Particle Acceleration and Radiation from Poynting Jets and Collisionless Shocks Edison Liang, Koichi...

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