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