  Electron(positron), proton and nuclei can be accelerated to very high energy
by local supernova remnants (SNR). The famous excesses of electron and proton
(nuclei) potentially come from such kind of local sources. Recently, the DAMPE
experiment measured the electron spectrum (including both electrons and
positrons) of cosmic rays with high-accuracy. It provides an opportunity to
further explore the excess of electrons. According to the gluon condensation
(GC) theory, once GC occurs, huge number of gluons condense at a critical
momentum, and the production spectrum of electron and proton showing typical GC
characteristics. There are exact correlations between the electron and proton
spectrum from a same GC process. It is possible to interpret the power-law
break of cosmic rays in view of GC phenomenon, and predict one from another
based on the relations between electron and proton spectrum. In this work, we
point out the potential existence of a second excess in the electron spectrum,
the characteristics of this excess is derived from experimental data of proton.
We hope that the future DAMPE experiments will confirm the existence of this
second excess and support the result of GC model.
