  We study a two-fluid description of high and low temperature components of
the electron velocity distribution of an idealized tokamak plasma. We refine
previous results on the laminar steady-state solution. On the one hand, we
prove global stability outside a parameter set of possible linear instability.
On the other hand, for a large set of parameters, we prove the primary
instabilities for varying temperature difference stem from the lowest spatial
harmonics. We moreover show that any codimension-one bifurcation is a
supercritical Andronov-Hopf bifurcation, which yields stable periodic solutions
in the form of traveling waves. In the degenerate case, where the instability
region in the temperature difference is a point, we prove that the bifurcating
periodic orbits form an arc of stable periodic solutions. We provide numerical
simulations to illustrate and corroborate our analysis. These also suggest that
the stable periodic orbit, which bifurcated from the steady-state, undergoes
additional bifurcations.
