New insights into the generalized Rutherford equation for nonlinear neoclassical tearing mode growth from 2D reduced MHD simulations

Two dimensional reduced MHD simulations of neoclassical tearing mode growth and suppression by ECCD are performed. The perturbation of the bootstrap current density and the EC drive current density perturbation are assumed to be functions of the perturbed ux surfaces. In the case of ECCD, this implies that the applied power is ux surface averaged to obtain the EC driven current density distribution. The results are consistent with predictions from the generalized Rutherford equation using common expressions for and . These expressions are commonly perceived to describe only the effect on the tearing mode growth of the helical component of the respective current perturbation acting through the modi cation of Ohm’s law. Our results show that they describe in addition the effect of the poloidally averaged current density perturbation which acts through modi cation of the tearing mode stability index. Except for modulated ECCD, the largest contribution to the mode growth comes from this poloidally averaged current density perturbation

Discretization methods for extremely anisotropic diffusion

In fusion plasmas there is extreme anisotropy due to the high temperature and large magnetic field strength. This causes diffusive processes, heat diffusion and energy/momentum loss due to viscous friction, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to $10^{12}$ times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. % Currently the common approach is to apply magnetic field aligned grids, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems in the case of crossing field lines, e.g., x-points and points where there is magnetic reconnection. This makes local non-alignment unavoidable. It is therefore useful to consider numerical schemes that are more tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this several discretization schemes are applied to the anisotropic heat diffusion equation on a cartesian grid

Numerical modelling of strongly anisotropic dissipative effects in MHD

In magnetically confined fusion plasmas there is extreme anisotropy due to the high temperature and large magnetic field strength to the extent that thermal conductivity coefficients can be up to $10^{12}$ times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods. A common approach uses field aligned coordinates but in case of magnetic x-points and reconnection local non-alignment is unavoidable. Accuracy in case of high levels of anisotropy for non-field aligned grids is needed for the simulation of instabilities and radial transport processes in the presence of magnetic reconnection, e.g. with edge turbulence. % We therefore consider $2^{nd}$ order numerical schemes which are suitable for non-aligned grids. A novel method for co-located grids, developed to take into account the direction of the magnetic field, has been applied to the unsteady anisotropic heat diffusion equation on a non-field-aligned grid and compared with several other discretisation schemes, including G{\"{u}}nter et al's symmetric scheme. Test cases include variable diffusion coefficients with anisotropy values up to $10^{12}$, and field line bending in divergence and non-divergence free (unit vector) field configurations. % One of the model problems is given by the unsteady heat equation % \begin{equation*} \begin{split} \mbf{q} &= - D_\bot\nabla T - (D_\|-D_\bot)\mbf{b}\mbf{b}\cdot\nabla T, \quad \diff{T}{t} = -\nabla\cdot\mbf{q} + f, \end{split} \label{eq:braginskii} \end{equation*} where $T$ represents the temperature, \mbf{b} represents the unit direction vector of the magnetic field line with respect to the coordinate axes, $f$ is some source term and $D_\|$ and $D_\bot$ represent the parallel and the perpendicular diffusion coefficient respectively. \\ % Preliminary conclusions are that for FDM's the preservation of self-adjointness is crucial for limiting the pollution of perpendicular diffusion to acceptable values. However it is not required for maintaining the order of accuracy in most cases as is demonstrated by our aligned method. Key goal is to improve the co-located method to obtain acceptable levels for the pollution of the pe

Discretization methods for extremely anisotropic diffusion

In fusion plasmas there is extreme anisotropy due to the high temperature and large magnetic field strength. This causes diffusive processes, heat diffusion and energy/momentum loss due to viscous friction, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to $10^{12}$ times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. % Currently the common approach is to apply magnetic field aligned grids, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems in the case of crossing field lines, e.g., x-points and points where there is magnetic reconnection. This makes local non-alignment unavoidable. It is therefore useful to consider numerical schemes that are more tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this several discretization schemes are applied to the anisotropic heat diffusion equation on a cartesian grid

B2.5-Eunomia simulations of Magnum-PSI detachment experiments: I. Quantitative comparisons with experimental measurements

Detachment experiments have been carried out in the linear plasma device Magnum-PSI by increasing the gas pressure near the target. In order to have a proper detailed analysis of the mechanism behind momentum and power loss in detachment, a quantitative match is pursued between B2.5-Eunomia solutions and experimental data. B2.5 is a multi fluid plasma code and Eunomia is a Monte Carlo solver for neutral particles, and they are coupled together to provide steady-state solution of the plasma and neutral distribution in space. B2.5-Eunomia input parameters are adjusted to produce a close replication of the plasma beam measured in the experiments without any gas puffing in the target chamber. Using this replication as an initial condition, the neutral pressure near the plasma beam target is exclusively increased during simulation, matching the pressures measured in the experiments. Reasonable agreement is found between the electron temperature of the simulation results with experimental measurements using laser Thomson scattering near the target. The simulations also reveal the effect of increased gas pressure on the plasma current, effectively reducing the current penetration from the plasma source. B2.5-Eunomia is capable of reproducing detachment characteristics, namely the loss of plasma pressure along the magnetic field and the reduction of particle and heat flux to the target. The simulation results for plasma and neutrals will allow future studies of the exact contribution of individual plasma-neutral collisions to momentum and energy loss in detachment in Magnum-PSI.</p

Strategies and performance of the CMS silicon tracker alignment during LHC Run 2

The strategies for and the performance of the CMS silicon tracking system alignment during the 2015–2018 data-taking period of the LHC are described. The alignment procedures during and after data taking are explained. Alignment scenarios are also derived for use in the simulation of the detector response. Systematic effects, related to intrinsic symmetries of the alignment task or to external constraints, are discussed and illustrated for different scenarios

Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with Subtype and Stage Inference

The heterogeneity of neurodegenerative diseases is a key confound to disease understanding and treatment development, as study cohorts typically include multiple phenotypes on distinct disease trajectories. Here we introduce a machine-learning technique\u2014Subtype and Stage Inference (SuStaIn)\u2014able to uncover data-driven disease phenotypes with distinct temporal progression patterns, from widely available cross-sectional patient studies. Results from imaging studies in two neurodegenerative diseases reveal subgroups and their distinct trajectories of regional neurodegeneration. In genetic frontotemporal dementia, SuStaIn identifies genotypes from imaging alone, validating its ability to identify subtypes; further the technique reveals within-genotype heterogeneity. In Alzheimer\u2019s disease, SuStaIn uncovers three subtypes, uniquely characterising their temporal complexity. SuStaIn provides fine-grained patient stratification, which substantially enhances the ability to predict conversion between diagnostic categories over standard models that ignore subtype (p = 7.18 7 10 124 ) or temporal stage (p = 3.96 7 10 125 ). SuStaIn offers new promise for enabling disease subtype discovery and precision medicine