Multiple Sheet Beam Instability of Current Sheets in Striped Relativistic Winds Inertial Parallel E in Neutron Star Magnetospheres: Return Cuurent Sheets and Pulsed Gammas Jonathan Arons University of California, Berkeley 1

Crab Vela G54.1 J2229 B1706 J0538 Ng & Romani Torii in rotational equator - small aspect ratio - /r ~ 0.1(Crab), smaller in others Rings and Torii As if energy fluxin a narrow latitude sector 2

Poynting Flux dominated wind strongest toward equator Magic: If, nebular response ~ images ( Komisssarov & Lyubarsky 2003; del Zanna et al 2004; Bogovalov et al 2005 ) “Unmagnetized” equatorial channel

Outer Wind Properties, : Current Sheet, carries return current Sheet Opening Angle: Like Split Monopole of Aligned Rotator Without Dissipation: Relativistic Beam: “protons” (i=0), e - (i=p) 4

PSRi Crab80 o Vela65 o o o o o Observed PSR = oblique rotators Gamma Ray PSR, i from Romani and Yadigarglou outer gap model Equatorial Current Sheet Frozen-in wave, Striped wind 5 Striped Jets: Spruit, Konigl

Force Free Simulation of i=60 o Rotator (Spitkovsky) Current Sheet Separating Stripes (Bogovalov) i=60 o i=9 o Inner Wind: Magnetically Striped 6

Stripe Dissipation If wrinkled current dissipates, striped field dissipates, magnetic energy coverts to flow kinetic energy, “heat” & high frequency radiation, strong waves - partition? Sheet Dissipation: Tearing of one locally ~ plane sheet? (Coroniti; too slow? - Kirk & co.) Cause: Current starvation? (everybody) sheet strong waves? - Melatos-vacuum) 7

Stream Instability of Multiple Sheets Current sheets = transmission lines Current = charged particle beam injected by source - Y or X line at LC | | =I GJ =Goldreich-Julian Current In absence of dissipation, beams flow adiabatically in narrow channel 8

2H (adiabatic EOS) Sheets swallow stripes (H > R L ): Simplified Sheet Structure (Crab)only if - sheets survive? 9 (protons)

Sheets Interact - Two Stream (Weibel-like) instability Thin Sheet (kr L <<1) dynamics as if each sheet is unmagnetized although intersheet medium MHD x 0 =R L << r x0x0 10

Two Symmetric Sheet Instability Imagine Magnetic disturbance at each sheet - Alfven pol j 0 x force compresses each sheet’s surface density into filaments parallel to j 0 Surface current filaments reinforce - Weibel instability in flatland RLRL Growth Rate 2 symmetric sheets = purely growing in proper frame 11

Proper Growth Rate (v A =c, v beam =c, sheet thickness = ) Growth rate > expansion rate for 12

Saturation - Magnetic Trapping beam particles scattered by self fields 13 Growth & Trapping Saturation of Spatially Distributed Weibel (Spitkovsky & JA) shock - transient growth and decay; current sheet is driven but end result will “always” be magnetic turbulence that scatters particles

Anomalous Resistivity in Sheets - rapid expansion of sheets, destruction of intersheet field? (Coroniti’s model) Resistive electric field in sheet - equilibrium beam energy (?) Many sheets, sheet strength j 0 declines with r: radiation of long wavelength EM waves (fast modes shocks) of relativistic amplitude? Anomalous resistance, scattering: radiation (synchroton), sheets radiate - pulsed emission? (Kirk et al; historically, JA)

15 Experiments Computational: 3D PIC, must be MHD between sheets (frozen-in pairs) resolve current layer: Larmor and c/  p scales of beam particles could use rectangular geometry Lab Experiment? Use laser on dense slab to launch relativistic electron-positron plasma onto field lines of reversed B (RFP?) Launch beams into field reversal region? Laser generated MHD electron-positron plasma XX Charged particle beam currents Strong Background B Perp E to give cross field plasma flow? Expt improves on simulation?

Parallel E in Pulsar return currents Pulsed Gamma Rays: Acceleration in Boundary layer along open field lines

Return Current Sheet Gamma rays radiated by some sort of sheet at or near the boundary layer Romani’s “outer gap” surface: quasi-vacuum E accelerator : thickness ~ r l (R L )(r/R L ) 3/2 Return current, precipitating plasma formed by reconnection at R Y Return current density huge: J ret ~ J[R L /r l (R L )] ~ J (e  /mc 2  ) >>>1  magnetospheric potential = B * R * (R * /R L ) 2 : V Particle inertia in the current channel:  ret = pair multiplicity, precipitating from Y-line, < 10 4 Y-line at r = R Y ~ R L Simulations? Experiments (Earth’s auroral currents, magnetotail reconnection informative)