1. Implications of HOMs on Beam Dynamics at ESS
Aaron Farricker
Aaron Farricker

2. Outline The European Spallation Source
The ESS Cavities and Mode Spectra
Impact of HOMs on the Beam
Methods of HOM Mitigation
The Wakefield From a Non-Relativistic Charge
Aaron Farricker

3. The European Spallation Source (ESS)
The ESS is a spallation neutron facility being build in Lund, Sweden.
The ESS collaboration consists of 19 countries from Europe
The facility consists of a superconducting proton linac which will collide a proton beam with a Solid target to produce neutron which will be directed into several experimental halls
Major Beam Parameters
Pulse Length (ms)
2.86
Energy (GeV) 2
Peak Current (mA)
62.5
Pulse Rep. Rate (Hz) 14
Average Power (MW) 5
Peak Power (MW)
125
Aaron Farricker

4. The ESS Linac Beta=0.5 Spoke Cavities # of CryoModules 13
Warm Section
Cold Section (2K SCRF)
Beta=0.5 Spoke Cavities
# of CryoModules 13
# of Cavities 26
Eacc (MV/m) 9
Frequency (MHz)
352.21
Beta=0.67 Elliptical Cavities
# of CryoModules 9
# of Cavities 36
Eacc (MV/m)
16.7
Frequency (MHz)
704.42
Beta=0.86 Elliptical Cavities
# of CryoModules 21
# of Cavities 84
Eacc (MV/m)
19.9
Frequency (MHz)
704.42
Aaron Farricker

5. Cavity Mode Spectra High Beta
In both cavities the accelerating mode is the one with the highest R/Q by more than an order of magnitude
All other modes have relatively low R/Q and it has been shown they are of little concern
However if a mode shifts onto a harmonic of the bunch frequency a resonant growth in the HOM voltage will occur
As a result of this ESS requires all HOMs are at least 5 MHz from any machine resonance
In all the designs a10 MHZ gap is found
HOMs of Concern
Accelerating Mode
Machine Harmonic
Medium Beta
Aaron Farricker

6. What Happens During Manufacturing
CEA Saclay have produced 2 prototypes which meet all requirements for the accelerating mode but not for the HOMs (TUPB007 SRF’15 Peauger et al.)
The ESS cavities will be manufactured from high purity niobium (RRR>250)
The process shaping the half cells will be carried out using the deep drawing process
Then half cells and end groups will be welded together
The structure is then mechanically stretched to tune the accelerating mode frequency and field shape
All of these processes introduce errors onto the original geometry and can shift HOM frequencies
As a result of this CEA asked for the ESS requirement to be looked at in detail.
Cavity ID
P01
P02
Design Frequency at 300 K
Measured
Voltage Build Up as a function of Mode Frequency
Aaron Farricker

7. Implications on the Beam
Impact of a single HOM lying on a Machine Resonance
Beam dynamics simulations following a drift-kick-drift scheme have been used
These simulations have indicated that even a single cavity can have a drastic impact on the beam (right)
As a result there is some limit which must be applied
The big question is whether the 5 MHz limit imposed by ESS is too strict or not
To ascertain this many simulations are required as the HOM frequency spread is random (hopefully)
Medium Beta
Q=108
Q=106
High Beta
Q=108
Q=106
Aaron Farricker

8. Is a HOM Frequency limit Needed?
Medium Beta
Clearly resonantly excited HOMs can have a significant impact on the beam (slide 7)
As a result of ESS not using HOM couplers a limit of at least 5 MHz separation is required
However this has proved problematic (slide 6)
The real question is 5 MHz adequate or too strict?
A reduction in this limit would make manufacturing much easier but at what cost to machine performance
On the right the Impact of randomly generated HOM frequencies following a 2 MHz wide uniform distribution is shown as a function of the central frequency difference from the machine resonance (mean of 1,000 simulations per point)
The transition between growth and no growth is less than 100 kHz wide
Q=108
Q=106
High Beta
Q=108
Q=106
Aaron Farricker

9. The Wakefield The wakefield for a beam of beta=1 is well understood
The wakefield is readily decomposed into a series of modes over which a sum can be taken (Condon Method)
This can be analytically for a closed pillbox
Comparison of the Wakefield from simulation (red) and the analytic form (blue)
Aaron Farricker

10. Beta<1
Beta=0.9 wakefield on axis
Red from simulation
Blue analytic
When beat<1 fields from the bunch can exist ahead and behind the charge
This means that a wakefield could be present ahead of the exciting bunch
Attempts are being made to reconcile the analytic form at beta<1 with simulations
The primary method considered is to integrate the wakefield off axis to remove the static component from space charge
Work on this is ongoing and much improvement has been seen
Beta=0.9 wakefield off axis
Aaron Farricker