Studies and calculations of transverse emittance growth in high-energy proton storage rings

The theory for stimulated transverse emittance growth of proton beams is presented. Given a random dipole kick each turn, quantitative predictions for the RMS (root mean square) beam centroid betatron oscillation amplitude and average emittance growth rate are made. Because the particles undergo deterministic betatron oscillations between kicks, the effects of successive kicks are correlated; hence, only the noise harmonics at the betatron frequency and multiples of the revolution frequency contribute to the emittance growth. An experiment was performed at the Fermilab Tevatron, where the effect of RF phase noise on transverse emittance growth was measured. The RF system was chosen because it was quantitatively understood, thus enabling an absolute calibration between the emittance growth rate and the injected phase noise amplitude. Applying the above theory to this experiment, it was found that the predicted and measured emittance growth rates were in agreement.<>