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The purpose of this memo is to put down, in one place, a number of commonly used accelerator formulae. I'll also comment briefly on the derivation of these relationships. Nothing in this memo is my original work. All of this was developed many years ago by the brilliant founders of the field of Accelerator Physics. The widely used differential relationships between beam momentum (p), dipole magnetic field (B), orbit length (L), and revolution frequency (f) are given in Table 1.

Differential Relationships Between Momentum Magnetic Field, Orbit Length, and Revolution Frequency