Nonlinear equilibria and transport processes in burning plasmas

Abstract

In this work, we put forward a general phase space transport theory in axisymmetric tokamak plasmas based upon the concept of zonal state (ZS). Within this theoretical framework, the ZS corresponds to a renormalized plasma nonlinear equilibrium consisting of phase space zonal structures (PSZS) and zonal electromagnetic fields (ZFs) which evolve self-consistently with symmetry breaking fluctuations and sources/collisions. More specifically, our approach involves deriving governing equations for the evolution of particle distribution functions (i.e, PSZS), which can be used to compute the corresponding macro-/meso-scale evolving magnetized plasma equilibrium adopting the Chew Goldberger Low description, separating the spatiotemporal microscale structures. The nonlinear physics of ZFs and of geodesic acoustic modes (GAMs)/energetic particle driven GAMs is then analyzed to illustrate the applications of our theory.

ATEP: an advanced transport model for energetic particles

“…To that end, comparisons with other reduced models will be carried out, e.g. with an ongoing extension of the DAEPS code [12,43] that uses explicit analytical expressions for calculating the phase space fluxes. Also, a 1d reduced model based on the beam-plasma bump-on-tail paradigm that is designed to go beyond the quasi-linear approximation and thus forecast possible EP transport transitions such as avalanching [36] will be used to determine the limits of the ATEP model.…”

“…In its simplest limit without sources, sinks and collisions, the transport equation is formulated as a continuity equation for the EP distribution function F z in the constants of motion (CoM) phase space (P ϕ , E, Λ) [12,29]:…”

“…⟨⟩ indicates orbit and phase (between particles and wave) averaging. Note that notations and definitions deviate slightly from [12]. If the initial F z is assumed to be a scalar function only of CoM, it will remain independent of any poloidal or toroidal angle since the phase space flow induced by the flow velocity v P ϕ ,E = (⟨…”

“…Large parameter scans, sensitivity studies, and multi-scale physics describing energetic particle (EP) transport on neoclassical transport time scales require tools that go beyond what is presently feasible with first-principles numerical codes. To this end, in recent years a set of comprehensive transport equations based on non-linear gyrokinetic theory [7][8][9] have been derived [10][11][12]. In particular, the special role of EPs has been addressed that not only introduce new classes of resonantly driven instabilities but also interact with micro-and macro-scale plasma perturbations, causing spatio-temporal cross-scale couplings [13,14].…”

Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

“…The phase space resonance islands of EP with different modes could easily overlap and decorrelate the coherent phase space structures. In this case, the EP transport may also exhibit a random-walk-like diffusive character [117,118]. The role of convective versus diffusive EP transport induced by RSAEs in the core of burning plasmas, of course, depends on the considered scenario, and both mechanisms might even coexist when inspecting different scales.…”