Perpendicular ion heating in turbulence and reconnection: magnetic moment breaking by coherent fluctuations

Abstract

We study the interaction of an ion with a fluctuation in the electromagnetic fields that is localized in both space and time. We study the scale-dependence of the interaction in both space and time, deriving a generic form for the ion's energy change, which involves an exponential cutoff based on the characteristic timescale of the electromagnetic fluctuation. This leads to diffusion in energy in both $v_\perp$ and $v_\parallel$. We show how to apply our results to general plasma physics phenomena, and specifically to Alfvénic turbulence and to reconnection. Our theory can be viewed as a unification of previous models of stochastic ion heating, cyclotron heating, and reconnection heating in a single theoretical framework.

Figures (4)

• Figure 1: The functional form (\ref{['eq:example']}) for the time-dependence of the electric field, with $a=-2$, $b=2$.
• Figure 2: Typical scalings for the magnetic and electric field fluctuation amplitudes as a function of $k_\perp\rho_p$, in the absence of strong dissipation. Here we have set $b=1/3$ and $a=3/4$, and the sub-ion-scale range is unrealistically long: in reality it would be cut off at the smaller of $k_\perp \sim 1/d_e$ or $k_\perp \sim 1/\rho_e$. We do not model electron-scale effects in this paper.
• Figure 3: The proton heating rate $Q_{\perp p}$ normalized to the turbulent energy flux through scales $\epsilon=\delta b_L^3/L$, for different values of the normalized outer-scale amplitude $A$, with $L/\rho_p = 10^{4}$ and $v_{th \rm p}/v_{\mathrm{A}}=0.1$. The horizontal black line denotes $Q_{\perp p}/\epsilon=1$, complete damping of the turbulent cascade: in reality, if the heating approaches this line the power-law behaviour of the spectra and the constancy of $\epsilon$ will no longer be accurate. The vertical solid black line denotes $k_\perp\rho_p=1$, and the vertical dashed line denotes $k_\perp\rho_e=1$: the small heating rates at or beyond the electron scales in our model (which neglects electron-scale physics) are an overestimate due to the much steeper spectrum in this range.
• Figure 4: A crude schematic of an ion-scale reconnection exhaust. The reconnecting field $\sim B_{0y}$ (blue) reverses across the exhaust. An ion enters the exhaust with a slow drift velocity (red) $v_{in}\sim R v_{Ay}$ with the reconnection rate $R\sim 0.1$ and $v_{Ay} = B_{0y}/\sqrt{4\pi n_p m_p}$. Within the exhaust, due to the strong electric field $E_x\sim c v_{Ay}/B_0$, where $B_0$ is the guide field, the ion takes up a drift at the Alfvénic outflow velocity $v_{out}\sim v_{Ay}$. If this process happens in a time comparable to the ion's gyroperiod, the magnetic moment is not conserved and strong heating occurs.