ETD

• fusion
• magnetic reconnection
• W7-X

Sawtooth-like core crashes observed in Wendelstein 7-X (W7-X) during electron-cyclotron current drive (ECCD) indicate that localized driven currents can trigger fast internal relaxations even in an optimized stellarator intended to operate with low net plasma current. These events motivate a quantitative assessment of which current-driven instabilities become accessible when ECCD perturbs the rotational transform profile and introduces low-order rational surfaces in the core. In particular, ECCD can produce a “humped” radial iota profile with two iota = 1 resonances, creating a double-resonant configuration that is favorable for current-driven magnetic reconnection. Here iota(r), the rotational transform, is proportional to the ratio of poloidal to toroidal turns of the equilibrium field. The goal of this thesis is to identify the dominant instability mechanisms supported by such equilibria in W7-X geometry and, crucially, to distinguish regimes governed by non-ideal reconnection physics (resistive or inertia-mediated tearing) from regimes in which the equilibrium is already unstable within ideal MHD.

The study employs a numerical workflow combining three-dimensional equilibrium reconstruction, ideal MHD stability analysis, and time-dependent nonlinear simulations with a radially global reduced gyrokinetic/fluid model in fully three-dimensional geometry. Equilibria are computed with the VMEC code under the nested-flux-surface assumption, prescribing an ECCD-like localized modification of iota that generates two iota = 1 surfaces. Ideal stability is assessed with the CAS3D code through the energy-principle eigenvalue problem, providing a direct criterion for the presence of global ideal instabilities in the reconstructed equilibrium. Non-ideal plasma evolution is investigated with the extended MHD model of the EUTERPE code, which includes finite plasma resistivity and electron inertia, and thus allows perturbed magnetic field lines to tear and reconnect. To highlight the role of current-density gradients, the time-dependent simulations are performed with flat plasma density and temperature profiles, so that the equilibrium pressure gradient is negligible and pressure-driven contributions are suppressed. Growth rates and mode structures are extracted from the simulations and compared with theoretical predictions, as well as with previous numerical and experimental results.

Controlled parameter scans are performed to probe the transition from collisional to weakly collisional regimes. Under collisional conditions, the dominant instability exhibits tearing parity and localizes primarily between the two resonant surfaces; its growth rate is consistent with resistive reconnection. As collisionality is reduced, an electron-inertia scan reveals an electron-inertia-dominated regime. These results support the interpretation that ECCD-driven double resonance in W7-X-like stellarator geometry can destabilize reconnecting modes under experimentally relevant conditions.

In the low-collisionality simulations at physical electron mass, however, the dynamics are dominated by a low-mode-number (m,n) = (1, -1) instability, whose growth rate shows only a weak dependence on plasma resistivity and approaches a finite value as the electron mass is reduced. This indicates that ideal MHD modes can also be destabilized. This outcome highlights the sensitivity of ideal stability to the background pressure: while flat density and temperature profiles in EUTERPE are useful for isolating current-gradient effects, they also imply an equilibrium with an essentially vanishing pressure gradient, which need not share the ideal-stability properties of the reference finite-pressure equilibrium. Accordingly, when an equilibrium consistent with the flattened pressure profile is recomputed with VMEC and reanalyzed with CAS3D, it is found to be ideally unstable, with a dominant (1, -1) eigenmode, matching the mode structure observed in the simulations for sufficiently small non-ideal effects. Importantly, boundary conditions on the magnetic axis proved essential for the extended EUTERPE code to capture ideal MHD eigenfunctions. In this thesis, the latest version of the code was used. The main conclusions are that (i) for equilibria that remain ideally stable, ECCD can produce double-resonant configurations that support reconnecting instabilities with resistive and inertial scaling, and (ii) pressure-profile simplifications can modify the equilibrium stability and introduce spurious ideal instabilities. A consistent strategy for future work is therefore to construct equilibrium families with pressure gradients and ECCD-driven current profiles that are verified to be marginally stable with CAS3D, and to perform matched extended MHD EUTERPE simulations on the same equilibria to better characterize ideal marginality.