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

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

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

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

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

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 1418.178 1402.254 1407.848 1418.674 1404.666 1408.258 Voltage Build Up as a function of Mode Frequency Aaron Farricker

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

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

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

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