Bunch-by-bunch feedback and LLRF at ELSA

Bunch-by-bunch feedback and LLRF at ELSA Dmitry Teytelman Dimtel, Inc., San Jose, CA, USA February 9, 2010

Outline 1 Feedback Feedback basics Coupled-bunch instabilities and feedback Beam and feedback models 2 Diagnostics Grow/Damp Measurements 3 ELSA Measurements Hardware Horizontal Vertical Longitudinal Digital LLRF

Closed-loop Feedback: Structure and Example Start with a physical system (plant). actuator u Plant y r controller sensor

Closed-loop Feedback: Structure and Example Start with a physical system (plant). actuator u Plant y Measure some property of the plant with a sensor. r controller sensor

Closed-loop Feedback: Structure and Example Start with a physical system (plant). actuator u Plant y Measure some property of the plant with a sensor. Plant behavior (state) can be affected by an actuator. r controller sensor

Closed-loop Feedback: Structure and Example actuator u y Take a household heating system as an example. Our plant is the house. r controller sensor

Closed-loop Feedback: Structure and Example u y Take a household heating system as an example. Our plant is the house. Actuator - furnace. r controller sensor

Closed-loop Feedback: Structure and Example u y Take a household heating system as an example. Our plant is the house. Actuator - furnace. Sensor - thermistor. r controller

Closed-loop Feedback: Structure and Example u y Take a household heating system as an example. Our plant is the house. Actuator - furnace. Sensor - thermistor. Controller - thermostat. r

Closed-loop Feedback: Structure and Example r u y Take a household heating system as an example. Our plant is the house. Actuator - furnace. Sensor - thermistor. Controller - thermostat. Loop signals Output y - temperature; Input u - heated air from the furnace; Reference r - temperature setpoint.

Dynamic System Descriptions and Models 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 00 11 K γ M F Mechanical system: mass on a spring with a damper. Described by Mẍ + γẋ + Kx = F. Differential equation is a time-domain description. Frequency domain - Laplace transform. Frequency response evaluated at s = iω.

Dynamic System Descriptions and Models Mechanical system: mass on a spring with a damper. F 1 Ms 2 +γs+k x Described by Mẍ + γẋ + Kx = F. Differential equation is a time-domain description. Frequency domain - Laplace transform. Frequency response evaluated at s = iω.

Dynamic System Descriptions and Models Mechanical system: mass on a spring with a damper. F 1 Mω 2 +γiω+k x Described by Mẍ + γẋ + Kx = F. Differential equation is a time-domain description. Frequency domain - Laplace transform. Frequency response evaluated at s = iω.

Coupled-bunch Instabilities Consider a single bunch in a lepton storage ring. Centroid motion has damped harmonic oscillator dynamics. Multiple bunches couple via wakefields (impedances in the frequency domain). At high beam currents this coupling leads to instabilities. In modern accelerators active feedback is used to suppress such instabilities.

Bunch-by-bunch Feedback Definition In bunch-by-bunch feedback approach the actuator signal for a given bunch depends only on the past motion of that bunch. BPM Sensor Beam Actuator Kicker structure Front end Controller Back end Bunches are processed sequentially. Correction kicks are applied one or more turns later.

Coupled-bunch Instabilities: Eigenmodes and Eigenvalues If we consider bunches as coupled harmonic oscillators, a system of N bunches has N eigenmodes. Without the wakefields these modes have identical eigenvalues determined by the tune and the radiation damping. Impedances shift the modal eigenvalues in both real part (damping rate) and imaginary part (oscillation frequency). Modeling all eigenmodes is computationally intensive.

MIMO model of the bunch-by-bunch feedback v0 v1. vn 1 φ0 φ1 Beam dynamics. G(s) φn 1 Feedback H(s) H(s)... H(s) Beam is a multi-input multi-output (MIMO) system. For N bunches there are N inputs and outputs. Individual bunch kicks are the inputs. Bunch positions are the outputs. Sequential processing, parallel analysis.

MIMO model of the bunch-by-bunch feedback v0 v1. vn 1 φ0 φ1 Beam dynamics. G(s) φn 1 Feedback H(s) H(s)... H(s) If feedback is the same for all bunches, it is invariant under coordinate transformations. Bunch-by-bunch feedback applies the same feedback H(s) to each eigenmode. Consequently it is sufficient to consider the most unstable eigenmode for modeling.

Detailed Scalar Feedback Model u(t) g 0 s 2 2λs+ω 2 n y(t) ge iφ Complex gain Beam Sampling u n H(Ω) y n Processing & cable delay Zero order hold Feedback filter

Grow/Damp Measurements Unstable systems are difficult to characterize. Transient measurements - open the loop for a short time to allow the unstable modes to grow. Record coordinates of all bunches. Longitudinal grow/damp in BEPC-II - HOMs in various vacuum structures. Vertical grow/damp in CESR-TA - electron cloud.

Estimating Eigenvalues R(y k ) (deg@rf) I(y k ) (deg@rf) 0.2 0.1 0 0.1 0.2 0.2 0.1 0 0.1 0.2 0 0.5 1 1.5 Time (ms) We post-process the data to estimate phase-space trajectories of the even-fill eigenmodes. Longitudinal mode 233 at the ALS is shown. Complex exponentials are fitted to the data to estimate the eigenvalues.

Estimating Eigenvalues Amplitude (deg@rf) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Data Fit Error 0 0 5 10 15 20 25 30 35 40 Time (ms) We post-process the data to estimate phase-space trajectories of the even-fill eigenmodes. Longitudinal mode 233 at the ALS is shown. Complex exponentials are fitted to the data to estimate the eigenvalues.

igp Highlights A 500+ MHz processing channel. Finite Impulse Response (FIR) bunch-by-bunch filtering for feedback. Control and diagnostics via EPICS soft IOC on Linux. External triggers, fiducial synchronization, low-speed ADCs/DACs, general-purpose digital I/O.

Front/Back-end Unit 1.5 GHz front-end detection frequency. 2-cycle comb generator. 1 GHz back-end frequency. Integrated control via igp GPIO: Front and back-end LO phase shifters; Front and back-end attenuators.

LLRF Prototype Full cavity control and monitoring; 6 RF inputs: forward, reflected, and probe signals; Klystron drive in open or closed-loop mode; Calibrated monitoring of channel amplitude and phase; Interlock options, digital I/O (tuners), EPICS controls.

Horizontal Drive/Damp Measurement at 30 ma, 2.3 GeV; Beam is stable, had to apply positive feedback; Band of modes centered at 270 (-4); Suggestive of ion-driven instability.

Horizontal Closed-loop Spectrum Measurement at 7 ma, 2.3 GeV; Feedback loop is closed; Notch at the betatron frequency; Can be used for parasitic tune measurement at 1 Hz rate.

Vertical Drive/Damp Measurement at 8.8 ma, 2.3 GeV; Two bands of modes: around -1 and 4; Combination of resistive wall and ions?

Bursting Longitudinal Motion Large amplitude (more than 30 degrees @ RF) longitudinal motion; Bursting at almost periodic intervals which change with beam current and energy; Time-domain plot of longitudinal position of one bunch; Spectrogram shows large tune shifts.

Bursting Longitudinal Motion Longitudinal position (ADC counts) 60 40 20 0 20 40 Time domain longitudinal motion of bunch 109, 14 ma, 1.2 GeV 60 0 10 20 30 40 50 Time (ms) Large amplitude (more than 30 degrees @ RF) longitudinal motion; Bursting at almost periodic intervals which change with beam current and energy; Time-domain plot of longitudinal position of one bunch; Spectrogram shows large tune shifts.

Bursting Longitudinal Motion Frequency (khz) 130 125 120 115 110 105 100 95 90 Spectrogram of bunch 109, 14 ma, 1.2 GeV 5 10 15 20 25 30 35 40 45 Time (ms) Large amplitude (more than 30 degrees @ RF) longitudinal motion; Bursting at almost periodic intervals which change with beam current and energy; Time-domain plot of longitudinal position of one bunch; Spectrogram shows large tune shifts.

Longitudinal Stabilization Ramping to 2.3 GeV allowed us to stabilize the motion; Used a stripline as a weak longitudinal kicker; Mode 252 dominates; Good growth and damping fits with no tune shifts.

Longitudinal Stabilization 0.06 0.05 feb0710/164202 Data, Fit and Error for Mode #252 Data Fit Error deg@rf 0.04 0.03 0.02 0.01 0 0 2 4 6 8 10 12 14 Time (ms) Ramping to 2.3 GeV allowed us to stabilize the motion; Used a stripline as a weak longitudinal kicker; Mode 252 dominates; Good growth and damping fits with no tune shifts.

Growth Rates Growth rate (ms 1 ) Oscillation frequency (khz) 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 86.5 85.5 84.5 Data Fit ELSA, feb0710, longitudinal: growth rates of mode 252 λ rad =0.6 ms 1 0 10 15 20 25 30 35 40 45 Beam current (ma) 86 85 84 10 15 20 25 30 35 40 45 Beam current (ma) Extract growth and damping rates from multiple transients; Fairly linear behavior versus beam current; Estimated radiation damping time of 1.66 ms; Added measurements below instability threshold (excite the motion, record open-loop decay); Most likely there are higher-order dynamics in play.

Growth Rates Extract growth and damping rates from multiple transients; Fairly linear behavior versus beam current; Estimated radiation damping time of 1.66 ms; Added measurements below instability threshold (excite the motion, record open-loop decay); Most likely there are higher-order dynamics in play.

Modeling Amplitude (arb. units) 1.5 1 0.5 0 0.5 1 Fs=85.2; gr=1.16; Fcl=85.0; dr=0.48 1.5 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Using measured growth and damping rates verify beam/feedback model; Simulated transient matches measurement at 26.7 ma; Extrapolate growth rate to 200 ma (10 ms 1 ), assume 200 W power amplifiers with 450 Ω kicker; Excellent damping performance.

Modeling Amplitude (arb. units) 0.15 0.1 0.05 0 0.05 0.1 0.15 Fs=85.2; gr=9.99; Fcl=83.2; dr=9.16 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (ms) Using measured growth and damping rates verify beam/feedback model; Simulated transient matches measurement at 26.7 ma; Extrapolate growth rate to 200 ma (10 ms 1 ), assume 200 W power amplifiers with 450 Ω kicker; Excellent damping performance.

LLRF Testing Results Used the prototype to monitor cavity signals when running with the existing analog LLRF; Switched to prototype LLRF system for driving the klystron; Several hours running with beam (open-loop); Open-loop cavity probe signal; Loop closed (5 ma @ 2.3 GeV).

Summary Successfully demonstrated bunch-by-bunch control in all three planes; Longitudinal stability has to come first, then transverse; Interesting longitudinal dynamics at large amplitudes; LLRF prototype performed well (and benefited from development with a real RF system).