Ring-shaped velocity distribution functions in energy-dispersed structures formed at the boundaries of a proton stream injected into a transverse magnetic field: Test-kinetic results

Abstract

In this paper we discuss the formation of ring-shaped and gyro-phase restricted velocity distribution functions at the edges of a cloud of protons injected into non-uniform distributions of the electromagnetic field. The velocity distribution function is reconstructed using the forward test-kinetic method. We consider two profiles of the electric field: (i) a non-uniform E-field obtained by solving the Laplace equation consistent with the conservation of the electric drift and (ii) a constant and uniform E-field. In both cases the magnetic field is similar to the solutions obtained for tangential discontinuities. The initial velocity distribution function is Liouville mapped along numerically integrated trajectories. The numerical results show the formation of an energy-dispersed structure due to the energy-dependent displacement of protons towards the edges of the cloud by the gradient-B drift. Another direct effect of the gradient-B drift is the formation of ring-shaped velocity distribution functions within the velocity-dispersed structure. Higher energy particles populate the edges of the proton beam while smaller energies are located in the core. Non-gyrotropic velocity distribution functions form on the front-side and trailing edge of the cloud; this effect is due to remote sensing of energetic particles with guiding centers inside the beam. The kinetic features revealed by the test-kinetic solutions have features similar to in-situ velocity distribution functions observed by Cluster satellites in the magnetotail, close to the neutral sheet.for an ensemble of charged particles injected into a stationary electromagnetic field distribution. 26 In Eq. ( 1) the electric field, E, and the magnetic field, B, are prescribed. One can compute any number of Vlasov characteristics and then "propagate" the VDF along them by applying the Liouville theorem. In this study we

Wave Excitation by Energetic Ring-distributed Electron Beams in the Solar Corona

“…Positive slopes of the particle distribution functions in the perpendicular direction were obtained by considering the particle acceleration in the outflow region of magnetic reconnection, where cup-like distribution functions are formed (Büchner & Kuska 1996). Energetic particles' magnetic gradient drifts can also cause a redistribution of the energy of parallel flowing beam particles to the perpendicular direction (Zhou et al 2015), forming ring-beam and gyro-phase restricted velocity distribution functions as it was shown by test particle calculations (Voitcu & Echim 2012) as well as crescent-shaped velocity distribution functions (Voitcu & Echim 2018). In addition, by means of self-consistent kinetic simulations it has been shown that positive slopes of the electron distribution function in the perpendicular velocity space survive due to the feedback of the self-generated plasma turbulence during magnetic reconnection (Muñoz & Büchner 2016).…”

Comparative study of forward and backward test-kinetic simulation approaches

“…Also, non-gyrotropic velocity distribution functions form in the front-side and trailing edge of the cloud due to remote sensing of energetic particles with guiding centers localized inside the beam. An explanation of the physical mechanism responsible for the formation of such an energy-dispersed structure and also a detailed analysis of the kinetic effects contributing to the formation of ring-shaped and non-gyrotropic velocity distribution functions is published elsewhere [21]. Here we limit our attention to the differences between the results obtained using both forward and backward test-kinetic approaches.…”

“…Another region of the magnetosphere where such electric and magnetic fields could be observed is the magnetopause. The relevance for this configuration of the electric and magnetic fields have been discussed in a previous publication [21].…”

The effects of density inhomogeneities on the radio wave emission in electron beam plasmas

“…Such a scenario applies when steep magnetic gradients are formed as in collisionless shocks and by magnetic reconnection at kinetic scales. Magnetic gradient drifts can redistribute the parallel beam particle energy into the perpendicular direction (Zhou et al 2015), thus forming ring-beam and gyro-phase restricted EVDFs (Voitcu & Echim 2012) as well as crescent-shaped EVDFs (Voitcu & Echim 2018). Ring distributions have been indeed found in particle-in-cell (PIC) simulations of magnetic reconnection (Bessho et al 2014; Shuster et al 2014) and in quasi-perpendicular shocks (Tokar et al 1986).…”