Exact Cancellation of Emittance Due to Coupled Transverse Dynamics in Solenoids and RF Couplers

Small, stray magnetic and RF fields in electron guns and injectors can perturb an electron beam and introduce correlations between the otherwise orthogonal transverse trajectories. These correlations couple the x and y dynamics which increases the transverse emittance. If the correlation becomes "diluted" or randomized in the beam transport then as the correlation disappears the 4D emittance increases. This paper discusses two important correlations common to most electron injectors. The first results from the coupling of a weak quadrupole field with beam rotation in a solenoid, and the second x-y coupling is generated by an asymmetric on-axis RF field due to a high-power RF coupler or cavity port. This paper shows that a small quadrupole field combined with solenoidal focusing can result in significant emittance growth due to coupled transverse dynamics. It also shows how adding a skewed quadrupole field can exactly cancel this correlation and its emittance. Similar emittance cancellation is demonstrated for asymmetric RF fields, with the degree of cancellation limited by the electron bunch length. Analytic expressions are derived and compared with simulations and experiments.