FIRST ASSIGNMENT: PHYSICS 8120 PLASMA PHYSICS: DUE 10 ...

FIRST ASSIGNMENT: PHYSICS 8120
PLASMA PHYSICS: DUE 10 SEPTEMBER 2007
Prof. Paul J. Wiita
If you haven’t already done so, read Chapters 1 and 2 in the Kulsrud text. Problem numbers
below refer to this book. The numbers in brackets after each question denote its point value.
The assignment is due at the beginning of class on Sept. 10th. I hope to have the
graded assignment back to you by the 12th, but will certainly have them returned by the 17th.
If you hand your paper in late, 5 points will be subtracted for every hour after 11:00 AM on
the 10th that it is received.
Before doing the problems, please note SOME ERRATA I found in the text and correct your
copy accordingly:
p. 4, para. 2, l. 5: add η: ... the resistivitiy, η, is the ...
p. 10, Eq. 10: the δ in the denominator should be the number 8
p. 29, 4th para, penultimate and antepenultimate lines:
Add and subtract question marks: .... moment µ change? The answer is no. ...
p. 32, 3rd para, 3rd line: DELETE “is”
p. 36, Eq. 49 The B in the denominator should have the subscript C, i.e, B C .
If you find any others, you will get one bonus point on this assignment for every
typo and grammatical error and three bonus points for every error in an equation
or mathematical point you detect.
1. Using Saha’s equation, plot the fractional ionization, p = [n i /n m ] as a function of temperature,
T, for at least four values of the total density n T = n i + n m . Determine the ratio p at
T = 10 4 K and n T = 10 21 cm −3 . Note that the constant in the form of this equation in the
notes changes to 2.4 × 10 15 if densities are in units of cm −3 instead of m −3 [10]
2. Estimate the number of particles in a Debye sphere for the following plasmas: (a) the earth’s
ionosphere; (b) the solar corona; (c) cometary tails; (d) an H II region near a hot star;
(e) the warm phase of the interstellar medium; (f) the hot, coronal phase of the ISM;
(g) the intracluster medium of a cluster of galaxies. (The plot on p. 6 of the notes will
be helpful, but you’ll need to to a little research to find appropriate numbers.) [14]
3. Show that, as mentioned in class, in the case of an inhomogenous magnetic field:
v D
= a ∇ ⊥B
v ⊥ 2B
[12]
4. Chapter 2, Problem 1 [15]
5. Consider the non-relativistic motion of particles of charge q and mass m in crossed static
electric and magnetic fields. Take the electric field to be ⃗ E = (0, Eĵ, 0) and the magnetic
field to be ⃗ B = (0, 0, Bˆk) (in Cartesian coordinates).
(a) Assuming that q, B, and E are all positive, sketch the orbit of a typical particle. [4]
(b) For the particular case that a particle is initially at rest at the origin, determine the form
of the orbit. Is this an example of the ‘typical’ particle you considered in (a)? [4]
1

6. A charged particle executing circular motion in a uniform magnetic field constitutes a current
loop. Show that this current loop produces a magnetic field in a direction opposite to
the original field. [10]
7. Determine the motion of a relativistic charged particle that obeys the equation:
d⃗p
dt = q c ⃗v × ⃗ B,
where ⃗p = γm⃗v and the Lorentz factor, γ = (1 − v 2 /c 2 ) −1/2 . Assume ⃗ B is constant and
⃗E = 0. [14]
8. Chapter 2, Problem 2 [17]
You may collaborate, if necessary, on Problems 3, 4, 7 and 8. If you do so, be sure to
list the names of those collaborators at the top of the first page of your solutions.
2