Magnetic Field Generation in Collisionless Shocks: Pattern Growth and Transport

Abstract

We present results from three-dimensional particle simulations of collisionless shock formation, with relativistic counter-streaming ion-electron plasmas. Particles are followed over many skin depths downstream of the shock. Open boundaries allow the experiments to be continued for several particle crossing times. The experiments confirm the generation of strong magnetic and electric fields by a Weibel-like kinetic streaming instability, and demonstrate that the electromagnetic fields propagate far downstream of the shock. The magnetic fields are predominantly transversal, and are associated with merging ion current channels. The total magnetic energy grows as the ion channels merge, and as the magnetic field patterns propagate down stream. The electron populations are quickly thermalized, while the ion populations retain distinct bulk speeds in shielded ion channels and thermalize much more slowly. The results help reveal processes of importance in collisionless shocks, and may help to explain the origin of the magnetic fields responsible for afterglow synchrotron/jitter radiation from Gamma-Ray Bursts.

Are Gamma‐Ray Burst Shocks Mediated by the Weibel Instability?

“…However, at the scale larger than the electron Larmor radius, which is of the order of $1/( 1/2 pp ), the field is already frozen into the electron gas; therefore, could hardly ever grow significantly beyond unity. One should also take into account that the current filaments are unstable to a kink-like mode ( Milosavljević & Nakar 2006; such an instability is actually observed in simulations by Frederiksen et al (2004) and Hededal (2005), which also stimulates the field decay. Therefore, we believe that there is no reason for the Weibel-driven shock transition to be significantly narrower than equation (26) predicts.…”

“…On the contrary, such a small-scale magnetic field should decay (Gruzinov 2001). There is evidence for hierarchical merging of current filaments (Silva et al 2003;Frederiksen et al 2004;Medvedev et al 2005;Kato 2005), so might exceed unity. However, at the scale larger than the electron Larmor radius, which is of the order of $1/( 1/2 pp ), the field is already frozen into the electron gas; therefore, could hardly ever grow significantly beyond unity.…”

“…Many authors have therefore assumed that the shock somehow manufactures field energy to meet this requirement, but no convincing mechanism has been proposed to date. One mechanism discussed is the Weibel instability ( Medvedev & Loeb 1999;Silva et al 2003;Frederiksen et al 2004;Jaroschek et al 2005;Medvedev et al 2005;Kato 2005;Nishikawa et al 2005), which has the fastest growth rate and produces relatively strong small-scale magnetic field even in an initially nonmagnetized plasma. It is expected that the thermalization of the upstream flow could occur via scattering of particles on the magnetic fluctuations.…”

Shock Vorticity Generation from Accelerated Ion Streaming in the Precursor of Ultrarelativistic Gamma‐Ray Burst External Shocks

“…On the other hand, since max is much larger than the plasma skin depth c/! pla , the magnetic field that the turbulent dynamo generates will not be susceptible to the fast collisionless decay discussed by Chang et al (2008) that affects the much smaller scale field that kinetic instabilities can generate in the shock transition layer (e.g., Gruzinov 2001; Frederiksen et al 2004;Medvedev et al 2005;Keshet et al 2008;Spitkovsky 2008b and references therein).…”

Synchrotron self-Compton flaring of TeV blazars

“…Experimentally (Kapetanakos 1974;Tatarakis et al 2003) and from numerous particle-in-cell (PIC) simulations (e.g. Lee & Lampe 1973;Nishikawa et al 2003;Silva et al 2003;Frederiksen et al 2004;Sakai et al 2004;Jaroschek et al 2005) such collisions of plasma shells lead to the onset of linear Weibel-type plasma instabilities perpendicular to the flow directions in both unmagnetised and slightly magnetised plasmas, and to the development of anisotropic relativistic plasma distributions. The PIC simulations of electron-proton and electronpositron plasmas demonstrate that these instabilities generate magnetic fields in the form of aperiodic fluctuations at almost equipartition strength on the shortest plasma time scale.…”