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\centerline{AS551 General Plasma Physics 1}
\centerline{September 20, 1996}
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\centerline{\bf Problem Set \#2 (due September 27)}
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\noindent 1. \quad
Since much of the galaxy is filled with an
electron-proton plasma,  one might expect that the propagation of starlight
reaching the earth could be affected.  Calculate the dispersion relation for
plane electromagnetic waves in this plasma, by modeling the plasma as a uniform
cold electron fluid.  If the electron density were 1 cm$^{-3}$, what
restriction is based on the observation of radio wave signals? What effect would
the inclusion of electron pressure have?  What other effects might have to be
included to obtain a realistic description of the propagation of  light in the
inter-stellar plasma.

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\noindent 2. \quad
In class, we derived the Debye shielding of the potential produced by a
test charge $Q$ in a plasma.  Calculate the resulting electron density and
verify than the test charge is indeed shielded by showing that the total
excess electon charge is $-Q$.  [Something to think about: Suppose the test
charge is {\it moving}.  How do you expect the Debye shielding to change?]


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\noindent 3. \quad
Assuming that the collision cross section is the square of the distance of
closest approach, derive the $v^{-3}$ dependence for the collision
frequency of electrons streaming through a field of stationary ions.
[Later in the course, we shall see this assumption underestimates the
collision frequency by about $\log(n\lambda_D^3)$.  The scaling is,
however, correctly given.]


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\noindent 4. \quad
Consider a homogeneous cold electron plasma, where the ions may be assumed to
be an infinitely massive neutralizing background.  Suppose that a small
fraction of the electrons in the slab $x_1<x<x_2$ are removed and then placed
at $x_1+L<x<x_2+L$.  Sketch the subsequent evolution of the electron density,
the electric field, and the electron fluid velocity.  Sketch the trajectory of
a single electron.

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