A uniform in space, oscillatory in time plasma equilibrium sustained by a time-dependent current density is analytically and numerically studied resorting to particle-in-cell simulations. The dispersion relation is derived from the Vlasov equation for oscillating equilibrium distribution functions, and used to demonstrate that the plasma has an infinite number of unstable kinetic modes. This instability represents a kinetic mechanism for the decay of the initial mode of infinite wavelength (or equivalently null wave number), for which no classical wave breaking or Landau damping exists. The relativistic generalization of the instability is discussed. In this regime, the growth rate of the fastest growing unstable modes scales with ${\gamma }_T^{-1/2}$, where ${\gamma }_T$ is the largest Lorentz factor of the plasma distribution. This result hints that this instability is not as severely suppressed for large Lorentz factor flows as purely streaming instabilities. The relevance of this instability in inductive electric field oscillations driven in pulsar magnetospheres is discussed.

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• Kinetic theory
• Plasma instabilities
• Plasma waves
• Wave-wave, wave-particle interactions
• Electron-positron plasmas
• Particle-in-cell methods