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Loizu, J.

Publications and source records attributed to Loizu, J..

6 records

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DOE OSTI2023

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by 'ideal interfaces', and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion6 101; Glasser et al 1975 Phys. Fluids18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Model for current drive induced crash cycles in W7-X

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι–profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Parallel convection and E × B drifts in the TCV snowflake divertor and their effects on target heat-fluxes

Parallel convection and E × B drifts act together to redistribute heat between the strike-points in the low field side snowflake minus (LFS SF–). The cumulative heat convection from both mechanisms is enhanced near the secondary X-point and is shown to dominate over heat conduction, partly explaining why the LFS SF– distributes power more evenly than the single null (SN) or other snowflake (SF) configurations. Pressure profiles at the entrance of the divertor are strongly affected by the position of the secondary X-point and magnetic field direction indicating the importance of E × B drifts. Pressure drops of up to 50% appear between the outer-midplane (OMP) and the divertor entrance enhancing the role of parallel heat convection. The electron temperature and density profiles and the radial turbulent fluxes measured at the OMP are largely unaffected by the changes in divertor geometry, even on flux surfaces where the connection length is infinite.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C 1 code and the tearing mode $\Delta^{^{\prime}}$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Overall, our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Direct prediction of nonlinear tearing mode saturation using a variational principle

It is shown that the variational principle of multi-region relaxed magnetohydrodynamics (MRxMHD) can be used to predict the stability and nonlinear saturation of tearing modes in strong guide field configurations without resolving the dynamics and without explicit dependence on the plasma resistivity. While the magnetic helicity is not a good invariant for tearing modes, we show that the saturated tearing mode can be obtained as an MRxMHD state of a priori unknown helicity by appropriately constraining the current profile. The predicted saturated island width in a tearing-unstable force-free slab equilibrium is shown to reproduce the theoretical scaling at small values of Δ' and the scaling obtained from resistive magnetohydrodynamics simulations at large Δ'.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Free-boundary MRxMHD equilibrium calculations using the stepped-pressure equilibrium code

Here the stepped-pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 , 112 502) is extended to enable free-boundary multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', , is computed, and the virtual-casing principle is used iteratively to compute the normal field on so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗