High intensity polarized protons can be stored in an all-electric ring to probe the proton electric dipole moment with high sensitivity. The expected sensitivity level is similar to 10(-29) e cm, better than any planned hadronic EDM experiment by one to two orders of magnitude. The protons at their magic momentum of 0.7 GeV/c are special in that they keep their spin vectors aligned with their momentum vectors in any transverse electric field. However, not all protons within the acceptance of the ring are exactly at the magic momentum. An RF-cavity is to be used to eliminate the first order effects responsible for the spread of angles between the spin and momentum vectors. We have used particle simulations with fourth-order Runge-Kutta integration to determine the second order effects. The spin precession time, which is a measure of the spin misalignment, is found to be adequate for a total storage time of 10(2)-10(3) s. Further improvements, using sextupoles and/or stochastic cooling, could bring further improvement in the statistical sensitivity of the method. (C) 2014 Elsevier B.V. All rights reserved.