On pair production in the Crab pulsar

We consider the widespread assumption that coherent pulsar radio emission i s based on extended pair production that leads to plasma densities highly e xceeding the Goldreich-Julian density. As an example, we show that the obse rved low-frequency (160 MHz) emission of the Crab pulsar is incompatible wi th the model of extended pair production. Our results rule out significant pair production if a plasma process is responsible for coherence and if the radio emission originates from inside the light cylinder.