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chris spencer deleted Math stuff.tex
about 10 years ago
Commit id: 4f7adb0dbd944596fab25073e68f944361ef07cd
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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=-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.
ω2=ωωcec2ωpe2k2
vgroup=dωdk=2kωcec2ωpe2 ω-1/2
Scratch latex work
\begin{equation}
a=\frac{f}{m}
\end{equation}
diff --git a/layout.md b/layout.md
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abstract.tex
Math stuff.tex
Introduction.tex
Introducation.tex