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We study electron-positron pair production in polar caps of energetic pulsarsto determine the maximum multiplicity of pair plasma a pulsar can produce underthe most favorable conditions. This paper complements and updates our study ofpair cascades presented in Timokhin & Harding (2015) with more accuratetreatment of the effects of ultra strong B>3x10^{12}G magnetic fields andemission processes of primary and secondary particles. We include pairsproduced by curvature and synchrotron radiation photons as well as resonantCompton scattered photons. We develop a semi-analytical model ofelectron-positrons cascades which can efficiently simulate pair cascades withan arbitrary number of microphysical processes and use it to explore cascadeproperties for a wide range of pulsar parameters. We argue that the maximumcascade multiplicity can not exceed ~ a few x 10^5 and the multiplicity has arather weak dependence on pulsar period on pulsar period. The highestmultiplicity is achieved in pulsars with magnetic field 4x10^{12}<B<10^{13}Gand hot surfaces, with T>10^6K. We also derive analytical expressions forseveral physical quantities relevant for electromagnetic cascade in pulsarswhich may be useful in future works on pulsar cascades, including the upperlimit on cascade multiplicity and various approximations for the parameter\chi, the exponential factor in the expression for photon attenuation in strongmagnetic field.

On the maximum pair multiplicity of pulsar cascades