RF Systems Design

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# RF Systems Design - PowerPoint PPT Presentation

RF Systems Design. Stephen Molloy RF Group ESS Accelerator Division. AD Seminarino 17 / 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

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### RF Systems Design

Stephen Molloy

RF Group

ESS Accelerator Division

17/02/2012

Outline
• Some basic concepts
• (Hopefully not *too* basic…)
• Optimising a cavity
• Optimising the linac
• Transient
• Filling a cavity
• Commissioning the machine
• Protecting the machine
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

Generator current after transformation by the coupler

Transmission 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.

Optimising a cavity for RF power
• Equivalent circuit allows tuning of parameters
• 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…

are equal

Tuning the frequency:Why use the wrong frequency?

Vcav= Vforward + Vreflected

Vbeam

Ibeam

φb

Vforward=Vg/2

Vg= Vcav - Vbeam

Vcav

A non-zero synchronous phase angle will always lead to reflected power, unless…

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?

Ibeam

Vg

ψ

φb

ψ

Vforward

Vbeam

Vcav

Forward voltage can be made equal to the cavity voltage  no reflected power!

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
• 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
• Integration by parts (twice)
• Cosine is an even function
• Sine is an odd function
• π phase advance per cell
• Five-cell cavity

Magic!

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:

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.

• 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
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 optimisation

Note the large reflected power from the spoke cavities

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
Klystron control & linac commissioning
• Choose klystron current to achieve correct phase & amplitude
• Vg + Vbeam = Vcav
• Must ensure that phase & amplitude are correct at beam arrival
• Vforwardmust change phase at beam arrival
• Due to synchronous phase angle
• 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