Particle acceleration, magnetic field generation, and emission in relativistic pair jets
K.-I.~Nishikawa\from{ins:x}\ETC
P.~Hardee\from{ins:y}
C. B.~Hededal\from{ins:z}
G.~Richardson\from{ins:a}
H.~Sol\from{ins:b}
R.~Preece\from{ins:c} \atque G. J.~Fishman\from{ins:d}
Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find that the growth times of Weibel instability are proportional to the Lorentz factors of jets. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of ``jitter'' radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.
nishikawa.tex
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      [1999/12/01 v1.4c Il Nuovo Cimento]
\documentclass[final]{cimento}

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\usepackage{graphicx}  % got figures? uncomment this
\title{Particle acceleration, magnetic field generation,
and emission in relativistic pair jets}
\author{K.-I.~Nishikawa\from{ins:x}\ETC,
P.~Hardee\from{ins:y}, C. B.~Hededal\from{ins:z},
G.~Richardson\from{ins:a}\\
H.~Sol\from{ins:b}, R.~Preece\from{ins:c}
        \atque
G. J.~Fishman\from{ins:d}}  %\thanks{The bad fellow.}}
\instlist{\inst{ins:x} National Space Science and Technology Center,
  Huntsville, AL 35805 USA
\inst{ins:y} Department of Physics and Astronomy,
  The University of Alabama,
  Tuscaloosa, AL 35487 USA
\inst{ins:z} Niels Bohr Institute, Department of Astrophysics,
Juliane Maries Vej30, 2100 K\o benhavn \O, Denmark

\inst{ins:a} Department of Mechanical and Aerospace Engineering
  University of Alabama in Huntsville Huntsville, AL 35899 USA

\inst{ins:b} LUTH, Observatore de Paris-Meudon, 5 place Jules Jansen
  92195 Meudon Cedex, France


\inst{ins:c} Department of Physics,
  University of Alabama in Huntsville,
  Huntsville, AL 35899 and National Space Science and Technology Center,
  Huntsville, AL 35805 USA


\inst{ins:d} NASA-Marshall Space Flight Center, \\
National Space Science and Technology Center,
  Huntsville, AL 35805 USA



inst{ins:y}} \PACSes{\PACSit{00.00}{By the way, which PACS is it,
the 00.00? GOK.} \PACSit{---.---}{\ldots}}
\begin{document}

\maketitle

\begin{abstract}
Shock acceleration is a ubiquitous phenomenon in astrophysical
plasmas.  Plasma waves and their associated instabilities (e.g.,
Buneman, Weibel and other two-stream instabilities) created in
collisionless shocks are responsible for particle (electron,
positron, and ion) acceleration. Using a 3-D relativistic
electromagnetic particle (REMP) code, we have investigated particle
acceleration associated with a relativistic  jet front propagating
into an ambient plasma. We find that the growth times of Weibel
instability are proportional to the Lorentz factors of jets.
Simulations show that
the Weibel instability created in the collisionless shock front
accelerates jet and ambient particles both perpendicular and
parallel to the jet propagation direction. The small scale magnetic
field structure generated by the Weibel instability is appropriate
to the generation of ``jitter'' radiation from deflected electrons
(positrons) as opposed to synchrotron radiation. The jitter
radiation resulting from small scale magnetic field structures may
be important for understanding the complex time structure and
spectral evolution observed in gamma-ray bursts or other
astrophysical sources containing relativistic jets and relativistic
collisionless shocks.
\end{abstract}

\section{Introduction}
Nonthermal radiation observed from astrophysical systems containing
relativistic jets and shocks, e.g., active galactic nuclei (AGNs),
gamma-ray bursts (GRBs), and Galactic microquasar systems usually
has power-law emission spectra. In most of these systems, the
emission is thought to be generated by accelerated electrons through
the synchrotron and/or inverse Compton mechanisms. Radiation from
these systems is observed in the radio through the gamma-ray region.
Radiation in optical and higher frequencies typically requires
particle re-acceleration in order to counter radiative losses.

Particle-in-cell (PIC) simulations can shed light on the physical
mechanism of particle acceleration that occurs in the complicated
dynamics within relativistic shocks.  Recent PIC simulations using
injected relativistic electron-ion jets show that acceleration
occurs within the downstream jet, rather than by the scattering of
particles back and forth across the shock as in Fermi acceleration
[1-7]. In general, these independent simulations have confirmed that
relativistic jets excite the Weibel instability [8]. The Weibel
instability generates current filaments with associated magnetic
fields [9], and accelerates electrons [1-7].

In this paper we present new simulation results of particle
acceleration and magnetic field generation for relativistic
electron-positron shocks using 3-D relativistic electromagnetic
particle-in-cell (REMP) simulations. In our new simulations, the
growthrates with different Lorentz factors of jets have been studied
without an initial ambient magnetic field.

\section{Simulation Setup and results}

Two simulations were performed using an $85 \times 85 \times 320$
grid with a total of 180 million particles (27
particles$/$cell$/$species for the ambient plasma) and an electron
skin depth, $\lambda_{\rm ce} = c/\omega_{\rm pe} = 9.6\Delta$,
where $\omega_{\rm pe} = (4\pi e^{2}n_{\rm e}/m_{\rm e})^{1/2}$ is
the electron plasma frequency and $\Delta$ is the grid size
(Nishikawa et al. 2004).
% In all
%simulations jets are injected at $z = 25\Delta$ in the positive $z$
%direction. Radiating boundary conditions were
%used on the planes at $z =0,z_{\rm max}$. Periodic boundary
%conditions were used on all other boundaries (Buneman 1993).
%

The electron number density of the jet is $0.741n_{\rm b}$, where
$n_{\rm b}$ is the density of ambient (background) electrons. The
average jet velocities for the two simulations are $v_{\rm j} =
0.9798c, 0.9977c$ corresponding to  Lorentz factors are 5 (2.5 MeV)
and 15 (7.5 MeV), respectively. The jets are cold ($v^{\rm e}_{\rm
j, th} = v^{\rm p}_{\rm j, th} = 0.01c$ and $v^{\rm i}_{\rm j, th} =
0.0022c$) in the rest frame of the ambient plasma. Electron-positron
plasmas have mass ratio $m_{\rm p}/m_{\rm e} = 1$. The thermal
velocity in the ambient plasmas is $v^{\rm e, p}_{\rm th} = 0.1c$
where $c$ is the speed of light. The time step $\Delta t =
0.013/\omega_{\rm pe}$.




% The jet makes contact with the ambient plasma at a 2D
%interface spanning the computational domain. Here only the dynamics
%of the propagating jet head and shock region is studied. Effectively
%we study a small uniform portion of a much larger shock. This
%simulation system is different from simulations performed using
%counter-streaming equal number density particles spanning the
%computational domain in the transverse direction. The important
%differences between this type of simulation and previous
%counter-streaming simulations is that the evolution of the Weibel
%instability is examined in a more realistic spatial way including
%the motion of the jet head, and we can have different number
%densities in beam and ambient medium.

Current filaments resulting from development of the Weibel
instability behind the jet front are shown in Figs. 1a  and 1b at
time $t = 28.8/\omega_{\rm pe}$ for unmagnetized ambient plasmas (a)
$\gamma = 5$ and (b) $\gamma = 15$. The maximum values of $J_{\rm
y}$ are (a) 15.63 and (b) 3.86, respectively. The slower jet shows
larger amplitudes than the faster jet at the same simulation time.
The effect of Lorentz factors of jets affects the growth rates of
Weibel instability as expected by the theory [8].

The differences in the growthrates between the differerent Lorentz
factors are seen more clearly in the $x$-component of the generated
magnetic fields as shown in Fig. 2. The amplitudes of $B_{\rm x}$ in
the slower jet (a) are much larger than those in the faster jet (b).
The comparisons in the saturated magnetic fields need much longer
simulations, which are in progress at the present time.

%The heating and acceleration of jet electrons in directions parallel
%and perpendicular to the flow is shown in Figure 1 for the
%electron-positron case (1c and 1e) and for the electron-ion case (1d
%and 1f).  The jet electrons are split into two parts: the injected
%(blue: rear half ($Z< 160\Delta$) and shocked (red: front half ($Z>
%160\Delta$). (The jet electrons are divided at $Z \sim 160\Delta$).)
%Since in the case of electron-ion jet the Weibel instability grows
%slightly the blue curves in Figs. 1d and 1f are considered as the
%distributions of injected jet electrons. In both parallel and
%perpendicular distributions, jet electrons are more accelerated in
%the electron-positron case than in the electron-ion case.
%It should be noted that the much stronger acceleration in the
%electrons occurs in the case where electron-ion jets are injected
%perpendicular to the strong ambient magnetic fields (Hededal and
%Nishikawa 2004).

\begin{figure}
\hspace*{1.2cm}
\includegraphics[height=.52\textheight]{nishikawa_f1}     % includes figure foo.eps
%\centerline{\psfig{figure=nishikawa_f1.ps,width=6.6in,height=3.5in}}
\caption{2D images show the current density ($J_{\rm y}$) at $t =
28.8/\omega_{\rm pe}$ (a) $\gamma = 5$ and (b) $\gamma = 15$. Colors
indicate the $y$-component of the current density, $J_{\rm y}$
[peak: (a) 15.63 and (b) 3.86], and the arrows indicate $J_{\rm z}$
and $J_{\rm x}$.}
\end{figure}

\begin{figure}
\includegraphics[height=.205\textheight]{nishikawa_f2}     % includes figure foo.eps
\caption{One-dimensional cuts along the $z$-direction ($25 \leq
z/\Delta \leq 314$) of a flat jet (a) $\gamma = 5$ and (b) $\gamma =
15$. Shown are the $x$-component of the magnetic field shown at $t =
28.8/\omega_{\rm pe}$. Cuts are taken at $x/\Delta = 38$ and
$y/\Delta = 33$ (blue-dotted), 43 (red-solid), 53 (green-dashed) and
separated by about one electron skin depth.}
\end{figure}


%\appendix

\section{Summary and Discussion}
We have performed self-consistent, three-dimensional relativistic
particle simulations of relativistic electron-positron jets
propagating into magnetized and unmagnetized electron-positron
ambient plasmas. The main acceleration of electrons takes place in
the region behind the shock front [5]. Processes in the relativistic
collisionless shock are dominated by structures produced by the
Weibel instability.  This instability is excited in the downstream
region behind the jet head, where electron density perturbations
lead to the formation of current filaments. The nonuniform electric
field and magnetic field structures associated with these current
filaments decelerate the jet electrons and positrons, while
accelerating the ambient electrons and positrons, and accelerating
(heating) the jet and ambient electrons and positrons in the
transverse direction.

The growthrates depend on the Lorentz factors of jet as expected by
the theory [9].  The $e$-fold time is written as $\tau \simeq
\sqrt{\gamma_{\rm sh}}/\omega_{\rm pe}$, where $\gamma_{\rm sh}$ is
the Lorentz factor of the shock. The simulation results show that
$\tau \propto \gamma_{\rm sh}$.

Other simulations with different skin depths and plasma frequencies
confirm that both simulations have enough resolutions and the
electron Weibel instability is characterlized by the electron skin
depth [5].
% An additional simulation in which an
%electron-ion jet is injected into a ambient plasma with
%perpendicular magnetic field shows magnetic reconnection due to the
%generation of an antiparallel magnetic field generated by bending of
%jet electron trajectories, consequently jet electrons are subject to
%strong non-thermal acceleration [8].
% (Hededal and Nishikawa 2004).

These simulation studies have provided new insights for particle
acceleration and magnetic field generation. Further research is
required to develop radiation models based on these microscopic
processes.


\acknowledgments K. Nishikawa is a NRC Senior Research Fellow at
NASA Marshall Space Flight Center. This research (K.N.) is partially
supported by the National Science Foundation awards ATM-0100997, and
INT-9981508. P. Hardee acknowledges partial support by a National
Space Science and Technology (NSSTC/NASA) award.  The simulations
have been performed on IBM p690 (Copper) at the National Center for
Supercomputing Applications (NCSA) which is supported by the
National Science Foundation.


\begin{thebibliography}{0}
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  \AA.}\TITLE{Collisionless Shocks - Magnetic Field Generation and Particle
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\BY{Hededal, C.B., Haugb\o lle, Frederiksen, J.T.,  Nordlund, \AA.}
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\bibitem{ref:nis03}
\BY{Nishikawa, K.-I., Hardee, P., Richardson, G., Preece, R., Sol,
H., Fishman, G.J.} \IN{ApJ} {595} {2003} {555}

\bibitem{ref:nishi04a}
\BY{Nishikawa, K.-I., Hardee, P., Richardson, G., Preece, R., Sol,
H., Fishman, G.J.}  \IN{ApJ} {623}{2005}{in press}
(astro-ph/0409702)

\bibitem{ref:nishi04b}
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\bibitem{ref:silva03}
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\bibitem{ref:weib59}
\BY{Weibel, E.S.} \IN{Phys. Rev. Lett.} {2}{1959} {83}

\bibitem{rf:medv99}
\BY{Medvedev, M. V. \atque  Loeb, A.} \IN{ApJ} {526}{1999} {697}



%\bibitem{ref:apo} \BY{Boccaccio~G. \atque de~Cam\~oes~L.}
%  \IN{Phys. Rev. A}{13}{1999}{12};
%  \SAME{69}{999}{1666}.
%\bibitem{ref:pul} \BY{Pulci~L.}
%  preprint INFN 8181.
%\bibitem{ref:bra} \BY{Bragg~B.}
%  \TITLE{Tender comrade},
%  in \TITLE{Workers Playtime},
%                  edited by \NAME{Tizio A. \atque Caio B.}
%                  (Unexeditor, Bologna) 1997, pp.~1-10.
\end{thebibliography}

\end{document}
\endinput
%%
%% End of file `cimsmple.tex'.

astro-ph0502331.extracted_bib
\begin{thebibliography}{0}
\bibitem{ref:fred02}
  \BY{Frederiksen, J.T., Hededal, C.B., Haugb\o lle, T.,  Nordlund,
  \AA.}\TITLE{Collisionless Shocks - Magnetic Field Generation and Particle
Acceleration}, in \TITLE{Proc.\ From 1st NBSI on Beams and Jets in
Gamma Ray Bursts, held at NBIfAFG/NORDITA, Copenhagen, Denmark,
August, 1-6, 2002} (astro-ph/0303360)
\bibitem{ref:fred04}
\BY{Frederiksen, J.T., Hededal, C.B., Haugb\o lle,  Nordlund, \AA.}
 \IN{ApJ} {608}{2004}{L13}
\bibitem{ref:hede04}
\BY{Hededal, C.B., Haugb\o lle, Frederiksen, J.T.,  Nordlund, \AA.}
\IN{ApJ} {617}{2004}{L107}
\bibitem{ref:nis03}
\BY{Nishikawa, K.-I., Hardee, P., Richardson, G., Preece, R., Sol,
H., Fishman, G.J.} \IN{ApJ} {595} {2003} {555}

\bibitem{ref:nishi04a}
\BY{Nishikawa, K.-I., Hardee, P., Richardson, G., Preece, R., Sol,
H., Fishman, G.J.}  \IN{ApJ} {623}{2005}{in press}
(astro-ph/0409702)

\bibitem{ref:nishi04b}
\BY{Nishikawa, K.-I., Hardee, P., Hededal, C. B., Richardson, G.,
Preece, R., Sol, H., Fishman, G.J.} \TITLE{Relativistic Shocks:
Particle Acceleration and Magnetic Field Generation, and Emission},
in \TITLE{Proceeding of International Symposium on High Energy
Gamma-Ray Astronomy (July 26-30, 2004)}, (astro-ph/0410193)

\bibitem{ref:silva03}
\BY{Silva, L. O., Fonseca, R. A., Tonge, J,.W., Dawson, J. M., Mori,
W.B.,  Medvedev, M. V.} \IN{ApJ} {596}{2003} {L121}

\bibitem{ref:weib59}
\BY{Weibel, E.S.} \IN{Phys. Rev. Lett.} {2}{1959} {83}

\bibitem{rf:medv99}
\BY{Medvedev, M. V. \atque  Loeb, A.} \IN{ApJ} {526}{1999} {697}



%\bibitem{ref:apo} \BY{Boccaccio~G. \atque de~Cam\~oes~L.}
%  \IN{Phys. Rev. A}{13}{1999}{12};
%  \SAME{69}{999}{1666}.
%\bibitem{ref:pul} \BY{Pulci~L.}
%  preprint INFN 8181.
%\bibitem{ref:bra} \BY{Bragg~B.}
%  \TITLE{Tender comrade},
%  in \TITLE{Workers Playtime},
%                  edited by \NAME{Tizio A. \atque Caio B.}
%                  (Unexeditor, Bologna) 1997, pp.~1-10.
\end{thebibliography}