  Several solenoids are usually installed in electron cooler device to guide
the motion of the electron beam in the cooler. However, the solenoids also have
influence to the ion beam in the cooler storage ring. The transverse motion of
the ion beam in storage ring will become coupled, if the solenoids installed in
the electron cooler are not compensated perfectly. In this paper, the coupled
transverse motion due to the uncompensated cooler's solenoids of CSRm (The main
storage ring in the IMP, Lan Zhou, China) is studied, and the coupled beam
envelopes are calculated by a new method.
