Higher Order Modes and Beam Dynamics at ESS Aaron Farricker

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

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

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

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

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

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

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

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

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

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