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We study a two-fluid description of high and low temperature components ofthe electron velocity distribution of an idealized tokamak plasma. We refineprevious results on the laminar steady-state solution. On the one hand, weprove global stability outside a parameter set of possible linear instability.On the other hand, for a large set of parameters, we prove the primaryinstabilities for varying temperature difference stem from the lowest spatialharmonics. We moreover show that any codimension-one bifurcation is asupercritical Andronov-Hopf bifurcation, which yields stable periodic solutionsin the form of traveling waves. In the degenerate case, where the instabilityregion in the temperature difference is a point, we prove that the bifurcatingperiodic orbits form an arc of stable periodic solutions. We provide numericalsimulations to illustrate and corroborate our analysis. These also suggest thatthe stable periodic orbit, which bifurcated from the steady-state, undergoesadditional bifurcations.

Global stability and local bifurcations in a two-fluid model for tokamak plasma