Submitted for the DPP17 Meeting of The American Physical Society Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations1 MATTHEW T BEIDLER, JAMES D CALLEN, CHRIS C HEGNA, CARL R SOVINEC, University of Wisconsin-Madison — Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state [1]. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extendedMHD code NIMROD, building on previous work [2] by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. [1] R. Fitzpatrick, Nucl. Fusion 33, 1049 (1993). [2] M.T. Beidler, J.D. Callen, C.C. Hegna, and C.R. Sovinec, Phys. Plasmas 24, 052508 (2017). 1Supported by DOE OFES grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664. Matthew T Beidler University of Wisconsin-Madison Date submitted: 13 Jul 2017 Electronic form version 1.4

The effects of collisions are often neglected in theoretical analyses of low collisionality plasmas where the collision rate nu is smaller than the frequency of waves or other physical processes being considered. However, small angle Coulomb collisions scatter the velocity vector v of charged particles and produce slightly probabilistic rather than fully deterministic charged particle trajectories in a plasma. These diffusive effects produce an effective collision rate nu(eff) similar to nu / (vertical bar delta v vertical bar/nu)(2) >> nu for relaxation of plasma responses localized to a small region delta v in velocity space. In particular, they create narrow dissipative boundary layers in the vicinity of resonant collisionless responses of the plasma to waves which resolve these singular responses and create temporal irreversibility. A new Green-function-based procedure is being developed for exploring these low collisionality effects. This new procedure is first used to explore Coulomb collisional scattering effects on the temporal evolution of the linear Landau damping of Langmuir waves. On collision and longer time scales the relevant plasma kinetic equation becomes an extended Chapman-Enskog type equation. Green function solutions of this kinetic equation can be used to determine self-consistent closures for fluid moment equations. A multiple time scale and systematic small gyroradius and perturbation level analysis has been used to develop descriptions of toroidal magnetically confined plasmas in tokamaks on collision and transport time scales. Some examples of low collisionality closures and their effects on the behavior of tokamak plasmas are noted.

A model is proposed for the edge electron temperature profile Te(ρ) in high (H) confinement mode, diverted tokamak plasmas based on the paleoclassical model for the minimum radial electron heat transport. Moving inward from the separatrix, Te profile predictions are: first an increasing Te gradient with ηe ≡ d ln Te/d ln ne 2, a maximum |∇Te| where q drops to < ∼ 5, then a decreasing |∇Te|, and finally a pedestal electron pressure determined by balancing collisional paleoclassical transport against gyro-Bohm-scaled anomalous electron heat transport: p e ≡ n e T ped e ∝ (ā/R̄q)B. Model predictions and transport modeling with it compare well with pedestal data from DIII-D.

This panel was set up by the U.S. Department of Energy's Fusion Energy Sciences Advisory Committee in response to a request from the department to prepare a strategy for the study of burning fusion plasmas. Experimental study of a burning plasma has long been a goal of the U.S. science-based fusion energy program. There is an overwhelming consensus among fusion scientists that we are now ready scientifically, and have the full technical capability, to embark on this step. The fusion community is prepared to construct a facility that will allow us to produce this new plasma state in the laboratory, uncover the new physics associated with the fusion burn, and develop and test new technology essential for fusion power. Given this background, the panel has produced a strategy to enable the United States to proceed with this crucial next step in fusion energy science. The strategy was constructed with awareness that the burning plasma program is only one major component in a comprehensive development plan for fusion energy. A strong core science and technology program focused on fundamental understanding, confinement configuration optimization, and the development of plasma and fusion technologies essential to the realization of fusion energy. The core program will also be essential to the successful guidance and exploitation of the burning plasma program, providing the necessary knowledge base and scientific workforce.