Possible Emittance Increase through Filamentation Due to Space Charge in Continuous Beams

The study of oscillations which can take place in a beam under space charge conditions has been extended to other distributions than the one described by Kapchinsky and Vladimirsky (K. V.) in 1959. Two sets of equations similar to the ones they established can be written provided axis and emittance values are replaced by rms expressions applicable to any type of distribution. In case of a non K. V. distribution, the comparison of these sets gives differential equations relating the rms emittances to correcting terms which depend on the charge distribution inside the beam. Such equations can be used to interpret some rms emittance increases observed either with a mismatch in a smooth focusing channel or with a matched beam in an AG focusing system.