13 research outputs found
Enhanced Preconditioner for JOREK MHD Solver
The JOREK extended magneto-hydrodynamic (MHD) code is a widely used
simulation code for studying the non-linear dynamics of large-scale
instabilities in divertor tokamak plasmas. Due to the large scale-separation
intrinsic to these phenomena both in space and time, the computational costs
for simulations in realistic geometry and with realistic parameters can be very
high, motivating the investment of considerable effort for optimization. In
this article, a set of developments regarding the JOREK solver and
preconditioner is described, which lead to overall significant benefits for
large production simulations. This comprises in particular enhanced convergence
in highly non-linear scenarios and a general reduction of memory consumption
and computational costs. The developments include faster construction of
preconditioner matrices, a domain decomposition of preconditioning matrices for
solver libraries that can handle distributed matrices, interfaces for
additional solver libraries, an option to use matrix compression methods, and
the implementation of a complex solver interface for the preconditioner. The
most significant development presented consists in a generalization of the
physics based preconditioner to "mode groups", which allows to account for the
dominant interactions between toroidal Fourier modes in highly non-linear
simulations. At the cost of a moderate increase of memory consumption, the
technique can strongly enhance convergence in suitable cases allowing to use
significantly larger time steps. For all developments, benchmarks based on
typical simulation cases demonstrate the resulting improvements
Nonlinear MHD modeling of soft limits in W7-AS
An important question for the outlook of stellarator reactors is their
robustness against pressure driven modes, and the underlying mechanism behind
experimentally observed soft limits. Towards building a robust answer
to these questions, simulation studies are presented using a recently derived
reduced nonlinear MHD model. First, the initial model implementation is
extended to capture fluid compression by including the influence of parallel
flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and
interchange modes in a finite , net-zero current carrying stellarator
with low magnetic shear are then used to demonstrate the modeling capabilities.
Finally, a validation study is conducted on experimental reconstructions of
finite W7-AS discharges. In agreement with past experimental analysis,
it is shown that (i) the MHD activity is resistive, (ii) a soft limit
is observed, when the plasma resistivity approaches the estimated experimental
value, and (iii) low MHD activity is observed at intermediate
values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is
mild, explaining the soft limit, because the plasma volume remains
separated into distinct sub-volumes in which field lines are ergodically
confined. For the assumed transport parameters, the enhanced perpendicular
transport along stochastic magnetic field lines can be overcome with the
experimental heating power. The limitations in the current modeling are
described, alongside an outlook for characterising soft limits in more
detail in future work.Comment: Submitted to Nuclear Fusio
MHD simulations of formation, sustainment and loss of Quiescent H-mode in the all-tungsten ASDEX Upgrade
Periodic edge localized modes (ELMs) are the non-linear consequences of
pressure-gradient-driven ballooning modes and current-driven peeling modes
becoming unstable in the pedestal region of high confinement fusion plasmas. In
future tokamaks like ITER, large ELMs are foreseen to severely affect the
lifetime of wall components as they transiently deposit large amounts of heat
onto a narrow region at the divertor targets. Several strategies exist for
avoidance, suppression, or mitigation of these instabilities, such as the
naturally ELM-free quiescent H-mode (QH-mode). In the present article, an ASDEX
Upgrade equilibrium that features a QH-mode is investigated through non-linear
extended MHD simulations covering the dynamics over tens of milliseconds. The
equilibrium is close to the ideal peeling limit and non-linearly develops
saturated modes at the edge of the plasma. A dominant toroidal mode number of
is found, for which the characteristic features of the edge harmonic
oscillation are recovered. The saturated modes contribute to heat and particle
transport preventing pedestal build-up to the ELM triggering threshold. The
non-linear dynamics of the mode, in particular its interaction with the
evolution of the edge safety factor is studied, which suggest a possible new
saturation mechanism for the QH-mode. The simulations show good qualitative and
quantitative agreement to experiments in AUG. In particular, the processes
leading to the termination of QH-mode above a density threshold is studied,
which results in the transition into an ELM regime. In the vicinity of this
threshold, limit cycle oscillations are observed.Comment: Revised version with modifications from review process include
Plasma Surrogate Modelling using Fourier Neural Operators
Predicting plasma evolution within a Tokamak reactor is crucial to realizing
the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal
evolution of plasma rapidly and accurately allow us to quickly iterate over
design and control strategies on current Tokamak devices and future reactors.
Modelling plasma evolution using numerical solvers is often expensive,
consuming many hours on supercomputers, and hence, we need alternative
inexpensive surrogate models. We demonstrate accurate predictions of plasma
evolution both in simulation and experimental domains using deep learning-based
surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that
FNO has a speedup of six orders of magnitude over traditional solvers in
predicting the plasma dynamics simulated from magnetohydrodynamic models, while
maintaining a high accuracy (MSE ). Our modified version of
the FNO is capable of solving multi-variable Partial Differential Equations
(PDE), and can capture the dependence among the different variables in a single
model. FNOs can also predict plasma evolution on real-world experimental data
observed by the cameras positioned within the MAST Tokamak, i.e., cameras
looking across the central solenoid and the divertor in the Tokamak. We show
that FNOs are able to accurately forecast the evolution of plasma and have the
potential to be deployed for real-time monitoring. We also illustrate their
capability in forecasting the plasma shape, the locations of interactions of
the plasma with the central solenoid and the divertor for the full duration of
the plasma shot within MAST. The FNO offers a viable alternative for surrogate
modelling as it is quick to train and infer, and requires fewer data points,
while being able to do zero-shot super-resolution and getting high-fidelity
solutions
Probing non-linear MHD stability of the EDA H-mode in ASDEX Upgrade
Regimes of operation in tokamaks that are devoid of large ELMs have to be
better understood to extrapolate their applicability to reactor-relevant
devices. This paper describes non-linear extended MHD simulations that use an
experimental equilibrium from an EDA H-mode in ASDEX Upgrade. Linear ideal MHD
analysis indicates that the operational point lies slightly inside of the
stable region. The non-linear simulations with the visco-resistive extended MHD
code, JOREK, sustain non-axisymmetric perturbations that are linearly most
unstable with toroidal mode numbers of n = \{6 \dots 9\}, but non-linearly
higher and lower n become driven and the low-n become dominant. The poloidal
mode velocity during the linear phase is found to correspond to the expected
velocity for resistive ballooning modes. The perturbations that exist in the
simulations have somewhat smaller poloidal wavenumbers (k_{\theta} \sim 0.1 to
0.5 cm^{-1} ) than the experimental expectations for the quasi-coherent mode in
EDA, and cause non-negligible transport in both the heat and particle channels.
In the transition from linear to non-linear phase, the mode frequency chirps
down from approximately 35 kHz to 13 kHz, which corresponds approximately to
the lower end of frequencies that are typically observed in EDA H-modes in
ASDEX Upgrade
Simulations of COMPASS vertical displacement events with a self-consistent model for halo currents including neutrals and sheath boundary conditions
The understanding of the halo current properties during disruptions is key to design and operate large scale tokamaks in view of the large thermal and electromagnetic loads that they entail. For the first time, we present a fully self-consistent model for halo current simulations including neutral particles and sheath boundary conditions. The model is used to simulate vertical displacement events (VDEs) occurring in the COMPASS tokamak. Recent COMPASS experiments have shown that the parallel halo current density at the plasma-wall interface is limited by the ion saturation current during VDE-induced disruptions. We show that usual magneto-hydrodynamic boundary conditions can lead to the violation of this physical limit and we implement this current density limitation through a boundary condition for the electrostatic potential. Sheath boundary conditions for the density, the heat flux, the parallel velocity and a realistic parameter choice (e.g. Spitzer's resistivity and Spitzer-Harm parallel thermal conductivity) extend present VDE simulations beyond the state of the art. Experimental measurements of the current density, temperature and heat flux profiles at the COMPASS divertor are compared with the results obtained from axisymmetric simulations. Since the ion saturation current density (Jsat) is shown to be essential to determine the halo current profile, parametric scans are performed to study its dependence on different quantities such as the plasma resistivity and the particle and heat diffusion coefficients. In this respect, the plasma resistivity in the halo region broadens significantly the Jsat profile, increasing the halo width at a similar total halo current