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Octupole Focusing Relativistic Self-Magnetometer Electric Storage Ring "Bottle"

A method proposed for measuring the electric dipole moment (EDM) of a charged fundamental particle such as the proton, is to measure the spin precession caused by a radial electric bend field $E_r$, acting on the EDMs of frozen spin polarized protons circulating in an all-electric storage ring. The dominant systematic error limiting such a measurement comes from spurious spin precession caused by unintentional and unknown average radial magnetic field $B_r$ acting on the (vastly larger) magnetic dipole moments (MDM) of the protons. Along with taking extreme magnetic shielding measures, the best protection against this systematic error is to use the storage ring itself, as a "self-magnetometer"; the exact magnetic field average $\langle B_r\rangle$ that produces systematic EDM error, is nulled to exquisite precision by orbit position control. By using octupole rather than quadrupole focusing the restoring force can be vanishingly small for small amplitude vertical betatron-like motion yet strong enough at large amplitudes to keep all particles captured. This greatly enhances the magnetometer sensitivity. Any average radial magnetic field error $\langleΔB_r\rangle$ causes a vertical orbit shift between CW and CCW beams. Self-magnetometry measures this shift, enabling its cancellation. For the octupole-only ring proposed here the accuracy of magnetic field control is $\langleΔB_r\rangle\approx \pm 3\times10^{-16}\,$Tesla. This is small enough to reduce the systematic error in the proton EDM measurement into a range where realistically small deviations from standard model predictions can be measured. Though novel, the theoretical analysis given here for relativistic bottles, magnetic or electric or both, is elementary, and their behavior is predicted to be entirely satisfactory.