# Aaron Farricker 107/07/2014Aaron Farricker Beam Dynamics in the ESS Linac Under the Influence of...

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### Transcript of Aaron Farricker 107/07/2014Aaron Farricker Beam Dynamics in the ESS Linac Under the Influence of...

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Aaron Farricker107/07/2014Aaron FarrickerBeam Dynamics in the ESS Linac Under the Influence of Monopole and Dipole HOMs

1OutlineThe European Spallation Source (ESS)Example of an ESS CavityBeam Dynamics Code including Beam-Higher Order Mode(HOM) interactionsLongitudinal Emittance DilutionTransverse Emittance Dilution + Alignment Tollerances

07/07/2014Aaron Farricker2Outline of the talk2European Spallation Source

ESS is a collaboration of more than 17 countriesExperiment is based in Lund SwedenAt the forefront of neutron fluxShould be operational around 2019ESS is going to be green, all power used by the machine during operation will be put back into the power grid using renewable energy sources on site

307/07/2014Aaron Farricker

ESSESS colaberation of 17 countriesMost powerful next gen neutron sourceIt is going to be green3ESS Linac

Beam power (MW)5Beam current (mA)62.5Linac energy (GeV)2Beam pulse length (ms)2.86Repetition rate (Hz)14Num. of CMsNum. of cavitiesSpoke1326Medium b (6-cell)936High b (5-cell)2184

Low energy section of the Linac is normal conducting taking the beam to 90 MeVSuperconducting Linac takes the beam to the final energy of 2 GeVThree families of SC cavities working across a range of velocities4At 352.2 MHz bunch spacing means 1 Million bunches07/07/2014Aaron FarrickerEarly stages NCLatter stages have three familier of SC CavityFocus on the SC section with example cavity as the high beta cavity4Example Cavity- ESS-like High Beta Cavity07/07/2014Aaron Farricker5

ParameterValueUnitsNumber of Cells5 Frequency704.42MHzCavity Length1.315mAccelerating Gradient18MV/mR/Q472Iris Diameter120mma/0.141ESS High beta cavity operating in the pi mode

Full Five Cell Structure in HFSS5Dispersion Curves For High Beta Cavity6

Single Cell Results as Red CirclesFull Cavity as Blue trianglesCircuit model fitted in purpleMachine lines in orangeLight line as a dashed line (beta=0.86)

Light line given by:07/07/2014Aaron FarrickerR/Q For Monopole And Dipole Bands

For the plot on the left note the high R/Q of the fundamental and also the high R/Q mode in the second pass band (blue)For the dipoles (right) the maximum R/Q is about 75 ohmsIt is important to remember that the velocity of the beam is changing so these values change on a cavity by cavity basisVariation in R/Q8As the proton beam is non-relativistic its velocity is changing on a cavity by cavity basisThis means that its experiencing a voltage from HOMs in each cavityThis variation can result in a mode that is not synchronous with the beam at the design beta becoming synchronous 07/07/2014Aaron Farricker

Drift-Kick-Drift Model

Monopoles and RF errors result in a difference in energy This difference in energy results in a time arrival error at the next cavity which is the same as a change in phase07/07/20149Aaron FarrickerFrom RF ErrorsFrom Monopole Modes

Monopole Interactions10Each bunch induces a voltage in every mode

It also gets acted on by the voltage already in each of the modesReal and Imaginary parts of the HOM voltageFundamental theorem of beam loading07/07/2014Aaron Farricker

Injection Pattern

07/07/2014Aaron Farricker11Voltage and Phase error from the klystronSynchronous particle energy gainTime arrival errorRF ErrorsRequirements on RF errors at ESS have been reduced significantly from 1 degree in phase and 1% in amplitude to from 0.1 degree in phase and 0.1% in amplitude.

This has a significant effect on the growth caused

Old RF errorsNew RF ErrorsDipole Interactions07/07/2014Aaron Farricker12The voltage induced in a dipole mode by an off axis bunch is given by:

Where the transverse R/Q and Voltage are defined through the Panofsky-Wenzel theorem as:These transverse voltages result in a transverse kick to subsequent bunches which results in a change in x given by (for small kicks):

Errors in Mode Frequencies13Due to the limitations in constructing SC cavities a spread in the frequencies of HOMs from cavity to cavity are expected

Studies were carried out by R.Sundalin and his empirical findings were confirmed at SNS (http://eval.esss.lu.se/DocDB/0000/000092/002/summary.pdf)

Therefore we expect a similar spread in frequencies at ESS

For modes in the higher pass bandsIncluding dipoles07/07/2014Aaron FarrickerFor modes in the first pass band

These significant frequency deviations are result of the manufacturing limitations fro SC CavitiesEffects of SOMs

14

90mA75mADesign-62.5mARF ErrorsThe emittance dilution at larger Q exceeds the effect of the RF by a significant margin for all of the currents

Q for these modes must be kept around 106 so that they arent the dominant source of dilution

It has been indicated that the Q will be at this level however more simulation will be required to confirm this

62.5mA is the baseline design and the other curves represent potential power upgrades07/07/2014Aaron Farricker

With SOMs

Modes Near Machine Lines

These two modes that lie near machine lines (orange line on the dispersion curve) are used in the next simulationsAlthough they have small R/Qs they will be resonantly excited

Variation of Emittance Dilution With Cavity Position07/07/2014Aaron Farricker16A single modal component is included in ONE cavity along the linacIts Frequency is shifted to lie exactly on the nearest machine line such that it is resonantly excitedThis is the case where the maximum dilution in emittance would be seen and the absolute worst case for ESSQ=106Q=106Variation of Emittance Dilution With Cavity Position07/07/2014Aaron Farricker17A single modal component is included in ONE cavity along the linacIts Frequency is shifted to lie exactly on the nearest machine line such that it is resonantly excitedThis is the case where the maximum dilution in emittance would be seen and the absolute worst case for ESS

Q=106Q=106Variation of Emittance Dilution With Cavity Position07/07/2014Aaron Farricker18

There is a significant reduction in the growth when the Q is reduced from 108 to 106.The shape of the growth approximately follows that of the R/Q with some small deviationsThese deviations require further investigation but will most likely be due to the shape of the phase space at that cavity.R/QR/QQ=106Q=106Q=108Q=108Transverse Plane

The five highest R/Q dipoles modes were used

The emittance dilution was found to be very small at various currents

Modes near machine lines have no effect as bunches arrive at a minima and low R/Q means they have very low voltages induced90mA75mADesign-62.5mA07/07/201419Aaron FarrickerTransverse Sum Wakefield07/07/2014Aaron Farricker20

Due to the large amount of computational time required we only plot the transverse wakefield for 50,000 bunches by applying the Condon method

It is therefore no surprise that we see little effect from dipole modes

Alignment Tolerances21In both cases uniformly distributed errors are usedAt possible and reasonable alignment errors there is little effect from dipole modesThe plot is extended to show the quadratic behaviour expected07/07/2014Aaron FarrickerTransverse kicks from the fundamental (bottom left) due to misalignments do have a significant effect and are the limit on alignment tolerancesAlignment tolerances for the machine are set to +/- 0.5 mm

SummaryBeam-HOM interactions can be tracked using a numerical codeModes in the first passband are a concern as they have an effect comparable with the RF errorsHOMs are of little concern in both the longitudinal and transverse planes unless a monopole mode is near a machine lineThe alignment requirements arise mainly as a result of transverse kicks from cavities at an angle to the beam axis07/07/2014Aaron Farricker22

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