Old Dominion University October 2012 2 2 2 f opt (b 1) fo IRQQ(/) where b oocos V Phase Amplitude Controller Controller Klystron 1.0 Limiter 0.9 0.8 Loop 0.7 Phase Amplitude 0.6 CEBAF 6 GeV Set Point 0.5 Amplitude CEBAF Upgrade Detector 0.4 Cavity 0.3 0.2 Energy Content (Normalized)Content Energy 0.1 Reference Phase 0.0 Phase -1,000 -800 -600 -400 -200 0 200 Set Point Detector Detuning (Hz) • RF Systems • What are you controlling? • Cavity Equations • Control Systems Cavity Models • Algorithms Generator Driven Resonator (GDR) Self Excited Loop (SEL) • Hardware Receiver ADC/Jitter Transmitter Digital Signal Processing • Cavity Tuning & Resonance Control Stepper Motor Piezo • RF Systems are broken RF Control Power down into two parts. Electronics Amplifier • The high power section consisting of the power amplifier and the high power transmission line Waveguide/ (waveguide or coax) Coax • The Low power (level) section (LLRF) consisting of the field and resonance control components Cavity • Think your grandfathers “Hi-Fi” stereo or your guitar amp. • Intensity modulation of DC beam by control grid • Efficiency ~ 50-70% (dependent on operation Triode Tetrode mode) • Gain 10-20 dB • Frequency dc – 500 MHz • Power to 1 MW • Velocity modulation with input Cavity • Drift space and several cavities to achieve bunching • It is highly efficient DC to RF Conversion (50%+) • High gain >50 dB • CW klystrons typically have a modulating anode for - Gain control - RF drive power in saturation • Power: CW 1 MW, Pulsed 5 MW • Frequencies 300 MHz to 10 GHz+ A. Nassiri CW SCRF workshop 2012 • Intensity modulation of DC beam by control grid • It is highly efficient DC to RF Conversion approaching 70% • Unfortunately low gain 22 dB (max) • Power: CW to 80 kW • Frequencies 300 MHz to 1.5 GHz As a tetrode As a klystron A. Nassiri CW SCRF workshop 2012 • RF Transistor RF Transistor • Efficiencies 40%+ (depends on operating mode) • Gain ~ 15 dB RF Transistor • Power mounted – 2 kW at 100 MHz – 1kW at 1000 MHz • Frequency to 3 GHz • Need to combine many transistors to get to very high power 5kW + A. Nassiri CW SCRF workshop 2012 • HVAC i.e. your house’s • Cavity RF control heating and A/C system • Set temperature • Set phase and • System applies amplitude heat/cooling to keep • System applies house at the set pointProportional phase/amplitude to Thermostat ControllerHVAC keep cavityHouseCavity field at the Phase/AmplitudeTemperature set points Set PointSet Point Sensor/DetectorThermometer Environment • Required Field Control to meet accelerator performance: – Proton/ion Accelerators: 0.5o and 0.5% – Nuclear Physics Accelerators: 0.1o and 0.05% – Light Source: 0.01o and 0.01% • Loaded Q Optimized for beam loading: Nuclear Physics < 1 mA, ERLs close to zero net current Light Sources 10’s of μA to 100 mA (high current in injectors) • Microphonics & Lorentz Detuning: Determined by cavity/cryomodule design and background environment. • Master Oscillator/Timing/Synchronization: Determined by application (light sources < 100 fs, frequently < 20 fs). • Accelerator Specific: Operational, Reliability/Maintainability Access etc. • For relativistic particles you want the electron bunch on crest.* Cavity Phase and Amplitude 1.2 • If the stability of the cavity Amplitude 1 error field effects the longitudinal emittance….energy spread 0.8 • Field control specification 0.6 Phase error folds back from the end Amplitude 0.4 users energy spread 0.2 requirements 0 -100 -50 0 50 100 Phase Degrees * There are special circumstances where the cavities are operated off crest. Examples particle bunching in injectors and FELS • Cavity: what's the frequency and Qext • Pulsed, CW, both • Cavity Gradient SNS Cavity • Lorentz detuning Mechanical Modes • Field regulation • Residual microphonic background • Beam current • Klystron/IOT/amplifier effects • Other cavity pass bands • He pressure drifts • Fault Recovery Phase Noise Spectrum Don’t Over Build the Control System ….KISS • Determines the feedback gain needed for operation • Determines the QL and the klystron power for lightly loaded cavities C100 HTB Cavity 7 10.000 120.0 1.000 40.2 15.0 26.7 65.7 90.3 0.100 RMS Hz) RMS ( 0.010 Center Frequency Shift Frequency Center 0.001 0 20 40 60 80 100 120 140 Vibration Frequency (Hz) References: 3 Microphonic Renascence C100 Microphonic Impact on cavity Detuning* (stiffened) power operating at 20 MV/m (100 mA of beam) RMS Amplitude 1.98 3.65 • C100 = 5.3 kW (Hz) • REN = 3.3 kW 6s(Hz) ~ Peak 11.9 21.9 Potential for cost reduction 1.2 Background Microphonics Histogram • Utility 1 • Power amplifier 0.8 C100 0.6 Renascen 0.4 ce Cryomodule design should 0.2 incorporate features to Normalized ProbablityNormalized 0 reduce microphonics. -0.2 -20 -15 -10 -5 0 5 10 Frequency Hz *Data Taken in Same Environment References: 3 • RF power produces radiation 1.00 0.90 2 2 pressures : P = (m0H – e0E )/4 0.80 0.70 • Pressure deformations 0.60 0.50 CEBAF 6 GeV produce a frequency shift : 0.40 CEBAF Upgrade 0.30 2 f = KLE acc 0.20 Energy Content (normalized) Content Energy 0.10 0.00 -1,000.00 -800.00 -600.00 -400.00 -200.00 0.00 200.00 Detuning (Hz) The Quadratic relationship with Outward pressure Gradient becomes an issue at the high at the equator Inward pressure at gradients (15+ MV/m) needed for new the iris accelerators References: 4,5 The simplest representation of a cavity is a parallel LRC circuit V (t)=v ejωt L R C cc Coupling to the cavity can be represented by a transformer and 11 then reduced to the following circuit Z=( + +jωC)-1 RjωL IG(t) I (t) ZO L R C G ZG L R C 1:k 2 1 R where ZGO k Z And the coupling is defined kZ2 References: 1 O Loaded Shunt R Shunt Impedance Ω R L Ω sh impedance r /Q Geometry Factor Ω Qo Intrinsic Quality Factor E Electric Field V/m QL Loaded Quality Factor l Electrical Length m Pg Generator Power W fo Cavity Frequency Hz Pc Cavity Dissipated Power W Stored Energy J Beam Phase W b Coupling Coefficient Ib Beam Current A Tuning Angle Vc Cavity Voltage V f Cavity Detuning Hz fo Cavity Bandwidth Hz fo Static Detuning Hz fm Microphonic Detuning Hz 1 QO C Substitutions for L & C o R LC o 22 Shunt Impedance VVcc RRsh or from circuit theory sh PPCC2 Q Loaded Q and Shunt O QL RLL (/) r Q Q Impedance 1 22 2 Generator VIRIRc(1 ) O L O L Pg1 cos b tan sin b Power RVV4 L c c f Detuning Angle tan 22 QLL Q OOf Total Detuning f fom f References: 1, 27 jωt jωt Vcc (t)=v e Igg (t)=I e L R C jωt Ibb (t)=I e • Beam and RF generator are represented by a current source Ib produces Vb with phase which is the detuning angle Ig produces Vg with phase Cavity Voltage Vc = Vg – Vb R R V =L II cos L cos C 22GB References: 1, 19 Im VC: VB VG IG IB Re R VIL cos BB2 1 2 1/2 PRI 2 VPR( )1/2 cos GR Sh G R GGL1/2 V =16L II cos L cos (1 ) C 22GB References: 1, 2, 19, 20 2 2 From generator power Vc 2 f Pg1 bQ L cos b 2 Q L bQ L sin b We can determine the r f 4 Q O Minimum power needed Q L IO r Substituting in for b where b VQ c Q Some assumptions QQ therefore O OL Q L Differentiating Pg with 1/2 ff respect to QL and setting it Q b22 4( ) 4( ) b sin to zero leads to optimum Lopt b ffOO Coupling Q 1/2 I rf Q (O )22 4( ) For beam on crest b=0 Lopt VcO Q f fO And if Io = 0 QLopt 2f And if Io >> 0 QLopt V/(/) I O r Q References: 1, 20 Beam on Crest QLopt f o /2 f 25000 Cavity Detuning 20000 0 Hz 5 Hz 15000 I = 10 mA Power 10 Hz 10000 20 Hz 5000 0 4.00E+06 4.00E+07 4.00E+08 Q References: 1 L Beam on Crest 100000 90000 Cavity Detuning 80000 0 Hz 70000 5 Hz 60000 Power 50000 10 Hz I = 1 mA 40000 20 Hz 30000 20000 10000 0 4.00E+06 4.00E+07 4.00E+08 Q QLopt V/(/) I O r Q References: 1 L fo is the static detuning or slow detuning …..< 1 Hz • Use active mechanical tuning to control cavity frequency fm is the fast detuning do to microphonics ……>10 Hz • Use active electronic feedback for field control Gray area between 1 and 10 Hz f fom f Classic “Plant-Controller” can be used to model the RF control system Cavity • Can be modeled a variety of ways. • Lorentz force can be added as a non-linear element • Mechanical modes can also be included Power Amplifier (Klystron, IOT, Solid State, etc.) • Saturation effects Hardware • Group delay (line delay, processing latency etc.) Modeling software such as Matlab/Simulink has made this rather easy. Controller Plant X(s) E(s) K(s) H(s) Y(s) G(s) Sensor Need to solve for close loop transfer function: Y/X E()()()() s X s G s Y s Y()()() s H s K s Y()()()() s K s H s E s X( s ) 1 H ( s ) K ( s ) G ( s ) References: 28 Want Output/Input (V/I) assume Parallel RLC circuit with current source VV I L R C I j CV V R j L V j RL 2 I RLC j L R Convert to s domain V() s sRL Gs() I() s s2 RLC sL R I(s) V(s) G(s) Sub for L&C R OLs Q Gs() L 22O V()()() s G s I s ssO References: 28 QL We are only interested in the time scale of the detuning microphonics.