The Weibel instability, driven by a plasma temperature anisotropy, is non-resonant with plasma particles: it is purely growing in time, and does not oscillate. The effect of a counterstreaming plasma is examined. In a counterstreaming plasma with an excess of transverse temperature, the Weibel instability arises along the streaming direction. Here it is proved that for large wave-numbers the instability becomes resonant with a finite real (oscillation) frequency, ωr ≠ 0. When the plasma flows faster, with a bulk velocity larger than the parallel thermal velocity, the instability becomes dominantly resonant. This new feature of the Weibel instability can be relevant for astrophysical sources of non-thermal emissions and the stability of counterflowing plasma experiments.
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