Resonant ion acceleration by plasma jets: Effects of jet breaking and the magnetic-field curvature

In this paper we consider resonant ion acceleration by a plasma jet originating from the magnetic reconnection region. Such jets propagate in the background magnetic field with significantly curved magnetic-field lines. Decoupling of ion and electron motions at the leading edge of the jet results in generation of strong electrostatic fields. Ions can be trapped by this field and get accelerated along the jet front. This mechanism of resonant acceleration resembles surfing acceleration of charged particles at a shock wave. To describe resonant acceleration of ions, we use adiabatic theory of resonant phenomena. We show that particle motion along the curved field lines significantly influences the acceleration rate. The maximum gain of energy is determined by the particle's escape from the system due to this motion. Applications of the proposed mechanism to charged-particle acceleration in the planetary magnetospheres and the solar corona are discussed.

Figure 1

Schematic view of formation of jet fronts in the planetary magnetosphere (top) and solar flare (bottom). Black curves show magnetic field lines.

Figure 2

Schematic view of the configuration of electric and magnetic fields at the front $(\phi$ is a scalar potential generated due to decoupling of ions and electron motions). The spatial scale of the front $l_x$ is also shown.

Figure 3

Schematic view magnetic-field line and system parameters. Calculation of the $\kappa$ parameter is shown.

Figure 4

Profiles of $f\left(\varphi \right),f^2\left(\varphi \right)$, and $d{f}^2/d\varphi$ functions.

Figure 5

(a) The profile of the $R\left(s\right)$ function given by Eq. (30). (b) The profiles of $h_z\left(X\right)$ for various values of $I_z$. (c) The profiles of $h_z^{\prime }\left(X\right)$ for various values of $I_z$.

Figure 6

Map in the $(X,q)$ plane: the gray color shows regions where Eq. (28) does not have a solution for given values of parameters.

Figure 7

Three phase portraits of Hamiltonian Eq. (26) for three sets of parameters. Here $\tilde{K}=K/L_x\sqrt{\kappa \overline{\sigma }}$.

Figure 8

Profiles of $S\left(X\right)$ and $S\left(h_z^{\prime }\right)$ normalized on $2^{2/3}{L}_x\sqrt{\kappa \overline{\sigma }}$ for several values of $I_z$.

Figure 9

Particle trajectory in $(\kappa x,p_x)$ plane (the gray color shows the trajectory segment before the trapping); two additional panels show trajectory fragments before the trapping and after escape from the resonance. Right panels show time profiles of $I_z$ invariant, $p_x$ component of the particle momentum, particle energy, and $z$ coordinate. Red dotted line shows profiles of $v_{\varphi }\left(t\right)$. System parameters are: $\kappa =0.1,\varepsilon =0.01,\delta B_z/B_n=3,L_x=0.1$.

Figure 10

Particle trajectory in $(\kappa x,p_x)$ plane (the grey color shows the trajectory segment before the trapping); two additional panels show trajectory fragments before the trapping and after escape from the resonance. Right panels show time profiles of $I_z$ invariant, $p_x$ component of the particle momentum, particle energy, and $z$ coordinate. Red dotted line shows profiles of $v_{\varphi }\left(t\right)$. System parameters are: $\kappa =0.1,\varepsilon =0.01,\delta B_z/B_n=3,L_x=0.01$.