6.9 Assignments 209
whereSP< 0 .By writing the source on thezaxis as
f(z)=
1
2 π
∫
eikzz−iωtdkz
and by solving the dispersion to givekx=kx(kz)show that the potential excited in
the plasma is singular along the resonance cone surfaces. Explain why thishappens.
Draw the group and phase velocity directions.
- What is the polarization (i.e., relative magnitude ofEx,Ey,Ez)of the QTO, QTX,
and the two QL modes? How should a microwave horn be oriented (i.e., in which way
should theEfield of the horn point) when being used for (i) a QTO experiment, (ii) a
QTX experiment. Which experiment would be best suited for heating the plasma and
which best suited for measuring the density of the plasma?
- Show that there is a simple factoring of the cold plasma dispersionrelation in the low
frequency limitω<<ωci.Hint - first find approximate forms ofS,P,andDin this
limit and then show that the cold plasma dielectric tensor becomes diagonal.Consider
a mode which has onlyEyfinite and a mode which only hasExandEzfinite. What
are the dispersion relations for these two modes, expressed in terms ofωas a function
ofk.Assume that the Alfvén velocity is much smaller than the speed of light.
