Status of TBTS PETS power and deceleration studies

Status of TBTS PETS power and deceleration studies Erik Adli, December 8 , 2010 Useful discussion with I. Syratchev, A. Dubrovskiy, R. Corsini, R. Ruber and CTF 3 team gratefully acknowledged. 1

Goal of this work CTF 3 Two-beam Test Stand (only part relevant for this study is shown) * Establish consistency and correlation between TBTS power production and deceleration * Identify unknown parameters, important for TBTS operation * Challenge: do this in robust way, with a set of model parameters and measurements we have confidence in 2

(reminder) TBTS PETS: feedback Particularity of TBTS PETS: field feedback. Proposed to use a simple model for the feedback, described in [Ruber, Ziemann, CTF 3 NOTE 092] and [EA, CTF 3 NOTE 096]. Basically, we consider the field is fed back into the PETS with a roundtrip gain, g<1, and a phase with respect to the beam produced field, f : with Ebeam function of pulse current. Shown in [EA, CTF 3 NOTE 096] to give reasonable results for varying pulse currents. Applicability: * no break down - (but can be used to detect break down) No break down * perfect bunch phase Before klystron Possible break down phase optimization [EA, CTF 3 -NOTE-096] After klystron phase optimization 3

Main principle: energy conservation As basis for this analysis, we suggest an approach where we start by considering the energy loss of the whole pulse (robust approach). Later, we complement with studies of energy loss along single pulses. Part 1) Energy loss in system, EP : (integration goes over whole pulse) Part 2) Energy loss in beam (deceleration) : Now, we want to verify: Two comments: 1) Equality holds for all splitter ratios and feedback phases -> robust with respect to data taken. 2) Since the beam pumps energy into the feedback loop, the equality only holds in general for the integrated quantity (in feedback steady-state, on the other hand the 4 equality holds at any point in time).

Feedback loop power budget ~ -50 d. B on choke [IS] From I. Syratchev. 5

Overview of measurements 6

Measurements – ctf 3 set-up • 3 GHz beam (sub-harmonic buncher disabled) • Combination using combiner ring only (x 4) to 12 GHz • Beam phase optimized (small phase variation of beam entering TBTS) 7

Measurements – rf Example rf data: We have span both split and phase in the measurement sets (to be discussed). Large noise (+/- 15 MW p 2 p on raw rf data. Needed heavy smoothing. Chose Savitzy-Golay filter which preserves features better than LP. Results is 8 reasonable, still, some precision lost.

Measurements – incoming beam Variation along pulse and pulse to pulse: Example transmission: in general perfect through PETS, sometimes small losses up to spectrometer. Relatively stable beam. Relatively flat pulses. Jitter on incoming beam parameters is contained, but of 9 2). significance, and must be compensated for (see part

Parameters, knowns, unknowns 10

Knowns and unknowns Assumed low confidence: • rf calibrations/electronics (ccalib) for all channels • logged values of power split and phase shifter (Tp, f) • form factor estimates (F) Assumed high confidence: • BPM measurement • spectrometer bending angle Assumed some confidence: • Feedback loop losses measurements (ohmic, reflection) We will treat as unknown: ccalib, Tp, f, F Main principle: “trust as little as possible” 11

Estimation strategy for unknowns One way to identify the unknown parameters (not unique) : ccalib and F cannot be disentangled in power measurement: P ~ ccalib F^2 However deceleration measurement: U ~ F^2 1) Use U and P to estimate ccalib for PPI 041 by comparing energy lost from beam by energy lost in system 1 a) However, energy lost in system depends strongly on split Tp 2) Then, from measured current I we can estimate form-factor F 3) Then, from calib of PPI 041 and split we can find calib of PSI 0431 12

Steady-state phase scan approach for 1 a) We want an independent way to estimate the split T (as we discuss later, we have some p reason to doubt the available information on the split). We suggest the following idea : Developing the feedback model we get the steady-state expression : i [EA, CTF 3 -NOTE-096] ("i" missing in org. refs. ) i The width (i. e. FWHM) is uniquely given by feedback gain (and split), independent of scaling (therefore also calib errors). Performing a phase-scan for given splitter setting, and measuring power, we should in principle be able to deduce gain (and split). 13

Steady-state conditions Depending on the split and the feedback phase, a certain time (number of loops) are needed to approach steady-state. Example: model used on square pulse, g=0. 75, f=-18 deg [EA, CLIC-NOTE-096] Calculated time needed to reach 95% s. s. (max. 5% diff from one step to another). Reminder: we have ~ 200 ns flat top of the pulse -> with current measurements we approach steadystate only up to Tp ~ 50% 14

Verifying phase-scan method We want to use method on measured power to estimate an unknown split. To build confidence in this approach (including details in data processing; i. e. I find last part of pulse, take average, norm. to current, then I do a constrained 3 parameter non-linear fit etc. ), we first test the method as follows : 1) we use measured current pulses 2) we use logged feedback phase settings 3) we use feedback model to reconstruct the power with a given split 4) we use the phase-scan analysis framework to estimate the (known) split, Tp [See extra material for example points from curve] 15

Verifying phase-scan method Error in estimates for phase scan based on reconstructed power (dominant error is lack of steady state conditions) -> within few % correct up to Tp = 50% (consistent with estimation of pulse length needed) 16

Estimating Tp from measurement Now: we estimate Tp from measured power (PPI 0431). Due to data quality (lower precision for low power) and longer steady state time for low power, we do not consider the valley, and only use down to 1/3 max). Example scan shown is with a logged Tp ~ 0. 67 (converted from cond. software "Tran" = 0. 54) 17

Summary of preliminary TP estimates * Fit and cond. software values are ~0. 3 apart. If cond. values are close to real, fit is not inside valid s. s. range, however, we do not expect this much underestimation -> can remove this doubt with a longer pulse. 18

Adding TP estimates for measurement. . . * We also have measured PSI and PPI, we do not believe any calib, however, by scaling the relative calib we should be able to get something consistent -> real Tp somewhere in between? Work in progress. I still consider a large error on Tp (or, Tp + losses) 19

Deceleration measurements 20

Deceleration measurements For a beam entering the spectrometer bend with zero offset and angle: However, must compensate for • jitter on, and static, incoming position and angle • jitter on, and static, incoming energy and the fact that • We don't have a precise knowledge of the Dpc, giving the reference momentum p 1 (p 1 is the momentum of particles bended q). What we have done is simply adjust bend to optimize 21 transmission.

Compensation of incoming position and angle [RR, VZ, EA, CTF 3 -NOTE-098] * Suggest using minimal information to take out angle; last three BPMs. No quadrupoles between 0510 and 0550 gives confidence in (relative) angle estimate. * Transverse kick in PETS due to break down/wake fields? Also compensated for. * In addition, we have minimized currents in last triplet to (6 A, 0 A, 6 A) for this measurement, after some suspicion on optics (however, later we verified, quite convincingly, the sign to be ok). * Ideally, would be good to have last triplet completely OFF, in order not to worry about different optics as function of deceleration Contribution to spectrometer BPM due to incoming position and angle : (M calculated with TBTS madx model)

Compensation of incoming energy [RR, VZ, EA, CTF 3 -NOTE-098] CM. BPM 0270 H CM. BPM 0230 H CM. BPM 0110 H We use similar strategy (3 BPMs, separating contribution of angle and dispersion through last bend upstream the PETS), yielding an incoming energy estimate, dincoming. = Dpi/p 0. We could deduce rel. energy loss in PETS d. PETS from the total rel. energy in spectrometer, dtotal=Dp/p 1, as

Relative energy loss measurements Since we have access to data of scans with large difference in power and deceleration (i. e. the phase scans), we suggest to disregards uncertainties in static incoming beam parameters (offset, angle, energy) by looking only at relative energy loss from pulse to pulse. We still get the information we need. This approach has the substantial advantage that : • We don't need to trust, nor take into account, BPM and quadrupole (mis)alignment • We don't need to trust, nor take into account, corrector settings and calibrations • We don't need to identify an absolute zero of the spectrometer readings For each pulse for which we calculate energy loss, we compensate for only for the relative incoming angle/position between this pulse and a given reference pulse. Similarly, we compensate only for the relative incoming energy between this pulse and a reference pulse [in formulas, see extra slide] 24

Correlations 25

Correlation power loss and deceleration (philosopy was: identify Tp first, then use this to identify calib; there I treat Tp as model parameters with errors, and calib as unknown) Data is from a single phasescan (fixed Tp). Here, for illustration: Tp = Tpfit (relative) 26

Sensitivity to Tp Extreme Tp estimates for this series: Tp_fit = 0. 34, Tp cond = 0. 60 [error on points not shown] Calib. estimates (and therefore also form factor estimates) shows large sensitivity to Tp 27

Deceleration along pulses We have looked at integrated energy loss from power and from spectrometer measurements (we believe this is more robust for parameter identification). However, it is also for interest to compare measured deceleration along pulses to the expected from the measurements/theory. We deduce deceleration from power measurements and model as : Alas, gain/Tp also enters here (does not help for identification of this) Measured (shifted, but not scaled) and calculated deceleration, with power scaled as identified (reasonable agreement). Measured (shifted, but not scaled) and calculated deceleration, with power not scaled (not good agreement).

Deceleration along pulse: examples Assuming a given Tp, the measured and calculated deceleration along the pulses shows reasonable agreement for all levels of absolute power: Measured (shifted, but not scaled) and calculated deceleration. For the measured we only look at relative variations along the pulse, so, we shift to absolute power calculation. Relative incoming energy, angle, position compensated for. 29

Summary: where are we? • • • Using energy conservation we get good correlation (relative) beam energy loss and system energy loss We also get reasonable agreement of relative measured deceleration verus calculated deceleration along pulse The power calculations depend strongly on the splitter ratio Tp. We have for them moment a large error on Tp The large error on Tb translates to a large error in power calibration estimates, and therefore also form factor estimates We work with an independent method to estimate Tp – need more data, see next slides • In parallell: would be good if others looked at Tp • In short: if we can pin down Tp to +/- 5% we could get power calibs and deceleration estimated to +/- < 10% In addition: estimate form factor and calib for PSI 0431 with same precision • For me: Tp (or rather gain which is Tp * eta) is the "bad gay" to be set straight.

Measurement data needed to complete work • Phase-scans for uncombined beam – steady-state conditions reached (~1000 ns) – need to show small bunch phase in order to validate applicability theory [no switches] – phase-scans at various Tp levels – rectangular pulse important • high current not that important • Ideally, we continue with factor 4 and also factor 8 in same session to complement data set -> estimate one day of measurement (before end of run) 31

Extra 32

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Some non-linearity in either IQ power or diode power. Already noticed and mentioned in [EA, CLIC-NOTE-096], where diode shows linear relation with current^2, while IQ 35 not -> we use diode.

From I. Syratchev 36

yr From I. Syratchev. 37

Example pulses from phase-scan calcs for reconstructed power. 38

Example pulses from phase-scan calcs for measured power.

Example of Chi 2 fits, with g fixed 40

Use of split scan and ss theory? Cannot draw very quantitative conclusions from this, however, it supports that Tp in program is too high by a significant amount.

In formulas, what I do to calculate the relative energy loss in a pulse :

Correlation for all three series (phasescans) 43