We consider the widespread assumption that coherent pulsar radio emission is based on extended pair production leading to plasma densities highly exceeding the Goldreich-Julian density. We show as an example that the observed low frequency (160 MHz) emission of the Crab pulsar is incompatible to the model of extended pair production. Our results rule out significant pair production if a plasma process is responsible for coherence and the radio emission originates from inside the light cylinder.Comment: accepted for publication in ApJ Letters; 4 pages, no figure

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On hand of 3D PIC simulations we show that in a strongly magnetized plasma a relativistic electron beam can be forced to emit highly coherent radio emission by self-induced nonlinear density fluctuations. Such slowly moving nonlinear structures oscillate with the local plasma frequency at which the relativistic electrons are scattered. Beam electrons dissipate a significant amount of their kinetic energy by inverse Compton radiation at a frequency of about g 2 v pe . Since the beam is sliced into pancake structures which experience the same electric field the inverse Compton scattering is coherent. Such a process is a very promising candidate for the coherent radio emission of pulsars.Neutron stars represent the most exotic state of matter with the highest densities accessible for direct observations in the universe. A subclass of neutron stars are sources of pulsating radio emission-the so called pulsars. Pulsars are fast rotating neutron stars~radius r NS ϭ 10 km, rotation periods P Ӎ 10 Ϫ3 Ϫ 10 s! with super strong surface magnetic fields of B 0 Ӎ 10 8 T and an induced quadrupolar electric field of 10 12 V0m which extracts particles out of the neutron star surface. This gives a density n gj ϭ 10 18 m Ϫ3

We develop a model for the infrared, optical, and soft X-ray emission of the Crab pulsar in terms of anisotropic synchrotron emission by relativistic particles in an outer gap scenario with a single energy distribution N(c) P c~2. It is shown that such a distribution is naturally produced in an efficient pair cascade and that the energy of the primary particles is limited by synchrotron radiation to c D 107. It is further shown that this synchrotron model is able to reproduce the spectral shape between the infrared and soft X-rays and also the corresponding luminosities. In particular, the long-standing problem of the rapid spectral decline toward infrared frequencies is understandable as emission at very small pitch angles from low-energy particles with c D 102. Finally, we show that the scaling of our synchrotron model explains the observed correlation between the X-ray luminosity and the spin-down luminosity of the neutron star found by Becker & L X D 10~3L sdTrumper.