BBCyclotronResonance/AbsorptionP(Luo&Melr0se20012006,Fusselletal.2003)の'=eB/mc.r=rcrscatteredE=C+VRCPabsorbedbyelectronsLCP absorbed by positronsOptical depth with >>12元n(1 - β cos B)%~ 0.62mB/2~-1/vg /3 P- (1 - β cos s)/3 ,73c/S2circular polarization can be generated by the asymmetric cyclotronabsorptionofelectronsandpositrons
ω′= eB/mc. r = rcr • RCP absorbed by electrons LCP absorbed by positrons • Optical depth with γ >>1 circular polarization can be generated by the asymmetric cyclotron absorption of electrons and positrons. B E = + scattered e Cyclotron Resonance/Absorption B p (Luo & Melrose 2001, 2006, Fussell et al. 2003)
不对称的正负电子回旋吸收对称的正负电子回旋吸收0.50.500110.50.500QQ-0.50.5-1-10.50.50UD00.5-0.5-1-10.50.5070-0.5-0.570-1vdeVdo-30-3088-60-6050100200500100020005010020050010002000s/R.S/R
对称的正负电子回旋吸收 不对称的正负电子回旋吸收
A small summarytopreviousstudiesDispersion relation and natural wave modes in some simpleapproximations was analytically derived A few kinds of propagation effects were studied qualitatively(early years) and using numerical calculations (recent works) Almost none of the previous studies has calculated the finalpolarization profiles with all of these propagation effects includedin a self-consistent way within a single theoretical framework
A small summary to previous studies • Dispersion relation and natural wave modes in some simple approximations was analytically derived. • A few kinds of propagation effects were studied qualitatively (early years) and using numerical calculations (recent works). • Almost none of the previous studies has calculated the final polarization profiles with all of these propagation effects included in a self-consistent way within a single theoretical framework
OurworksWaveand modes amplitude evolution eguationOn some specialpropagation effectsVacuum resonance (Wang,Lai& Han 2007)_Wave mode coupling (Wang, Lai & Han 2010)Quasi-tangential effect (Wang&Lai 2009)- Intrinsic Faraday Rotation in magnetosphere(Wang,Han &Lai2011)· Numerical calculations on Polarization profilechanges considering all the propagation effects.(Wang,Lai&Han2010)
Our works • Wave and modes amplitude evolution equation • On some special propagation effects – Vacuum resonance (Wang, Lai & Han 2007) – Wave mode coupling (Wang, Lai & Han 2010) – Quasi-tangential effect (Wang & Lai 2009) – Intrinsic Faraday Rotation in magnetosphere (Wang, Han & Lai 2011) • Numerical calculations on Polarization profile changes considering all the propagation effects. (Wang, Lai & Han 2010)
Wave evolution eguationSome propagation effects have not analytic solutionsDifferent effects are coupled and not easy to be separated=> numerical ray integrations is necessaryWave evolution eguationexx=1+Jsf.(y)dysdAxikooxxOXYA2exy =-Eyy=ifs12f.(s)dysds2AyAyoYxQYYEx2 = E =-2sfanfs(ydyswhereeye = e2y - / sfai2f()dys,=oxxExX --Determined by=oxyEXY,e =1+E / (fs.n +fan) f(y)dys.dielectric tensorOYX=EYX,with=OYYEYY-1usy-'(I+iyad)fs.11=(1 + iynd)2 us)-2 (1 - nβ, cos O)-2Wavefrequencysign(g)/2sy-2(—ncos@)-1fs.12 :(1 + iynd)2 usy-2 (1 nβ, cos Og)-2UsPlasmapropertiesfs.n(1+iyad)y(1nβ,cos )2npsingg5sMagneticfield1-npscos0B
Wave evolution equation => numerical ray integrations is necessary. • Wave evolution equation Determined by dielectric tensor ✓ Some propagation effects have not analytic solutions. ✓ Different effects are coupled and not easy to be separated. Plasma properties Wave frequency Magnetic field