Benoit Salvant

Control of Intra-Bunch Vertical Motion in the SPS with GHz Bandwidth Feedback

A GHz bandwidth vertical beam feedback system has been in development at the CERN SPS for control of unstable vertical beam motion in single bunch and bunch train configurations. We present measurements and recent studies of stable and unstable motion for intensities up to 2 × 1011 p/bunch [1]. The system has been operated at 3.2 GS/s with 16 samples across a 5-ns RF bucket (4.2 ns 3σ bunch at injection) and experimental results confirm damping of intra-bunch instabilities in Q20, Q22 and Q26 optics configurations. Instabilities with growth rates of 1/200 turns are well-controlled from injection, consistent with the achievable gains for the 2 installed stripline kickers with 1 kW broadband power. Measurements from multiple studies in single-bunch and bunch train configurations show achieved damping rates, control of multiple intra-bunch modes, behavior of the system at injection (including interaction with the existing vertical damper) and final damped noise floor. The work is motivated by anticipated intensity increases from the LIU and HL-LHC upgrade programs [2], and has included the development of a new 1 GHz bandwidth slotline kicker structure and associated amplifier system. TRANSVERSE WIDEBAND INTRA-BUNCH FEEDBACK DEMONSTRATION SYSTEM A single-bunch wideband digital feedback system was initially commissioned at the CERN SPS in November 2012 [3]. Over time the system has has been extended to include control for trains of 64 bunches [4] and configured with two 500-MHz bandwidth stripline kickers, each powered with 500W of broadband RF power. Over time the system has been used to study single bunch and multi-bunch beams at the SPS in Q26, Q20 and most recently Q22 optics. The essential goals in al these studies is to try to quantify the behavior of the feedback in terms of damping intra-bunch motion from impedance mechanisms, TMCI, or Ecloud mechanisms. ∗ Work supported by the U.S. Department of Energy under contract # DE-AC02-76SF00515, the US LHC Accelerator Research (LARP) program, the CERN LHC Injector Upgrade Project (LIU) and the US-Japan Cooperative Program in High Energy Physics. Figure 1: Vertical motion signal showing 16 samples across the bunch for 20,000 turns. Positive feedback is applied from turns 3500 6500, there is no feedback applied after turn 6500. The bunch motion is excited and continues without being damped.

Experimental studies on the SPS electron cloud

One of the most important limitations in the performances of the CERN-SPS is presently the Electron Cloud Instability (ECI). Hence, defining its dependence on energy with confidence is an indispensable asset to direct the efforts for all the upgrade studies. Macroparticle simulations carried out with the HEADTAIL code [1] have shown that the ECI mechanism is subtle and the scaling laws valid for the Transverse Mode Coupling Instability cannot be applied to it [2]. The reason lies in the fact that the electron dynamics, while a bunch is going through an electron cloud, is heavily affected by the transverse beam size. In fact, transversely smaller beams can enhance the electron pinch and lower the intensity threshold for the bunch to be unstable. Hence, higher energy beams, though more rigid, can be more unstable due to their smaller transverse size (with constant transverse normalized emittance). During the 2007 run a measurement campaign has been carried out at the CERN-SPS to prove experimentally the outcomes of macroparticle simulations. INTRODUCTION AND MOTIVATIONS Plans for the Large Hadron Collider (LHC) performance upgrade include the improvement of the existing LHC injectors and/or the design of possible new rings in the injector chain [3]. Several scenarios, aimed at overcoming the existing bottlenecks, are presently being taken into consideration. One option, based on the replacement of the Proton Synchrotron (PS) ring with the PS2 [4], foresees an increase of the injection energy into the existing SPS from the present 26 GeV/c to 50 GeV/c. This is believed to be beneficial for the machine in many regards (e.g., less space charge and intra beam scattering, more rigid beams against coupled bunch instabilities, no transition crossing, lower injection and capture losses) [2]. Furthermore, it would allow for an upgrade of the SPS to a 1 TeV extraction energy ring, with the related advantages for injection into the LHC. However, the SPS upgrade plan crucially depends on the effect of a higher injection energy on the collective phenomena that are presently believed to be the real limitation in the SPS performance. One of them is TMCI, which was observed in the SPS for special intense bunches with low longitudinal emittance [5, 6]. Therefore, it could be a potential limiting factor in the future, especially taking ∗Giovanni.Rumolo@cern.ch into account the enhancement of the impedance of the SPS caused by the installation of 9 new extraction kickers in the ring since 2003 and the higher charge per bunch that should be injected into the SPS [7]. In addition, the vertical single bunch ECI has been limiting for a long time the number of batches that could be injected into the SPS and it could be overcome by beam scrubbing and subsequently operating the ring with a high vertical chromaticity (which nonetheless can be harmful for the beam lifetime) [8]. A detailed study on the energy dependence of the threshold for the onset of these instabilities is essential to assess a global beneficial effect of the pre-injector upgrade without unwanted side effects. The scaling law of the TMCI threshold with energy was already addressed in [9]. Under conservation of the longitudinal emittance and assuming bunches always matched to their buckets, the TMCI threshold only depends linearly on the slip factor |η|, and therefore a higher injection energy would certainly help to operate the machine farther from this limitation. Besides, preliminary studies of the dependence of the ECI threshold on energy were done, which showed that the related scaling law cannot be trivially derived from the existing TMCI theories. In fact, a first attempt of analytical approach using a broad-band resonator with beam dependent parameters showed that it may become surprisingly unfavourable at high energies far from transition, under the further assumptions of conservation of the bunch length and the normalized transverse emittances. A comprehensive study of the effect of higher injection energy on the ECI has been therefore carried out numerically and experiments are being done in the CERN-SPS with an LHC-type beam to verify it. SUMMARY OF SIMULATION RESULTS AND CODE-TO-CODE BENCHMARK Table 1 shows a list of the essential parameters used for the numerical study (typical LHC-type bunch in the SPS). The main assumptions of our model are: • The longitudinal emittance and the bunch length are kept constant. The momentum spread ∆p/p0 is re-scaled and the matched voltage re-adjusted accordingly when changing the energy. The matched voltage goes like |η|/γ with energy. This constraint could be relaxed by increasing the longitudinal emittance. • The normalised transverse emittances are constant. BEAM’07 PROCEEDINGS