Spark model for pulsar radiation modulation patterns

A nonstationary polar gap model first proposed by Ruderman & Sutherland is modified and applied to spark-associated pulsar emission at radio wavelengths. It is argued that under physical and geometrical conditions prevailing above pulsar polar cap, highly nonstationary spark discharges do not occur at random positions. Instead, sparks should tend to operate in well determined preferred regions. At any instant the polar cap is populated as densely as possible with a number of two-dimensional sparks with a characteristic dimension as well as a typical distance between adjacent sparks being about the polar gap height. Our model differs, however, markedly from its original hollow cone version. The key feature is the quasi-central spark driven by gamma-B pair production process and anchored to the local pole of a sunspot-like surface magnetic field. This fixed spark prevents the motion of other sparks toward the pole, restricting it to slow circumferential E x B drift across the planes of field lines converging at the local pole. We argue that the polar spark constitutes the core pulsar emission and that the annular rings of drifting sparks contribute to conal components of the pulsar beam. We found that the number of nested cones in the beam of typical pulsar should not exceed three; a number also found by Mitra & Deshpande using a completely different analysis. We confront predictions of our model with a variety of pulsar data, including mean profiles morphology and their predicted correlations with properties of the P-(P) over dot pulsar diagram as well as detailed studies of drifting subpulses. We demonstrate that, if the observing geometry is known, the average profile as well as the apparent drift pattern are fully determined by the values of P and (P) over dot. In the accompanying Paper II we develop a self-consistent theory of coherent pulsar radio emission based on the modified polar gap model explored in this paper.