Theoretical astrophysics and plasma physics at RPC

Abstract:

Curvature-driven instabilities are ubiquitous in magnetised fusion plasmas. By analysing the conservation laws of the gyrokinetic system of equations, we demonstrate that the well-known spatial localisation of these instabilities to regions of ‘bad magnetic curvature’ can be explained using the conservation law for a sign-indefinite quadratic quantity that we call the gyrokinetic field invariant. Its evolution equation allows us to define the local effective magnetic curvature whose sign demarcates the regions of ‘good’ and ‘bad’ curvature, which, under some additional simplifying assumptions, can be shown to correspond to the inboard (high-field) and outboard (low-field) sides of a tokamak plasma, respectively. We find that, given some reasonable assumptions, electrostatic curvature-driven modes are always localised to the regions of bad magnetic curvature, regardless of the specific character of the instability. More importantly, we also deduce that any mode that is unstable in the region of good magnetic curvature must be electromagnetic in nature. As a concrete example, we present the magnetic-drift mode, a novel good-curvature electromagnetic instability, and compare its properties with the well-known electron-temperature-gradient instability. Finally, we discuss the relevance of the magnetic drift mode for high- fusion plasmas, and in particular its relationship with microtearing modes.

Abstract:

Electron energisation by magnetic reconnection has historically been studied in the Lagrangian guiding-centre framework. Insights from such studies include that Fermi acceleration in magnetic islands can accelerate electrons to high energies. An alternative Eulerian fluid formulation of electron energisation was recently used to study electron energisation during magnetic reconnection in the absence of magnetic islands. Here, we use particle-in-cell simulations to compare the Eulerian and Lagrangian models of electron energisation in a set-up where reconnection leads to magnetic island formation. We find the largest energisation at the edges of magnetic islands. There, energisation related to the diamagnetic drift dominates in the Eulerian model, while the Fermi related term dominates in the Lagrangian model. The models predict significantly different energisation rates locally. A better agreement is found after integrating over the simulation domain. We show that strong magnetic curvature can break the magnetic moment conservation assumed by the Lagrangian model, leading to erroneous results. The Eulerian fluid model is a complete fluid description and accurately models bulk energisation. However, local measurements of its constituent energisation terms need not reflect locations where plasma is heated or accelerated. The Lagrangian guiding centre model can accurately describe the energisation of particles, but it cannot describe the evolution of the fluid energy. We conclude that while both models can be valid, they describe two fundamentally different quantities, and care should be taken when choosing which model to use.