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LLRF tools and models e-Cloud/TMCI Publications

LHC LLRF Models, tools and Studies Feedback Control of SPS E-Cloud/TMCI Instabilities

LARP DOE Review July 16 2010 J.D. Fox1

LARP LLRF Contributors:

• T. Mastorides1, C. Rivetta1, D. Van Winkle1,

P . Baudrenghien2, A. Butterworth2, J. Molendijk2 LARP Ecloud Contributors:

• A. Bullitt1, J. D. Fox1, G. Ndabashimiye1, M. Pivi1, C. Rivetta1, O. Turgut1,
• R. De Maria2, G. Arduini2, W. Hofle2, G. Rumolo2,
• J. Byrd3, M. Furman3, M. Venturini3, S. De Santis3, R. Secondo3, J.-L. Vay3

1Accelerator Technology Research Department, SLAC 2BE-RF Group, CERN 3LBL

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LLRF tools and models e-Cloud/TMCI Publications

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LLRF tools and models

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Motivation: LHC LLRF Optimization tools

Investigate the operational limits and impact on beam dynamics from the impedance-controlled RF systems. Look ahead to high current operations, possible upgrades and understand the role of the technical implementation.

Based on PEP-II experience, where limits of machine were understood, and

• vercome, via models and simulation studies of new control techniques

As part of these studies, CERN requested model-based commissioning tools - they are part

• f the beam/LLRF simulation.

These tools operate remotely and allow identifying the RF station transfer function and designing the feedback loops using model-based techniques. Remote operation was crucial under the new stricter CERN polices preventing tunnel access when the magnets are energized.

Klystron

• +

+ + + +

• Setpoint

Beam Feedback Analog RF RF 1Turn(comb) Klystron Polar Loop Driver Digital RF Feedback Feedback cav.

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LLRF tools and models e-Cloud/TMCI Publications

Motivation: RF Noise Effect on Beam Diffusion Studies

The noise power spectrum of the RF accelerating voltage can strongly affect the longitudinal beam distribution and contribute to beam motion and diffusion.

Increased bunch length decreases luminosity and eventually leads to beam loss due to the finite size of the RF bucket.

The choices of technical and operational configurations can have a significant effect on the noise sampled by the beam.

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LLRF tools and models e-Cloud/TMCI Publications

FY 2010 Results

LLRF Optimization tools The LLRF configuration tools have been used by the CERN BE-RF group to remotely commission the LLRF feedback loops of the RF stations during start up in both November 09 / February 10.

Tools reduced commissioning from 1.5 days/station to 1.5 hours/station. Model based configuration adds consistency and reliability. CERN BE-RF group have repeatedly expressed their support and enthusiasm for this collaboration.

RF Noise Effect on Beam Diffusion Studies To better understand the RF-beam interaction we developed a theoretical formalism relating the equilibrium bunch length with beam dynamics, accelerating voltage noise, and RF system configurations Conducted measurements at LHC (May) which confirmed our theoretical formalism and models

• T. Mastorides defended his Ph.D. thesis, with significant LARP funded LHC work

Multiple publications in peer-reviewed journals and conference proceedings.

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LLRF tools and models e-Cloud/TMCI Publications

Technical examples: LHC LLRF Optimization tools

Tool calculation and adjustment of RF station closed loop gain/phase.

−2 −1.5 −1 −0.5 0.5 1 1.5 2 −20 −10 10 Closed−Loop Transfer Function Frequency (MHz) Gain (dB) Initial Final −2 −1.5 −1 −0.5 0.5 1 1.5 2 −600 −400 −200 200 Frequency (MHz) Phase (degrees) Initial Final −2 −1.5 −1 −0.5 0.5 1 1.5 2 −60 −40 −20 20 Frequency (MHz) Gain (dB) Fit Data −2 −1.5 −1 −0.5 0.5 1 1.5 2 −1000 −500 500 Frequency (MHz) Phase (degrees)

1-turn feedback models ready. Waiting for hardware commissioning.

−150 −100 −50 50 100 150 −20 20 40 60 Frequency (kHz) Gain (dB) Fit Data −150 −100 −50 50 100 150 −500 500 Frequency (kHz) Phase (degrees) −150 −100 −50 50 100 150 −4 −2 2 Frequency (kHz) Gain (dB) Fit Data −150 −100 −50 50 100 150 −220 −200 −180 −160 −140 Frequency (kHz) Phase (degrees)

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LLRF tools and models e-Cloud/TMCI Publications

RF Noise Effect on Beam Diffusion Studies

Determined that the RF reference dominates beam diffusion related to RF noise Collaboration with BE-RF on technical means to improve noise spectrum

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180 160 140 120 100 80 60 40 20

Frequency (Hz) Noise (dBc/Hz)

10MHz Ref 10MHz Ref (scaled) 400MHz Ref Sum B2 BPL Off Sum B2 BPL ON

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LLRF tools and models e-Cloud/TMCI Publications

RF Noise Effect on Beam Diffusion Studies

Anticipated a close relationship between RF station noise spectrum and beam diffusion rate. April 2010 measurements showed clear correlation between the bunch length as estimated by our theoretical formalism and the longitudinal emittance growth

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5

Time (s) Bunch Length (cm) Data G = 1125 G = 562.5 G=70 G=0 G=10 G=2

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FY2011 Research Plan

LLRF Optimization tools The 1-Turn Feedback routines of the optimization tools suite have been tested on the RF station prototype and on one real LHC station. LHC operations has not yet commissioned the 1-Turn Feedback. As currents increase, the 1-Turn feedback will be commissioned for all RF stations. The optimization tools will be validated and available for this commissioning. Final validation measurements of the complete suite will be conducted. Ongoing collaboration with the CERN BE-RF group on new features for future high-current

• perations.

RF Noise Effect on Beam Diffusion Studies Research plan: inject noise at specific frequencies and with varying amplitudes in a second round of measurements. Better quantify the relationship between the RF noise and longitudinal emittance blowup. Our earlier measurements identified the RF reference (Local Oscillator distribution) as the dominating component affecting the beam diffusion. Studies are being conducted to identify alternative technical LO implementations to reduce this effect. We would like to develop a formalism to estimate more accurately the time evolution of the bunch length growth with the simulation and models.

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LLRF tools and models e-Cloud/TMCI Publications

Ecloud Project Motivation and Progress July 2009 - July 2010

Motivation - control Ecloud and TMCI effects in SPS and LHC via GHz bandwidth feedback Complementary to Ecloud coatings, grooves, etc. Also applicable to TMCI.

Technical formalism similar to 500 Ms/sec feedback implemented at PEP-II, KEKB, DAFNE Ecloud/TMCI Modeling, dynamics estimation, feedback simulation efforts Dynamics analysis techniques to quantify nonlinear unstable oscillators MD results June 2009 (Instability Dynamics) April 2010 (pickup and kicker studies) Hardware efforts (4 GS/sec. synchronized excitation) near-term plans (MD, models, lab) - Response to Chamonix emphasis on SPS intensities

Multi-lab effort - coordination on

Non-linear Simulation codes (LBL - CERN - SLAC) Dynamics models/feedback models (SLAC - Stanford STAR lab) Machine measurements- SPS MD (CERN - SLAC - LBL) Hardware technology development (SLAC)

FY2010 first year of LARP SLAC staff support

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LLRF tools and models e-Cloud/TMCI Publications

Organization and Staffing

Greater activity, increased progress winter 2010 Program emphasis on coordinating models, machine measurements, and feedback estimation. Develop more realistic feedback model in WARP (R. Secondo) Multi-lab WEB meetings on Ecloud/TMCI feedback

www.slac.stanford.edu/∼jdfox/ecloudwebfeb10.pdf

Biggest Change - step-up FY2010 SLAC Funding

Allows 2 Stanford grad students Alex Bullitt (working on excitation system) Ozhan Turgut (system identification, dynamics models) LARP support 25 % for J. Fox, C. Rivetta

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SPS Studies

Vertical Instability develops after injection of second batch, within 100 turns. Time domain shows bunch charge, and transverse displacement 1E11 p/bunch (June 2009) Use this technique to compare models, MD data - extract beam dynamics necessary to design feedback. Roughly 25 slices (250 ps) between displacement maxima and minima April 2010 - characterize existing SPS pickups and drive tapered pickup as kicker pickups - very successful Noise, transverse resolution well-quantified 25 microns rms at 0.5E11 (vertical) Kicker and Beam Excitation, mixed results difficult to excite measurable response 1/f Kicker response, limited power Chamonix Implications-> kicker fab?

50 100 400 300 200 100 100 200 300 400 500

Vertical displacement of bunch 119

slice SUM / DIFF signals (a.u) 50 100 1 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1 slice Vertical displacement (a.u) SUM DIFF

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Analysis of Ecloud simulations and Ecloud MD data

Observations

tune shifts within bunch due to Ecloud, bursting, positions of unstable bunches information in SUM signal frequencies within bunch - estimated bandwidth of instability signal, correction signal Growth rates of eigenmodes - initial fits and stability observations

Simulations - access to all the beam data. What effects are not included? Machine measurements - what can we measure? with what resolution? What beam conditions?

Tune versus Position found between turn 100 and turn 200

Z position [sample] Tune

20 40 60 80 100 120 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 500 1000 1500 2000 2500 3000a.u

MD data June 2009 WARP simulation

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Identification of Internal Bunch Dynamics: Reduced Model

characterize the bunch dynamics - same technique for simulations and SPS measurements critical to design the feedback algorithms Specify requirements for pickup, receiver, processing, power stages and kicker systems. Ordered by complexity, the reduced models could be

linear models with uncertainty bounds (family of models to include the GR/tune variations) ’linear’ with variable parameters (to include GR/tune variations-different op. cond.) non-linear models

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LLRF tools and models e-Cloud/TMCI Publications

Closed-Loop feedback around the Reduced Model

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Use the reduced model, with realistic feedback delays and design a simple FIR controller Each slice has an independent controller This example 5 tap filter has broad bandwidth - little separation of horizontal and vertical tunes But what would it do with the beam? How can we estimate performance?

1 1.5 2 2.5 3 3.5 4 4.5 5 1 0.5 0.5 1

Taps Coefficients

Transfer function for a 5 TAP FIR Filter

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 20 10 10 20

Normalized frequency Magnitude [dB.]

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 200 100 100 200

Normalized frequency Phase [deg.]

Nominal Tune = 0.19

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LLRF tools and models e-Cloud/TMCI Publications

Root Locus Study - Tune shifted from 0.185 to 0.21

We study the stability for a range of tunes This filter can control both systems- Maximum damping is similar in both cases Is this realistic case to design? We need more data from simulations and MD We need models for dynamics vs. beam energy, interaction with ramp

1 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1 1 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1

Real Imag

Rootlocus for fractional tune 0.185 and 0.21 (Detail)

frac.tune = 0.21 (red) frac.tune = 0.185 (blue)

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1

Real Imag

Rootlocus for fractional tune 0.185 and 0.21 (Detail)

frac.tune = 0.21 (red) frac.tune = 0.185 (blue)

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LLRF tools and models e-Cloud/TMCI Publications

Design study - 4 Gs/sec. 1 stack SPS feedback channel

Can we build a ’small prototype’ style feedback channel? What fits in our limited LARP hardware budget? what to do in 2010/ 2011? Develop for closed loop tests in SPS Idea - build 4 GS/sec. channel via evaluation boards and SLAC-developed Vertex 5 FPGA processor

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Summary - 2010 LARP Ecloud/TMCI effort

Understand Ecloud dynamics via simulations and machine measurements

Participation in E-Cloud studies at the SPS (next opportunity July 2010) Analysis of SPS and LHC beam dynamics studies, comparisons with Ecloud models

Modelling, estimation of E-Cloud effects

Validation of Warp and Head-Tail models, comparisons to MD results comparisons with machine physics data (driven and free motion), Critical role of Ecloud simulations in estimating future conditions, dynamics extraction of system dynamics, development of reduced (linear) coupled-oscillator model for feedback design estimation

Lab effort -development 4 GS/sec. excitation system for SPS

Modify existing system to synchronize with selected bunches - data for system ID tools Identify critical technology options, evaluate difficulty of technical implementation Explore 4 Gs/sec. ’small prototype’ functional feedback channel for 2011 fab and MD use Evaluate SPS Kicker options re: CERN request, 2012 shutdown window

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Request for SPS Feedback System

What can we do for the SPS shutdown? CERN’s interest - very high. Critical missing element - useful high-power kicker and power amplifier components in SPS

Identify the Kicker technology as an accelerated research item, design prototype kicker and vacuum components for SPS fabrication and installation Kicker design/fab requires joint CERN/US plans, they are ready to collaborate Specify power amplifiers, cable plant, loads, diagnostics, all vacuum components

FY 2011 Accelerated research and design report on Kicker System

design report, suggested implementation, test low power lab models, RF simulation

FY2012 - detailed design and fab of prototype kicker, vacuum components FY2013 - installation in SPS with Amplifiers and Cable plant

Vacuum components essential for shutdown

Dovetails with parallel system estimation and development of ’quick prototype processor’

Model closed-loop dynamics, estimate feedback system specifications Evaluate possible control architectures, implementations, via technology demonstrations SPS Machine Physics studies, development of ’small prototype’, closed loop studies

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FY2011 Plans

LLRF Tools, Models and High-Current estimation

We need to pace LHC RF system commissioning, validate comb model for setup tools Continuation of noise studies, estimate longitudinal emittance growth, system limits Staffing 0.25 FTE, plus 0.5 FTE new student Travel budget $11.5K

Ecloud/TMCI Feedback

Consistent with plans, continue MD effort, simulations, model feedback options Lab effort to build ’quick prototype’ 4 GS/sec processing model Staffing LBL 0.4 FTE, SLAC 1.75 FTE staff, 2 FTE Students M&S $75K Travel $26K (SLAC and LBL)

Extra effort on Kicker for SPS 2013 upgrade installation

FY 2011 0.5 - 0.75 FTE staff to develop Kicker design options report, $25K M&S , $6K travel FY 2012 1 - 1.5 FTE staff, $250K M&S for kicker and cables, $50K for amplifiers, $6K travel

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LLRF tools and models e-Cloud/TMCI Publications

• T. Mastorides et. al., LHC Beam Diffusion Dependence on RF Noise: Models and

Measurements, in preparation for submission to Physical Review ST-AB.

• T. Mastorides et. al., RF system models for the LHC with Application to

Longitudinal Dynamics, submitted to Physical Review ST-AB.

• T. Mastorides et. al., LHC Beam Diffusion Dependence on RF Noise: Models and

Measurements, Proceedings IPAC 2010, 23-28 May 2010, Kyoto, Japan.

• D. Van Winkle et. al., Commissioning of the LHC Low Level RF System Remote

Configuration Tools, Proceedings IPAC 2010, 23-28 May 2010, Kyoto, Japan.

• J. D. Fox et. al., SPS Ecloud Instabilities - Analysis of Machine Studies and

Implications for Ecloud Feedback, Proceedings IPAC 2010, 23-28 May 2010, Kyoto, Japan. J.-L. Vay et. al., Simulation of E-cloud Driven Instability and its Attenuation Using a Feedback System in the CERN SPS, Proceedings IPAC 2010, 23-28 May 2010, Kyoto, Japan. WEBEX Ecloud Feedback mini-workshop February 2010 (joint with SLAC, Stanford, CERN, and LBL).

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J.D. Fox, et. al., Feedback Techniques and Ecloud Instabilities - Design Estimates, SLAC-PUB-13634, May 18, 2009. 4pp. Presented at Particle Accelerator Conference (PAC 09), Vancouver, BC, Canada, 4-8 May 2009.

• J. R. Thompson et. al., Initial Results of Simulation of a Damping System of

Electron Cloud-Driven Instabilities in the CERN SPS, Presented at Particle Accelerator Conference (PAC 09), Vancouver, BC, Canada, 4-8 May 2009. Performance of Exponential Coupler in the SPS with LHC Type Beam for Transverse Broadband Instability Analysis 1 R. de Maria BNL, Upton, Long Island, New York, J. D. Fox SLAC, Menlo Park, California, W. Hofle, G. Kotzian, G. Rumolo, B. Salvant, U. Wehrle CERN, Geneva Presented at DIPAC 09 May 2009 WEBEX Ecloud Feedback mini-workshop August 2009 (joint with SLAC, CERN, BNL, LBL and Cornell). J.D. Fox et. al., Feedback Control of Ecloud Instabilities, CERN Electron Cloud Mitigation Workshop 08.

• W. Hofle, E-cloud feedback activities for the SPS and LHC, CERN Electron Cloud

Mitigation Workshop 08.

• R. De Maria, Observations of SPS e-cloud instability with exponential pickup,

CERN Electron Cloud Mitigation Workshop 08.

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• G. Rumolo, Experiments on SPS e-cloud instability, CERN Electron Cloud

Mitigation Workshop 08.

• M. Venturini, Progress on WARP and code benchmarking, CERN Electron Cloud

Mitigation Workshop 08.

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