148 Chapter 4. Elementary plasma waves
an oscillating electric field ̃E⊥where⊥means in the direction perpendicular toz.ˆ
What is the polarization current associated withE ̃⊥? By substituting this polarization
current into the MHD approximation of Ampere’s law, find a relationship between
∂E ̃⊥/∂tand a spatial operator onB ̃.Use Faraday’s law to obtain a similar relationship
between∂B⊥/∂tand a spatial operator onE ̃.Consider a mode whereE ̃x(z,t)and
B ̃y(z,t)are the only finite components and derive a wave equation. Do the same for
the pairE ̃y(z,t)andB ̃z(z,t).Which mode is the compressional mode and which is
the shear mode?