Particle-in-cell simulations of electron-positron cyclotron maser forming pulsar radio zebras

Abstract: The microwave radio dynamic spectra of the Crab pulsar interpulse contain fine structures represented via narrowband quasiharmonic stripes. The pattern significantly constrains any potential emission mechanism. Similar to the zebra patterns observed, for example, in type IV solar radio bursts or decameter and kilometer Jupiter radio emission, the double plasma resonance (DPR) effect of the cyclotron maser instability may allow for interpretion of observations of pulsar radio zebras. We present electromagnetic relativistic particle-in-cell (PIC) simulations of the electron-positron cyclotron maser for cyclotron frequency smaller than the plasma frequency. In four distinct simulation cycles, we focused on the effects of varying the plasma parameters on the instability growth rate and saturation energy. The physical parameters were the ratio between the plasma and cyclotron frequency, the density ratio of the "hot" loss-cone to the "cold" background plasma, the loss-cone characteristic velocity, and comparison with electron-proton plasma. In contrast to the results obtained from electron-proton plasma simulations, we find that the pulsar electron-positron maser instability does not generate distinguishable X and Z modes. On the contrary, a singular electromagnetic XZ mode was generated in all studied configurations close to or above the plasma frequency. For low density ratios, the highest peak of the XZ mode is at double the frequency of the highest peak of the Bernstein modes, indicating that the radio emission is produced by a coalescence of two Bernstein modes with the same frequency and opposite wave numbers. Our estimate of the radiative flux generated from the simulation is up to $\sim$30 mJy from an area of 100 km$^2$ for an observer at 1 kpc distance without the inclusion of relativistic beaming effects, which may account for multiple orders of magnitude.