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\centerline{AS551 General Plasma Physics 1}
\centerline{September 20, 2002}
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\centerline{\bf Problem Set \#2 (due September 27)}

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\noindent 1. \quad
In class, we derived the Debye shielding by electrons 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 $-Q$.  

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\noindent 2. \quad
In the Debye shielding calculation done in class, we assumed the ion
density remained uniform and used a Boltzmann equilibrium distribution for
the electrons only.  Extend the Debye shielding calculation to include a
Boltzmann equilibrium distribution for the ions as well, where the ions
have charge $Z_i$ and density $n_{i0} = n_{e0}/Z_i$ (the plasma is neutral in
the absence of the test charge).  Allow the ion temperature temperature
$T_i$ to be different than the electron temperature $T_e$ (we will discover
later in this class that the electron-ion temperature equilibration rate
can be relatively slow).  Which species provides the dominant shielding if
$T_i \ll T_e$?    [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
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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\noindent 4. \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, with a uniform background of stationary ions.  (This calculation
will be related to the $\omega_{pe}$ plasma oscillation calculation we did
in class, but you will need to include the fluctuating magnetic field
also.)  If the electron density were 1 cm$^{-3}$, what restriction is based
on the observation of radio wave signals?  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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