During these 20 seconds the beam makes 1,000,000 turns around the 6.28 km circumference. Therefore, on the average the beam picks up 650 kV more energy from the RF cavities on each revolution. Energy stays proportional to magnetic field. The force on a charged particle is given by the Lorentz Force.
Electric forces are small.
The protons in the Fermilab synchrotrons are bent in a circle by magnets and kept focused by quadrupoles, another type of magnet. The magnetic force is perpendicular to both the velocity of the particle and the direction of the magnetic field lines. Motion in a uniform magnetic field is a circle. Focusing of charged particles is done with quadrupole magnets. This method of keeping the beam particles tightly constrained inside a vacuum chamber is used in all the Fermilab synchrotrons, and also in the many beam lines at Fermilab.