Rahul Singh Betatron Tune Measurements 1 Beam Physics for FAIR Workshop May, 2012 Odenwald, Germany R. Singh 1,2, O. Chorniy 1, P. Forck 1, P. Kowina 1, W. Kaufmann 1, K. Lang 1, T. Weiland 2 1 GSI SD, Darmstadt, Germany 2 TEMF, TU Darmstadt, Germany

Rahul Singh Betatron Tune Measurements 2 Outline Introduction Methods Tune, Orbit and Position Measurement System (TOPOS) Base Band Tune Measurement System (BBQ) Results April 2011 April 2012 Opportunities and Conclusion

Rahul Singh Betatron Tune Measurements 3 Outline Introduction Methods Tune, Orbit and Position Measurement System (TOPOS) Base Band Tune Measurement System (BBQ) Results Opportunities and Conclusion

Rahul Singh Betatron Tune Measurements 4 Goal of Work Continuous tune monitoring throughout the acceleration cycle Measurement as “non-destructive” as possible, measure the destructiveness Explain the spectra under normal operations, distinguish between beam physics and technical imperfections

Rahul Singh Betatron Tune Measurements 5 What is betatron tune? The number of spatial oscillations, the particle traverses during one turn around the synchrotron Tune primarily depends on the optics of the synchrotron

Rahul Singh Betatron Tune Measurements 6 How is tune measurement done? Incoherent motion, BPM measures centre of mass Excite the beam

Rahul Singh Betatron Tune Measurements 7 GSI SIS-18 Synchrotron Important parameters of SIS-18 Circumference216 m Inj. typeMultiturn Energy range11 MeV → 2 GeV Acc. RF0.8 → 5 MHz Harmonic number4 (no. of bunches) Bunching factor0.4 → 0.08 Ramp duration0.06 → 1.5 s Ion range (Z)1 → 92 (p to U) Beam Diagnostic Devices 1)BPMs 2)Schottky Pick-up 3)DC Current transformers 4)Fast transformers 5)Beam profile monitors 6)SEM Grid 7)Scintillation Screens 8)Beam Loss Monitors

Rahul Singh Betatron Tune Measurements 8 Outline Introduction Methods Tune, Orbit and Position Measurement System (TOPOS) Base Band Tune Measurement System (BBQ) Results Opportunities and Conclusion

Rahul Singh Betatron Tune Measurements 9 Tune Measurement System Details ADC Beam Position Pre-Amp DSP in FPGA Noise Generator Concentrator Servers FFT, Averaging 25W 50dB 180˚ 0˚ RF Clock Stripline Exciter Linear cut BPM Tune Orbit GUI Bunched beam E

Rahul Singh Betatron Tune Measurements 10 Beam Exciter (RF Noise) Pseudo Random noise generator Tunable noise frequency and its bandwidth Strip line exciters with maximum power of 50W Frequency Time Output of tunable noise generator over the ramp, frequency increasing with time 0.2 s

Rahul Singh Betatron Tune Measurements 11 Position Calculation Algorithms Bunch Detection Position Calculation FPGA Time Windows Baseline Restoration Linear Regression (OLS)

Rahul Singh Betatron Tune Measurements 12 Bunch Detection 1) A minimum is found between two adjacent bunches. 2) Using the minimum level Smin, two thresholds are calculated at 1/2 Smin and -5/8 Smin 3) When the bunch signal passes through all these thresholds, it is detected. 4) Time window for the bunch is calculated which is passed to position calculation part of the algorithm S min -5/8S min 1/2S min

Rahul Singh Betatron Tune Measurements 13 Baseline Restoration Algorithm

Rahul Singh Betatron Tune Measurements 14 GUI (TOPOS) Online positon and tune measurement during the whole acceleration cycle Tune versus time horizontal vertical Working Diagram Tune at fixed time vertical horizontal vertical Maximum Position Variation  Q y  0.02  Q x  mm 5 mm

Rahul Singh Betatron Tune Measurements 15 Outline Introduction Methods Tune, Orbit and Position Measurement System (TOPOS) Base Band Tune Measurement System (BBQ) Designed by Marek Gasior et al (BE/BI/QP), CERN Results Opportunities and Conclusion

Rahul Singh Betatron Tune Measurements 16 BBQ System Details LB Amplifiers & Filters Peak Detectors Tune Noise Generator Real time Spectrum Analyzer 25W 50dB 180˚ 0˚ RF Clock Stripline Exciter Linear cut BPM Bunched beam

Rahul Singh Betatron Tune Measurements 17 BBQ Details Time constant (R*C 2 ) has to be optimized to be > 10*T rev to suppress revolution frequency C 1 / C 2 determines the transfer impedance

Rahul Singh Betatron Tune Measurements 18 BBQ Details Bandwidth 10 KHz to 1 MHz 50 dB common mode rejection (CMRR) Variable gain upto 65 dB

Rahul Singh Betatron Tune Measurements 19 System Comparison TOPOS BBQ Position, orbit, tune, Longitudinal profile etc., Versatile system Dedicated tune measurement Low sensitivity: It can detect ~ 0.1mm oscillations with 6dB Signal to Noise Ratio (SNR) Higher sensitivity: It can detect ~0.01 mm oscillations with 6dB SNR Fast ADCs required to resolve high frequencies in bunch structure Reduces the data directly in detectors, slower high res. ADCs could be used Bunched beams Also with coasting beams

Rahul Singh Betatron Tune Measurements 20 System Comparison TOPOS BBQ Position, orbit, tune, Longitudinal profile etc., Versatile system Dedicated tune measurement Low sensitivity: It can detect ~ 0.1mm oscillations with 6dB Signal to Noise Ratio (SNR) Higher sensitivity: It can detect ~0.01 mm oscillations with 6dB SNR Fast ADCs required to resolve high frequencies in bunch structure Reduces the data directly in detectors, slower high res. ADCs could be used Bunched beams Also with coasting beams Both are required at the moment, they have mutually exclusive applications!!!

Rahul Singh Betatron Tune Measurements 21 BBQ vs TOPOS BBQ : SNR~55dBTOPOS : SNR~40dB Horizontal tune spectra with 300 mV chirp excitation at 2e9 U 73+ Different BPM sensitivities and ADC types

Rahul Singh Betatron Tune Measurements 22 Frequency Spectra BBQ vs TOPOS BBQTOPOS Same form but differences in relative amplitudes Coupling Second Peak

Rahul Singh Betatron Tune Measurements 23 Outline Introduction Methods Tune, Orbit and Position Measurement System (TOPOS) Base Band Tune Measurement System (BBQ) Results/Applications Opportunities and Conclusion

Rahul Singh Betatron Tune Measurements 24 Applications Online tune measurements on acceleration ramp to observe the tune while changing optics Change in tune spectra with beam intensity Machine set-up in case of control system errors

Rahul Singh Betatron Tune Measurements 25 Tune Measurement on Ramp Tune measurement on Ramp Tune movement due to change in optics from triplet to doublet focussing Tune versus time horizontal vertical Working Diagram Tune at fixed time vertical horizontal vertical Maximum Position Variation  Q y  0.02  Q x  mm 5 mm 0.7 s

Rahul Singh Betatron Tune Measurements 26 Experimental Details Time Energy (MeV/u) Injection Plateau Tune Measurements at various intensities with different excitation types and power Comparison of the two tune measurement systems Continuous current and beam transverse profile measurements RampExtraction Flat-top

Rahul Singh Betatron Tune Measurements 27 April 2011 Beam Conditions : Intensity variation 2e9 to 2.5e10 injected Ar 18+ particles Excitation power 0.01mW/Hz to 1mW/Hz Beam losses without excitation at high intensities Goals : Compare the width of horizontal and vertical tune spectra Compare influence of excitation type white noise vs RF noise excitation Test and compare the raw data mode in TOPOS

Rahul Singh Betatron Tune Measurements 28 Coherent Tune Shift Horizontal coherent tune-shift (Expected) Vertical coherent tune-shift (Expected) Horizontal coherent tune-shift (Expected)~-0.001~ Vertical coherent tune-shift (Measured)~-0.01~-0.02 Where: z is charge state r 0 is atomic radius I is the peak current R is radius of the ring A is the atomic mass β is relativistic beta γ is relativistic gamma is averaged beta function h is the height of the boundary How to find this? Taken as 50mm(V) and 150 mm(H)

Rahul Singh Betatron Tune Measurements 29 Horizontal Plane: Tune Spectra Coherent tune shift in dependence of current visible. Ar MeV/u 600 ms The third spectra is noisy due to improper gain settings Set Tune = 0.17

Rahul Singh Betatron Tune Measurements 30 Vertical Plane: Tune Spectra Coherent tune shift in dependence of current visible. The various peaks in the spectrum are attributed to intra-bunch motion, not well understood. Form of spectra relatively independent of intensity. ~0.02 ~0.01 Set Tune = 0.29 ~0.003 Ar MeV/u 600 ms

Rahul Singh Betatron Tune Measurements 31 Tune Peaks 2e10 Ar 18+, 1mW/Hz excitation Baseband spectra changing with time Clear instances of various (higher order) modes getting excited and damped 1-13 turns turns Same Bunch, same cycle, 100 turns later

Rahul Singh Betatron Tune Measurements 32 Intra Bunch Movement Sum Difference DSP

Rahul Singh Betatron Tune Measurements 33 Intra Bunch Motion at High Intensity Bunch Length (μs) No. of stored Ar 18+ Ions ~ Energy = 11.4 MeV/u F rev = KHz Excitation ~ 1mW/Hz Intra bunch oscillations i.e Head tail modes

Rahul Singh Betatron Tune Measurements 34 Dependence on Excitation

Rahul Singh Betatron Tune Measurements 35 April 2012 Beam Conditions : U 73+, 1e8 to 2e9 injected particles Measurements only on injection flat-top Goals : Sweep through the spectra to have phase information, and test one more excitation type Compare the TOPOS vs BBQ spectra Coupling between the two planes

Rahul Singh Betatron Tune Measurements 36 Frequency Sweep vs. Band Limited Noise Width of tune spectra in vertical plane is bigger than horizontal plane Coupling between vertical and Horizontal planes Tune visible without external excitation Horizontal Tune Vertical Tune Coupling RF Noise/BL Noise Frequency Sweep

Rahul Singh Betatron Tune Measurements 37 Frequency Sweep in Vertical Plane Excitation power only changes signal to noise ratio Coupling between vertical and Horizontal planes 300 mV Excitation30 mV Excitation

Rahul Singh Betatron Tune Measurements 38 Frequency Sweep in Horizontal Plane Width of tune spectra in vertical plane is larger than horizontal plane Coupling between vertical and horizontal planes 300 mV Excitation30 mV Excitation

Rahul Singh Betatron Tune Measurements 39 Width of Spectra, Vertical vs Horizontal Linear Scale : The Vertical tune spectrum has a certain form!

Rahul Singh Betatron Tune Measurements 40 Width of Spectra, Horizontal vs Vertical

Rahul Singh Betatron Tune Measurements 41 Width of Spectra, Horizontal vs Vertical The Vertical tune spectrum has a certain form! Relatively independent of beam intensity V Tune Sidebands H Tune Sidebands RF Noise Averaged Over 5000 turns

Rahul Singh Betatron Tune Measurements 42 Opportunities What do these higher order modes signify? What can we deduce from the width of tune spectrum? More questions to ask for systematic understanding of TOPOS data? Technical improvements for beam physics users?

Rahul Singh Betatron Tune Measurements 43 Conclusions Two parallel working and comparable tune measurement systems TOPOS offers possibilities for detailed beam investigations More work to be done to de-couple physics and technical imperfections

Rahul Singh Betatron Tune Measurements 44 Acknowledgement European ITN- DITANET for funding the work and associated people for providing this opportunity CERN BI group especially M. Gasior for help on BBQ system Highly Supportive Beam Diagnostics Group at GSI Thanks for attention! Questions?

Rahul Singh Betatron Tune Measurements 45 High Intensity Effects Δ BPM Signal Δ Signal Σ Signal

Rahul Singh Betatron Tune Measurements 46 Width of Spectra, Horizontal vs Vertical (Noise) F rev V Tune Sidebands 2e9 Ar 18+ 1e8 Ar 18+ Dependent of intensity not significant

Rahul Singh Betatron Tune Measurements 47 Width of Spectra, Horizontal vs Vertical

Rahul Singh Betatron Tune Measurements 48 BBQ Results Particle numbers (U39+) ~ 7e8 40 V ~ 1mW/Hz Time Frequency TOPOS BBQ Tune Sidebands Suppressed Revolution Frequency

Rahul Singh Betatron Tune Measurements 49 What is tune? Tune spread due to momentum spread! Chromaticity

Rahul Singh Betatron Tune Measurements 50 Why measurement of tune?

Rahul Singh Betatron Tune Measurements 51 Why measurement of tune? Not to lose particles or lose particles at will(slow extraction) Correct unwanted tune movements, i.e control it Precise control of the tune is crucial for high current operations especially for the storage of low energy ion beams (Tune shifts depending on intensity)

Rahul Singh Betatron Tune Measurements 52 Tune Orbit and Position measurement system (TOPOS) Tunable Pseudo Random Noise Generator Stripline Line Exciter (50W Max.) Shoe-Box BPM with high impedance termination Fast ADCs with 125 MSa/s to digitize the BPM signals Real time evaluation of BPM signals to calculate position of the bunches* Position data transfer to the concentration servers for each BPM FFT of the beam position to acquire tune Display of tune and closed orbit in the control room *Possibility to acquire raw bunch signals from all BPM plates simultaneously.

Rahul Singh Betatron Tune Measurements 53 Shoe-Box BPMs Linear spatial sensitivity High pass with high input impedance of amplifier

Rahul Singh Betatron Tune Measurements 54 Algorithm for position calculation Present algorithm : Does the following steps on both upper and lower BPM plate  Identifying bunches using double threshold algorithm.  Finds appropriate windows  Shifts the baseline inside the windows  Integrates the values inside the windows Calculates the position using (X+) - (X-)/ (X+) + (X-)

Rahul Singh Betatron Tune Measurements 55 Common beam parameters Parameter nameTypical ValueUnits Atomic Mass40 Charge State18 Energy per nucleon1.14E+01MeV/u rms x size (radius)1.50E-02m rms y size (radius)1.00E-02m rms z size (bunch length)5.00E-07s Accelerator radius3.44E+01m Horizontal tune4.16E+00 Vertical tune3.29E+00 RF Harmonics4.00E+00 RF Voltage6.00E+03V Particles in one bunch5.00E+09 Natural Chromaticity-1.30E+00 Radius of vacuum pipe (x,y)0.1, 0.035m

Rahul Singh Betatron Tune Measurements 56 Beam Parameters 2 Magnetic Rigidity1.08E+00T-m Betatron beta x8.27E+00m Betatron beta y1.05E+01m Relativistic gamma1.01E+00 Revolution time4.60E-06s Relativistic beta1.54E-01 Slip Factor9.36E-01 Average current in the ring1.25E-02A Peak current in a bunch3.73E-02A Total particles in the ring2.00E+10 Total charge in the ring5.76E-08C Synchrotron tune7.54E-03 Bunching factor3.5E-01 Horizontal emittance EH(2s)7.2E+01mm-mrad Vertical emittance EV(2s)1.38E+01mm-mrad Rms momentum spread1.5E-03

Rahul Singh Betatron Tune Measurements 57 High Current Tune Spectrogram Number of stored Ions ~ 2e10 Spectra changing with time!

Rahul Singh Betatron Tune Measurements 58 Intra bunch motion – Acceleration Beam parameter: Ar 18+ acc. 11  300 MeV/u within 0.7 s Number of stored Ions  2E10 Excitation  1mW/Hz Bunch Length (μs) Δ BPM Signal

Rahul Singh Betatron Tune Measurements 59 Tune Spectra during acceleration Time (ms) Tune FFT Amplitude (a.u.)

Rahul Singh Betatron Tune Measurements 60 Effect of excitation on tune spectra

Rahul Singh Betatron Tune Measurements 61 Linear Regression Linear regression with ordinary least square estimator Better variance and bias properties

Rahul Singh Betatron Tune Measurements 62 Bunch Motion RF Noise

Rahul Singh Betatron Tune Measurements 63 Bunch Motion White Noise