Transverse Feedback System at SOLEIL

Let us start by recalling that the SOLEIL ring was designed to operate principally in the following two modes: the so called “multibunch maximum flux” mode (with the goal of storing 500 mA beam distributed in a large number of bunches up to the maximum of 416), and the so called “time structure” mode consisting of a small number of bunches (typically 8 bunches of 10 mA each separated by roughly 140 ns). In addition, the single bunch mode, as well as a hybrid mode (3/4 of the ring filled with a multibunch and a high intensity single bunch sitting on the opposite side) were also envisaged.
In the longitudinal plane, the RF system uses superconducting cavities, which were especially designed to dampen higher-order modes so to avoid longitudinal multibunch instabilities.
In the transverse plan, it was necessary to create a very powerful transverse feedback system to combat the instabilities in the above two configurations:
 

1. “Multibunch”: so called “resistive-wall” instability due to the interaction of the electromagnetic field of the beam with various vacuum chamber components that couples different bunches. In addition, there is the instability arising from the interaction of electrons with ions (not only the multi turn interactions in which ions are trapped in the electro-static potential of the electrons, but also of the type “Fast Beam Ion Instability (FBII)” involving short interactions lasting less than one turn.
   
   
2. “Time structure”: Instabilities arising from coherent oscillation modes within a bunch called “head-tail”, as the mechanism involves synchrotron oscillation that renders particles in the head of a bunch to be in the tail a half period later. In particular, those that involve coupling of different modes may provoke strong beam blow ups called “Transverse Mode Coupling Instability (TMCI)”.
   

Although the machine performance aimed at is very challenging (in both the total and the bunch current), the vertical opening of the vacuum chambers adopted is small all along the ring so as to match the “low gap” of insertion devices, while simulations had predicted relatively low instability thresholds and high growth rates. The choice was therefore made to develop a bunch by bunch digital feedback system, which is far more powerful than a mode by mode one.

Figure 1 : Layout of a transverse feedback chain developed at SOLEIL.

The digital system selected was developed at SPring-8. On the basis of the betatron motion measured for each bunch, this performs FIR (Finite Impulse Response) filtering to re-inject a signal necessary for oscillation damping of a given bunch turn by turn. The whole operation is performed by an FPGA board with a latency of less than one turn.
The feedback chains are integrated into the SOLEIL Tango control system. We have up to now constructed three chains (Figure 2).

In the absence of feedback, the multibunch instability threshold at zero chromaticity¹ is very low: it is of the order of 30 mA in the vertical plane and 40 mA in the horizontal. The application of feedback allows the beam to be stabilised under the same conditions of up to about 400 mA. Figure 4 shows the spectrum of such a beam observed between F_RF, the RF frequency (352 MHz), and F_RF + 10xF₀ (F₀: revolution frequency). Only the harmonics of revolution frequency (nF₀, n=1,…,10) are present and no unstable lines appear.
In most cases when one is above the instability threshold, the unstable beam stabilizes itself by losing a part of itself (in particular the tail of a bunch train while the head part remains unchanged, as if the beam is “torn into pieces”). In certain other configurations, however, the beam the beam may remain constantly blown up (with a large increase in beam size)

Nevertheless, high values of chromaticity imply stronger magnetic fields and may spoil the original beam quality.
Fig. 5 presents the spectra of such beams in two different situations:

1. Instability regime dominated by the “resistive-wall” effect. The unstable lines correspond to the vertical betatron frequencies. The largest amplitude corresponds to the lowest frequency, namely FRF + (1-ν)xF₀ (ν: Vertical betatron tune). The amplitude of the unstable lines dampens rapidly as the number of harmonics n in (n - ν) x F₀ increases (n=1,…).
   
   
2. Instability regime dominated by ions. The amplitude of the unstable lines is maximum for the harmonics n = 4, 5 and 6, which we call an “ion bump”.
   
   A mixture of the two regimes is often observed.

Figure 4 : Spectrum of a stable beam (with feedback)

Figure 5 : Instability due to “resistive-wall” (left) and “ions” (right)

Figure 6 : Observed transverse beam sizes (pinhole) with (left) and without feedback (right)

To ensure good functioning of the machine for users with the designated beam characteristics (stability, low emittance and good lifetime) irrespective of the configuration of insertion devices, we combine the use of two feedback chains with the application of moderate values of chromaticities.
Beam stability is presently maintained up to 450 mA, relatively close to the target current of 500 mA. Nevertheless, sudden beam losses still occur occasionally showing characteristics of fast beam-ion instability.


It should be noted that the FPGA architecture is very powerful:

• It allows the instability of all bunches to be characterized.
  
• It also allows the individual excitement of one of the 416 bunches to measure its betatron tune constantly on-line. It is then possible to apply feedback to the quadrupole magnets to keep the tunes of the machine constant against the variation of insertion device parameters, which is indispensable for the good functioning of the entire machine.
  
• It also allows differentiation of the feedback gain between high and low intensity bunches as in the hybrid mode.

The feedback performance attained against a single bunch is remarkable: indeed, improvements by more than a factor of 3 have been achieved on the TMCI threshold, namely at zero chromaticity (9 mA instead of 2.5 mA), and up to 20 mA for a moderate value of chromaticity (instead of 2 mA without feedback). In order to measure the betatron tunes online (and correct their variations against insertion device gap motions), we have no other option than to switch off the feedback over 20 ms every 2 seconds and excite the beam during this short interruption. This technique, yet to be perfected, was successfully used during the last week of the first block of runs in 2010, when a single bunch was delivered to the users. On the other hand, feedback in the 8-bunch mode still requires some study.