1. Relativistic Plasmas in Astrophysics and in Laser Experiments I:
PIC Simulations of Poynting Jets and
Collisionless Shocks
Edison Liang, Koichi Noguchi
Rice University
Acknowledgements: Scott Wilks, Bruce Langdon
(lecture series at LANL July, 2006)
Work supported by LLNL, LANL, NASA, NSF

2. acceleration and radiation of: 1. Poynting jets = EM-dominated
This talk will focus on particle
acceleration and radiation of:
1. Poynting jets = EM-dominated
directed outflows
2. Relativistic collisionless shocks

3. Relativistic
Plasma Physics
High Energy
Astrophysics
Particle
Acceleration
New
Technologies
Ultra-Intense
Lasers

4. Phase space of laser plasmas overlaps most of relevant high energy astrophysics regimes
PulsarWind
GRB 4 3 2 1
High-b
Blazar
log<g>
INTENSE LASERS
Low-b
Galactic Black Holes
We/wpe

5. Pulsar equatorial striped wind from oblique rotator
(Lyubarsky 2005)
collisionless shock

6. Gamma-Ray Bursts: Two Competing
Paradigms: “to B(magnetic) or not to B?”
Woosley & MacFadyen,
A&A. Suppl. 138, 499 (1999)
e+e-
e+e-
Internal shocks:
Hydrodynamic
Outflow
What is primary energy source?
How are the e+e- accelerated?
How do they radiate?
Poynting flux:
Electro-magnetic
-dominated
Outflow

7. Relativistic Plasmas Cover Many Regimes:
1. kT or internal <g> > mc2
2. Flow speed vbulk ~ c (G >>1)
3. Strong B field: vA/c = S1/2 = We/wp > 1
4. Vector potential ao=eE/mcwo > 1
Most of these regimes are “collisionless”
They can be studied mainly via
Particle-in-Cell (PIC) simulations

8. Moreover, nonlinear collective processes
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 v=c limit.

9. x y (into plane) Example of in NN code. x is open
in Zohar code.
In dynamic problems, we often use
zones << initial Debye length to
anticipate density compression

10. 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

11. Particle acceleration by relativistic
j x B force
EM pulse
Entering By
Plasma
JxB force snowplows all surface particles upstream:
<g> ~ max(B2/4pnmec2, ao)
“Leading Poynting
Accelerator” (LPA) By x y z Ez Jz
JxB k Ez Jz x
Exiting
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:
<g> >> B2 /4pnmec2, ao “Trailing Poynting Accelerator”(TPA).
(Liang et al. PRL 90, , 2003) x

12. We/wpe =10 Lo=120c/We t.We=800 t.We=10000 TPA reproduces many GRB
signatures:
profiles,
spectra
and spectral
Evolution
(Liang &
Nishimura
PRL 91, )
magnify
We/wpe =10
Lo=120c/We

13. Details of early e+e- expansion
E+e- slab run
Momentum gets more and
more anisotropic with time

14. Fourier peak wavelength scales as ~ c.gm/ wpe
tWe=1000
hard-to-soft
GRB spectral
evolution
5000
10000
diverse
and
complex
BATSE
light
curves
18000
Fourier peak wavelength scales as ~ c.gm/ wpe

15. (movie by Noguchi 2004)

16. 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=(n+1)/2
the maximum gmax ~ e E(t)bzdt /mc where E(t)
is the comoving electric field

17. m(t) = (2fe(t)t + Co)1/2 t ≥ Lo/c
e/wep=10
e/wep=100
f= Co=27.9
m(t) = (2fe(t)t + Co)1/2 t ≥ Lo/c
This formula can be derived analytically from first principles

18. 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: d<g2>/dt ~ 2 po We(t)<h> Integrating we obtain: <g2>(t) = 2f We(t).t + go2

19. The power-law index seems remarkably robust
independent of initial plasma size or temperature
and only weakly dependent on B
Lo=105rce
f(g)
Lo= 104rce
-3.5 g

20. 3D cylindrical geometry with toroidal fields
(movies by Noguchi)

24. 3D donut geometry with pure toroidal fields
(movies by Noguchi)

28. PIC simulation allows us to compute the
radiation directly from the force terms
Prad = 2e2(F|| 2+ g2F+2) /3c
where F|| is force along v
and F+ is force orthogonal to v
TPA does NOT radiate synchrotron radiation.
Instead Prad ~ We2pz2sin2a << Psyn ~We2g2
where pz is momentum orthogonal to both B and
Poynting vector k, and a is angle between v and k.

29. TPA Prad asymptotes to ~ constant level at late times .
Lo=120c/We
po=10
Lo=105c/We

30. TPA of initially cold plasma results in much lower radiation
po=0.5

31. Asymptotic Prad scales with We/wpe between 2nd and 3rd power
103
104

32. 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/c=10-3
Averaged Radiated Power by the highest energy electrons

33. Using ray-tracing Noguchi has computed intensity and polarization
histories seen by detector at infinity
We/wpe=10
We/wpe=102

34. TPA e-ion run e
ion

35. e+e-
In pure e-ion plasmas, TPA transfers EM energy mainly to ion component due to charge separation
e-ion

36. TPA of e-ion plasma gives weaker electron radiation

37. ions get most of energy via charge separation
In mixture of e-ion and e+e- plasma, TPA selectively accelerates only the e+e- component e
ion
100% e-ion:
ions get most of energy via charge separation
e+e-
10%e-ion, 90%e+e-: ions do not get accelerated, e+e- gets most energy
ion

38. cold clumpy e+e- (Noguchi et al 2005)
PIC simulations of Relativistic Collisionless Shocks
3D run of e+e-
running into
cold clumpy e+e- (Noguchi et al 2005)

39. Interaction of e+e- Poynting jet with cold ambient e+e- shows broad
(>> c/We, c/wpe) transition region with 3-phase “Poynting shock”
By*100 px
ejecta
ambient
f(g)
ambient
spectral
evolution
ejecta
spectral
evolution g g

40. Prad of “shocked” ambient electron is lower than ejecta electron

41. 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
px/mc pi
ambient e-
ambient ion
ejecta e+ x
pi*10 By
By*100

42. Poynting shock in e-ion plasma is very complex with 5 phases
and broad transition region(>> c/Wi, c/wpe). Swept-up electrons are
accelerated by ponderomotive force. Swept-up ions are accelerated by
charge separation electric fields.
100pxi
100By
ejecta e-
Prad
100Ex
f(g)
ejecta e+
-10pxe
-10pxej
ambient
ion
ambient e- g

43. Prad of shocked ambient electron is comparable to the e+e- case
ejecta e-
shocked ambient e-

44. ejecta hi-B, hi-g weak-B, moderate g B=0, low g
Examples of collisionless shocks: e+e- running into B=0 e+e- cold plasma
ejecta hi-B, hi-g weak-B, moderate g B=0, low g
100By
ejecta
100By
100Ex
100By
swept-up
100Ex
-px swept-up
-pxswrpt-up
swept-up
ejecta
swept-up
swept-up

45. 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 e+e- and e-ion plasmas, TPA preferentially accelerates
The e+e- component and leave the e-ion plasma behind.