Radio Emission of Pulsars. II. Coherence Catalyzed by Cerenkov-Unstable Shear Alfvén Waves

Abstract: This paper explores small-scale departures from force-free electrodynamics around a rotating neutron star, extending our treatment of resistive instability in a quantizing magnetic field. A secondary, Cerenkov instability is identified: relativistic particles flowing through thin current sheets excite propagating charge perturbations that are localized near the sheets. Growth is rapid at wavenumbers below the inverse ambient skin depth $k_{p,\rm ex}$. Small-scale Alfv\'enic wavepackets are promising sources of coherent curvature radiation. When the group Lorentz factor $\gamma_{\rm gr} \lesssim (k_{p,\rm ex}R_c)^{1/3} \sim 100$, where $R_c$ is the magnetic curvature radius, a fraction $\sim 10^{-3}$-$10^{-2}$ of the particle kinetic energy is radiated into the extraordinary mode at a peak frequency $\sim 10^{-2}ck_{p,\rm ex}$. Consistency with observations requires a high pair multiplicity ($\sim 10^{3-5}$) in the pulsar magnetosphere. Neither the primary, slow resistive instability nor the secondary, Alfv\'enic instability depend directly on the presence of magnetospheric `gaps', and may activate where the mean current is fully supplied by outward drift of the corotation charge. The resistive mode is overstable and grows at a rate comparable to the stellar spin frequency; the model directly accommodates strong pulse-to-pulse radio flux variations and coordinated subpulse drift. Alfv\'en mode growth can track the local plasma conditions, allowing for lower-frequency emission from the outer magnetosphere. Beamed radio emission from charged packets with $\gamma_{\rm gr} \sim 50-100$ also varies on sub-millisecond timescales. The modes identified here will be excited inside the magnetosphere of a magnetar, and may mediate Taylor relaxation of the magnetic twist.