The ESS LLRF Control System. Rihua Zeng, SLHiPP-2,Catania RF Group, Accelerator Division, ESS

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1 The ESS LLRF Control System Rihua Zeng, SLHiPP-2,Catania RF Group, Accelerator Division, ESS

2 Outline Outline LLRF Introduction and Requirements Issues in LLRF Control Control Methods Consideration Summary May 4, 211 2

3 Cavity Field Stability Requirement Control and maintain the specified phase and amplitude stability of accelerating field in RF cavity during beam traveling Also maintain the filling stage of the RF pulse Vcav/ MV Without Beam T fill The stability requirement is from the beam dynamic: V acc, n = V c V tot = N! n=1 # E E = V 2 tot ( 1+! V )cos(! b +"! ) V acc, n " V tot 2 V tot 2 In the case of fixed sync. phase:! # "! # "! # "! E E! E E! E E $ & % $ & % $ & % corr. uncorr. 2 ' 1 cos(" b ) '! =! $ E # & " E % 1 N 2 corr. 1 ( 2 1+ cos ( 2" b) )! 2 V + 1 ( 2 1( cos ( 2" b) )! 2 " cos 2" 2 ( ( b) (1)! " 1 cos(" b ) 2! +! $ E # & " E % 1 ( 2 1+ cos ( 2" b) )! 2 V + 1 ( 2 1( cos ( 2" b) )! 2 " cos 2" 2 ( ( b) (1)! " uncorr. Further reading: A. Mosnier ; J. M. Tessier, Field StabilizaKon for Tesla. Tesla reports KraQ, G ; Merminga, L, Energy Spread from RF Amplitude and Phase Errors, EPAC 96. May 4, 211 3

4 Stability Requirements in different accelerators The stability requirement varies in different accelerators, determined by specific application. XFEL ILC SNS JPARC Amp./Phase Stability.1%,.1 (rms).1%,.1 (rms) ±.5%, ±.5 ±1%, ±1 The stability is specified in peak to peak rather than in rms in proton machine due to beam velocity is dependent on energy gain. In some case, the requirement on phase stability differs by time scale, short term( during the pulse), medium term (pulse to pulse), long term (minutes to hours). At XFEL, the requirement is:.1 (short term),.3 (medium term),.1-.5 (Long term). The stability at ESS? May 4, 211 4

5 Requirments at ESS Source MHz 74.42MHz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! LEBT RFQ MEBT DTL Spokes Low! High! HEBT Target 75keV 3MeV 5MeV 18MeV 66MeV 25MeV RF Source Cavity phase and amplitude stability, frequency control Minimize the required overhead power for control Automated operakon, remote control Availability, maintenance, upgradability High intensity, 5mA Long pulse, 2.9ms High gradient Spoke cavity High Efficiency High availability; 95% Support Linac commissioning

6 The ideal cases Consider an ideal beam current inject into an ideal superconducting cavity at ideal time Ideal beam current: no synchronous phase, continuous current during pulse Ideal superconducting cavity: optimized Q L for beam current, no reflection power at beam duration Ideal injection time V ref, I ref V for, I for V cav = V ref +V for = V g +V b V cav V g, generator current I g induced voltage; V g, beam current I b induced voltage; I b = 2I b, I b is average DC current QL opkmizing: At steady state : P g = P c + P b + P r, (P r = )! = P g P c =1+ P b P c! P b P c, (P b >> P c, for superconducting cavity) Q L = Q 1+!! Q P 2 c V = cav P b P b (R / Q) P b = V cav I b for beam induced voltage, V b = 1 2 (R / Q)Q L " 2I b = I b (R / Q)Q L # V b = V cav Ideal injeckon Kme: Steady state for V g, (don't consider beam) :! = V ref V for =! "1! +1, V g = V ref +V for = 2!! +1 V for At filling stage : (const. V for input) V g (t) = V ref (t)+v for V ref (t) = V g (1" e "t/" )"V for V ref (t) = # t inj = " ln( 2!! "1 ) for superconducting cavity,! >>1, t inj $ " ln2 = 2Q L # ln2 V cav = V g (t inj ) = 1+! 2! V g = V for $.5V g Further reading: D. McGinnis, A Simple Model for a SuperconducKng RF cavity with a Vector Phase Modulator, 27. T. Schilcher, Vector Sum Control of Pulsed AcceleraKng Fields in Lorentz Force Detuned SuperconducKng CaviKes. Ph. D. Thesis of DESY, 1998 May 4, 211 6

7 The ideal cases Vcav/MV Pg/MW Without Beam x Vcav/ MV Pfor/ MW t inj With Beam Generator Induced Voltage Vg Vcav=Vg+Vb Beam Induced Voltage Vb Vcav/ MV Pfor/ MW Without Beam Vref t / s x 1 3 WithoutBeam x Pref t / s x 1 3 Vref/ MV Pref/ Mw t/ s x 1 3 WithBeam t / s x 1 3 Vref/ MV Pref/ MW t inj t/ s x 1 3 WithoutBeam t / s x 1 3 May 4, 211 7

8 PerturbaKons in real world Beam Loading Synchronous phase Beam chopping Pulse beam transient Charge fluctuations Non-relativistic beam Pass band modes HOMs, wake-field Phase reference distribukon Reference thermal drift Master oscillator phase noise Cavity Lorentz force detuning Microphonics Thermal effects (Quench ) Power Supply Modulator drop and ripple Klystron nonlinearity Electronics crates Crates power supply noise Cross talk, thermal drift Clock jitter, nonlinearity Further reading: LLRF Experience at TTF and Development for XFEL and ILC, S. Simrock, DESY, ILC WS 25 May 4, 211 8

9 Lorentz Force Detuning The radiation pressure on cavity walls cavity shape changes by a volume ΔV cavity resonance frequency is shifted Lorentz force detune is repetitive from pulse to pulse Lorentz force detuning coefficient K typically a few Hz/(MV/m) 2 Radiation pressure : P s = 1 ( 4 µ H!"! 2!! E!" 2 ) Cavity perturbation theory: " E!" 2!"! 2 # (! µ H ) dv!!! "V =!! E!" 2!"! 2 #! µ H dv V ( ) TM 1 induced static detuning: 2 "f =!K $ E acc Number of cavity 12 1 MB, avg = 2.1 HB, avg = LFD Coef. (Hz/(MV/m) 2 ) Further reading: T. Schilcher. Vector Sum Control of Pulsed AcceleraKng Fields in Lorentz Force Detuned SuperconducKng CaviKes. Ph. D. Thesis of DESY, 1998 May 4, 211 9

$Lorentz Force Detuning Dynamic effects of cavity detuning Observed detuning agrees with expectations in a g fraction of cavities.$ cavities respectively. eigenmodes Some of vibration.

cavities respectively. eigenmodes Some of vibration.

rates as show Fig. 7, implying dynamic resonance condition. 2nd-order differential equation of dynamic detuning,!!! n + 2!! n + " 2 n!

! n& = #2#% K n $ E acc n n n Dynamic Detuning (Hz) 1 8 6 4 2 6Hz 3Hz 15Hz filling flattop -2 5 1 15 Time (us) May 4, 211 Figure 7.

10 Lorentz Force Detuning Dynamic effects of cavity detuning Observed detuning agrees with expectations in a g fraction of cavities. The detuning coefficients are a 3~4 Hz/(MV/m) 2 and 1-2 Hz/(MV/m) 2 in medium Any cavity has an infinite number high beta of mechanical cavities respectively. eigenmodes Some of vibration. cavities show hi A 2 nd -order differential equation detuning can be coefficients used to describe at higher the repetition dynamics. rates as show Fig. 7, implying dynamic resonance condition. 2nd-order differential equation of dynamic detuning,!!! n + 2!! n + " 2 n!! n = #2#K n " 2 n $ E 2 acc (t)+ n(t) " m,n!!(t) = %!! n (t), K = % K n n In steady state: 2!! & = %!! n& = #2#% K n $ E acc n n n Dynamic Detuning (Hz) Hz 3Hz 15Hz filling flattop Time (us) May 4, 211 Figure 7. Lorentz force detuning at various repetition r observed in some of the SNS high beta cavities. In S. Kim, I. E. Campisi, F. Casagrande et al, Status of the SNS Cryomodule Test, PAC7. M.Doleans, Studies of EllipKcal SuperconducKng CaviKes at Reduced Beta, PhD thesis, example the accelerating gradient is 12.7 MV/m.

11 Overhead calculakon for LFD in ellipkcal cavity It makes calculation easier to discuss detuning according to the rate Δf/f 1/2 Below f 1/2, ( K~1.5 for high beta, K~2 for med beta), most cavity overhead is <7%. 25% or more are required for detuning > 2 f 1/2 (K~3 for high beta, K~4 for med beta) Appropriate pre-detuning for both sync. phase and LFD is assumed May 4,

12 Overhead for LFD in Spoke cavity 18.% 16.% 14.% 12.% 1.% 8.% 6.% 4.% 2.%.% LFD=1*Cavity half bandwidth LFD=.5*Cavity half bandwidth R. Zeng, Power Overhead CalculaKon for Lorentz Force Detuning, ESS- tech notes, 212 May 4,

Klystron droop and ripple Perturbations in the cathode voltage results in the change = ( + of the ) ( beam + ) velocities, and then led to the variations of

variation = in RF output phase = High frequency ripple with larger amplitude is hard to be eliminated by feedback, especially in normal conducting cavity =

variation JPARC[1] 312 3.4% 25 8%(power) SNS [2,3] 85 3% 5(max) 8%(power) PEPII[4] 476 14 /kv SACLAY[5] 74.4 2V@95kV 1 /kv@92kv t = L! = L, " = #t ev m d" =!

13 Klystron droop and ripple Perturbations in the cathode voltage results in the change = ( + of the ) ( beam + ) velocities, and then led to the variations of the RF output phase 1% error in cathode voltage leads to more = than 1 deg. variation = in RF output phase = High frequency ripple with larger amplitude is hard to be eliminated by feedback, especially in normal conducting cavity = Table 1: Measurement for the phase and amplitude variations in other labs RF freqency Cathode Phase variation Amplitude /MHz voltage change /deg. variation JPARC[1] % 25 8%(power) SNS [2,3] 85 3% 5(max) 8%(power) PEPII[4] /kv SACLAY[5] V@95kV 1 /kv@92kv t = L! = L, " = #t ev m d" =! #L " dv 2eV V m relativistic case: d" =! e#lv mc 3 $ 3 % 3 " dv V P out!v 5/2 1/2 V out! P out V out!v 5/4 dv out! 5 dv V out 4 V Further reading: R. Zeng et, al. The Droop and Ripple s Influence on Klystron Output, ESS tech- note. SNS ( ) JPARC May 4,

14 Droop and ripple control by feedback The errors can be suppressed in feedback loop a factor of loop gain G. The loop gain is limited by loop delay and also by pass-band mode Integral gain of Ki=2πf HBW is intorduced to eliminate the steady errors and reduce low frequency noises Assuming that 15 degree phase error is induced by per 1% error from modulator, to control the error to.5, we should restrict the droop and ripple number from modulators: Magnitude (db) System: T Frequency (Hz): 16 Magnitude (db): 4 Bode Diagram System: T Frequency (Hz): 428 Magnitude (db): 3 System: T Frequency (Hz): 1.48e+4 Magnitude (db): 3 System: T Frequency (Hz): 5.81e+4 Magnitude (db): Frequency (Hz) May 4,

15 Synchronous phase The purpose of beam off-crest acceleration by a sync. phase is to minimize the energy spread resulted from wake fields. By pre-detuning the cavity with motor tuner, the effect of the sync. phase acceleration is compensated. It can be also compensated by extra power overhead, which was the case in LEP at CERN to avoid ponderomotive oscillation (CW, 8 cavity/klystron) in cavity RLC circuit, in steady state, dv cav =, dt R V cav = L! I total, R # 1 1" ir L % $!L "!C & L = 1 2 ( R Q)Q L ( ' # 1 tan! D = R L % $ "L ""C & #" ( = Q L ' " " " & *" % ( ) 2Q L $ " ' ", I total = I g " I b = ( I gr " ii gi ) + ( I br " ii bi ) + ( I gr " I br ) + i( I gi " I bi ) = V cav, I gr = V cav. R + L -. I gi = " V cav /. R L R L + I br = V cav + I b cos! b R L ( 1" itan! D ) tan! D + I bi = " V cav R L tan! D " I b sin! b (note defination! b ) 2V To minimize RF power, have Q L = cav and I gi =, ( R Q)I b cos! b + tan! D = " I b sin! b I b cos! b = "tan! b Further reading: ElectroacousKc instabilikes in the LEP- 2 superconduckng cavikes, D. Boussard, et, al. 7 th RF superconduckng workshop, 1995 May 4,

Beam loading One bunch of the beam travelled through an RF cavity will experience the RF voltage, the induced field from previous bunches, and half of the selfinduced field (Fundamental Theory of

16 Beam loading One bunch of the beam travelled through an RF cavity will experience the RF voltage, the induced field from previous bunches, and half of the selfinduced field (Fundamental Theory of Beam Loading) Beam loading effects is not so significant, but get worst when there are charge fluctuation and beam chopping I DC = q T b = q! 2"!C!! C = Q L R L = V b = q C = 1 2 ( ) 4! R Q 2 R Q ( ), q =! ( R Q)" I DC assume no det une and other perturbation, V b " ( t) =! 1 2 V be!(t!nt b )! +V b e!(t!(n!1)t b )! +V b e!(t!(n!2)t b )! +!+V b e!(t!t b ) % $! +V b e!t! ' # & V cav (t) = V g (t)+v b (t) = V g( ( 1! e!t! ) +V b (t),! = 2Q L " Further reading: InteracKon between RF- System, RF- Cavity and Beam, Thomas Weis, 25 May 4,

17 An beam chopping example in JPARC Further reading: T. Kobayashi, M. Ikegami, BEAM TEST OF CHOPPED BEAM LOADING COMPENSATION FOR THE J- PARC LINAC 4- MEV UPGRADE, Linac 1. May 4,

18 Non- relakviskc beam, HOMs, Passband mode Non-relativistic beam HOMs and pass band modes are excited in the cavity during beam loading. The pass band mode closest to the fundamental mode is to be concerned. It is one of the reasons causes instabilities and limit the loop gain This mode can be excited by the chopped beam pulses and the switching edges of the rf pulses. Phys. Rev. ST Accel. Beams 9, 32 HENGJIE MA et al. Normalized magnitude spectrum 1 A special filter can be applied to suppress this mode in digital domain RF off Further reading: Hengjie Ma et al., Low- level rf control of SpallaKon Neutron Source: System and characterizakon, Physical Review Special Topics - Accelerators and Beams 9, no. 3, 26 FIG. 13. (Color) 5=6" mode excited by the switching of rf power. The measurement was made on cavity SCL-13a runni Time (µs) Feedback on.5 Frequency (MHz) RF on loop control. May 4, 211 R. Zeng, SLHiPP- 2, ofcatania running the cavities in a simplistic feedback control only mode all the time without the assistance of a feed forward drive for cavity filling. At the beginning of each rf pulse, 18 The operation of the SC cavities does requ dure of an initial cavity filling so that the follow loop control during the flat top will be able to

Microphonics Caused by the mechanical vibrations in the accelerator environment, such as vacuum pumps, helium pressure fluctuations, traffic, ground motion, ocean waves It is a slow perturbation, not

19 Microphonics Caused by the mechanical vibrations in the accelerator environment, such as vacuum pumps, helium pressure fluctuations, traffic, ground motion, ocean waves It is a slow perturbation, not predictable, and usually of the order of several Hz to several 1Hz Avoid the domain frequencies in the microphonics spectrum close to the cavity mechanical modes 1.E+1 RMS Amplitude (Hz rms) 1.E+ 1.E-1 1.E-2 1.E Frequency (Hz) Figure 3: Typical background microphonics spectrum Further reading: S. Simrock, M. Grecki, 5th LC School, Switzerland, 21, LLRF & HPRF. J.R. Delayen, G. Davis, Microphonics and Lorentz Transfer FuncKon Measurements on the SNS Cryomodules, 23. May 4,

20 Thermal drir and crates noise Thermal drift in phase reference line and down converter, master oscillator and crate noise are out of the feed back control loop. Special cautions should be taken: Temperature-stabilized phase reference line; Low phase noise master oscillator; Down convert board temperature and channels cross talk control; Crate power noise; ADC non-linearization (non-iq sampling); Drift calibration in digital control; May 4, 211 2

21 Feedback The errors could be suppressed in feedback loop a factor of loop gain G. The loop gain is limited by loop delay and also by pass-band mode Large loop gain will result in more overshoot. Average loop gain at SNS is about 5 for superconducting cavity, less than 1 for normal cavity ( ) = + ( ) H o (f) ( = ) GH = cav e jτf, G H o (f) =, = f f hbw ϕ = H o (f) = arctan f τf. f hbw The instability is happening when: H( o ) (f) = 1, ϕ = 18 + n 36, n = ±1, ±2,... May 4,

22 Integral- proporkonal controller Integral gain of Ki=2πf HBW is then introduced to eliminate the steady errors and reduce low frequency noises The PI feedback loop can suppresses effectively low frequency noise but the performance degrades as frequency increases, while the far higher frequency noise is filtered by cavity itself Ki H o(f) = K p 1 + Hcav (f) e j2πτf j2πf Bode Diagram = K p j2πf + Ki j2πf H o(f) = K p 1 + K i 2πf 2 f hbw e jπτf, jf + f hbw 2 f 1 +, f hbw ϕ = H o(f) = arctan 2πf arctan f π K i f hbw 2 2πτf. Bode Diagram Magnitude (db) System: T Frequency (Hz): 32 Magnitude (db): 4 System: T Frequency (Hz): 6.83e+4 Magnitude (db): 4 Magnitude (db) > ( ) Ki<2pi*fhbw Ki= Ki=.1K Ki=.1K Ki=.1K Ki=K Ki=1K Ki=1K Ki=1K 8 Phase (deg) 9 Ki=2pi*fhbw Frequency (Hz) Ki<2pi*fhbw Frequency (Hz) Figure 13: Noise suppression performance of PI feedback closed loop as a function of frequency for superconducting cavity(k p = 5,K i = 2π 518) Figure 11: Phase margin reduced in open loop under different integral gains (without delay, K = 2πf hbw ) Bode Diagram Further reading: R. Zeng et, al. The Droop and Ripple s Influence on Klystron Output, ESS tech- note. 1 May 4, System: T Frequency (Hz): 7.53e+3 Magnitude (db): 2 System: T Frequency (Hz): 1.53e+5 Magnitude (db): 2 System: T Frequency (Hz): 2.85e Bode Diagram Ki= Ki=.1K Ki=.1K Ki=.1K 22

23 Feedforward Feed forward is to deal with the repetitive errors from pulse to pulse. In simplicity, It adds the errors learned to every pulse by feed forward table " $ # $ % $ I gr = V cav R L I gi =! V cav R L + I br = V cav R L + I b cos! b tan! D + I bi =! V cav R L tan! D! I b sin! b note here we take V cav as the reference V cav = V cav + i & Amplitude / MV Cavity Field by Feedforward (only predetuning for Sync. Phase) K = 1 Hz/MV 2 tao m = 1 ms Predetuning = Hz Sync. phase = 14deg Phase Power / rad. MW Forward, Reflect Power P for P ref Time / s x Time / s x 1 3 May 4,

24 Feedforward The oscillation is happening when feedback is applied during beam loading due to loop delay and high loop gain. Feedforward compensation DESY SNS May 4,

AdapKve Feed forward The RepeKKve perturbakons and the system performance may vary slowly with the Kme(thermal drir, microphonics, cathode voltage

25 AdapKve Feed forward The RepeKKve perturbakons and the system performance may vary slowly with the Kme(thermal drir, microphonics, cathode voltage variakons, component aging). AdapKve algorithm is crucial here in order to compensate the possible changes of the environmental and operakng condikons May 4,

26 AdapKve feedforward at DESY TTF measure the step responses conknually to maintain a current system model. The step size should be select carefully It is direct, straighuorward, but need large computakon capacity, measurement response not fast LLRF Development for TTF II and Applicability to X- FEL & ILC, S. Simrock, ILC WS 24 May 4,

AdapKve feedforward at SNS " # LðsÞ ¼a sb 1 z ðb 1 z A z ðdo L Þ K P Þþ 1 s K I in time domain, the learning controller is Z ðtþ ¼f uk F ðtþþab 1 z e k a B 1 t z A z ðdo L Þ K P e k ðtþþak I e k ðtþ

27 AdapKve feedforward at SNS " # LðsÞ ¼a sb 1 z ðb 1 z A z ðdo L Þ K P Þþ 1 s K I in time domain, the learning controller is Z ðtþ ¼f uk F ðtþþab 1 z e k a B 1 t z A z ðdo L Þ K P e k ðtþþak I e k ðtþ dt v kþ1 F : Q- filter is added to suppress the high frequency component due to that modeling of high- frequency dynamics are difficult and may lead to an inadequate model and unstable behavior L- filter (self learning filter) that compensates well for low frequencies, and it has the characteriskcs of PID a forgewng factor is introduced to put different weights to the past feedforward controller outputs S.I. Kwon, A.H. Regan, SNS SuperconducKng RF. Cavity Modeling - IteraKve Learning Control,. Nuclear Instruments and Methods in Physics Research A 482 (22) May 4,

New AdapKve Feedforward at FLASH A possible scheme: take the current drive signal of the pulse as the feedforward input for the next pulse Unfortunately, it is unstable Instead, add a

compensate loop delay Lowpass: Time-reversed lowpass: FF new = TRLP(FB last )+FF last is surprisingly stable :) time-reversed low-pass Further reading: Alexander Brandt, LLRF AutomaKon

28 New AdapKve Feedforward at FLASH A possible scheme: take the current drive signal of the pulse as the feedforward input for the next pulse Unfortunately, it is unstable Instead, add a time-reversed low-pass filter: record feedback error signal e(t), time reverse e(t) e(-t), low pass filter e(-t), reverse filtered signal in time again, shift signal in time to compensate loop delay Lowpass: Time-reversed lowpass: FF new = TRLP(FB last )+FF last is surprisingly stable :) time-reversed low-pass Further reading: Alexander Brandt, LLRF AutomaKon and AdapKve Feedforward, FLASH Seminar, 26 Alexander Brandt, Development of a Finite State Machine for the Automated OperaKon of the LLRF Control at FLASH, PhD thesis, DESY, 27. May 4,

29 Summary LLRF has to maintain the stability of the RF field, and minimize the required overhead power. Automated operation and easy maintenance should be taken into account, especially in large-scale facilities. A variety of perturbations can be seen everywhere in the accelerator environment PI Feedback is an effective and classical way to deal with the perturbations but at the cost of the more overhead consumption and rising instability. Feedforward is essential for the repetitive perturbations and need automatically update. We should look into more advanced control methods to be able to achieve better performance May 4,

30 Thank you for the ayenkon! May 4, 211 3

Field Stability Issue for Normal Conducting Cavity under Beam Loading

Field Stability Issue for Normal Conducting Cavity under Beam Loading Rihua Zeng, 3- - Introduction There is cavity field blip at the beginning of beam loading (~several ten micro-seconds) under PI control