Presentation on theme: "Stephen Molloy RF Group ESS Accelerator Division"— Presentation transcript:
1 Stephen Molloy RF Group ESS Accelerator Division RF Systems DesignStephen MolloyRF GroupESS Accelerator DivisionAD Seminarino17/02/2012
2 Outline Some basic concepts Steady-state analysis Transient (Hopefully not *too* basic…)Steady-state analysisOptimising a cavityOptimising the linacTransientFilling a cavityCommissioning the machineProtecting the machine
4 Lumped elements: RF cavity Parallel LCR circuit, where L, C, & R, depend on geometry & material.Resonant with a certain quality factor, Q0.
5 Lumped elements: RF system Generator current after transformation by the couplerTransmission line impedance seen from “the other side” of the transformer.Note it is in parallel with the cavity resistance, R.Note that loaded R & Q both scale in the same way when shunted by the coupler.Therefore R/Q is unchanged.R/Q is a function of the geometry only, and so the circuit resistance, (R/Q)QL, is set by choosing the coupler loading.
6 Optimising a cavity for RF power Equivalent circuit allows tuning of parametersLoaded quality factor, QLTransformer ratio of the couplerLocation and dimensions of coupler & conductorFrequencyInductance & capacitanceDimensions of the cavityCoupling to beam, R/QAlso the inductance & capacitanceCavity dimensions
7 Optimising the coupling How best to squeeze RF into the cavity?Minimise QL to speed power transfer from klystron?Maximise QL to improve efficiency of the cavity?Match voltages excited by klystron & beamRequires a specific value for QLFor a specific forward power…Thus, steady state signalsare equal
8 Tuning the frequency: Why use the wrong frequency? Vcav= Vforward + VreflectedVbeamIbeamφbVforward=Vg/2Vg= Vcav - VbeamVcavA non-zero synchronous phase angle will always lead to reflected power, unless…
9 Break the phase relationship Driving a resonator off-resonance leads to a drop in the amplitude and a rotation of the phase of the excited signal.The higher power required to achieve the same cavity field could be easily compensated by the elimination of the reflected power
10 Tuning the frequency: Why use the wrong frequency? IbeamVgψφbψVforwardVbeamVcavForward voltage can be made equal to the cavity voltage no reflected power!
11 Linac & cavity optimisation For a single cavityReflected power can be eliminatedCorrectly choose:DetuningQL due to the couplerFor a linac, it is not so simpleDetuning is easyForgetting about Lorenz detuning for the momentCouplerProhibitively expensive to design individual couplers for each cavitySo, optimise the QL for the total reflected power
12 An aside: Beam cavity coupling Coupling composed of 2 signalsCavity field vector (depends on position)Cavity phase (depends on time)MagicIntegration by parts (twice)Cosine is an even functionSine is an odd functionπ phase advance per cellFive-cell cavityMagic!See ESS Tech Note: ESS/AD/0025
13 DiscussionVelocity bandwidth may be approximated by the closest zeros of the cosine:That the optimum β is greater than β0 is a well known phenomenon.This curve agrees very well with simulation/measurement.R/Q depends on square of V.β=β0 may seem problematic as the cosine will go to zero, however the denominator also goes to zero. In this limit:
14 Additional spatial harmonics? 2nd term is negligibleResult is the same as for 1 spatial harmonicNo advantage in velocity bandwidth12.5% improved accelerationWith no increase in peak voltage!
15 Transit-time factor conclusions Note assumptions:Fixed cell lengthNo significant velocity changeπ-mode cavityObserved voltage dependent on lots of thingsCavity β, particle β, peak voltage, frequency, etc.Velocity bandwidth depends….Only on the number of cells!Increase effective voltage:Increase number of cellsIncrease 1st order spatial componentAdd additional components to maintain reasonable peak field
17 Goals, technique, assumptions Minimise the total reflected powerVary the QL’s, and sum the reflected powersNominal beam 50 mA, 2.8 msEach section has a single QLSpoke, medium/high betaEach cavity detuned optimallyVelocity dependence of impedance includedTheoretical for elliptical cavitiesSpoke based on field profile from S. Bousson
18 Result of optimisation Note the large reflected power from the spoke cavities
23 Klystron control & linac commissioning Choose klystron current to achieve correct phase & amplitudeVg + Vbeam = VcavOnly in steady-state!Must ensure that phase & amplitude are correct at beam arrivalVforward must change phase at beam arrivalDue to synchronous phase angleIn addition:How much power is reflected when commissioning with low current beam?
25 Beam trip!In reality, LLRF would detect the incorrect cavity amplitude & phase, and the large reflected power, and act to prevent this.
26 Dynamic effects – work in progress Nominal beamControl klystron to achieve required RF conditionsCommissioningShorten RF pulses to match beam durationLower peak current will cause problemsQL matching done for 50 mAPreferable to run with same bunch chargeMachine faultsHow much power can we reflect back to the loads?Klystrons tripped by MPS within a pulse?
27 Conclusions Steady-state analysis Transient analysis Linac optimised using 5 families of couplersMismatches between the voltage profile and R/Q profile are simple to fixReflected power per cavity reduced to <10 kWTransient analysisA work in progress…Reflected energy/pulse calculated for all cavitiesBegun investigating:Commissioning strategiesFault scenarios
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