Longitudinal Emittance Growth from Transition Crossing

A. G. Ruggiero and S. M. Pruss

September 11, 1989

A suggestion was made that much higher intensities (>1014) might be desirable from the Main Injector. among the many problems such high intensities present is longitudinal emittance blow-up for the standard main injector design with no transition jump. Using a value of 5 Ohms for the imaginary part of z/n, we find tat as the intensity increases there is a minimum value of longitudinal emittance after transition that can be achieved. If one starts with a very small emittance, it blows up to very large. As the emittance at injection increases, the amount of blow-up decreases such that the resultant emittance after transition decreases. As the emittance at injection continues to increase eventually the emittance after transition passes through a minimum and starts to increase again. The minimum after transition emittance occurs for a blow-up of about 40%. The minimum after transition emittance scales about as 1 eV-sec/1011 per bunch for 500 bunches in the main injector. Thus 3 × 1013 from the main injector probably will have 0.6 eV-sec rather than 0.4 eV-sec quoted in the standard main injector parameter list. The attached table and graph show this data in more detail and illustrate how these conclusions were reached. If a transition jump is added to the standard main injector wit a 100msec jump speed, then the minimum after transition emittance is reduced by a factor of four. This calculation took space charge and the realistic wall impedance into account, but neglected any possible problems from non-uniform beam loading of the RF system (i.e. the missing 90 bunches for the abort kicker risetime gap.)