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Spatial Dependent Diffusion of Cosmic Rays and the Excess of Primary Electrons Derived from High Precision Measurements by AMS-02

The precise spectra of Cosmic Ray (CR) electrons and positrons have been published by the measurement of AMS-02. It is reasonable to regard the difference between the electrons and positrons spectra ( $\triangle Φ= Φ_{e^-}-Φ_{e^+}$ ) as being dominated by primary electrons. Noticing that the resulting electron spectrum shows no sign of spectral softening above 20 GeV, which is in contrast with the prediction of standard model. In this work, we generalize the analytic one dimensional two-halo model of diffusion to a three dimensional realistic calculation by implementing a spatial variant diffusion coefficients in DRAGON package. As a result, we can reproduce the spectral hardening of protons observed by several experiments, and predict an excess of high energy primary electrons which agrees with the measurement reasonably well. Unlike the break spectrum obtained for protons, the model calculation predicts a smooth electron excess and thus slightly over predicts the flux from tens of GeV to 100GeV. To understand this issue, further experimental and theoretical studies are necessary.