Relativistic Current Sheets
in Electron-Positron Plasmas
Seiji Zenitani
NASA Goddard Space Flight Center
Collaborators: M. Hoshino (U. Tokyo), M. Hesse, A.
Klimas (NASA/GSFC)

Outline• Introduction• Basic processes in a relativistic current sheet– 2D Reconnection– 2D Drift Kink Instability– 3D Evolution– 3D Guide field effect– Weibel instability• Discussions• Large-scale MHD problem (option)• Summary + Open questions

Sites of relativistic current sheets• Pulsar winds– Magnetic dissipation in relativistic outflow ofelectron positron plasma winds• Magnetars– giant flare models for SGR• Various potential sites

1015G– Active galactic nuclei– Gamma ray bursts
Reconnectionin the current sheet

Lyutikov 2006 MNRASStriped pulsar wind
• Magnetic dissipation process ishighly demanded in the striped
current sheets (Coroniti 1990 ApJ,
Lyubarsky & Kirk 2001 ApJ, Kirk &Skjaeraasen 2003 ApJ)
Kirk et al. 2007 astroph/0703116

currentsheetsmagnetic
field lines

Coroniti 1990 ApJe+, e- flow

Basic processes
in a relativistic current sheet

Relativistic Current Sheet (RCS)
ee+BＺＸ

ＹJ•••••

Antiparallel magnetic field lines
Dense plasma current sheet at the center
Current : the counter-streaming of electrons and positrons
Relativity : T~mc2, cA ~ c
Relativistic Harris model (Hoh 1966, Kirk & Skjaeraasen 2003)

Magnetic Reconnection (RX)Ｚ

B
J

YZ : drift kinkinstability (DKI)ＸＹ

XZ ： magnetic
reconnection (RX)2D PIC simulation• Fast reconnection occurs• Particle acceleration around the X-region
Energy spectra

Zenitani & Hoshino 2001 ApJ

DC particle acceleration
ZEyX~ -1E2-B2>0Y

Zenitani & Hoshino 2001 ApJ

Ey

Trapping condition~ Gyro motion by Bz (Speiser orbit)==> extended in the Y direction

BzXc$ m 0c 2rL "=%&#CeBZ

Large-scale dynamic evolution
Ey-Ey

↑
te+

Zenitani & Hoshino 2007 ApJ~ -3
Jaroschek et al. 2004 ApJ•Powerful motional electric fields
at multiple magnetic islands•Entire acceleration mechanism:
not yet well understood

Jaroschek et al. 2004 Phys. Plasmas

Drift Kink Instability (DKI)ＺBJYZ : drift kinkinstability (DKI)ＸＹXZ ： magneticreconnection (RX)2D PIC simulation• A kink-type instability, driven by the electron-positron counterstreaming (Zhu & Winglee 1996 JGR, Ozaki et al. 1996 Phys.
Plasmas, Pritchett et al 1996 JGR, Daughton 1999 Phys.
Plasmas)

+Bx
e--Bx

e+

Electric field

Energy spectra

(1)

(2)

E・ J
Joule dissipation(3)

Plasmaheating

Zenitani & Hoshino 2005 ApJ

Two competing modes
RX (nonthermal acceleration) vs DKI (plasma heating).
In the relativistic regime, DKI grows faster.

• PIC simulation• Analytical estimateRXDKIτc γDKI

τc γRXnonrela.
regimerelativistic
regimenonrela.

relativistic

T/mc2

thin RCS

T/mc2
thick RCS

3D evolution

DKI dominates
Micro RXoccurs here

Turbulent
Zenitani & Hoshino 2008 ApJ

Guide field case

The Guide field (By)ＺＸ

•Harris field + Uniform By = Twisted equilibrium

BBy

YZ : drift kinkinstability (DKI)

XZ ： magnetic
reconnection (RX)BBＹGrowth rate: guide field dependency• RX is insensitive• DKI is stabilized by themagnetic tension• We expect that RX
dominates in 3DDKIRX

Guide field (|By|/B0)

3D evolution with guide field
B

Hybrid oblique modes
between RX and the driftsausage mode (an oddparity cousin of DKI)

Hybrid modes triger
secondary RX

Zenitani & Hoshino 2005 PRL

Energy distribution

3D DKI - plasma heating
3D RX (guide field)
particle acceleration

Magnetic topology changes
the destination of released energy;
plasma heat or non-thermal energy.
Zenitani & Hoshino 2005 PRL

Recent discovery:
Weibel instability

Weibel-type instability in reconnection• Anisotropy-driven Weibel instability (WBI)generates out-of-plane magnetic field at the outflow jet front• Small scale mode of (L ~ γ1/2c/ωp)
By

Charge separation

Zenitani & Hesse 2008 Phys. Plasmas• The WBI quickly widens the magnetic island

Weibel• The WBI works as a shock-downstream scatterer
Magnetic wall
(Tangential Discon.)

Reconnection
Outflow

Weibel fields• The WBI seems to be universal (Nonrelativistic case; Swisdak’s Talk)

Discussions

On the dissipation problem• Radial 1D flow model (Lyubarsky & Kirk 2001 ApJ, Kirk &Skjaeraasen 2003 ApJ)

Kinetic energy

EM energy

Termination Shock– A realistic rate by RX (the collisionless tearing mode; Zelenyi &Krasnosel’skikh 1979)" RTI = # c $ RTI = " 3 / 2– The DKI will give better dissipation" RDKI ~ " > " RTI• Dissipation & particle acceleration
at the shock!

– Lyubarsky 2005 MNRAS, Pétri!& Lyubarsky!2007 A&A, Nagata et al.
2008 ApJ– 2D/3D instabilities would enhance magnetic dissipation - evenwhen (rL/L)~O(0.1), 2D instabilities grows fast in such a thin RCSLarge scale PIC simulation• 3D evolution in a nonrelativistic pair plasma is more
dynamic than expected• DKI saturates, RX grows, and again kink-like mode in the thinreconnection CS• At least the linear physics would be similar

DKIRXLin et al. 2008 PRL
Large-scale evolution of RCS remains unclear
It should be checked by large-scale PIC simulation

Spectral index• Magnetic reconnection– Acceleration region --- s ~ 1.x• Theory: Romanova & Loverace 1992 A&A, Larrabee et al. 2003ApJ• PIC: Zenitani & Hoshino 2001 ApJ– Universal index --- s ~ 3 (2.x)• PIC: Jaroschek et al. 2004 Phys. Plasmas, Zenitani & Hoshino
2007, 2008 ApJ, Bessho & Battarachargee 2007 Phys. Plasmas,Karlíky 2008 ApJ• Moderate guide field may make it harder– Further enhanced in pulsar-wind driven configuration• Lyubarsky & Liverts 2008 ApJ• 1D RCS problem– Nonadiabatic acceleration in an individual RCS : s=2-4• Jaroschek et al. 2008 Adv. Space. Res.

– Shock - RCSs interaction : s=4• Nagata et al. 2008 ApJ

Large-scale MHD
evolution of RCS
Beyond the kinetic scale …

Resistive RMHDreconnection• RCS processes dissipate magneticenergy• Limited number of resistive
relativistic MHD (RMHD) studies• Watanabe & Yokoyama 2006 ApJ– Relativistic resistive MHD simulation
in weakly magnetized regime– Ohm’s law: localized resistivity at
the center• Petschek reconnection
with a pair of slow shocks

Watanabe & Yokoyama 2006 ApJ

Two-fluid RMHD reconnection (1)• Independent electronpositron motion• Resistivity = an inter-species
friction force• Localized resistivity profileux
Zenitani et al. 200x in prepTwo-fluid RMHD reconnection (2)•When the inflow is more magnetic-dominated, we observe
Sweet-Parker-type fast reconnection of the rate ~1.

preliminary•The system evolution highly depends on the resistivity profile,which essentially comes from the small-scale kinetic physics.
•RMHD + kinetic joint study required.

Summary• Basic instabilities in RCS– Magnetic Reconnection (RX; nonthermal acceleration)– Relativistic Drift Kink Instability (DKI; plasma heating)– Hybrid oblique modes– The Weibel Instability (WBI)• RCS 3D evolution– Antiparallel : RX < DKI (?) → Plasma heating– Guide field : RX > DKI → Nonthermal acceleration– DKI will be the better dissipation mechanism– Power Law : universal index of s ~ 3– RMHD simulation: important tools to study large-scaleastrophysical problems, with PIC• Open Questions (Next slide)Open questions• Large scale kinetic evolution• Large scale RMHD evolution, and its consistency with kineticmodel• RX––––Acceleration rate or power-law index
Dependence to the upstream σOrigin of the resistivity, and how to scale it?
The steady reconnection model and its reconnection rate?

• DKI– Saturation mechanism– Compressed configuration• and many more…
– Radiative effect (→ Jaroschek’s Talk)– Positron-ion-electron plasmaDziękuję(Thank you!)