Relativistic Plasmas in Astrophysics

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Relativistic Plasmas in Astrophysics and in
Laser Experiments I PIC Simulations of
Poynting Jets and Collisionless Shocks Edison
Liang, Koichi Noguchi Rice University Acknowledge
ments Scott Wilks, Bruce Langdon (lecture series
at LANL July, 2006) Work supported by LLNL,
LANL, NASA, NSF
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• This talk will focus on particle
• acceleration and radiation of
• 1. Poynting jets EM-dominated
• directed outflows
• 2. Relativistic collisionless shocks

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Relativistic Plasma Physics
High Energy Astrophysics
Particle Acceleration
New Technologies
Ultra-Intense Lasers
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Phase space of laser plasmas overlaps most of
relevant high energy astrophysics regimes
PulsarWind
GRB
4 3 2 1 0
High-b
Blazar
logltggt
INTENSE LASERS
Low-b
Galactic Black Holes
100 10 1 0.1
0.01
We/wpe
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Pulsar equatorial striped wind from oblique
rotator
(Lyubarsky 2005)
collisionless shock
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Gamma-Ray Bursts Two Competing Paradigms
to B(magnetic) or not to B?
Woosley MacFadyen, AA. Suppl. 138, 499 (1999)
ee-
ee-
Poynting flux Electro-magnetic -dominated Outflow
Internal shocks Hydrodynamic Outflow
What is primary energy source? How are the ee-
accelerated? How do they radiate?
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• Relativistic Plasmas Cover Many Regimes
• 1. kT or internal ltggt gt mc2
• 2. Flow speed vbulk c (G gtgt1)
• 3. Strong B field vA/c S1/2 We/wp gt 1
• 4. Vector potential aoeE/mcwo gt 1
• Most of these regimes are collisionless
• They can be studied mainly via
• Particle-in-Cell (PIC) simulations

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• Side Note
• MHD, and in particular,
• magnetic flux freezing, often fails in the
  relativistic regime, despite small gyroradii.
• This leads to many novel, counter-intuitive
  kinetic phenomena unique to the
• relativistic regime.
• Moreover, nonlinear collective processes
• behave very differently in the ultra-
• relativistic regime, due to vc limit.

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Example of
x
y (into plane)
in NN code. x is open
in Zohar code.
In dynamic problems, we often use zones ltlt
initial Debye length to anticipate density
compression
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What astrophysical scenarios may give
rise to Poynting jet driven
acceleration?
Popular GRB Scenario
magnetic tower head w/ mostly toroidal field lines
local cylinder
rising flux rope from BH accretion disk
collapsar envelope
global torus rapid deconfinement
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Particle acceleration by relativistic j x B force
EM pulse
Entering
By
Plasma
JxB force snowplows all surface particles
upstream ltggt max(B2/4pnmec2, ao) Leading
Poynting Accelerator (LPA)
Ez
Jz
x
Exiting
Plasma
JxB force pulls out surface particles. Loaded EM
pulse (speed lt c) stays in-phase with the fastest
particles, but gets lighter as slower particles
fall behind. It accelerates indefinitely over
time ltggt gtgt B2 /4pnmec2, ao Trailing Poynting
Accelerator(TPA). (Liang et al. PRL 90, 085001,
2003)
x
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t.We800
t.We10000
TPA reproduces many GRB signatures
profiles, spectra and spectral Evolution (Liang
Nishimura PRL 91, 175005 2004)
magnify
We/wpe 10 Lo120c/We
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Details of early ee- expansion
Momentum gets more and more anisotropic with time
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tWe1000
hard-to-soft GRB spectral evolution
5000
10000
diverse and complex BATSE light curves
18000
Fourier peak wavelength scales as c.gm/ wpe
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(movie by Noguchi 2004)
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TPA produces Power-Law spectra with low-energy
cut-off. Peak Lorentz factor gmcorresponds
roughly to the profile/group velocity of the EM
pulse
Typical GRB spectrum
gm
b(n1)/2
the maximum gmax e E(t)bzdt /mc where E(t)
is the comoving electric field
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?e/wep10
?e/wep100
f1.33 Co27.9
?m(t) (2f?e(t)t Co)1/2 t Lo/c This formula
can be derived analytically from first
principles
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Lorentz equation for particles in an EM pulse
with E(t ,t), B(t, t) and profile velocity
bw d(gbx)/dt - bzWe(t)h(t) d(gbz)/dt
-(bw- bx)We(t)h(t) d(gby)/dt 0 dg/dt
-bw bzWe(t)h(t) For comoving particles with bw
bx we obtain bz -??o/g by ??yo /g bx
(g2 -1- ?o2 -?yo2)1/2/g po transverse jitter
momentum due to Ez Hence dg2/dt 2 po
We(t)h(t)bx As g???, bx 1 dltg2gt/dt 2
po We(t)lthgt Integrating we obtain ltg2gt(t) 2f
We(t).t go2
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The power-law index seems remarkably robust
independent of initial plasma size or
temperature and only weakly dependent on B
Lo105rce
Lo 104rce
f(g)
-3.5
g
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3D cylindrical geometry with toroidal fields
(movies by Noguchi)
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3D donut geometry with pure toroidal fields
(movies by Noguchi)
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PIC simulation allows us to compute the
radiation directly from the force terms
Prad 2e2(F 2 g2F2) /3c where F
is force along v and F is force orthogonal to
v TPA does NOT radiate synchrotron
radiation. Instead Prad We2pz2sin2a ltlt
Psyn We2g2 where pz is momentum orthogonal to
both B and Poynting vector k, and a is angle
between v and k.
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TPA Prad asymptotes to constant level at late
times .
Lo120c/We
Lo105c/We
po10
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TPA of initially cold plasma results
in much lower radiation
po0.5
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Asymptotic Prad scales with We/wpe between
2nd and 3rd power
We/wpe102
103
104
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We have added radiation damping to PIC code using
the Dirac-Lorentz Equation (see Noguchi 2004) to
calculate radiation output and particle motion
self-consistently
reWe/c10-3
Averaged Radiated Power by the highest energy
electrons
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Using ray-tracing Noguchi has computed intensity
and polarization histories seen by detector at
infinity
We/wpe10
We/wpe102
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TPA e-ion run
e
ion
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In pure e-ion plasmas,TPA transfersEM
energymainly to ioncomponent dueto charge
separation
ee-
e-ion
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TPA of e-ion plasma gives weaker electron
radiation
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In mixture of e-ion and ee- plasma, TPA
selectively accelerates only the ee- component
e
ion
100 e-ion ions get most of energy via charge
separation
ee-
10e-ion, 90ee- ions do not get accelerated,
ee- gets most energy
ion
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PIC simulations of
Relativistic Collisionless Shocks
3D run of ee- running into cold clumpy ee-
(Noguchi et al 2005)
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Interaction of ee- Poynting jet with cold
ambient ee- shows broad (gtgt c/We, c/wpe)
transition region with 3-phase Poynting shock
By100
ejecta
px
ambient
f(g)
ambient spectral evolution
ejecta spectral evolution
g
g
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Prad of shocked ambient electron is lower than
ejecta electron
ejecta e-
shocked ambient e-
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Propagation of ee- Poynting jet into cold
e-ion plasma acceleration stalls after
swept-up mass gt few times ejecta mass.
Poynting flux decays via mode conversion and
particle acceleration
pi
px/mc
ambient ion
ambient e-
ejecta e
x
pi10
By
By100
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Poynting shock in e-ion plasma is very complex
with 5 phases and broad transition region(gtgt
c/Wi, c/wpe). Swept-up electrons are accelerated
by ponderomotive force. Swept-up ions are
accelerated by charge separation electric
fields.
100pxi
ejecta e-
100By
Prad
100Ex
f(g)
ejecta e
-10pxe
-10pxej
ambient ion
ambient e-
g
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Prad of shocked ambient electron is comparable to
the ee- case
shocked ambient e-
ejecta e-
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Examples of collisionless shocks ee- running
into B0 ee- cold plasma ejecta hi-B,
hi-g weak-B, moderate g B0,
low g
100By
ejecta
100By
100By
100Ex
swept-up
100Ex
-px swept-up
-pxswrpt-up
swept-up
ejecta
swept-up
swept-up
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• SUMMARY
• Poynting jet (EM-dominated outflow) can be a
  highly efficient, robust comoving accelerator,
  leading to ultra-high Lorentz factors.
• TPA reproduces many of the telltale signatures of
  GRBs.
• In 3D, expanding toroidal fields mainly
  accelerates particles along axis, while expanding
  poloidal fields mainly accelerates particles
  radially.
• Radiation power of TPA is higher than
  collisionless shocks. But in either case it is
  much lower than classical synchrotron radiation.
• This solves the cooling problem of synchrotron
  shocks.
• 5. Structure and radiation power of collisionless
  shocks is highly sensitive to EM field strength.
• 6. In hybrid ee- and e-ion plasmas, TPA
  preferentially accelerates
• The ee- component and leave the e-ion
  plasma behind.