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Abstract

Context. Several important mechanisms that explain coherent pulsar radio emission rely on streaming (or beam) instabilities of the relativistic pair plasma in a pulsar magnetosphere. However, it is still not clear whether the streaming instability by itself is sufficient to explain the observed coherent radio emission. Due to the relativistic conditions that are present in the pulsar magnetosphere, kinetic instabilities could be quenched. Moreover, uncertainties regarding specific model-dependent parameters impede conclusions concerning this question.

Aims. We aim to constrain the possible parameter range for which a streaming instability could lead to pulsar radio emission, focusing on the transition between strong and weak beam models, beam drift speed, and temperature dependence of the beam and background plasma components.

Methods. We solve a linear relativistic kinetic dispersion relation appropriate for pulsar conditions in a more general way than in previous studies, considering a wider parameter range. In doing so, we provide a theoretical prediction of maximum and integrated growth rates as well as of the fractional bandwidth of the most unstable waves for the investigated parameter ranges. The analytical results are validated by comparison with relativistic kinetic particle-in-cell (PIC) numerical simulations.

Results. We obtain growth rates as a function of background and beam densities, temperatures, and streaming velocities while finding a remarkable agreement of the linear dispersion predictions and numerical simulation results in a wide parameter range. Monotonous growth is found when increasing the beam-to-background density ratio. With growing beam velocity, the growth rates firstly increase, reach a maximum and decrease again for higher beam velocities. A monotonous dependence on the plasma temperatures is found, manifesting in an asymptotic behaviour when reaching colder temperatures. A simultaneous change of both temperatures proves not to be a mere linear superposition of both individual temperature dependences. We show that the generated waves are phase-coherent by calculating the fractional bandwidth.

Conclusions. Plasma streaming instabilities of the pulsar pair plasma can efficiently generate coherent radio signals if the streaming velocity is ultra-relativistic with Lorentz factors in the range 13 <  γ <  300, if the background and beam temperatures are small enough (inverse temperatures ρ₀; ρ₁ ≥ 1, i.e., T₀; T₁ ≤ 6 × 10⁹), and if the beam-to-background plasma density ratio n₁/(γ_bn₀) exceeds 10⁻³, which means that n₁/n₀ has to be between 1.3 and 20% (depending on the streaming velocity).