Usually we think a X-ray source may be a compact(neutron) binary star on which the X-ray radiation might be generated by gravitational acceleration for the particles coming from the primary and going along magnetic field lines of the compact star to the poles. But, in the past, people don't consider well the problem of particle acceleration. It seems to be simplified for the situation only to consider the gravitation effect, because some electric-magnetic effect in a strong magnetic field could not be neglected. However, it is unreasonable to neglect the plasma turbulent waves in an electric-magnetic field, because strong enough turbulent waves such as Alfven waves, whistlers generated nearby the surface of neutron stars probably contribute energy to accelerate particles, which may be more important than gravitation sometimes. For a binary system with a neutron star if ion number density N > 1017 /cm3 in its surface atmosphere, the turbulent wavess will be stimulated that will accelerate the particles reaching a speed over 108cm/s. they strike the atmosphere of the compact star in the system, so that a shock wave is formed which turns part of kinetic energy to heat to form hot spots of about 108K to emit X-ray.