accelerator laboratory of tsinghua university research on deflecting cavities for spx project in aps...
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Accelerator Laboratory of Tsinghua University
Research on deflecting cavities for SPX project in APS
Yawei YangTsinghua University, Argonne National Lab
Institute of Modern Physics, Lanzhou, China
Accelerator Laboratory of Tsinghua University2
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 University3
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 experimentsR&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 University5
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 University6
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 University7
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 University8
Wakefield Analysis of SC deflecting cavity in APS
Wake potential and impedance
L
zz dzcszzEq
s0
,1
W
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.
L
edzcszzFq
s0
/,1
W
Accelerator Laboratory of Tsinghua University9
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.
(CLm) (VC-1L-2m) (VC-1L1-2m)
Wake potential in circular symmetric structure
Accelerator Laboratory of Tsinghua University10
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 University11
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 University12
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 University13
Wakefield Analysis of SC deflecting cavity in APS
Current design options
Mark I Mark II
Power couplerPower coupler
LOM damper
HOM damper 1
HOM damper 2
HOM damper 1
LOM damper
Accelerator Laboratory of Tsinghua University14
Wakefield Analysis of SC deflecting cavity in APS
Eigen mode analysis
Mode Freq(GHz) Qext R/Q longi R/Q trans Longi (Ohm) Trans (Ohm/m)TM010 (cavity) 2247.4 67.96 62.777 1.121 4266.346 3542.000
TM110(working mode) 2812.1 1.1E-04 36.715TE110 (cavity)-1 2985.1 273.47 2.0E-03 0.940 0.536 16082.449TE110 (cavity)-2 3027.2 515.75 9.5E-05 0.990 0.049 32395.233TM110(cavity) 3371.5 74.02 3.8E-03 2.777 0.280 14523.148
Mark I Mark II
Mode Freq(GHz) Qext R/Q longi R/Q trans Longi (Ohm) Trans (Ohm/m)TM010 (cavity) 2419.3 260 58 4.1 15080 1.30E+05
TM110(working mode) 2814.05 9.00E-05 37.103TE110 (cavity)-1 2985.1 295.31 1.81E-01 0.626 53.41 11475.54 TE110 (cavity)-2 3003.02 578.83 4.10E-05 0.3 0.02 7427.33
TM110(cavity) 3295.2 11662 3.00E-03 5.35 35.5 4.31E+06
Mark I
Mark II
Accelerator Laboratory of Tsinghua University15
Design of on-cell damping deflecting cavity
探寻宇宙起源
On-cell damping single cell designTM010 mode has been
Significantly lowered
Single beam excitation @(0,0)
TM010 mode
Accelerator Laboratory of Tsinghua University16
Design of on-cell damping deflecting cavity
探寻宇宙起源
On-cell damping single cell design
TM110hori is not a problem
any more
Dipole beam excitation @(2mm,0)(-2mm,0)
TM110 hori mode
Qext 11000
Accelerator Laboratory of Tsinghua University17
Design of on-cell damping deflecting cavity
探寻宇宙起源
On-cell damping single cell designMark-II has been chosen as the
design for SPX-0 in ring test.Dipole beam excitation @(0, 2mm)(0,-2mm)
Deflecting Mode
Accelerator Laboratory of Tsinghua University18
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 excitation @(0,0)
Accelerator Laboratory of Tsinghua University19
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 excitation @(-4mm,0)
Or Dipole beam excitation @(2mm,0)&(2mm,0)
Accelerator Laboratory of Tsinghua University20
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 excitation @(0,0)
Hybrid mode Q is low
TM010
No high Q mode (above 5000) below 5GHz
Accelerator Laboratory of Tsinghua University21
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 excitation @(2mm,0) (-2mm,0)
TE111
Accelerator Laboratory of Tsinghua University22
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 excitation @(0,0)
TM010 mode
Accelerator Laboratory of Tsinghua University23
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 excitation @(0,0)
TM010 mode
Accelerator Laboratory of Tsinghua University24
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 excitation @(0,0)
Accelerator Laboratory of Tsinghua University25
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 excitation @(2mm,0)&(-2mm,0)
Accelerator Laboratory of Tsinghua University26
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 excitation @(0,2mm)&(0mm,-2mm)
Accelerator Laboratory of Tsinghua University27
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 University28
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 University29
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 University30
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-0.1 -7.2365
0 2.80960.1 12.999350.2 23.05180.3 32.8906
positive
Integration displacement (mm)
Accelerating voltage
Accelerator Laboratory of Tsinghua University31
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 University32
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 University33
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 University34
SPX beamline and new superconducting cavity
Approaches to produce Short Pulsed X-ray
Accelerator Laboratory of Tsinghua University35
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 University36
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)
Polarization CST simulation Measurement Difference
TM010 X 2295.82 2299.085 0.142%
TM110 vertical 2812.19 2809.955 -0.080%
TE111 horizontal 2975.325 2977.692 0.079%
TE111 vertical 3036.44 3038.175 0.057%
TM110 horizontal 3346.72 3368.568 0.649%
We could detect the TM110 peak through the LOM damper, indicating that Qext around 106
Accelerator Laboratory of Tsinghua University37
Copper Prototyping of on-cell damping deflecting cavity
探寻宇宙起源
Copper prototype measurementMagnetic 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 Mode H field profile of Deflecting Mode
I am working on better way to measure the H-field profile.
Simulation
Measurement Measurement
Simulation
Accelerator Laboratory of Tsinghua University38
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 University39
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 modesMode Single cell 2cell 0 mode 2cell pi mode ratio (2cell/1cell)
TM010 72.71 20.62 115.8 1.59 TM110_y 32.56 0.78 65.64 2.02 TE111_y 5.075 4.32 2.86 0.85 TE11_x 4.71 1.69 8.1417 1.73
TM110_x 5.159 9.1 1.5 1.76
Accelerator Laboratory of Tsinghua University40
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 increasedfrom 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 University41
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 cavity@ 100mT
40mmCoupling coefficient from -0.015 to 0.0033
Mode separation from 85MHz to 19MHz
Accelerator Laboratory of Tsinghua University42
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 670 mode R/Q 0.1
Accelerator Laboratory of Tsinghua University43
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