Abstract
In this paper, we extend the multiscale approach developed in Abel et al (2012 Rep. Prog. Phys. submitted) by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the reduced electron model. We prove that ion-scale electromagnetic turbulence cannot change the magnetic topology, and argue that to lowest order the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response to ion-scale turbulence is derived. All fast electron timescales have been eliminated from these equations. We also use these magnetic surfaces to construct transport equations for electrons and for electron heat in terms of the reduced electron model.
Highlights
The energy, particle, and momentum confinement of present-day fusion experiments and proposed future devices is limited by turbulent, rather than collisional transport
The turbulence that causes this transport has an essentially multiscale character. It occurs on spatial scales smaller than those associated with the equilibrium and on timescales shorter than those associated with transport of mean quantities but much longer than the gyroperiod
This is the basis for the multiscale gyrokinetic approach presented in [1, 2], characterised by the small parameter = ρ/a, where ρ is the thermal gyroradius and a is a typical equilibrium length scale
Summary
The energy, particle, and momentum confinement of present-day fusion experiments and proposed future devices is limited by turbulent, rather than collisional transport. It occurs on (perpendicular) spatial scales smaller than those associated with the equilibrium and on timescales shorter than those associated with transport of mean quantities but much longer than the gyroperiod This is the basis for the multiscale gyrokinetic approach presented in [1, 2], characterised by the small parameter = ρ/a, where ρ is the thermal gyroradius and a is a typical equilibrium length scale. We derive for the first time a set of equations governing the electron behaviour in the presence of ion-scale fluctuations. The second major result of this paper is a simplified system of transport equations for electrons
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