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Abstract:

Multiple space and time scales arise in plasma turbulence in magnetic confinement fusion devices because of the smallness of the square root of the electron-to-ion mass ratio ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$ and the consequent disparity of the ion and electron thermal gyroradii and thermal speeds. Direct simulations of this turbulence that include both ion and electron space–time scales indicate that there can be significant interactions between the two scales. The extreme computational expense and complexity of these direct simulations motivates the desire for reduced treatment. By exploiting the scale-separation between ion scales (IS) and electron scales (ES), and expanding the gyrokinetic equations for the turbulence in ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$, we derive such a reduced system of gyrokinetic equations that describes cross-scale interactions. The coupled gyrokinetic equations contain novel terms which provide candidate mechanisms for the observed cross-scale interaction. The ES turbulence experiences a modified drive due to gradients in the IS distribution function, and is advected by the IS $E\times B$ drift, which varies in the direction parallel to the magnetic field line. The largest possible cross-scale term in the IS equations is sub-dominant in our ${\left({m}_{{\rm{e}}}/{m}_{{\rm{i}}}\right)}^{1/2}$ expansion. Hence, in our model the IS turbulence evolves independently of the ES turbulence. To complete the scale-separated approach, we provide and justify a parallel boundary condition for the coupled gyrokinetic equations in axisymmetric equilibria based on the standard 'twist-and-shift' boundary condition. This approach allows one to simulate multi-scale turbulence using ES flux tubes nested within an IS flux tube.

Abstract:

Here we present details of a mixed implicit-explicit numerical scheme for the solution of the gyrokinetic-Poisson system of equations in the local limit. This scheme has been implemented in a new code called $\texttt{stella}$, which is capable of evolving electrostatic fluctuations with full kinetic electron effects and an arbitrary number of ion species in general magnetic geometry. We demonstrate the advantages of this mixed approach over a fully explicit treatment and provide linear and nonlinear benchmark comparisons for both axisymmetric and non-axisymmetric magnetic equilibria.

Abstract:

© 2018 IOP Publishing Ltd. Differential rotation is induced in tokamak plasmas when an underlying symmetry of the governing gyrokinetic-Maxwell system of equations is broken. One such symmetry-breaking mechanism is considered here: the turbulent acceleration of particles along the mean magnetic field. This effect, often referred to as the 'parallel nonlinearity', has been implemented in the δf gyrokinetic code stella and used to study the dependence of turbulent momentum transport on the plasma size and on the strength of the turbulence drive. For JET-like parameters with a wide range of driving temperature gradients, the momentum transport induced by the inclusion of turbulent acceleration is similar to or smaller than the ratio of the ion Larmor radius to the plasma minor radius. This low level of momentum transport is explained by demonstrating an additional symmetry that prohibits momentum transport when the turbulence is driven far above marginal stability.

Abstract:

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion–electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, βi: It ranges from ∼0.05 at βi=0.1 to at least 30 for βi≳10. This energy partition is approximately insensitive to the ion-to-electron temperature ratio Ti/Te. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high βi and hotter electrons at low βi. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high βi and a tendency for the ion heating to be mediated by nonlinear phase mixing (“entropy cascade”) when βi≲1 and by linear phase mixing (Landau damping) when βi≫1.