Abstract:This paper explores the behavior of runaway electrons in tokamak plasmas at low electron density, plasma current, and magnetic field using experimental data from the Madison Symmetric Torus (MST) and computational data from the NIMROD nonlinear resistive 3D MHD code. Density thresholds for the onset and suppression of runaway electrons are determined experimentally in steady tokamak plasmas, and in plasmas with a population of runaway electrons, resonant magnetic perturbations with different poloidal mode numb… Show more
“…[5] from runaway electron deconfinement experiments in the Madison Symmetric Torus (MST) reported in Ref. [21]. The NIMROD spatial representation uses structured, C 0 -continuous, Lagrange spectral elements in the poloidal plane and a finite series of Fourier modes in the toroidal direction.…”
An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L 2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergencefree condition is incorporated as a constrain in the cost function allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.
“…[5] from runaway electron deconfinement experiments in the Madison Symmetric Torus (MST) reported in Ref. [21]. The NIMROD spatial representation uses structured, C 0 -continuous, Lagrange spectral elements in the poloidal plane and a finite series of Fourier modes in the toroidal direction.…”
An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The coefficients of the expansion are obtained by minimizing a cost function defined as the L 2 norm of the difference between the ground truth and the reconstructed magnetic field evaluated on the training data. The divergencefree condition is incorporated as a constrain in the cost function allowing the method to achieve arbitrarily small errors in the magnetic field divergence. An exponential decay of the approximation error is observed and compared with the less favorable algebraic decay of local splines. Compared to local methods involving computationally expensive search algorithms, the proposed method exhibits a significant reduction of the computational complexity of the field evaluation, while maintaining a small error in the divergence even in the presence of magnetic islands and stochasticity. Applications to the computation of Poincaré sections using data obtained from numerical solutions of the magnetohydrodynamic equations in toroidal geometry are presented and compared with local methods currently in use.
“…The most studied mitigation method is massive material injection (gas or shattered pellet) either before or after RE beam formation [6][7][8][9]. RE avoidance has also been pursued via applied 3D magnetic fields, with the resulting stochasticity transporting REs out of the plasma [10][11][12][13][14][15][16][17]. While initial results are promising, fully stochastic fields have not yet been achieved [18,19], and this is still an active mitigation scheme.…”
The potential formation of multi-mega-ampere beams of relativistic ‘runaway’ electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak’s development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium–tritium plasmas.
“…The most studied mitigation method is massive material injection (gas or shattered pellet) either before or after RE beam formation [6][7][8][9]. RE avoidance has also been pursued via applied 3D magnetic fields, with the resulting stochasticity transporting REs out of the plasma [10][11][12][13][14][15][16][17]. While initial results are promising, fully stochastic fields have not yet been achieved [18,19], and this is still an active mitigation scheme.…”
The potential formation of multi-mega-ampere beams of relativistic "runaway" electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak's development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium-tritium plasmas.
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