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Person# Ankit Kumar

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Antoine Baillod, Ankit Kumar, Joaquim Loizu Cisquella

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-C1 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. 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.

2021Sameer Kumar, Rohit Kumar, Ankit Kumar, Harshita Raj, Abhijit Sen

The influence of background plasma poloidal rotation on the rotation frequency of the m/n = 2/1 drift tearing mode (DTM) has been studied in ADITYA-U tokamak. The poloidal rotation velocity of the background plasma in the ion diamagnetic direction is increased or decreased by inducing an outward or inward radial electric field, respectively, through a biased-electrode placed in the edge region of the plasma. The rotation frequency of the preexisting drift tearing mode, rotating in the electron diamagnetic direction, concomitantly decreased or increased with the application of bias depending on its polarity. The positive-bias increases the background plasma rotation in the ion-diamagnetic direction from its pre-bias value, hence decreasing the DTM rotation frequency, whereas the negative bias reduces the plasma rotation velocity in the ion-diamagnetic direction, hence increasing the mode rotation. In addition to that, a short gas puff introduced during the positive and negative bias pulse further reduces the mode frequency, however, with different amplitudes in different bias-polarities. These observations suggest that the background plasma rotation contributes significantly toward the rotation of DTMs, and the rotation frequency of the magnetohydrodynamic modes can be modified by varying the poloidal rotation of the background plasma and/or the diamagnetic drift frequency.

2021Ankit Kumar, Joaquim Loizu Cisquella

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.

2023