1. Higher Order Modes and Beam Dynamics at ESS
Aaron Farricker

2. The European Spallation Source
ESS is a high intensity accelerator driven neutron source
It is driven by a 5 MW superconducting proton linac
Takes a 62.5 mA, 2.86 ms long pulse up to 2 GeV
Collides with a rotating Tungsten target to produce neutrons via spallation
Utilises well known technology (elliptical cavites) as well relatively new spoke cavities
ESS will not be using HOM couplers to damp unwanted modes in the cavities

3. HOMs
Decompose the field inside the cavity into different modes (two shown to the right)
We drive the cavity at the frequency of the accelerating mode and use this to accelerate the beam
The Beam excites all other possible mode by varying degrees
These slowly decay and can effect subsequent bunches
On the right is the Wakefield from a single bunch
Accelerating Mode
HOM

4. HOM-Beam Effects at ESS
We track the effect of HOMS on the beam using a drift-kick drift model
Modes in the first passband (SOMs) are not a problem if Q<106 (top right)
Q’s of this order are anticipated as they should be similar to the accelerating mode which is controlled
We found that HOMs are not an issue for ESS as long as they are not near a machine resonance.
90mA
75mA
62.5mA (design)
Effect of RF errors

5. HOMs Near Machine Lines
Q=106
Q=108
R/Q
If modes lie on or near a machine resonance then large voltages can build up in that mode
This can cause significant growth in the energy spread and also result in bunches being lost
If even a small part of the 5 MW beam is lost it could do significant damage to the machine

6. Alignment Study
Cavities must be aligned properly to prevent the unintentional excitation of dipole mode and transverse kicks from the accelerating mode due to an angular offset
Dipole modes are not an issue at ESS due to them only interacting weakly with the beam
The alignment tolerances are set by the transverse kick the accelerating mode can give if it is at an angular offset

7. HOMSC ‘14 I attend HOMS’14 at Fermi lab
Presented my work on the effects of HOMs on the beam at ESS
Paper will be published in Physics Procedia

8. Error Analysis Using the Circuit Model
We model a cavity as a series of coupled RLC circuits, where we find the eigenvalues to find the frequency of the modes
In this model we can add frequency errors by adding an error to the leading diagonal.
Applying uniformly distributed errors and solving allows us to build a picture of how various magnitudes of errors effect the mode frequency
The circuit model suggests if errors are around 8-9 MHz it is possible to hit the machine line.
Machine Line
Average including 1,2 and 3 sigma error bars

9. Why Is The Average Increasing?
It would be expected that applying uniform errors the average effect would be zero how ever it is increasing
Errors are applied to a single cell in both the circuit model and in superfish (by changing the radius of a cell in a three cell pillbox)
This shows that the circuit model is correct and there is a tendency for the bands to shift upwards and could be a problem for ESS
Endcell
Midcell
Circuit Model
End Cell
Mid Cell
Superfish

10. Single Cell Simulations
To work out what effect errors have on the resonant frequency we need to perform simulation including the errors.
This needs to be done in a 3D code such as HFSS which is computationally expensive.
If a large enough set of data can be simulated then the distribution found can be fed back into the circuit model to predict the effects.
This will need to be corroborated by having some full cavity simulations to compare to
200 micron errors
500 micron errors

11. Future Work Visit ESS for the first time in January
Complete study on the effects of manufacturing errors for (IPAC paper)
Investigate the effects on the other cavities at ESS