Emittance Growth Caused by Current Variation in a Beam-Transport Channel

Time variation of space-charge forces in a beam-transport channel will lead to a time-averaged emittance growth of the beam. The Kapchinskii-Vladimirskii (K-V) equations have been used to follow the envelope of a round beam with effective beam current fluctuation i through a transport channel. The area of the ellipse that encloses the varying ellipses at the end has been used as the criterion for emittance growth. Simple formulae give the relation between i, initial emittance ¿, allowable fractional emittance growth ¿¿, effective average current I, average beam radius R, and transport length. For example, for a long transport channel a nominally compensated beam must have i <(ß¿¿2I0/R2)¿¿, where I0 = 4¿¿0Mc3/e, and ß¿ is the usual relativistic factor. Results for other conditions are presented. A comparison with a numerical calculation from the TRACE code for transport of a 100-keV, 100-mA beam is made.