Discovered in 1967, pulsars are the rapidly rotating core left behind by exploding Type II supernovae. More than a thousand have now been observed in our Galaxy, in halo globular clusters, and in the LMC and SMC. Radio observations of these rapidly pulsating stars provide information on the plasma densities and magnetic field strengths of the intervening interstellar medium over base lines of tens of kiloparsecs.

The electrodynamic properties of a plasma are functions of the frequency of the electromagnetic wave that traverses the plasma. The group velocity of a wave in a plasma is

where is the angular frequency and
_{p} is the plasma
frequency defined by
^{2}_{p}
= 4 *n e*^{2} / *m*,
for which *n*, *e* and *m* are the number density, charge
and mass of the free electrons.

Because the group velocity of a wave depends on its frequency, the fourier
components of a pulse will traverse a total distance *d* through a plasma
in a time *t*_{} given by

where *s* defines a small increment of distance through the plasma.
Plasma frequencies in interstellar space are typically very low so
we can expand eqn. 3 and substitute into eqn. 5 such that the time taken for
the fourier component of a pulse to traverse a plasma is

The first term is the time taken to traverse a distance *d* in vacuo, and
the second term is the plasma correction.

Studies of the arrival times of the various fourier components indicate that the highest frequencies arrive ahead of the low frequency components. What is actually measured is the derivative of eqn. 5,

The dispersion measure, defined as *D*_{m} =
_{0}^{d} *n*_{e} *ds*,
is a measure of the total column of free electrons along the path to
the pulsar in units of pc cm^{-3}. A column of 10^{20}
electrons results
in a *D*_{m} of 30 pc cm^{-3} and a delay of 12 sec
for a signal at 100 MHz
relative to infinite frequency. Dispersion measures were first obtained by
the pulsar discovery team. Since then, we have come to learn
(Fig. 5)
from pulsars in distant globular clusters and
the Magellanic Clouds that the warm atmosphere in the Galaxy
extends to about a kiloparsec above the Galactic plane.

The radio signals reveal other important properties about the diffuse
gas. In the presence of a magnetic field along the path to the pulsar,
*B*_{||}, the plane of polarization of the propagating wave
will rotate
by an angle equal to the phase
delay between the ordinary and
extraordinary components of the electric field. The so-called Faraday
rotation angle is given by

for which _{B} is the
cyclotron frequency. We define a quantity called the rotation measure,

in the traditional units of rad m^{-2}, and
where *B*_{||} is in units of microgauss
(*µ*G). The ratio of *R*_{m} to
*D*_{m} is the average galactic magnetic field strength
along the path,