particle acceleration and radiation from poynting jets and collisionless shocks edison liang, koichi...
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Particle Acceleration and Radiation from Poynting Jets and Collisionless Shocks
Edison Liang, Koichi NoguchiRice University
Acknowledgements: Scott Wilks, Bruce Langdon
Talk given at Xian AGN Meeting 2006
Internal shocksHydrodynamic Outflow
Poynting fluxElectro-magnetic-dominated outflow
Two Distinct Paradigms for the Energeticsof Relativistic Jets
e+e-ions
e+e-
What is primary energy source?How are the e+e- accelerated? How do they radiate?
shock-raysSSC, IC… -rays
B
What astrophysical scenarios may give rise to Poynting-flux driven acceleration?
magnetic towerhead w/ mostlytoroidal fieldlines
internal via toroidal EM expansion
rising flux rope
from BH
accretion disk
smallsection
modeledas cylinder
Reconnectionleads to freeexpansion of
EM-dominatedtorus
Bulk from hoop stress
t.e=800 t.e=10000
e/pe =10 Lo=120c/e
Poynting flux
Is an efficient
accelerator(Liang &
NishimuraPRL 91,175005 2004)
By
Ez
Jz
Plasma
JxB force snowplows all surface particles upstream:<> ~ max(B2/4nmec2, ao)“Leading PonderomotiveAccelerator” (LPA)
Plasma
JxB force pulls out surface particles. Loaded EM pulse (speed < c) stays in-phase with the fastest particles, but gets “lighter” as slower particles fall behind. It accelerates indefinitely over time: <> >> B2 /4nmec2, ao “Trailing Ponderomotive Accelerator” (TPA).
(Liang et al. PRL 90, 085001, 2003)
Entering
Exiting
Particle acceleration by relativisticj x B force
x
x
EM pulse
By
x
y
z
Ez
Jz JxB
k
The power-law index seems remarkably robust independent of initial plasma size or temperature
and only weakly dependent on B
f()
-3.5
Lo=105rce
Lo= 104rce
Radiation detected at infinity is strongly linearly polarized
e/pe=10
e/pe=102
3D magnetic e+e- donut with pure toroidal fields
(movies by Noguchi)
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PIC simulation can compute the radiation power directly from the force terms
Prad = 2e2(F|| 2+ 2F+2) /3c
where F|| is force along vand F+ is force orthogonal to v
Poynting jet does NOT radiate synchrotron radiation. Instead Prad ~ e
22sin4<< Psyn ~e22
where is angle between v and Poynting vector k.Alsocr ~ e2sin2crsyn
(movie by Noguchi 2004)
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Poynting Jet Prad asymptotes to ~ constant level at late timesas increase in is compensated by decrease in and B
Lo=120c/e Lo=105c/e
po=10
Prad
10*By
Prad
Inverse Compton scattering against ambient photons can slow or stop acceleration (Sugiyama et al 2005)
n=10-4ne n=10-2ne n=ne
1 eV photon field epe=100
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B
px
By*100
f()
Interaction of e+e- Poynting jet with cold ambient e+e- shows broad
(>> c/e, c/pe) transition region with 3-phase “Poynting shock”
ejecta
ambient
ejectaspectralevolution
ambientspectral evolution
ejecta e- shocked ambient e-
Prad of “shocked” ambient electron is lower than ejecta electron
Propagation of e+e- Poynting jet into cold e-ion plasma: acceleration stalls after “swept-up” mass > few times ejecta mass. Poynting flux decays via mode conversion and particle acceleration
ejecta e+ ambient e- ambient ion
px/mc
By
x
By*100
pi*10
pi
ejecta e+
ejecta e-
ambient ion
ambient e-
f()-10pxe-10pxej
100pxi
100Ex
100By
Prad
Poynting shock in e-ion plasma is very complex with 5 phases and broad transition region(>> c/i, c/pe). Swept-up electrons are
accelerated by ponderomotive force. Swept-up ions are accelerated by charge separation electric fields.
ejecta e- shocked ambient e-
Prad of shocked ambient electron is comparable to the e+e- case
Examples of collisionless shocks: e+e- running into B=0 e+e- cold plasma ejecta hi-B, hi- weak-B, moderate B=0, low
swept-up
swept-up
swept-up
100By
ejecta
swept-up100By
100Ex
100By100Ex
-px swept-up
-pxswrpt-up
ejecta
SUMMARY
1. Poynting jet (EM-dominated directed outflow) is a highly efficient, robust accelerator, leading to ultra-high energy particles.
2. In mixed e+e- and e-ion plasmas, Poynting flux preferentially captures and accelerates e+e- component and leave e-ion behind.
3. In 3D, expanding toroidal fields mainly accelerates particles along axis.
4. Intrinsic radiation power of both Poynting jet and collisionless shocks are much lower than classical synchrotron radiation. This may favor IC over SSC in some cases.
4. Structure and radiation power of collisionless shocks are highly dependent on ejecta B field strength and Lorentz factor.
(Lyubarsky 2005)
Pulsar equatorial striped wind from oblique rotator
collisionless shock
High Energy Astrophysics
Ultra-IntenseLasers
Relativistic Plasma Physics
ParticleAcceleration
New Technologies
e/pe
log<>
100 10 1 0.1 0.01
4
3
2
1
0
GRB
Galactic Black Holes
INTENSE LASERS
Phase space of laser plasmas overlaps most of relevant high energy astrophysics regimes
High-
Low-
PulsarWind
Blazar
x
y (intoplane)
in NN code. x is open in Zohar code.
Example of
In dynamic problems, we often usezones << initial Debye length to anticipate density compression
TPA produces Power-Law spectra with low-energy cut-off.Peak Lorentz factor mcorresponds roughly to the
profile/group velocity of the EM pulse
logdN/dE
logE
Epk~200 keV
~0--1.5
~-2--2.5
time
Epk
dN/dt
m
the maximum max ~ e E(t)zdt /mc where E(t) is the comoving electric field
Typical GRB spectrum
=(n+1)/2
m(t) = (2fe(t)t + Co)1/2 t ≥ Lo/cThis formula can be derived analytically from
first principles
f=1.33 Co=27.9
e/ep=10e/ep=100
Lorentz equation for particles in an EM pulse with E(t ,),B(t, ) and profile velocity w
d(x)/dt = - ze(t)h()d(z)/dt = -(w- xe(t)h()d(y)/dt = 0d/dt = -wze(t)h()
For comoving particles with w~ x we obtain:z = -o/; y = yo /; x = (2 -1- o
2 -yo2)1/2/
po ~ transverse jitter momentum due to Ez
Hence: d2/dt = 2 po e(t)h()x
As x ~ 1: d<2>/dt ~ 2 po e(t)<h>Integrating we obtain: <2>(t) = 2f e(t).t + o
2
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3D cylindrical geometry with toroidal fields
(movies by Noguchi)
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We have added radiation damping to PIC code using theDirac-Lorentz Equation (see Noguchi 2004) to
calculate radiation output and particle motion self-consistently
ree/c=10-3
Averaged Radiated Power by the highest energy electrons
TPA e-ion run
e
ion
In pure e-ion plasmas,
TPA transfersEM energy
mainly to ioncomponent due
to charge separation
e+e-
e-ion
e-ion Poynting jet gives weaker electron radiation
100% e-ion: ions get most of
energy via charge separation
10%e-ion, 90%e+e-: ions do
not get accelerated, e+e- gets most
energy
e ion
e+e- ion
In mixture of e-ion and e+e- plasmas, Poynting jet selectively accelerates only the e+e- component
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te=1000
5000
10000
18000
Fourier peak wavelength scales as ~ c.m/ pe
logdN/dE
logE
Epk~200 keV
~0--1.5
~-2--2.5
time
Epk
dN/dthard-to-soft GRB spectralevolution
diverseandcomplexBATSElightcurves
Relativistic Plasmas Cover Many Regimes:1. kT or internal <> > mc2
2. Flow speed vbulk ~ c ( >>1)
3. Strong B field: vA/c = ep > 1
4. Vector potential ao=eE/mco > 1
Most relativistic plasmas are “collisionless”They need to be modeled correctly via
Particle-in-Cell (PIC) simulations
Side Note
MHD, and in particular,magnetic flux freezing, often fails in the
relativistic regime, despite small gyroradii.
Moreover, nonlinear collective processesbehave very differently in the ultra-
relativistic regime, due to the v=c limit.
Momentum gets more and more anisotropic with time
Details of early e+e- expansion
Poynting jet Prad increases with initial temperature roughly as (kTo)2
po=0.5
Asymptotic Prad scales as (e/pe)n with n ~ 2 - 3
e/pe=102 103 104