The fastest millisecond pulsar PSR B1937+21 presents an interpulse separated from the main pulse by nealy 180 o at radio frequencies. Recently, the ASCA observations (Takahashi et al. 2001) detected pulsed X-ray emission from this pulsar. Only a single narrow X-ray pulse is observed, which is coincident with the radio interpulse in phase. We investigate the possible origin of the pulsed X-rays from the polar cap (PC) accelerators or the outer gap (OG) accelerators in the frame of PC model and OG model, respectively, by assuming a dipolar magnetic field structure and the same radio emission pattern from its poles for the pulsar. The OG model can naturally explain the main observational facts. For the PC model, the coincidence between the X-ray pulse and the radio interpulse can not be reproduced in the assumed case. However when considering possible deviation from our assumption, PC model may still be valid for this pulsar in some cases. Subject headings: pulsar: PSR B1937+21: X-rays: emission mechanism 1. introduction Even more than 30 years after the discovering of high energy pulsars, the theoretical reproduction of X-ray and γ-ray emission from such pulsars is still a matter of debate. It is commonly agreed that there are two scenarios on modelling X-ray and γ-ray creation: the outer ga
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