Prof Michael Barnes

Abstract:

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio Qi/Qe as a function of the compressive-to-Alfvénic driving power ratio Pcompr/PAW, of the ratio of ion thermal pressure to magnetic pressure βi, and of the ratio of ion-to-electron background temperatures Ti/Te. It is shown that Qi/Qe is an increasing function of Pcompr/PAW. When the compressive driving is sufficiently large, Qi/Qe approaches ≃Pcompr/PAW. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfvén waves is absent for both low and high βi, meaning that the compressive driving is directly connected to the ion-entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low βi and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.

Abstract:

Magnetised plasma turbulence can have a multiscale character: instabilities driven by mean temperature gradients drive turbulence at the disparate scales of the ion and the electron gyroradii. Simulations of multiscale turbulence, using equations valid in the limit of infinite scale separation, reveal novel cross-scale interaction mechanisms in these plasmas. In the case that both long-wavelength (ion-gyroradius-scale) and short-wavelength (electron-gyroradius-scale) linear instabilities are driven far from marginal stability, we show that the short-wavelength instabilities are suppressed by interactions with long-wavelength turbulence. Two novel effects contributed to the suppression: parallel-to-the-field-line shearing by the long-wavelength <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022377820001294_inline2.png" /> <jats:tex-math>${{\boldsymbol {E}} \times \boldsymbol {B}}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> flows, and the modification of the background density gradient by the piece of the long-wavelength electron adiabatic response with parallel-to-the-field-line variation. In contrast, simulations of multiscale turbulence where instabilities at both scales are driven near marginal stability demonstrate that when the long-wavelength turbulence is sufficiently collisional and zonally dominated the effect of cross-scale interaction can be parameterised solely in terms of the local modifications to the mean density and temperature gradients. We discuss physical arguments that qualitatively explain how a change in equilibrium drive leads to the observed transition in the impact of the cross-scale interactions.

Abstract:

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for $k_y \rho_i \gtrsim 0.1$ in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, $k_y$ is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and $\rho_i$ is the ion gyroradius. At $k_y \rho_i \gtrsim 1$, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as $k_y \rho_i \sim (\rho_i/\rho_e) L_{Te} / R_0 \sim 1$ and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, $K_x \rho_e \sim 1$, where $K_x$ is the effective radial wavenumber. Here, $\rho_e$ is the electron gyroradius, $R_0$ is the major radius of the last closed flux surface, and $1/L_{Te}$ is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by $\mathbf{ E} \times \mathbf{ B} $ shear. ETG modes are very resilient to $\mathbf{ E} \times \mathbf{ B}$ shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.