PHYS 519: Plasma Kinetic Theory
Homework 1
Due before the beginning of class on Thursday January 26, 2017.
Email your solution as a PDF file to [email protected]. (A scan of a hand-written document is fine.)
1. Quantum effects in a plasma
(a) Compare the temperature T of a nonrelativistic electron-proton plasma to the Fermi
energy EF of the electrons to obtain an approximate formula for the density nQ above
which quantum effects dominate.
(b) Obtain a numerical version of the formula in part (a) with nQ in cm−3 and T in eV.
(c) Evaluate nQ in cm−3 for T = 1 keV and compare the corresponding mass density to the
mass density of hydrogen gas and lead (both at STP).
2. Basic plasma parameters: A reading assignment
Please read sections 1.1 to 1.5 in Introduction to Plasma Theory by D. R. Nicholson (see
handout). Once you have read those sections, write “I have read sections 1.1 to 1.5 of
Nicholson” on your homework solutions.
3. The Klimontovich equation
(a) Show that the Klimontovich equation
∂Ns
qs
1
+ v · ∇x Ns +
E m (x, t) + v × B m (x, t) · ∇v Ns = 0
∂t
ms
c
(1)
can be written as a continuity equation in the 6-dimensional x-v phase space.
(b) Show that at any time t, the integral of the Klimontovich density Ns over all phase space
yields the total number of particles of species s.
(c) In class we assumed that there were no external fields E ext and B ext . Give the Klimontovich equation for nonzero external fields.
(d) Modify our in-class derivation of equation (1) to obtain the relativistic Klimontovich
equation for Ns (x, p, t), where p = mγv is the relativistic momentum.