D.P. Brennan, E. Startsev, A.H. Boozer NSTX-U / PPPL Theory collaboration on Disruptions

1. Self-consistent nonlinear simulation of generated runaway electron current coupled with resistive MHD D.P. Brennan, E. Startsev, A.H. Boozer NSTX-U / PPPL Theory collaboration on Disruptions October 25, 2013

2. Implement runaway electron current density within MHD : Ohm’s law only diffuses background Algorithm in DEBS: Remove runaway electrons from diffusion term in Ohm’s law Include full current in VxB term in momentum equation Advance Jre source (or sink!) with parallel electric field

3. Research Plan: Precondition study based on MHD instabilities of varying character Evolve nonlinearly with a series of variations in profiles in advance of avalache. First cases as simple as possible: force free linearly stable. - characterize self consistent n=0 evolution – this alone is new Study two equilibria: sheared and flat core FRS equilibrium: well known basis for resistive 2/1 or multiple m/n Holmes equilibrium: flat q in core - Higher Jq -> E|| -> Jre Differences in shear affects core and outer mode Br and thus Jre Holmes, et al, Phys. Fluids 26, 2569 (1983). Furth, et al, Phys. Fluids 16, 1054 (1973).

4. First preliminary result: animations show evolution (m/n=0/0 only) of Jre in MHD Initial simulations have included verification of the numerical method, variation of the initial Jre, and variation of the threshold Electric field (constant for now) Compare two cases in Holmes equilibrium m/n=0/0 only (would be unstable to n=1) Seed Jre varies from peaked on axis to peaked outer minor radius In axis peak case: Jre inductively consumes the background current, forms background Jb shell, reduces the E|| below threshold, and saturates, as q(0) is raised >>1. In outer peak case: Jre forms shell, highly localized Jb driven on axis, q(0) decreased <<1 -> likely strongly unstable to n>=1.

5. First preliminary result: animations show evolution (m/n=0/0 only) of Jre in MHD As Jre grows and becomes on order of Jb Jb inductively forms current shell, E|| drives edge of Jre System saturates as electric field decays, as expected. - need to reconsider E||<Ec effect on Jre? Or ok? E-folds issue requires resistive wall -> readily available, near term study - these runs have effectively had infinite flux available

6. Nonlinear MHD+Jre is new physics that is critical to our burning plasmas, though largely absent in present day experiments We have: cylindrical tokamak, nonlinear resistive MHD, anisotropic heat conduction, resistive wall, and runaway electrons self-consistently coupled. Near term plans: Characterize the n=m=0 evolution of the runaways with Jb peak 2/1 and more m>1 resistive MHD 1/1 kink mode + m>1 modes, nonlinearly evolving Include temperature equation with anisotropic heat conduction and resistive wall NSTX experimental disruptions could be used to study the variations of the preconditions to expect based on state of the equilibrium and stability on entry into the thermal quench. The computations can answer what the outcome of these preconditions would be in burning plasma conditions. This has never been done, is a critical physics study for ITER, and may lead to a predictive tool for avoidance of catastrophic Jre