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D 1D  wave has index of refraction n=cvphase If waves propagate along the background magnetic field and no collision in the plasma then index of refraction is n2=1-ωpe2(ω+ωci)(ω-ωce) but we can ignore the effects of the ion contribution because ω>>ωci  plasma frequency ωpe=ne2mε0 ,where n is density, e is electron charge, m is mass of electrons.  cyclotron frequency, for electrons ωce=eBme, for ions its the same but with mass of the ion.   maxwells equations. ∇ x E=-dBdt. E=-dB/dt.  when solving this the left side becomes a line integral over a length and the right side becomes an integral over area of magnetic flux. Vmeasured=Nloop*Area* dBnormdt where N loop and area are talking about the loops and the area of the probe. Its a 6 coils arranged in the plasma. Tim says to think about it like 6 sides of a cube. B norm is the direction of the magnetic field through that loop.   the reduced equation for index of refraction (with ω>>ωci) is n2=1-ωpe2(ω)(ω-ωce)  vphase =ωk= ωωcec2ωpe2 solve for ω.