PHYS 480: Introduction to Plasma Physics
Homework 6
Due 1pm, Thursday, October 17, 2013
Email a single PDF file to the grader, with a CC to the instructor, with HW06 in the Subject line.
1. Reflection of oblique electromagnetic waves by a cold unmagnetized plasma
Electromagnetic waves in vacuum are incident on a slab of plasma at an angle θ as shown below. The
plasma has a uniform plasma frequency ωp .
(a) Using Snell’s law, find the critical angle θc for total reflection as a function of frequency.
(b) Plot sin θc versus ω/ωp and shade the region of total reflection. Note that for large incident angles,
total reflection can occur at frequencies well above the plasma frequency.
2. The dispersion tensor for cold magnetized electron OCP
As in lectures the equation of motion for electrons may be written
f = − e δE
f
(−iω − Ω×) δv
me
(1)
where Ω ≡ (eB0 /me )b
z = ωceb
z.
(a) Apply the “conjugate operator” (iω − Ω×) to both sides of equation (1), solve for each of the three
f write the solutions in matrix form δv
f = A · δE,
f where A is a 3×3 matrix
Cartesian components of δv,
f into δJ
f = −en0 δv
f = σ · δE
f to obtain the conductivity tensor σ.
(tensor), and substitute δv
(b) From σ obtain the corresponding dielectric tensor and the dispersion tensor
D=
ω2
+ nn − n2 I
2
c
(2)
where n = kc/ω is the vector index of refraction.
3. Reading and exercise(s) from Plasma Dynamics by R.O. Dendy:
(a) Read Section 3.4. After reading Section 3.4, for full credit write “I have read Section 3.4 of Dendy”,
and for bonus points write a brief summary.
(b) Exercise 3.2. Please attempt to complete each exercise before looking at the solution in the book.
You may look at the solution in the book, but you must not just copy it.