Non-adiabatic Ion Acceleration in the Earth Magnetotail and Its Various Manifestations in the Plasma Sheet Boundary Layer

Abstract

Many physical phenomena in space involve energy dissipation which generally leads to charged particle acceleration, often up to very high energies. In the Earth magnetosphere energy accumulation and release occur in the magnetotail, namely in its Current Sheet (CS). The kinetic analysis of non-adiabatic ion trajectories in the CS region with finite but positive normal component of the magnetic field demonstrated that this region is essentially non-uniform in terms of scattering characteristics of ion orbits and contains spatially localized, well-separated sites of enhanced and reduced chaotization. The latter represent sources from which accelerated and energy-collimated ions are ejected into Plasma Sheet Boundary Layer (PSBL) and stream towards the Earth. Numerical simulations performed as part of a Large-Scale Kinetic Model have shown the multiplet ion structure of the PSBL is formed by a set of ion beams (beamlets) localized both in physical and velocity space. This structure of the PSBL is quite different from the one produced by CS acceleration near a magnetic reconnection region in which more energetic ion beams are generated with a broad range of parallel velocities. Multi-point Cluster observations in the magnetotail PSBL not only showed that non-adiabatic ion acceleration occurs on closed magnetic field lines with at least two CS sources operating simultaneously, but also allowed an estimation of their spatial and temporal characteristics. In this paper we discuss and compare the PSBL manifestations of both mechanisms of CS particle acceleration: one based on the peculiar properties of non-adiabatic ion trajectories which operates on closed magnetic field lines and the other representing the well-explored mechanism of particle acceleration during the course of magnetic reconnection. We show that these two mechanisms supplement each other and the first operates mostly during quiescent magnetotail periods.

Appendix: Model of Particle Energization in the Vicinity of Dynamic X-Line

Let us assume that reconnection magnetic field could be presented in a form: B={B ₀tanh(Z/L _Z ),0,B _0Z tanh(X/L _X )}, where B ₀ is the lobe magnetic field, L _X and L _Z are the spatial scales of the system in (XZ) plane. We also assume that a constant electric field E _Y is applied to the system. Relations between the magnitudes of magnetic field components b _n =B _0z /B ₀ and spatial scales L _x /L _z are governed by the value of X-line angle α (see Fig. 36). The modeling domain is limited in the dawn-dusk direction: |Y|<12L _Z . All spatial variables are normalized to L _z (r/L _z =r ^∗) and time is normalized to the ion gyrofrequency t→teB ₀/mc. Velocity will be correspondingly normalized to V ₀=eB ₀ L _Z /m _i c and energy to $V_{0}^{2}$. Ions arriving at the CS from a number of sources are placed at X=4L _X ,Z=4b _n L _X with different Y-positions.

Fig. 36

Test particle trajectories in 2D magnetic X-line geometry. Magnetic field lines are shown by thin dotted lines. The black circle indicates the start position of test particles

To study effects of particle isotropization and acceleration by inductive electric fields, Veltri et al. (1998) and Artemyev et al. (2009) used a model of turbulent electromagnetic fields consisting of an ensemble of plane electromagnetic waves:

(3)

Here $g_{\mathbf{k}} = \cos( \mathbf{kr} +\phi_{\mathbf{k}}^{2} - t\omega_{\mathbf{k}} ), h_{\mathbf{k}} =\sin( \mathbf{kr} + \phi_{\mathbf{k}}^{1} - t\omega_{\mathbf{k}}), k_{ \bot} = \sqrt{k_{z}^{2} + k_{y}^{2}}$ and $k =\sqrt{k_{z}^{2} + k_{y}^{2} + k_{x}^{2}}$. Initial phases $\phi_{\mathbf{k}}^{1}$ and $\phi_{\mathbf{k}}^{2}$ have a random values within the interval [0,2π]. Each harmonic has the frequency: ω _k =v _ϕ |k|. We assume for simplicity that v _ϕ has the same value for all waves (Zelenyi et al., 2008; Artemyev et al., 2009). Wave magnitudes are described by the power distribution: δB(k)=C(1+(lk)²)^−η. Here l is the correlation vector (|l|=L _z /10) and the value η=7/8 is derived from observations (Hoshino et al., 1994; Petrukovich, 2005, and references therein).

One can find the components of electric field from the Maxwell equations, using the expressions (3):

$$ \begin{array}{rll}\nabla\times\delta\mathbf{E} &=& - c^{-1}\partial\delta\mathbf{B}/\partial t \\[6pt]\nabla\delta\mathbf{E} &=& 0\end{array}$$

(4)

The magnitude of turbulence can be characterized by free parameter $\delta = \sqrt{\langle \delta \mathbf{B} \cdot \delta \mathbf{B} \rangle}/B_{0}$. Wave numbers have the following distributions: k _z L _z =2πn _z (n _z =1..4),k _x L _z =2πn ₀cosθ and k _y L _z =2πn ₀sinθ (n ₀=1..10,θ∈[0,2π]). We assume that there are 600 harmonics in the system.

In our modeling we consider two different cases. In the first case, we take a weak level of turbulence, δ=0.3, and a relatively large value of the angle, α=π/9. The second case corresponds to the strong turbulence level δ=0.6, and small angle, α=π/18. In the first case, the increase of X-line angle leads to particle thermalization: the value of ion thermal velocity V _T∥ approaches to the value of their bulk velocity V _D (V _D /V _T∥→1). In the second case, the increase of the turbulence level, δ, results in strong particle acceleration (V _D grows) and particles acquire energies which could significantly exceed the characteristic value of potential drop across the magnetotail. Electromagnetic turbulence in this case also leads to some particle thermalization, even in systems with a small value of X-line angle, so that ion V _D /V _T∥≥1.