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.
High-brightness injectors for hadron colliders
The counterrotating beams in collider rings consist of trains of beam bunches with N{sub B} particles per bunch, spaced a distance S{sub B} apart. When the bunches collide, the interaction rate is determined by the luminosity, which is defined as the interaction rate per unit cross section. For head-on collisions between cylindrical Gaussian beams moving at speed {beta}c, the luminosity is given by L = N{sub B}{sup 2}{beta}c/4{pi}{sigma}{sup 2}S{sub B}, where {sigma} is the rms beam size projected onto a transverse plane (the two transverse planes are assumed identical) at the interaction point. This beam size depends on the rms emittance of the beam and the focusing strength, which is a measure of the 2-D phase-space area in each transverse plane, and is defined in terms of the second moments of the beam distribution. Our convention is to use the rms normalized emittance, without factors of 4 or 6 that are sometimes used. The quantity {tilde {beta}} is the Courant-Synder betatron amplitude function at the interaction point, a characteristic of the focusing lattice and {gamma} is the relativistic Lorentz factor. Achieving high luminosity at a given energy, and at practical values of {tilde {beta}} and S{sub B}, requires a large more » value for the ratio N{sub B}{sup 2}/{var epsilon}{sub n}, which implies high intensity and small emittance. Thus, specification of the luminosity sets the requirements for beam intensity and emittance, and establishes the requirements on the performance of the injector to the collider ring. In general, for fixed N{sub B}, the luminosity can be increased if {var epsilon}{sub n} can be reduced. The minimum emittance of the collider is limited by the performance of the injector; consequently the design of the injector is of great importance for the ultimate performance of the collider. « less
Prediction of net pressure on pressure equalized cavities
Abstract A numerical model has been developed for prediction of net pressure on pressure equalized cavities. The results based on this model show good agreement with those obtained from mock-up tests. Parametric studies verify that reductions in cladding load are possible, with proper design of curtain walls.