Accelerator Laboratory of Tsinghua University Research on deflecting cavities for SPX project in APS Yawei Yang Tsinghua University, Argonne National Lab Institute of Modern Physics, Lanzhou, China

Accelerator Laboratory of Tsinghua University 2 Content R&D activity of deflecting cavity in Tsinghua Research and Analysis I.Wakefield Analysis of SC deflecting Cavity for APS SPX (focus) II.Power leaking analysis and ways to solve the problem III.Copper prototyping measurement IV.Towards two cell cavity design

Accelerator Laboratory of Tsinghua University 3 R&D activity of deflecting cavity in Tsinghua 探寻宇宙起源 Completed Cavity Design and Fabrication L-band deflecting cavity for ANL emittance exchange experiment S-band deflecting cavity for Tsinghua beamline diagnostics International Collaboration on SC deflecting cavity Compressing X-ray pulse at the APS, ANL I am in the visiting graduate student program. Large part of my thesis work will be finished there C-band deflecting cavity R&D for ultrashort electron diffraction

Accelerator Laboratory of Tsinghua University Measurement experiments R&D activity of deflecting cavity in Tsinghua Bunch-train diagnostics using RFD 2 pC case 15 pC case 35keV 1keV Yawei Yang, et al, Proceedings of IPAC2011, TUPC110 4

Accelerator Laboratory of Tsinghua University 5 Content R&D activity of deflecting cavity in Tsinghua Research and Analysis I.Wakefield Analysis of SC deflecting Cavity for APS SPX (focus) II.Power leaking analysis and ways to solve the problem III.Copper prototyping measurement IV.Towards two cell cavity design

Accelerator Laboratory of Tsinghua University 6 Wakefield Analysis of SC deflecting cavity in APS Motivations of the long-range wake field analysis Ali Nassiri, Oral Presentation on Deflecting/Crabbing Cavity Mini-Workshop 2010 Preservation of present operations Hundreds of mA current could excite lots of modes in the cavity Wakefield could lead to beam instability and emittance growth Control the collective effect is very important.

Accelerator Laboratory of Tsinghua University 7 Wakefield Analysis of SC deflecting cavity in APS Long-range wake field (My focus) How the wake field act on following bunch. The way to damp the long-range wake is to add damper. Described by wake impedance (Impedance threshold) Robinson instability and transverse Robinson instability Short-range wake field How much wake is generated and act on itself Described by loss factor (longitudinal) and kick factor (transverse) Head-tail instability

Accelerator Laboratory of Tsinghua University 8 Wakefield Analysis of SC deflecting cavity in APS Wake potential and impedance The wake potential is given by the integral of the fields that are left behind by a driving bunch. Generally, the Fourier transform of wake potential could be called impedance. However, the wake potential is determined by the parameter of the driving bunch, like transverse position and bunch length. We need a definition that is independent of this.

Accelerator Laboratory of Tsinghua University 9 Wakefield Analysis of SC deflecting cavity in APS Calculate the wake impedance of deflecting cavity Wake function : it describes the shock response of a structure to a delta function of beam which carries an mth momentum. All kinds of bunch could be expended as a sum of different moments of the beam. Impedance: The Fourier transform of the wake function is called the wake impedance. This definition is independent of beam parameters. (CL m ) (VC -1 L -2m ) (VC -1 L 1-2m ) Wake potential in circular symmetric structure

Accelerator Laboratory of Tsinghua University 10 Wakefield Analysis of SC deflecting cavity in APS Impedance budget How the impedance was related to beam instability ---- Robinson Instability or BBU. Longitudinal: Transverse: Growth rate:

Accelerator Laboratory of Tsinghua University 11 Wakefield Analysis of SC deflecting cavity in APS How to calculate the impedance? Ali Nassiri, Oral Presentation on Deflecting/Crabbing Cavity Mini-Workshop 2010 Delta function of beam only exist in mathematic. Time domain analysis: GdfidL\CST particle studio\ T3P spectrum of Gaussian bunch : could calculate the impedance in low frequency as Delta Frequency domain analysis : Calculate R/Q and Q value The eigen mode determines where the long range wakefield tend to be trapped.

Accelerator Laboratory of Tsinghua University 12 Wakefield Analysis of SC deflecting cavity in APS Panofsky-Wenzel theory It is the nature property of Maxwell equation. It is independent of boundary condition. The boundary could be dielectric, lossy material or even plasma. And for the wake field. But there is a lot derivation based on Panofsky-Wenzel, which is not always the case. (standing wave resonator) (circular symmetric)

Accelerator Laboratory of Tsinghua University 13 Wakefield Analysis of SC deflecting cavity in APS Current design options Mark I Mark II Power coupler LOM damper HOM damper 1 HOM damper 2 HOM damper 1 LOM damper

Accelerator Laboratory of Tsinghua University 14 Wakefield Analysis of SC deflecting cavity in APS Eigen mode analysis ModeFreq(GHz)QextR/Q longiR/Q transLongi (Ohm)Trans (Ohm/m) TM010 (cavity) TM110(working mode) E TE110 (cavity) E TE110 (cavity) E TM110(cavity) E Mark I Mark II ModeFreq(GHz)QextR/Q longiR/Q transLongi (Ohm)Trans (Ohm/m) TM010 (cavity) E+05 TM110(working mode) E TE110 (cavity) E TE110 (cavity) E TM110(cavity) E E+06 Mark I Mark II

Accelerator Laboratory of Tsinghua University 15 Design of on-cell damping deflecting cavity 探寻宇宙起源 On-cell damping single cell design TM010 mode has been Significantly lowered Single beam TM010 mode

Accelerator Laboratory of Tsinghua University 16 Design of on-cell damping deflecting cavity 探寻宇宙起源 On-cell damping single cell design TM110 hori is not a problem any more Dipole beam TM110 hori mode Qext 11000

Accelerator Laboratory of Tsinghua University 17 Design of on-cell damping deflecting cavity 探寻宇宙起源 On-cell damping single cell design Mark-II has been chosen as the design for SPX-0 in ring test. Dipole beam 2mm)(0,-2mm) Deflecting Mode

Accelerator Laboratory of Tsinghua University 18 Wake field analysis of deflecting cavity in storage ring 探寻宇宙起源 Long Range wake field effect: circular symmetric structure Single beam

Accelerator Laboratory of Tsinghua University 19 Wake field analysis of deflecting cavity in storage ring 探寻宇宙起源 Long Range wake field effect: circular symmetric structure Single beam Or Dipole beam

Accelerator Laboratory of Tsinghua University 20 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: Mark II cavity The transverse wake is present for monopole mode in the asymmetric cavity Single beam Hybrid mode Q is low TM010 No high Q mode (above 5000) below 5GHz

Accelerator Laboratory of Tsinghua University 21 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: Mark II cavity The transverse wake is present for monopole mode in the asymmetric cavity Single beam (-2mm,0) TE111

Accelerator Laboratory of Tsinghua University 22 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: Mark II cavity The transverse wake is present for monopole mode in the asymmetric cavity Transverse kick due to the TM010 mode. Strong dipole component of dipole in TM010 field Strength is 1/10 of the longitudinal Single beam TM010 mode

Accelerator Laboratory of Tsinghua University 23 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: Mark II cavity The transverse wake is present for monopole mode in the asymmetric cavity For single bunch excitation, the transverse kick due to the TM010-like mode is event stronger than the dipole mode evern if there is offset 500um. Remember the number of 2*10^4Ohm/m Single beam TM010 mode

Accelerator Laboratory of Tsinghua University 24 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: SPX-0 in ring test See how the wakefield spectrum change with the cavity interval. TM01 cutoff frequency Single beam

Accelerator Laboratory of Tsinghua University 25 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: SPX-0 in ring test See how the wakefield spectrum change with the cavity interval. Beam pipe TE11 cutoff frequency Dipole beam

Accelerator Laboratory of Tsinghua University 26 Wake field analysis of deflecting cavity in storage ring Long Range wake field effect: SPX-0 in ring test See how the wakefield spectrum change with the cavity interval. Beam pipe TE11 cutoff frequency Dipole beam

Accelerator Laboratory of Tsinghua University 27 Wake field analysis of deflecting cavity in storage ring 探寻宇宙起源 Wakefield and Instability Current Estimation of wake field threshold It is not valid for asymmetric structure Robinson Instability It is not valid for asymmetric structure The wake field excitation is quite complicated in asymmetric structure. I will work more on the beam cavity interacting and how this will affect beam instability.

Accelerator Laboratory of Tsinghua University 28 Wake field analysis of deflecting cavity in storage ring 探寻宇宙起源 Summary Briefly review the wake impedance definition. Use two ways to analyze the wake field: Eigen mode and time domain Mark II is better than Mark I in time domain and frequency domain Frequency vs Time domain Pros of Frequency: Qext of HOM could be easily calculated. Pros of Time domain: Wake excitation process could be calculated in detail. Cons of Frequency: Wake excitation of asymmetric structure might be complicated and different. Cons of Time domain: Better for low frequency, if there is high Qext mode and high frequency, time domain might be problems.

Accelerator Laboratory of Tsinghua University 29 Power Leaking Analysis The possibility of power leaking through LOM damper Deflecting mode frequency is above the cutting off frequency of LOM damper. Ideally, the LOM damper is located in the center, and it will not couple with TE10 mode. The TM110 center offset due to Y-end group The error of fabrication

Accelerator Laboratory of Tsinghua University 30 Power Leaking Analysis The magnetic center calculation The accelerating voltage integration along (0mm, ymm) Magnetic center: -26.7um due to y-end group Integration path y (mm)Accelerating Voltage positive Integration displacement (mm) Accelerating voltage

Accelerator Laboratory of Tsinghua University 31 Power Leaking Analysis Qext of deflecting mode coupling with on cell damper Move the damper location up and down, to see how the Qext of deflecting mode changes with displacement Qext Damper location offset (mm) The Qext proves to be very sensitive to the location of the damper and also the tilt.

Accelerator Laboratory of Tsinghua University 32 Power Leaking Analysis 探寻宇宙起源 Approaches to solve the problem T junction like stop band filter Disk like stop band filter

Accelerator Laboratory of Tsinghua University 33 SPX beamline and new superconducting cavity 探寻宇宙起源 Approaches to produce Short Pulsed X-ray RF window Flange before taper post like stop band filter

Accelerator Laboratory of Tsinghua University 34 SPX beamline and new superconducting cavity Approaches to produce Short Pulsed X-ray

Accelerator Laboratory of Tsinghua University 35 Copper Prototyping of on-cell damping deflecting cavity 探寻宇宙起源 Copper prototyping Purpose: To verify the design with measurement result. Copper prototype has been fabricated. We are testing the field distribution and Qext

Accelerator Laboratory of Tsinghua University 36 Copper Prototyping of on-cell damping deflecting cavity 探寻宇宙起源 Copper prototype measurement We have identified all the important modes. The measured frequency is very consistent with simulation. Next step is to measure the Qext after adding the damper on it. Frequency(MHz) PolarizationCST simulationMeasurementDifference TM010X % TM110vertical % TE111horizontal % TE111vertical % TM110horizontal % We could detect the TM110 peak through the LOM damper, indicating that Qext around 10 6

Accelerator Laboratory of Tsinghua University 37 Copper Prototyping of on-cell damping deflecting cavity 探寻宇宙起源 Copper prototype measurement Magnetic field is where most of the transverse kick comes from. Using dielectric bead to measure the E field, Using metal bead to measure E and H field Try to get magnetic field by subtracting electric from metal one E field profile of Deflecting ModeH field profile of Deflecting Mode I am working on better way to measure the H-field profile. Simulation Measurement Simulation

Accelerator Laboratory of Tsinghua University 38 Research and design of multi-cell deflecting cavity 探寻宇宙起源 The motivation of a multi-cell deflecting cavity For SPX-0, wake field damping is biggest concern of design. Single cavity is the easiest way. To generate X-ray around 1ps, we need deflecting voltage of 4MV, preliminary result has shown that single cavity can only provide deflecting voltage of 0.5MV. And space is limited. Multi-cell deflecting cavity could potentially increase the deflecting voltage per cavity, and reduce the cost. My work is focus 2-cell deflecting cavity.

Accelerator Laboratory of Tsinghua University 39 Research and design of multi-cell deflecting cavity 探寻宇宙起源 2-cell approach III.The benefit of 2-cell cavity 1. Increase the deflecting voltage per cavity from 0.5MV to 1MV 2. Lower the R/Q of other modes so as to lower mode excitation 3. Save more damper and space R/Q of different modes ModeSingle cell2cell 0 mode2cell pi mode ratio (2cell/1cell) TM TM110_y TE111_y TE11_x TM110_x

Accelerator Laboratory of Tsinghua University 40 Research and design of multi-cell deflecting cavity 探寻宇宙起源 2-cell approach III.Challenge of 2 cell cavity 1. Field Enhancement between the two cell 2. Damping the 0 mode and pi mode simultaneously Bmax/Vdef increased from 175mT/MV (single cell) to 220mT/MV (2 cell) R/Q will be around 66 compared with 34 for single cavity

Accelerator Laboratory of Tsinghua University 41 Research and design of multi-cell deflecting cavity 探寻宇宙起源 2-cell approach III.To change the iris geometry to lower to the surface magnetic field. 1. Field Enhancement between the two cell To make the iris shape similar to cavity shape The coupling of TM110 could be lowered Bmax/Vdef lowered from 160mT/MV (single cell) to 97mT/MV (2 cell)\ 1MV per 100mT 40mm Coupling coefficient from to Mode separation from 85MHz to 19MHz

Accelerator Laboratory of Tsinghua University 42 Research and design of multi-cell deflecting cavity 探寻宇宙起源 2-cell approach Due to increase of the transverse wake Bmax/Vdef=104mT/MV Pi mode R/Q 67 0 mode R/Q 0.1

Accelerator Laboratory of Tsinghua University 43 Wake field analysis of SC cavity 探寻宇宙起源 The short-range wake The squashed iris will lower the magnetic field significantly, but it make short- range transverse wave stronger. And the kick factor will be different. We need to investigate how the kick factor changes with a race-track iris so as to know how it affect beam instability