Electron dynamics in the HERA luminosity upgrade lattice of the year 2000

It is planned to upgrade the HERA luminosity to 7.10³¹ cm^-2s^-1, which is 4 times the original design luminosity. This is to be achieved by decreasing the proton beam size by moving quadrupoles closer to the interaction point and by increasing their strength. Similar measures decrease the electron beam size. However, to match the smaller proton beam size, the horizontal electron emittance additionally has to be decreased. The electron emittance can be decreased either by stronger focusing in the arcs, or by changing the damping partition numbers. In the HERA case, however, both methods have to be applied simultaneously, since changing the damping partition numbers increases the longitudinal emittance, which can only be tolerated with the current RF parameters if the bucket is increased by a stronger focusing in the arcs. These two methods of decreasing the emittance have competing effects on long term stability. Stronger focusing usually leads to a greater reduction of the dynamic aperture than of the emittance; whereas a change of the damping partition numbers tends to increase the dynamic aperture relative to the emittance. Playing the two competing effects against each other, it is possible to decrease the electron emittance while keeping the relative dynamic aperture as well as the requirements on the RF system tolerable