1. Aaron Farricker 107/07/2014Aaron Farricker Beam Dynamics in the ESS Linac Under the Influence of Monopole and Dipole HOMs

2. ESS ESS is a collaboration of more than 17 countries Experiment is based in Lund Sweden At the forefront of neutron flux Should be operational around 2019 2 Power=I x E x Pulse Length x Rep Rate ESS 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 07/07/2014Aaron Farricker

3. Neutron Experiments CsZrMnSOCLiH X-rays Neutrons Thermal neutrons have a wavelength comparable to the inter atomic spacing of materials and an energy comparable to excitations in a solid The scattering cross-section varies between elements and isotopes (Hydrogen is particularly important) Neutrons can easily penetrate into the bulk of a material unlike EM waves allowing not just the surface to be seen Neutrons can probe a whole variety of different materials 3 Spallation- Incoming proton produces many neutrons (20-30) 07/07/2014Aaron Farricker

4. ESS Linac Beam power (MW)5 Beam current (mA)62.5 Linac energy (GeV)2 Beam pulse length (ms)2.86 Repetition rate (Hz)14 Num. of CMs Num. of cavities Spoke1326 Medium  (6-cell) 936 High  5-cell) 2184 Low energy section of the Linac is normal conducting taking the beam to 90 MeV Superconducting Linac takes the beam to the final energy of 2 GeV Three families of SC cavities working across a range of velocities 4 At 352.2 MHz bunch spacing means 1 Million bunches 07/07/2014Aaron Farricker

5. Example Cavity- ESS High Beta Cavity 07/07/2014Aaron Farricker5 ParameterValueUnits Number of Cells5 Frequency704.42MHz Cavity Length1.315m Accelerating Gradient 18MV/m R/Q472Ω Iris Diameter120mm

6. Dispersion Curves For High Beta Cavity 6 Single Cell Results as Red Circles Full Cavity as Blue triangles Circuit model fitted in purple Machine lines in orange Light line as a dashed line (beta=0.86) Light line given by: 07/07/2014Aaron Farricker

7. Variation in R/Q 7 As the proton beam is non-relativistic its velocity is changing on a cavity by cavity basis This means that its experiencing a voltage from HOMs in each cavity This variation can result in a mode that is not synchronous with the beam at the design beta becoming synchronous 07/07/2014Aaron Farricker

8. 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 phase 07/07/20148Aaron Farricker

9. Monopole Interactions 9 Each bunch induces a voltage in every mode It also gets acted on by the voltage already in each of the modes Real and Imaginary parts of the HOM voltage Fundamental theorem of beam loading Voltage and Phase error from the klystron Synchronous particle energy gain Time arrival error RF Errors Errors for RF at ESS are expected to be at the 0.1% level in amplitude and 0.1 degree in phase 07/07/2014Aaron Farricker

10. Errors in Mode Frequencies 10 Due 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 Therefore we expect a similar spread in frequencies at ESS For modes in the first pass band For modes in the higher pass bands 07/07/2014Aaron Farricker

11. Effects of SOM’s 11 90mA 75mA Design-62.5mA RF Errors The emittnce dilution at larger Q exceeds the effect of the RF by some margin for all of the currents Q for these modes must be kept around 10^6 so that they aren’t 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 07/07/2014Aaron Farricker

12. Effects of HOMs 12 Effect of HOMs away from machine lines are extremely small and of no consequence However modes near machine lines are of particular concern By moving just a Single mode in ONE cavity that is near a machine line to lie on that line large dilution is seen The position in the linac also has significant effect on the size of this dilution One cavity like this could compromise the operability of the machine General shape follows that of the R/Q as would be expected f= 1409.82 MHz f=2464.80 MHz Simulation Data R/Q Simulation Data R/Q Q=10^8 07/07/2014Aaron Farricker

13. Transverse Plane The 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 induced 90mA 75mA Design- 62.5mA 07/07/201413Aaron Farricker

14. Alignment Tolerances 14 At possible and reasonable alignment errors there is little effect from dipole modes (Left fitted with model from SLAC-PUB-) Transverse kicks from the fundamental (bottom left) due to misalignments do have a significant effect and are the limit on the alignment tolerances In both cases uniformly distributed errors are used Alignment tolerances for the machine are set to +/- 0.5 mm 07/07/2014Aaron Farricker