High-energy emission from pulsars in polar-cap models with CR-induced   cascades
  For a subclass of polar-cap models based on electromagnetic cascades induced by curvature radiation (CR) we calculate broad-band high-energy spectra of pulsed emission expected for classical and millisecond pulsars. The spectra are a combination of curvature and synchrotron components. The spectrum of curvature component breaks at 150MeV, and neither its slope nor level below this energy are compatible with phase-averaged spectra of pulsed X-ray emission inferred from observations. Spectral properties in the combined energy range of ROSAT and ASCA (0.1 - 10 keV) depend upon the location of cyclotron turnover energy epsilon_ct=\hbar{e B \over m_e c} /sin(psi) in the synchrotron component. Unlike in outer-gap models, the available range of pitch angles psi is rather narrow and confined to low values. For classical pulsars, a gradual turnover begins already at 1MeV, and the level of the synchrotron spectrum decreases. At 10keV the curvature component eventually takes over, but with photon index alpha = 2/3, in disagreement with observations. For millisecond pulsars, the X-ray spectra are dominated by synchrotron component with alpha \simeq 1.5, and a sharp turnover into alpha \simeq -1 at epsilon_ct \sim 100eV. Relations of pulsed luminosity L_X to spin-down luminosity \edot are presented for classical and millisecond pulsars. We conclude that spectral properties and fluxes of pulsed non-thermal X-ray emission of some objects, like the Crab or the millisecond pulsar B1821-24, pose a challenge to the subclass of polar-cap models based on curvature and synchrotron radiation alone. 
B.Rudak, J.Dyks