Modeamplitude evolution equationBTwo elliptically polarized modes in theE.labframeKpBtangm=Eu/(iE)Theellipticity ofthemodes.X0°or 90°: linearly polarized;45°: circularly polarizedSBTheorientationofthemodes,dominatedbyBfieldAxicosOmcospB-sinOmsinB-isinOmcosB-cosOmsinpBA+E++A_E-E+AyicosmsinB+sinOmcosB-isinOmsinpB+cosmcosBModeamplitudeevolutionequation-△k/2+Φgsin20mi0m+Φgcos20mddsi0m+igcos20m△k/2-Φgsin20m△k/2-ΦBsin20mAdiabaticTad =>10m+Φgcos 20mCondition
Mode amplitude evolution equation E+ E- Two elliptically polarized modes in the lab frame The ellipticity of the modes, 0 o or 90o : linearly polarized; 45o : circularly polarized The orientation of the modes, dominated by B field Mode amplitude evolution equation x y Y X B⊥ Adiabatic Condition i i
Our works on propagation effectsVacuumresonance(Wang&Lai2007,MNRAS)Wave mode coupling(Wang,Lai&Han2010,MNRAS)Quasi-tangential effect(Wang&Lai2009,MNRAS)Intrinsic Faraday Rotation effect in pulsarmagnetosphere(Wang,Han&Lai201i,MNRAS)
Our works on propagation effects • Vacuum resonance (Wang & Lai 2007, MNRAS) • Wave mode coupling (Wang, Lai & Han 2010, MNRAS) • Quasi-tangential effect (Wang & Lai 2009, MNRAS) • Intrinsic Faraday Rotation effect in pulsar magnetosphere (Wang, Han & Lai 2011, MNRAS)
Vacuumresonance(thecompetition betweenplasmaandQEDeffect)X-rayband, Vacuum polarization (orQED effect)dominates thedispersion relationRadioband,plasmaeffectdominatesWhereistheboundary?WhathappensintheboundaryregimeQEDdominatedplasmadominatedVacuumresonanceThetwoeffects“cancled”witheachothel1.Correction to dielectric tensor△e(v) = (α-1)I+qBBE = e(pP) + △e(v)2.Inversepermeabilitytensorμ-1 =aI +mBB
Vacuum resonance (the competition between plasma and QED effect) 1. Correction to dielectric tensor 2. Inverse permeability tensor • X-ray band, Vacuum polarization (or QED effect) dominates the dispersion relation • Radio band, plasma effect dominates Where is the boundary? What happens in the boundary regime QED dominated plasma dominated Vacuum resonance The two effects “cancled” with each other
WavemodeswithQEDeffect"Avoid modecrossing" occurs, the two modes (O-mode & E-mode)coupleddefinetwonewmodes:modemode.Q-mode+ modeX-modeX-mode1/(Bcos0B）modem/yo=O-modeC1.801251.8013subluminous O-mode1/coseX-mode/w)-3/2/β+1/(βcos8g.superluminous-modsS10.51.520(ap/0)-3/2
Wave modes with QED effect • “Avoid mode crossing” occurs, the two modes (O-mode & E-mode) coupled. ➔ define two new modes: “＋” mode “－” mode. O-mode O-mode X-mode X-mode
Mode conversiondueto vacuum resonanceQEDVacuumplasmadominatedResonancedominatedHelicityunchangedOQO-modeX-mode-W?一X-mode-=YK0O-mode11.21.31.41.17n = N/NGJ
QED dominated plasma dominated Vacuum Resonance O-mode O-mode X-mode X-mode Mode conversion due to vacuum resonance Helicity unchanged