Electron space charge and solenoidal field effects on the proton cooling ring

Problems of the electron space charge and solenoidal fields are treated analytically. An exact matrix formalism is used for calculating the tune shifts and the change in the betatron functions, which are due to the electron space charge. A Hamiltonian formalism is then used for solving the motion equations resulting from a coupling field. Both of the analytic results are applied to the present Fermilab cooling ring design and discussed for protons and antiprotons. To cancel the space charge effects, the ring tunes or cooling ring insertion have to be changed and the electron current has to be reduced or neutralized. The coupling effect of the solenoid can easily be compensated with two small skew quadrupoles