Equilibrium and transport for quasi-helical reversed field pinches

Abstract

We provide a survey of the recent progresses in theoretical/numerical studies on the physics of the quasi helical RFP regime. Such regime systematically characterizes RFX-mod experiments at high currents (Ip>1.2 MA), producing clear electron transport barriers about mid-radius. Several approaches, ranging from macroscopic to microscopic description, have been used to tackle the related complex physics. MHD analytical calculation of ohmic helical states by perturbation theory has been developed. A necessary criterion for field reversal at the edge is derived, proved to be satisfied in a large database of RFX-mod pulses. Numerical simulations show that the criterion works for large perturbations of the pinch configuration too, in particular those leading to states with a single helical axis. The addition of heat transport dynamics is expected to improve the 3D nonlinear MHD modelling of RFP self-organization. To this end the PIXIE3D initial value code has been implemented for RFP dynamics. Recently, for the first time in MHD simulation, the mandatory step of numerical verification has been completed by careful benchmarking PXIE3D and SpeCyl codes. The effect of chaos healing by separatrix expulsion, believed to favor the formation of transport barriers, has been reviewed using a volume preserving field line tracing code (NEMATO). The nature of additional physical mechanisms responsible for the actual transport in such regimes is matter of study. ITG microturbulence has been considered first. In 2008 Guo showed analytically that ITG modes are more stable in RFPs than in tokamaks because of a stronger Landau damping. In the last two years different numerical tools have been adapted to the RFP: the nonlinear gyrokinetic GS2 code and the fluid TRB code. An integral eigenvalue approach, retaining finite Larmor radius effects has also been used. All approaches agree that ITG modes can hardly become linearly unstable but could be envisaged in future higher-current experiments. Impurities and trapped electrons effect on ITGs are under consideration, first results show a destabilizing effect by impurities, while a negligible one by trapped electrons. Trapped Electron Modes may appear across high density gradient regions. Microtearing turbulence is expected to play an important role at the transport barriers.

How to Face the Complexity of Plasmas?

“…Indeed with general assumptions, the supplementary terms of a generalized Ohm's law do not contribute into the parallel Ohm's law used in such calculations (see section 2.1 of [25]). This does not prove the validity of the simplest Ohm's law.…”

“…This motion explains the dynamo component of the electromotive force driving the currents in the plasma, which was a mystery for the previous TRT paradigm. At present, single helicity states are understood as a mere extension of the saturated tearing mode, in particular as far as the electric drift nature of the dynamo is concerned [19,25]. As yet, MHD simulations remain the main way to address theoretical issues, since the analytical description of these states is just in its infancy 15 [18,25].…”

“…At present, single helicity states are understood as a mere extension of the saturated tearing mode, in particular as far as the electric drift nature of the dynamo is concerned [19,25]. As yet, MHD simulations remain the main way to address theoretical issues, since the analytical description of these states is just in its infancy 15 [18,25]. In many other fields of plasma physics too, numerical simulations are the irreplaceable tool for investigating complexity 16 .…”

“…This is all the more important that this fluid motion is a simple example of a dynamo, i.e. the production of an electromotive force from a fluid motion [25]. The RFP single helicity equilibrium provides another instance which is an extension of the simplest case.…”

“…Because of the limited capabilities of models, the status of analytical calculations is different from more axiomatic fields of physics. Heuristically, they are a powerful tool to uncover new hidden physics, but pedagogically one may avoid them to start with, and keep the physical ideas and the corresponding images 25 . Another incentive to diminish 22 In the fluid description of screw pinches, a classical model is provided by the combination of Faraday-Ohm's law and of Navier-Stokes equation with Lorentz force.…”