The Large Hadron Collider rf station-beam interaction strongly influences the longitudinal beam dynamics, both single-bunch and collective effects. Nonlinearities and noise generated within the radio frequency (rf ) accelerating system interact with the beam and contribute to beam motion and longitudinal emittance blowup. Thus, the noise power spectrum of the rf accelerating voltage strongly affects the longitudinal beam distribution. Furthermore, the coupled-bunch instabilities are also directly affected by the rf components and the configuration of the low level rf (LLRF) feedback loops. In this work we present a formalism relating the longitudinal beam dynamics with the rf system configurations, an estimation of collective effects stability margins, and an evaluation of longitudinal sensitivity to various LLRF parameters and configurations.

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1438&context=phy_fac

RF system models for the CERN Large Hadron Collider with application to longitudinal dynamics

Several high-current accelerators use feedback techniques in the accelerating RF systems to control the impedances seen by the circulating beam. [1, 2] These Direct and Comb Loop architectures put the high power klystron and LLRF signal processing components inside feedback loops, and the ultimate behavior of the systems depends on the individual sub-component properties. Imperfections and non-idealities in the signal processing leads to reduced effectiveness in the impedance controlled loops. In the PEP-II LLRF systems non-linear effects have been shown to reduce the achievable beam currents, increase low-mode longitudinal growth rates and reduce the margins and stability of the LLRF control loops. We present measurements of the driver amplifiers used in the PEP-II systems, and present measurement techniques needed to quantify the small-signal gain, linearity, transient response and image frequency generation of these amplifiers.

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Selecting rf amplifiers for impedance controlled LLRF systems - nonlinear effects and system implications

The interaction between beam dynamics and the radio frequency (rf) station in circular colliders is complex and can lead to longitudinal coupled-bunch instabilities at high beam currents. The excitation of the cavity higher order modes is traditionally damped using passive devices. But the wakefield developed at the cavity fundamental frequency falls in the frequency range of the rf power system and can, in theory, be compensated by modulating the generator drive. Such a regulation is the responsibility of the low-level rf (llrf) system that measures the cavity field (or beam current) and generates the rf power drive. The Large Hadron Collider (LHC) rf was designed for the nominal LHC parameter of 0.55 A DC beam current. At 7 TeV the synchrotron radiation damping time is 13 hours. Damping of the instability growth rates due to the cavity fundamental (400.789 MHz) can only come from the synchrotron tune spread (Landau damping) and will be very small (time constant in the order of 0.1 s). In this work, the ability of the present llrf compensation to prevent coupled-bunch instabilities with the planned high luminosity LHC (HiLumi LHC) doubling of the beam current to 1.1 A DC is investigated. The paper conclusions are based on the measured performances of the present llrf system. Models of the rf and llrf systems were developed at the LHC start-up. Following comparisons with measurements, the system was parametrized using these models. The parametric model then provides a more realistic estimation of the instability growth rates than an ideal model of the rf blocks. With this modeling approach, the key rf settings can be varied around their set value allowing for a sensitivity analysis (growth rate sensitivity to rf and llrf parameters). Finally, preliminary measurements from the LHC at 0.44 A DC are presented to support the conclusions of this work.

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APS : Fundamental cavity impedance and longitudinal coupled-bunch instabilities at the High Luminosity Large Hadron Collider

We explore the possibility of operating a self-amplified spontaneous emission free electron laser with a storage ring. We use a semi-analytical model to obtain the evolution inside the undulator, by taking into account the interplay on the laser dynamics due to the induced energy spread and the radiation damping. We obtain the Renieri's limit for the stationary output power, and discuss the possibility of including in our model the effect of the beam instabilities.

SASE FEL Storage Ring

We explore the possibility of operating a SASE FEL with a Storage Ring. We use a semi-analytical model to obtain the evolution inside the undulator by taking into account the interplay on the laser dynamics due to the induced energy spread and to the radiation damping. We obtain the Renieri's limit for the stationary output power and discuss the possibility of including in our model the effect of the beam instabilities.

SSRL and SLAC groups are developing a long-range plan to transfer its evolving scientific programs from the SPEAR3 light source to a much higher performing photon source that would be housed in the 2.2-km PEP-II tunnel. While various concepts for the PEP-X light source are under consideration, including ultimate storage ring and ERL configurations, the present baseline design is a very low-emittance storage ring. A hybrid lattice has double bend achromat (DBA) cells in two of the six arcs that provide a total 30 straight sections for insertion device (ID) beam lines extending into two new experimental halls. The remaining arcs contain TME cells. Using 90 m of damping wigglers the horizontal emittance at 4.5 GeV would be 100 pm-rad with 1.5-A stored beam. PEP-X will produce photon beams having brightnesses near 10{sup 22} (ph/s/mm{sup 2}/mrad{sup 2}/0.1% BW) at 10 keV. Studies indicate that a 90-m undulator could have FEL gain and brightness enhancement at soft x-ray wavelengths with the stored beam. Crab cavities or other beam manipulation systems could be used to reduce bunch length or otherwise enhance photon emission properties. The present status of the design of PEP-X as a storage ring is presented.

Concepts for the PEP-X Light Source

The LHC Low Level RF System (LLRF) is a complex multi-VME crate system which is used to regulate the superconductive cavity gap voltage as well as to lower the impedance as seen by the beam through low latency feedback. This system contains multiple loops with several parameters to be set before the loops can be closed. In this paper, we present a suite of MATLAB based tools developed to perform the preliminary alignment of the RF stations and the beginnings of a closed loop model based alignment routine. We briefly introduce the RF system and in particular the base band (time domain noise based) network analyzer system built into the LHC LLRF. The main focus of this paper is the methodology of the algorithms used by the routines within the context of the overall system. Measured results are presented that validate the technique. Because the RF systems are located in a cavern 120 m underground in a location which is relatively un-accessible without beam and completely un-accessible with beam present or magnets are energized, these remotely operated tools are a necessity for the CERN LLRF team to maintain and tune their LLRF systems in a similar fashion as to what was done very successfully in PEP-II at SLAC.

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Feedback configuration tools for lhc low level rf system

PEP-II plans to achieve the final goal in luminosity will require an increase of the beam currents to 4 A for LER and 2.2 A for HER. These magnitudes are challenging in part because they will push the longitudinal low-order mode (LOM) beam stability and the station stability to the limit. To analyze the behavior of both rings at high currents and to understand the limits in the longitudinal feedback systems, a simulation tool has been developed at SLAC. This tool is based on a reduced model of the longitudinal LOM dynamics of the beam interacting with the effective impedance presented by the RF stations. Simulations and measurements of the longitudinal beam behavior in both rings have been performed to understand the ultimate limits of the systems. These studies have defined the impact of control loop parameters in the longitudinal beam dynamics, identified the limiting behavior of RF devices affecting the optimal performance of the RF stations and quantified the behavior of the longitudinal LOM beam dynamics. Results of sensitivity to parameter variations in the beam dynamics and limits in the maximum current that LER/HER can achieve based on the longitudinal beam stability are reported in this paper.

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Analysis of the longitudinal low-order mode beam dynamics in PEP-II rings at high current beams

CBP 839 FEEDBACK TECHNIQUES AND SPS ECLOUD INSTABILITIES - DESIGN ESTIMATES ∗ J.D. Fox, T. Mastorides, G. Ndabashimiye, C. Rivetta, D. Van Winkle, Stanford Linear Accelerator Center, Stanford, CA , USA J.Byrd, J-L Vay, Lawrence Berkeley Laboratory, Berkeley, CA, USA W. Hoﬂe, G. Rumolo, CERN, Geneva, Switzerland R. De Maria, Brookhaven National Laboratory, Upton, NY, USA Abstract The SPS at high intensities exhibits transverse single- bunch instabilities with signatures consistent with an Ecloud driven instability. While the SPS has a coupled- bunch transverse feedback system, control of Ecloud- driven motion requires a much wider control bandwidth capable of sensing and controlling motion within each bunched beam. This paper draws beam dynamics data from the measurements and simulations of this SPS instability, and estimates system requirements for a feedback system with 2-4 GS/sec. sampling rates to damp Ecloud-driven transverse motion in the SPS at intensities desired for high- current LHC operation. via numeric simulation models as well as from machine measurements themselves [1] [6] [5] [8]. One important effort of 2009 has been to focus attention on comparisons of these multiple estimates, and highlight areas of agree- ment and understand disagreements in the data. The data from the non-linear time domain simula- tions provides time slice displacements of a bunch, for the MD data wideband exponential stripline pickups and sum/difference hybrids are recorded at a 10 - 20 GS/sec rate for post analysis. [8] The ﬁrst quantitative information to be extracted is thge oscillation frequency of each slice ( longitudinal FFTs of each slice over turns) . Figures 1, 2 and 3 show this sim- ple tune vs. slice analysis for the WARP, HeadTail 1 and MD measurement. In the two simulation cases, there is no coherent excitation or centroid kick at the beginning of the transient - the motion is from the growing Ecloud effect. Tune vs Position WARP simulation 26 GeV INTRODUCTION AND MOTIVATION The SPS suffers from an electron cloud driven transverse instability [1] for intensities above 1.2E11 per bunch and bunch trains of 72 bunches with 25 ns bunch spacing. In the nominal LHC ﬁlling scheme the intensity per bunch is 1.15x11 per bunch and up to 4 batches of 72 bunches are foreseen to be accelerated in the SPS. Mitigation methods to control the Ecloud driven insta- bility in SPS operation have been developed via scrub- bing techniques, adjustment of chromaticity, special vac- uum chamber coatings and special chamber geometries. A high frequency vertical feedback system is a complemen- tary approach to the vacuum chamber upgrade, as it could also cure the anticipated single bunch TMC instability [3] [4].Development of a wideband front-end and processing channel also offers improved transverse diagnostics. The basic system formalism studied in our design es- timate is a single-pickup transverse receiver, with a high sampling rate channel which has sufﬁcient bandwidth to sample the bunch vertical coordinate multiple times across the several ns bunch length.The feedback control ﬁlter is estimated as a multi-tap FIR ﬁlter, though the design study can explore IIR and more complex ﬁlter options. Frac. Tune Z position [cm] Figure 1: 26 GeV WARP Tune vs.Position data 300 turns of evolution. 1.1E11 p/bunch. We see unstable motion evolve as the tails of the bunch start growing at shifted tune above the 0.185 betatron tune ( the base tune is seen as a weak line in the HeadTail data set). It is very encouraging that all three data sets show shifted Ecloud tunes, though the MD measurement shows motion in all portions of the beam at the shifted tune. The MD measurements also show signiﬁcant spectral power at low frequencies far from the betatron or shifted Ecloud 1 The HeadTail simulation code uses a ﬁxed number of samples across the bunch, and as the bunch longitudinal distribution evolves the sampling intervals are not ﬁxed in time. For this sliding window tune analysis we post-process the HeadTail data via an interpolation code which upsamples the bunch coordinates to a higher sampling frequency, then re-samples the bunch information to a ﬁxed sampling interval ESTIMATES OF SYSTEM DYNAMICS FROM SIMULATIONS AND MD EFFORTS Estimation of feedback system speciﬁcations must begin with knowledge of the beam and Ecloud dynamics obtained ∗ Work supported by the U.S. Department of Energy under contract # DE-AC02-76SF00515 and the US LARP program. This work was also supported by the U.S. Department of Energy under Contract DE-AC02-05CH11231.

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Feedback techniques and SPS Ecloud instabilities - design estimates

A non-linear time-domain simulation has been developed that can determine technical limitations, effects of non-linearities and imperfections, and impact of additive noise on the interaction of the beam with the Impedance Control Radio Frequency (RF) systems [1]. We present a formalism for the extraction of parameters from the time domain simulation to determine the sensitivity of the beam longitudinal emittance and dilution on the RF system characteristics. Previous studies [2], [3] have estimated the effect of a noise source on the beam characteristics assuming an independent perturbation source of the RF voltage and a simplified beam model with no coupling. We present the methodology for the time-domain simulation study of the dependence of the accelerating voltage noise spectrum on the various RF parameters and the technical properties (such as non-linearities, thermal noise, frequency response etc.) of the Low Level RF (LLRF) system components. Future plans to expand this formalism to coupled bunch studies of longitudinal emittance growth in the LHC at nominal and upgraded beam currents are briefly summarized.

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T. Mastorides

Papers

Concepts for the PEP-X Light Source

Feedback configuration tools for lhc low level rf system

Analysis of the longitudinal low-order mode beam dynamics in PEP-II rings at high current beams

Feedback techniques and SPS Ecloud instabilities - design estimates

Application of Non-Linear Time-Domain RF Simulations to Longitudinal Emittance Studies for the LHC