Transverse multibunch instabilities for two bunch trains on separated orbits

Transverse multibunch instabilities including the resistive wall instability and ion instabilities are investigated analytically and numerically for two bunch trains on separated orbits in a storage ring. The two separated orbits’ operating mode appears more stable against transverse multibunch instabilities than the conventional single orbit operating mode and may be beneficial to high current operations for colliders or synchrotron light sources.

Figure 1

Sketch of the two spatially separated bunch trains in the SSRF storage ring. (A quarter of the full ring lattice is shown here. The blue line is the golden orbit and the red one is the distorted orbit that is kicked by $100\mu \mathrm{rad}$ in the vertical plane by a fast kicker located at the end of the second straight section.)

Figure 2

Vertical tune shift produced by the vertical kicker (located at the end of the second straight section) at the SSRF storage ring.

Figure 3

Tracking results showing the resistive wall instability for three different cases. (a) average beam oscillation amplitude of two bunch trains on the golden orbit; (b) average amplitude of two bunch trains with $200\mu \mathrm{rad}$ separation; (c) average amplitude of two bunch trains with $400\mu \mathrm{rad}$ separation. The amplitude approaching a constant value indicates that an instability threshold has been found.

Figure 4

The integral term in Eq. (18) as a function of $\mathrm{y}/{\sigma }_y$.

Figure 5

The oscillation amplitude of ions with respect to the circulation time in the SSRF storage ring, tracking 5 turns. (a) 1 bunch train with 700 bunches followed by a 20 bunch empty gap; (b) 2 bunch trains with 350 bunches each, separated by a 10 bunch empty gap; (c) two spatially separated bunch trains of 350 bunches each, separated by a 10 bunch empty gap, run at different closed orbits with displacement $200\mu \mathrm{m}$ at the observation point.

Figure 6

Growth of the maximum oscillation amplitude of the electron bunch centroid for the same parameters used in the ion trapping simulation in Fig. 5.

Figure 7

Dynamic apertures for on-momentum and off-momentum beams for different operating modes (blue lines indicate on-momentum particles and green and red lines indicate off-momentum particles).