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observations of astrophysical objects with relativistic plasma outflows generally show frequency spectra dominated by power - law segments .
these objects count gamma ray bursts ( grbs ) and active galactic nuclei .
the general interpretations of such observations are that 1 ) electrons are accelerated to power - law distributions @xmath0 in the collisionless shock interface between the relativistic ejecta and the surrounding media and 2 ) the accelerated electrons radiate through synchrotron radiation in the downstream region of the shock .
the magnetic field strength required to account for the observed radiation spectra is typically of the order of percents of equipartition . a complete physical model for relativistic collisionless shocks should account for both the origin of such strong magnetic fields and for acceleration of electrons to power - law distributions .    regarding the origin of the magnetic field
, particle - in - cell ( pic ) simulations have shown that the weibel two - stream instability can generate a small scale , but strong , magnetic field transverse to the jet flow ( @xmath1 where @xmath2 describes the fraction of total injected kinetic energy that is converted to magnetic energy ) @xcite .
other pic simulations have found that the ambient large scale magnetic field neccesary to quench this instability has to be significantly stronger than the @xmath3 g field typically found in the interstellar medium ( ism ) @xcite .    regarding the non - thermal electron acceleration , monte carlo test - particle simulations have shown that fermi acceleration can provide electron power - law distributions under some assumptions about the shock and magnetic field @xcite .
this mechanism has , however , not been conclusively demonstrated to occur in ab initio particle simulations .
pic simulations have shown that both thermal and non - thermal particle acceleration take place in the shock transition region @xcite .    in this paper , we discuss the particle dynamics in collisionless shocks based on results from a three dimensional relativistic pic code . we propose a new particle acceleration mechanism that is itself a consequence of the weibel two - stream instability @xcite .
we have performed computer experiments using a charged particle - in - cell code .
the code works from first principles by solving maxwell s equations for the electromagnetic fields and the lorentz force equation of motion for the particles .
the fields are defined on a numerical grid and the particles are defined in a continuous phase space .
we use a computational box with @xmath4 grid points and a plasma consisting of @xmath5 ions and electrons .
the ion rest - frame plasma frequency is @xmath6 , rendering the box 150 ion skin depths long .
the electron rest - frame plasma frequency is @xmath7 in order to resolve the microphysics of the electrons .
hence , the ion - to - electron mass ratio is @xmath8 .         in the experiments we study the microphysics of two colliding plasma populations .
the experiments are carried out in the rest frame of one of the populations ( downstream , e.g. , a jet ) . in this frame , a less dense population ( upstream , e.g. the ism ) is continuously injected at the leftmost boundary @xmath9 .
we have performed two runs with relativistic velocities corresponding to lorentz factors @xmath10 and @xmath11 . initially , the jet plasma is denser by a factor of three and both plasma populations are unmagnetized .
the boundaries in the direction transverse to the jet flow ( @xmath12 ) are periodic . at the @xmath13-boundaries ,
electromagnetic waves are absorbed and we allow particles to escape in order to avoid unphysical feedback .
the experiment last until @xmath14 340 @xmath15 , which is sufficient for the continuously injected upstream ism - plasma to travel 2.3 times the length of the box .
the results from the experiments show how the weibel two - stream instability forms current filaments in the region where the two plasma populations interpenetrate and how these filaments merge into increasingly larger patterns further downstream ( fig .
[ fig : current ] _ left panel _ ) ( see also @xcite ) .
the induced magnetic field grows to @xmath16 .
we identify two mechanism that accelerate electrons .
the first is thermalization caused by random deflections by the generated small scale electromagnetic field .
this mechanism is dominant for the @xmath10 run . in the @xmath11
run a second acceleration mechanism becomes important .
here we briefly discuss this mechanism ( for details please see @xcite ) :    the generated ion current channels are debye shielded by the heated electrons . at distances less than the debye length ,
the current channels are surrounded by transverse electric fields that accelerate the electrons toward the current channels .
the acceleration happens in an approximately electrostatic field and is a simple consequence of potential energy being converted into kinetic energy .
therefore , the electrons are decelerated again when leaving the current channel and reach their maximal velocities at the centers of the current channels ( fig .
[ fig : current ] ) .
it has been shown that a spatial fourier decomposition of the transverse ion filaments in the box exhibits power - law behavior @xcite .
hence , the number of accelerated electrons is expected to reflect this power - law behavior .
this relation is confirmed in fig .
[ fig : powerlaw ] .
the left panel shows a scatter plot of electron momentum ( @xmath17 ) plotted against the strength of the electric current sampled at each electrons position . there is a power - law correlation between the electron energy and the local current density . some deviations from the power - law
is found : cold trapped thermal electrons ( indicated with the ellipse ) exist inside the ion current channel and count towards lowering the average four velocity at high @xmath18 .
also , heated electrons are found outside the current channels which increase the average four velocity at low @xmath18 .
the electron distribution function can be seen in the right panel of fig .
[ fig : powerlaw ] .
it show a thermal distribution with a power - law component at high energies .
the slope of the power - law segment corresponds to a spectral index of p=2.7 .     versus the four velocity of the electrons in a region downstream of the shock .
overplotted is a line ( thin ) showing the average four velocity as a function of @xmath18 , and a line ( thick ) showing a straight line fit .
_ right panel : _ the normalized electron particle distribution function downstream of the shock .
the dot  dashed line is a power law fit to the non  thermal high energy tail , while the dashed curve is a lorentz - boosted thermal electron population .
the horizontal line at @xmath19 indicates the plasma injection velocity.,title="fig:",scaledwidth=50.0% ]   versus the four velocity of the electrons in a region downstream of the shock .
overplotted is a line ( thin ) showing the average four velocity as a function of @xmath18 , and a line ( thick ) showing a straight line fit . _
right panel : _ the normalized electron particle distribution function downstream of the shock .
the dot  dashed line is a power law fit to the non  thermal high energy tail , while the dashed curve is a lorentz - boosted thermal electron population .
the horizontal line at @xmath19 indicates the plasma injection velocity.,title="fig:",scaledwidth=50.0% ]
we have investigated magnetic field generation and particle acceleration in collisionless shocks using three dimensional charged particle - in - cell experiments . the results are applicable to interactions between relativistic outflows and the interstellar medium .
such relativistic outflows occur in grbs and in jets from compact objects .
we observe how the weibel two - stream instability is excited and find that the non - linear stage of the instability penetrates at least 150 ion skin depths into the shock ramp . extrapolating to the real electron - ion mass ratio , this is more than 6000 electron skin depths .
the instability efficiently creates a strong , small - scale magnetic field ( @xmath16 ) .    regarding particle acceleration ,
the results show that thermalization dominates the electron distribution in the simulation run where a jet is expanding with @xmath10 . at @xmath11 ,
a new acceleration mechanism becomes important in the high energy tail of the spectrum .
the acceleration is non - thermal and the resulting electron distribution function has a power - law segment .
the slope of this segment corresponds to @xmath20 .
we emphasize that the generation of magnetic field and the non - thermal acceleration of electrons are two highly interconnected processes in collisionless shocks . the acceleration is closely tied to the spatial distribution of electric current filaments .
further large scale simulations are need to determine how this slope depends on different parameters .
when the injected ism ions has traveled through the simulation box they are not merged with the jet ions to a single population .
this indicates that larger simulations are needed to cover the whole shock ramp .
the outflows from gamma ray bursts , active galactic nuclei and relativistic jets in general interact with the surrounding media through collisionless shocks . with three dimensional relativistic particle  in  cell simulations we investigate such shocks . 
 the results from these experiments show that small  scale magnetic filaments with strengths of up to percents of equipartition are generated and that electrons are accelerated to power law distributions @xmath0 in the vicinity of the filaments through a new acceleration mechanism . the acceleration is locally confined , instantaneous and differs from recursive acceleration processes such as fermi acceleration . 
 we find that the proposed acceleration mechanism competes with thermalization and becomes important at high lorentz factors .    
 [ 1999/12/01 v1.4c il nuovo cimento ]