Relativistic plasma emission due to a beam instability in the polar cap reg
ions is examined critically as a pulsar radio emission mechanism. Wave disp
ersion in the pulsar plasma is discussed, based on the use of a relativisti
c plasma dispersion function. The growth rate for the beam instability is e
stimated in the rest frame of the plasma for parallel Langmuir waves, L-O m
ode waves, and oblique Alfven waves. The first two of these imply frequenci
es that are much higher than the observed frequencies for plausible paramet
ers, suggesting that they are not viable as pulsar radio emission mechanism
s. Growth of Alfven waves requires that the beam speed equal the phase spee
d of the Alfven waves, and this condition cannot be satisfied within the li
ght cylinder, except for an extremely high energy beam. It is suggested tha
t either the plasma parameters in the source region are quite different fro
m what is currently considered plausible or the emission mechanism does not
involve a beam instability. Alternative pulsar radio emission mechanisms s
hould be explored further.