Runaway electrons may be generated in a tokamak during the start up, during normal operation and during a plasma disruption. During a disruption, runaway electrons can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode number tearing modes. We have developed a fluid runaway electron model for the 3D MHD code M3D-C1 (Jardin et al 2012 J. Comput. Sci. Discovery 6 014002). To benchmark, we have reproduced the MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous analytic studies (Helander et al 2007 Phys. Plasmas 14 104142) and have extended them here with a numerical eigenvalue calculation. We find that the low mode number tearing mode has a rotation caused by the MHD - runaways interaction and the perturbed toroidal current scale length is much smaller with runaways than without and decreases as the runaway speed increases.
We investigate the effects of runaway electron current on the dispersion relation of resistive magnetohydrodynamic modes in tokamaks. We present a new theoretical model to derive the dispersion relation, which is based on the asymptotic analysis of the resistive layer structure of the modes. It is found that in addition to the conventional resistive layer, a new runaway current layer can emerge whose properties depend on the ratio of the Alfvén velocity to the runaway electron convection speed. Due to the contribution from this layer, both the tearing mode and kink mode will have a real frequency in addition to a growth rate. The derived dispersion relation has been compared with numerical results using both a simplified eigenvalue calculation and a M3D-C1 linear simulation, and good agreement is found in both cases.
Relativistic electron (RE) beams at high current density (low safety factor, q
a
) yet very low free-electron density accessed with D2 secondary injection in the DIII-D and JET tokamak are found to exhibit large-scale MHD instabilities that benignly terminate the RE beam. In JET, this technique has enabled termination of MA-level RE currents without measurable first-wall heating. This scenario thus offers an unexpected alternate pathway to achieve RE mitigation without collisional dissipation. Benign termination is explained by two synergistic effects. First, during the MHD-driven RE loss events both experiment and MHD orbit-loss modeling supports a significant increase in the wetted area of the RE loss. Second, as previously identified at JET and DIII-D, the fast kink loss timescale precludes RE beam regeneration and the resulting dangerous conversion of magnetic to RE kinetic energy. During the termination, the RE kinetic energy is lost to the wall, but the current fully transfers to the cold bulk thus enabling benign Ohmic dissipation of the magnetic energy on longer timescales via a conventional current quench. Hydrogenic (D2) secondary injection is found to be the only injected species that enables access to the benign termination. D2 injection: (1) facilitates access to low q
a
in existing devices (via reduced collisionality & resistivity), (2) minimizes the RE avalanche by ‘purging’ the high-Z atoms from the RE beam, (3) drives recombination of the background plasma, reducing the density and Alfven time, thus accelerating the MHD growth. This phenomenon is found to be accessible when crossing the low q
a
stability boundary with rising current, falling toroidal field, or contracting minor radius—the latter being the expected scenario for vertically unstable RE beams in ITER. While unexpected, this path scales favorably to fusion-grade tokamaks and offers a novel RE mitigation scenario in principle accessible with the day-one disruption mitigation system of ITER.
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