Relativistic Plasmas in Astrophysics and in Laser Experiments I:

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. 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 0 High-b Blazar log<g> INTENSE LASERS Low-b Galactic Black Holes 100 10 1 0.1 0.01 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- Poynting flux: Electro-magnetic -dominated Outflow Internal shocks: Hydrodynamic Outflow What is primary energy source? How are the e+e- accelerated? How do they radiate?

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. 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. Example of x y (into plane) 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 y By Ez JxB Jz x z k EM pulse Entering By Plasma JxB force snowplows all surface particles upstream: <g> ~ max(B2/4pnmec2, ao) “Leading Poynting Accelerator” (LPA) 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, 085001, 2003) x

12. t.We=800 t.We=10000 TPA reproduces many GRB signatures: profiles, spectra and spectral Evolution (Liang & Nishimura PRL 91, 175005 2004) magnify We/wpe =10 Lo=120c/We

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

14. 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 ~ eE(t)bzdt /mc where E(t) is the comoving electric field

17. e/wep=10 e/wep=100 f=1.33 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 poWe(t)h(t)bx As g,bx ~ 1: d<g2>/dt ~ 2 poWe(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 Lo= 104rce f(g) -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 Lo=105c/We po=10

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 We/wpe=102 103 104

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. In pure e-ion plasmas,TPA transfersEM energymainly to ioncomponent dueto charge separation e+e- e-ion

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

37. 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. 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 ejecta px ambient f(g) ambient spectral evolution ejecta spectral evolution g g

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

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 pi px/mc ambient ion ambient e- 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 shocked ambient e- ejecta e-

44. 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.