Charged-particle acceleration in braking plasma jets

In this paper we describe the mechanism of the charged particle acceleration in space plasma systems. We consider the interaction of nonrelativistic particles with a sub-Alfvenic plasma jet originated from the magnetic reconnection. The sharp front with increased magnetic field amplitude forms in the jet leading edge. Propagation of the jet in the inhomogeneous background plasma results in front braking. We show that particles can interact with this front in a resonance manner. Synchronization of particle reflections from the front and the front braking provides the stable trapping of particles in the vicinity of the front. This trapping supports the effective particle acceleration along the front. The mechanism of acceleration is potentially important due to the prevalence of the magnetic reconnection in space and astrophysical plasmas.

Figure 1

Schematic view of the system (a). Profile of the $f\left(\varphi \right)$ function (b).

Figure 2

Magnetic field profiles $B_f(x/L_x)f\left(\varphi \right)$ for two values of $\sigma$ and three time moments. We take $L_x/L_f=20$ and $s_0=10$ for illustration. Grey area shows the leading edge of fronts where $df/d\varphi <0$.

Figure 3

Profiles of $h(\alpha ,\sigma )$ function for four values of $\alpha$.

Figure 4

Maximum energy gained by protons due to resonant acceleration $\sim max|v_y{|}^2$ is shown as a function of system parameters.

Figure 5

The particle trajectory is shown in the $(x,y)$ plane (a) and in the $(x,v_x)$ plane (b). The fragment of the particle trajectory in the trapping is shown in the $(\varphi ,d\varphi /dt)$ plane (c). The particle energy and $d\varphi /dt$ as functions of time are shown in (d), (e). Grey and black colors are used for fragments before the trapping and after the escape from the resonance, while the red color shows the fragment of the trapped motion. System parameters are $L_x=100{\rho }_0$, $v_{\varphi }=3v_0$, $L_f=0.3{\rho }_0$, $\alpha =1$, $\sigma =0$, where the initial particle energy is $H=v_0^2/2$ and the initial particle Larmor radius is ${\rho }_0=v_0/{\overline{\Omega }}_0$. The front magnetic field is nonzero only for $y/{\rho }_0\in [-5,5]$. For the typical conditions in the Earth magnetotail ${\rho }_0\sim 1000–2000$ km and, thus, we have $\left|y\right|<{10}^4$ km in agreement with spacecraft observations [27].

Figure 6

Three particle trajectories are shown in the $(x,y)$ plane (a,c,e) and in the $(v_x,v_y)$ plane (b,d,f). The black color is used for fragments before the trapping and after the escape, while the red color shows the fragment of the trapped motion. System parameters are the same as in Fig. 5.

Figure 7

The dependence of $v_x$ on time is shown with the ${\widehat{v}}_{\varphi }\left(x\right)$ profile (in blue) for the trajectory presented in top panels of Fig. 6. Fragment of ${\widehat{v}}_{\varphi }\left(x\right)$ variation along the trajectory in the resonance (indicated by grey color in the top panel) is shown in the bottom panel.

Figure 8

(a) and (b) show two particle trajectories. The black color is used for fragments before the trapping and after the escape, while the red color shows the fragment of the trapped motion. (c) shows the energy distribution for the particle ensemble (the total number of particles is ${10}^6$). The grey color indicates the tail of the distribution containing resonantly accelerated particles. System parameters are the same as in Fig. 5.