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Model on pulsed GeV radiation from magnetars

We discuss a possible scenario for radiation mechanism of pulsed GeV gamma-rays from magnetars. The magnetars have shown frequent X-ray bursts, which would be triggered by crust fractures and could release the energy of order of ~10^{41-42}erg. If the location of the crust cracking of the magnetic field is close to the magnetic pole, part of the released energy may excite the Alfevn wave that can propagate into outer magnetosphere. The oscillation of the magnetic field induces the available potential drop ~10^{15}Volts, which can accelerate the electrons and/or positrons to the Lorentz factor ~10^{7} in the outer magnetosphere. The curvature radiation process at outer magnetosphere can produce GeV gamma-rays. If the radiation process is occurred above r~5x 10^7cm from the stellar surface, the emitted GeV gamma-rays can escape from the pair-creation process with the X-rays and/or the magnetic field. The expected luminosity of the GeV emissions is order of L_γ< 10^{35} erg/s, and the radiation process will last for a temporal scale of years. The expected pulse profiles have a broad shape with sometimes sharp peaks. We apply the model to AXP 1E~2259+586.