Chapter 11: Plasma physics61For disturbances in thez-direction in a cold, homogeneous, magnetized plasma:±B=B0±ez+±ˆBei(kz-ωt)andn=n0+ˆnei(kz-ωt)(externalEfelds are screened) ±ollows, with the defnitionsα=ωp/ωandβ=Ω/ωandω2p=ω2pi+ω2pe:±J=±±σ±E,with±=iε0ω±sα2s11-β2s-iβs1-β2s0iβs1-β2s11-β2s0001where the sum is taken over particle speciess. The dielectric tensorE, with property:±k·(±±E·±E)=0is given by±±E=±±I-±/iε0ω.With the defnitionsS=1-±sα2s1-β2s,D=±sα2sβs1-β2s,P-±sα2s±ollows:±±E=S-iD0iDS0PThe eigenvalues o± this hermitian matrix areR=S+D,L=S-D,λ3=P, with eigenvectors±er=12√2(1,i,0),±el=12√2(1,-i,0)and±e3=(0,0,1).±eris connected with a right rotating feld ±or whichiEx/Eyand±elis connected with a le±t rotating feld ±or whichiEx/Ey=-1. Whenk
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.