significantly different dynamics between cases computed with and without runaway electrons. Though it is not yet feasible to achieve fully realistic runaway electron velocities close to the speed of light in complete simulations of slowly evolving plasma instabilities, the code is demonstrated to be suitable to study various kinds of MHD-RE interactions in MHD-active and disruption relevant plasmas.

Resistive reduced MHD modeling of multi-edge-localized-mode cycles in Tokamak X-point plasmas.

The full dynamics of a multi-edge-localized-mode (ELM) cycle is modeled for the first time in realistic tokamak X-point geometry with the nonlinear reduced MHD code jorek. The diamagnetic rotation is found to be instrumental to stabilize the plasma after an ELM crash and to model the cyclic reconstruction and collapse of the plasma pressure profile. ELM relaxations are cyclically initiated each time the pedestal gradient crosses a triggering threshold. Diamagnetic drifts are also found to yield a near-symmetric ELM power deposition on the inner and outer divertor target plates, consistent with experimental measurements.

Mechanism of edge localized mode mitigation by resonant magnetic perturbations.

A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the jorek code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number n=2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to n=2 RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n=2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.