Multiple Sheet Beam Instability of Current Sheets in
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
Rings and Torii Crab G 54. 1 B 1706 Vela J 2229 Ng & Romani J 0538 Torii in rotational equator - small aspect ratio - /r ~ 0. 1(Crab), smaller in others As if energy flux latitude sector 2 in a narrow
Poynting Flux dominated wind strongest toward equator Magic: If , nebular response ~ images “Unmagnetized” equatorial channel (Komisssarov & Lyubarsky 2003; del Zanna et al 2004; Bogovalov et al 2005)
Outer Wind : Properties, Like Split Monopole of Aligned Rotator Without Dissipation: Current Sheet, carries return current Relativistic Beam: “protons” (i=0), e- (i=p Sheet Opening Angle: 4
Observed PSR = oblique rotators PSR Crab Vela 1509 -58 1706 -44 0630+17 1055+08 i 80 o 65 o 60 o 40 o 25 o 70 o Gamma Ray PSR, i from Romani and Yadigarglou outer gap model Equatorial Current Sheet Striped Jets: Spruit, Konigl 5 Frozen-in wave, Striped wind
Inner Wind: Magnetically Striped Force Free Simulation of i=60 o Rotator (Spitkovsky) Current Sheet Separating Stripes (Bogovalov) i=60 o i=9 o 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? -7 Melatos-vacuum)
Stream Instability of Multiple Sheets Current sheets = transmission lines Current = charged particle beam injected by source - Y or X line at LC | | =IGJ=Goldreich-Julian Current In absence of dissipation, beams flow adiabatically in narrow 8 channel
Simplified Sheet Structure 2 H (adiabatic EOS) Sheets swallow stripes (H > RL): (Crab) only if - sheets survive? 9 (protons)
Sheets Interact - Two Stream (Weibel-like) instability x 0 =RL<< r Thin Sheet (kr. L<<1) dynamics as if each sheet is unmagnetized although intersheet medium MHD x 0 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 RL Growth Rate 2 symmetric sheets = purely growing in proper frame 11 Surface current filaments reinforce Weibel instability in flatland
Proper Growth Rate (v. A=c, vbeam=c, sheet thickness = ) Growth rate > expansion rate for 12
Saturation - Magnetic Trapping beam particles scattered by self fields 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 13
Anomalous Resistivity in Sheets - rapid expansion of sheets, destruction of intersheet field? (Coroniti’s model) Resistive electric field in sheet - equilibrium beam energy (? ) Anomalous resistance, scattering: radiation (synchroton sheets radiate - pulsed emission? (Kirk et al; historically Many sheets, sheet strength j 0 declines with r: radiation long wavelength EM waves (fast modes shocks) of relativistic amplitude?
Experiments Computational: 3 D 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? Charged particle beam currents X X Laser generated MHD electron-positron plasma Perp E to give cross field plasma flow? Expt improves on simulation? Strong Background B 15
Parallel E in Pulsar return currents Pulsed Gamma Rays: Acceleration in Boundary layer along open field lines
Return Current Sheet : thickness ~ rl(RL)(r/RL)3/2 Y-line at r = RY ~ RL Gamma rays radiated by some sort of sheet at or near the boundary layer Return current, precipitating plasma formed by reconnection at Return current density huge: Jret ~ J[RL/rl(RL)] ~ J (e /mc 2 ) >>>1 magnetospheric potential = B*R*(R*/RL)2: 1012 -1017 V Particle inertia in the current channel: ret = pair multiplicity, precipitating from Y-line, < 104 Romani’s “outer gap” surface: Simulations? Experiments (Earth’s auroral currents, quasi-vacuum E accelerator magnetotail reconnection informative)
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