RF Systems Design
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Transcript of RF Systems Design
RF Systems Design
Stephen MolloyRF Group
ESS Accelerator Division
AD Seminarino17/02/2012
Outline
• Some basic concepts– (Hopefully not *too* basic…)
• Steady-state analysis– Optimising a cavity– Optimising the linac
• Transient– Filling a cavity– Commissioning the machine– Protecting the machine
RF SYSTEM CONCEPTS
Lumped elements: RF cavity
Parallel LCR circuit, where L, C, & R, depend on geometry & material.Resonant with a certain quality factor, Q0.
Lumped elements: RF system
Transmission line impedance seen from “the other side” of
the transformer.Note it is in parallel with the
cavity resistance, R.
Generator current after transformation
by the coupler
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.
Optimising a cavity for RF power
• Equivalent circuit allows tuning of parameters• Loaded quality factor, QL
• Transformer ratio of the coupler– Location and dimensions of coupler & conductor
• Frequency• Inductance & capacitance
– Dimensions of the cavity
• Coupling to beam, R/Q• Also the inductance & capacitance
– Cavity dimensions
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 & beam• Requires a specific value for QL
– For a specific forward power…
• Thus, steady state signalsare equal
Tuning the frequency:Why use the wrong frequency?
Vbeam Ibeam
Vcav
Vg= Vcav - Vbeam
φb Vforward=Vg/2
A non-zero synchronous phase angle will always lead to reflected power,
unless…
Vcav= Vforward + Vreflected
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
Tuning the frequency:Why use the wrong frequency?
Vbeam
Ibeam
Vcav
Vg
φb
Vforward
Forward voltage can be made equal to the cavity voltage no reflected
power!
ψ ψ
Linac & cavity optimisation
• For a single cavity– Reflected power can be eliminated• Correctly choose:
– Detuning– QL due to the coupler
• For a linac, it is not so simple– Detuning is easy
» Forgetting about Lorenz detuning for the moment
– Coupler• Prohibitively expensive to design individual couplers for
each cavity• So, optimise the QL for the total reflected power
An aside: Beam cavity coupling
• Coupling composed of 2 signals– Cavity field vector (depends on position)
– Cavity phase (depends on time)
Magic! See ESS Tech Note: ESS/AD/0025
Magic• Integration by parts (twice)• Cosine is an even function• Sine is an odd function• π phase advance per cell
• Five-cell cavity
Discussion
β=β0 may seem problematic as the cosine will go to zero, however the denominator also goes
to zero. In this limit:
Velocity bandwidth may be approximated by the closest
zeros of the cosine:
R/Q depends on square of V.
That the optimum β is greater than β0 is a well known
phenomenon.This curve agrees very well with
simulation/measurement.
Additional spatial harmonics?
• 2nd term is negligible• Result is the same as for 1 spatial harmonic
– No advantage in velocity bandwidth• 12.5% improved acceleration
– With no increase in peak voltage!
Transit-time factor conclusions
• Note assumptions:• Fixed cell length• No significant velocity change• π-mode cavity
• Observed voltage dependent on lots of things• Cavity β, particle β, peak voltage, frequency, etc.
• Velocity bandwidth depends….• Only on the number of cells!
• Increase effective voltage:• Increase number of cells• Increase 1st order spatial component
– Add additional components to maintain reasonable peak field
OPTIMISING THE SC LINAC
Goals, technique, assumptions
• Minimise the total reflected power• Vary the QL’s, and sum the reflected powers
– Nominal beam 50 mA, 2.8 ms
• Each section has a single QL • Spoke, medium/high beta
• Each cavity detuned optimally• Velocity dependence of impedance included
• Theoretical for elliptical cavities• Spoke based on field profile from S. Bousson
Result of optimisationNote the large reflected power from the
spoke cavities
Why are the spokes problematic?R/
Q
Spoke reflected power
• Fixes:• Redesign spokes for a lower beam velocity• Begin spoke section at a higher beam energy• Use multiple coupler designs in the spoke section
Re-optimise
DYNAMIC (NOT STEADY STATE) PERFORMACE
Klystron control & linac commissioning
• Choose klystron current to achieve correct phase & amplitude
• Vg + Vbeam = Vcav
– Only in steady-state!• Must ensure that phase & amplitude are correct at
beam arrival
• Vforward must change phase at beam arrival• Due to synchronous phase angle
• In addition:• How much power is reflected when commissioning
with low current beam?
Beam trip!
In reality, LLRF would detect the incorrect cavity amplitude & phase, and the large reflected power, and act to prevent this.
Dynamic effects – work in progress
• Nominal beam– Control klystron to achieve required RF conditions
• Commissioning– Shorten RF pulses to match beam duration– Lower peak current will cause problems• QL matching done for 50 mA
– Preferable to run with same bunch charge
• Machine faults– How much power can we reflect back to the loads?– Klystrons tripped by MPS within a pulse?
Conclusions
• Steady-state analysis– Linac optimised using 5 families of couplers– Mismatches between the voltage profile and R/Q
profile are simple to fix– Reflected power per cavity reduced to <10 kW
• Transient analysis• A work in progress…
– Reflected energy/pulse calculated for all cavities– Begun investigating:• Commissioning strategies• Fault scenarios