Measurement and Compensation of Space Charge Induced Q-Shifts in the CERN Intersecting Storage Rings (ISR)

The space charge induced Q-shifts were measured either by comparing the radial positions of a given nonlinear resonance with and without a stack, or by means of RF deflecting fields. The first consequence of these Q-shifts is a displacement of the working line in the stability diagram towards low order non-linear resonances. A secondary effect is a progressive reduction of the radial derivatives of the Q\´s at the edges of the stack with increasing intensity, which makes the stack unstable in these regions. These results were used to derive "prestressed" working lines which are suited to high intensity stacks.