JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line bending and field compression) and velocity ( E × B flow, field-aligned flow and fluid compression), which are amenable to three-dimensional treatment. Once the representations are inserted into the MHD equations, appropriate projection operators are applied to Faradays law and the Navier-Stokes equation to obtain a system of scalar equations that is closed by the continuity and energy equations. If the background vacuum field is sufficiently strong and the β is low, MHD waves are approximately separated by the three terms in the velocity representation, with each term containing a specific wave. Thus, by setting the appropriate term to zero, we eliminate fast magnetosonic waves, obtaining a reduced MHD model. We also show that the other two velocity terms do not compress the magnetic field, which allows us to set the field compression term to zero within the same reduced model. Dropping also the field-aligned flow, a further simplified model is obtained, leading to a fully consistent hierarchy of reduced and full MHD models for 3D plasma configurations. Finally, we discuss the conservation properties and derive the conditions under which the reduction approximation is valid. We also show that by using an ordering approach, reduced MHD equations similar to what we got from the ansatz approach can be obtained by means of a physics-based asymptotic expansion.

Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by Cα-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between Cα-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.