RF Control of Heavy Ion Linear Accelerators An Introduction

Transcription

1 RF Control of Heavy Ion Linear Accelerators An Introduction RF Control- essential functions Typical Architecture of RF system Reference Phase Distriubution- an example High power RF system RF system architectures Disturbances and control strategies Architecture of computer control

2 RF Control- essential functions RF Linear Accelerator Series of resonators mounted along the beam-line Energy Gain E. cos(ø) E : Magnitude of the electric field Ø: Phase of the electric field when particle at the gap centre RF Control Set-up and stabilize E ø Resonance Frequency To reduce RF power for control, and - Distribution of stable phase reference signals

3 MASTER CLOCK REMOTE CONTROL PICK UP TUNER TC TC FP RP RESONATOR CONTROLLER RF POWER AMPLIFIER FP RP COUPLER DIRECTIONAL COUPLER CIRCULATOR QUARTER WAVE RESONATOR (QWR) Local COMPUTER CONTROL CONTROL & MONITORING IDENTICAL SYSTEMS PICK UP TUNER TC TC FP RP FP RP COUPLER DIRECTIONAL COUPLER QWR RESONATOR CONTROLLER RF POWER AMPLIFIER CIRCULATOR Local COMPUTER CONTROL CONTROL & MONITORING PARTICLE BEAM TRAJECTORY OVERVIEW OF A TYPICAL RF SYSTEM

4 ION SOURCE F/16 LOW ENERGY BUNCHERS F/8 BEAM LINE LEB RC LEB RC -VOLTAGE CONTROLLED PHASE SHIFTER X2 PD PD REF. CLOCK ~ F DC PU-PICK UP PR-PHASE REFERENCE RC-RESONATOR CONTROLLER FB-FEED BACK SIGNAL PD-POWER DIVIDER FD-FREQUENCY DIVIDER DC-DIRECTIONAL COUPLER DC FB FD PD 1:4 SPLITTER 1:4 SPLITTER P E L L E T R O N 1/2 1/2 1/2 1/2 1/2 PR PHASE DETECTOR ELECTRONICS TO CRYOSTAT-2 PU ANALYSING MAGNET TO PELLETRON BEAM HALL PU RC PR SWEEPER PU RC CORRECTOR PR PHASE DETECTOR PU F/32 F/32 F/4 F RC PR SUPER BUNCHER PR PR PR PR PU PU PU PU RC RC RC RC F F F F SUPER CONDUCTING RESONATORS CRYOSTAT-1 BLOCK DIAGRAM OF THE RF SYSTEM FOR THE BARC-TIFR LINAC BOOSTER Generation & Distribution of phase reference signals - TO C R Y O S T A T -2

5 Reference Phase Distribution Voltage to Time-Difference Conversion (RF phase of Bunchers) Delay (Through Pelletron) Compensation Timing Jitter + Time-Difference to Phase-angle Conversion (Phase Detector) - + Ref. Phase Phase-Difference to Voltage Converter Correction of Timing-Jitter Reference phase distribution: stability very important Electronics temperature, power supplies, low noise/jitter components use of phase stable cables

6 Elements of an RF system for one resonator in a Linac Drive Power Amplifier Plant High Power Transport Directional Coupler Coupling Tuner Resonator Pick-up Controller For. Ref. RF Control Electronics RF Reference Amplitude and Phase set points

7 RF System- Large no. of possibilities Resonator Normal-conducting, superconducting Architecture of RF Power System Generator Driven/Self-excited Loop based one RF source one resonator/ multiple resonators one resonator multiple power sources Application may demand extremes of stability Operation CW/pulsed beam loading high/low Implementation Primarily Analog/Digital

8 High Power System electrical model I S Z s Z0 =R/β1, α R I b Power Amplifier (ρ s ) L Transmission line Resonator (ω c, τ) Beam Equivalent circuit transformed to terminals of the main resonator i g L i v C R i b Simplified Equivalent Circuit Rg Source Resonator Beam

9 High Power System electrical model i g L i v C R i b Simplified Equivalent Circuit Rg Source Resonator Beam In systems that employ circulators- i 2v f g = = Zo R g = R 2v f β ( R / β ) Where is the coupling coefficient and is the forward wave as transformed to the resonator terminal

10 v + v / (RC) + v/(lc) = i /C v + (2/τl) v + ωc 2 v = (2/τl) Req.( ig + ib), Req is the parallel combination of Rg and R τl = 2 Req C ωc = (LC) 1/ i g L i v C R i b ig = R(Ig. e jωt ), ib=r(ib. e jωt ), v =R( V e jωt ) Rg τl V + (1 + j(ω - ωc) τl)v= Vg, where, Vg = Req ( Ig +. Ib) = Vg Vg = Ii + j Qi and V= I + j Q I = (-1/τl).I (ωc - ω) Q + (1/ τl).ii (i) and Q = (-1/τl).Q + (ωc - ω)i + (1/ τl).qi (ii) Source Resonator Beam Efficient power transfer requires- 1. Adjusting the coupling 2. Detuning of the cavity

11 RF Power System- steady state contd. Quadrature Power Control Locus of the resonator current for constant voltage Resonator voltage Output Resonator current needed to achieve lock Drive current before beam Beam Current Addition of Quadrature Signal Drive Current with beam Steady-state solution

12 Electro-mechanical effect in a RF resonator Presence of electromagnetic field exerts pressure on the walls of the resonator: 1 2 ( µ H ε oe 2 ) 4 o Motion of the walls of the resonator can be expressed as a sum of mechanical modes of the resonator It can be established that: 2 d ωμ 2 dωμ Ω 2 μ ωμ dt τ dt μ = k μ Ω 2 μ VV * 2 d ωμex 2 dωμex Ωμ ωμ μ Ωμ η 2 ex = k ex dt τ dt μ Total detuning ( ω ω) = + ω + ω c 0 µ n µ exn

13 Mathematical Model of the RF system V g = (I i +. j Q i ) =R eq ( I g +. I b ) I i d di 1.I Δ.Q 1 i dt = τ + l τ I l dq = 1.Q+ Δ.I+ 1 Qi dt τ τ VV 2 Q i 2 ω dt d ω dt l = I + Q * 2 2 l 1 dω. Ω K Ω μn μn 2 2 * μnωμn = μn μnvv τμ n dt 2 dω. Ω Ω μexn μexn μn ωμexn = kμexn μn τμ n dt η I Q η ( ω ω) = ( ω ω) + ω + ω c 0 µ n µ exn

14 1. High Power RF System Model Models help in: understanding the behaviour of RF system Transients in pulsed systems High beam loading Cavity Filling Electro-mechanical effects Multi-feed systems development of control algorithms Models Developed at base-band using complex amplitude concept for Typical single and double-feed systems with tubes having resonant output network Transistor based with broadband output Methodology can be applied for any no. of power feeds

15 Procedure for the development of the RF power system model: 1. Transform the system in the plane of the main resonator 2. Express the dynamics of the voltage on the tank circuits in the standard form- τ d V + [1+ j(ω ωc) τ] V dt = by identifying the appropriate time constant and the drive 3. Concatenate the model of the tank circuits with that of the transmission lines Prepare scheme of computations Express the resulting set of equations in real variables 4. Apply transformation in the reverse direction to obtain voltages/currents in the actual system V g

16 Procedure for the development of the RF power system model: 1. Transform the system in the plane of the main resonator Beam example Transmission Transmission Line1 Line2 TUBE1 Main Resonator TUBE2 N Z β = R β s1.z 01 R I b β s2.z 02 I 1 Z 01 = R/β 1 V Z 02 = R/β 2 I 2 ω 1, τ 1 L 1 ω L 2 c, τ ω 2, τ 2 Tank circuits joined by transmission lines

17 2. Express the dynamics of the voltage on the tank circuits in the standard form by identifying the appropriate time constant and the drive τ Time Constant d V + [1+ j(ω ωc) τ] V dt = V τ /( 1+ β1 + β βn) g Drive V g V g = [R/ ( 1 + β 1 + β 2 + β n )] { I b + [(2V f1 β 1 )/ R ] + [ (2V f2 β 2 )/ R] + + [ (2V fn β n )/ R] }, Transmission Lines V jω ( α + ) L c L 0( t) = e Vi ( t c )

18 3. Concatenate the model of the tank circuits with that of the transmission lines - prepare scheme of computations in phasor domain get equations in real variables V = V i + jv q 2β s1 1+β s1 + R β β s1 Tube1 Dynamics τ l = ω 1 ω _ T. L. 1 V r1 _ T. L. 1 (Delay, attenuation, phase shift) V f1 + 2β 1 1+β 1 +β 2 Tube1 Current I b R 1+β 1 +β Main Tank + Dynamics V 2β s2 1+β s2 R β β s2 Tube2 Dynamics τ l = ω 2 ω _ T. L. 2 T. L. 2 V r2 (Delay, attenuation, phase shift) _ V f2 + 2β 2 1+β 1 +β 2 τ l = ω c -ω Tube2 Current 4: Apply transformation in the reverse direction to obtain voltages/currents in the actual system

19 Developed the model for the CERN Linac2 RF power system Matched system with beam Helped in identifying setting-up problems

20 RF System Architectures: Generator Driven Resonator (GDR) Self Exited Loop (SEL) Choice depends primarily on Band-width of sourceresonator system in relation to resonant frequency deviation

21 GDR RF Reference Phase Modulator Amplitude Modulator Reference Phase Shifter Amplifier Measurement & Control Phase Comparison X Amplitude Set-Point Amplitude Measurement Resonator Convenient: Stable Drive in the absence of feedback used for normal-conducting resonators Possibility of electro-mechanical instability!

22 GDR- possibility of electromechanical instability Resonator Walls Move Under the change of Radiation Pressure (mechanical modes of the resonator) Resonance Frequency Changes The tuning berween the source and resonator is changed The RF Field in the resonator changes (electrical mode of the resonator)

23 Control of Super-conducting Resonators High Q ~10 8 to 10 9 Band-width ~1 Hz at 150 MHz Resonant Frequency variation several bandwidths due to tuning tolerances, mechanical vibrations and liquid Helium pressure changes, electromechanical coupling Setting-up RF field using a fixed frequency generator not very convenient Instead a Self Excited Loop is used

24 SEL Resonator (Filter) Amplifier Loop Phase Shifter Attenuator Limiter ELEMENTS OF A Free-running SELF EXCITED LOOP A convenient starting point for subsequent amplitude and phase locking: - Smooth adjustment across the resonance curve using the Loop Phase Shifter. - Immune to electro-mechanical instability

25 SEL RF Reference Phase Modulator Amplitude Modulator Reference Phase Shifter Limiter Loop Phase Shifter Phase Comparison X Amplitude Set-Point Amplitude Measurement Amplifier Resonator Measurement & control SEL with amplitude and phase feedback

26 Disturbances & Control Strategies 1. Resonance frequency variation: Quadrature Power Control τ l V + [(1 + j(ω - ω c ) τ l )]V= V g, under steady state resonator output/input = 1/ (1 + jx), x= j(ω - ω c ) τ l x detuning in terms of no. of half band-widths Increase the drive V g by (1 + ix) Used when- adequate power is available low power systems mechanical tuning system too slow

27 Disturbances & Control Strategies contd. Quadrature Power Control Resonator Input to achieve Amplitude and Phase Lock Addition of Quadrature Signal Resonator Input Before Lock Resonator Output Locus of the Input Steady-state solution

28 Disturbances & Control Strategies contd. Resonance Curve phase shift across resonator: monotonic function of detuning maximum sensitivity around resonance Static: Dynamic: sensor for the frequency deviation Φ = tan -1 [τ (ωc - ω)] y= [τ (ωco - ω)] ((1 + sτ) 2 + y 2 ) δφ = τ (1 + sτ) δ(ωc - ω)

29 Disturbances & Control Strategies contd. Resonator Power Amplifier Control Element Directional Couplers Limiter 90 Gain 0 Phase Ref. Input Gain Phase Detector Loop Phase Shifter 0 Gain 0 Output Gain Ref. Phase Shifter Field Amplitude Detector - Phase Error Amplifiers Amplitude Ref. + Amplitude Error Amplifiers Quiescent Power SEL WITH AMPLITUDE & PHASE LOCK

30 Controller_SEL SEL dynamics: dva τ dt + V a = in phase Drive τ(ω ω0 ) V = quadrature Drive V a Disturbances & Control Strategies contd. a : amplitude of RF in the resonator τ : decay time of the resonator field ω : loop oscillation frequency ω 0 : resonant frequency Dominant disturbance - Variation of ω 0 1. Phase Control - modulation of Quadrature drive 2. Amplitude control - modulation of In-phase drive

31 yr=τ (ω r ω o ) Resonator Input to achieve Amplitude and Phase Lock yl =τ (ω lo ω o ) Addition of Quadrature Signal Resonator Input Before Lock Resonator Output Locus of the Input Steady-state solution for yl=yr=0

32 A a -1 δp 1/(1+sτ) -2K μ Ω μ2 Vo δv SEL + 1/(s 2 +2.τ μ s+ω μ2 ) δω o δω ex δq 1/τ δ(ω l ω o ) + 1/s δφ -1 Aϕ System Model: Linearised yl=yr=0

33 Disturbances & Control Strategies contd. Tuning: Electronic using voltage variable reactance Correction Mechanical Plunger Cooling Water Temperature Mechanical Deformation of Resonator Walls

34 Disturbances & Control Strategies contd. Counteract x electronically: Voltage Controlled Reactance Method High Power RF VCX Attenuator Amplifier Resonator Pick-up X Amplitude Ref. Amplitude Demodulator Limiter Amplitude Ref. Ref. phase X An SEL with VCX Control band-width extending to khz range Can counteract vibration induced variations

35 Disturbances & Control Strategies contd. Electronic Damping of microphonics ω 2 ofb = ω 2 o 1+ 2k µ 1 2 Ωµ V 2 ( ) τ µ 2 0 k f

36 Disturbances & Control Strategies contd. Mechanical Deformation of resonator walls Slow variations stepper motor, helium gas pressure variations cooling water temperature variations Piezo

37 Disturbances & Control Strategies contd. Piezo based control: Can counteract microphonics Active area of R&D especially for pulsed systems Source: Bhuban Sahu et al., NIMA 777, 2015,

38 Disturbances & Control Strategies contd. 2. Random amplitude and phase fluctuations in the drive: & Beam Current -Feedback control based on measurement of resonator output -Frequency range of control limited by the delay and other high frequency dynamics PHASEDETECTOR LOOP PHASE SHIFTER PHASE FEEDBACKSWITCH Q COMPENSATION PHASEERROR LOWPASS FILTER F/ VECTOR MODULATOR 0 BIAS REF.PHASE SHIFTER I RF POWER AMP. QUIESCENTPOWER RESONATOR AMPLITUDE FEEDBACKSWITCH FIELDLEVELRF DEMODULATOR FIELDLEVELDC COMPENSATION FIELD LEVEL CONTROL C DEMODULATOR COUPLED CONTROL AMPLITUDEERROR - + AMP. REF. PHASEREFERENCE

39 Disturbances & Control Strategies contd. 3. High speed but predictable variations in pulsed systems Adaptive Feedforward Model of the system Effectively increases the bandwidth of the system

40 Cavity Field Detection & Actuators: Implementation Issues: Detectors Analog Stability of this part crucial 1. Temperature stabilization, power supply 2. Use of external signal for gain stabilization

41 Implementation Issues: Digital Input RF sampled using a synchronous clock Resulting discrete-time sequence processed Digital systems: Clock jitter manifests itself as phase jitter in the demodulated signals. Phase jitter, δϕ(t), in the digitized RF input due to timing jitter in the sampling clock σ(t), is given by equation : δφ() t = 2 π f σ () t in 1. Stabilization of clocks 2. Removed as common mode jitter in Reference and RF input

42 Offset tone based gain correction: Implementation Issues:

43 Thanks