accelerator laboratory of tsinghua university research on deflecting cavities for spx project in aps...

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



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


Content


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


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.



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



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



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



Impedance budget How the impedance was related to beam instability ---- Robinson Instability or BBU.

Longitudinal:

Transverse:

Growth rate:



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.



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)



Current design options

Mark I Mark II

Power couplerPower coupler

LOM damper

HOM damper 1

HOM damper 2

HOM damper 1

LOM damper



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


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



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



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


Wake field analysis of deflecting cavity in storage ring

探寻宇宙起源

Long Range wake field effect: circular symmetric structure




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)



Long Range wake field effect: Mark II cavity The transverse wake is present for monopole mode in the asymmetric cavity


Hybrid mode Q is low

TM010

No high Q mode (above 5000) below 5GHz




Single beam excitation @(2mm,0) (-2mm,0)

TE111




Transverse kick due to the TM010 mode. Strong dipole component of dipole in TM010 field

Strength is 1/10 of the longitudinal


TM010 mode




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


TM010 mode



Long Range wake field effect: SPX-0 in ring test See how the wakefield spectrum change with the cavity interval.

TM01 cutoff frequency





Beam pipe TE11 cutoff frequency

Dipole beam excitation @(2mm,0)&(-2mm,0)




Beam pipe TE11 cutoff frequency

Dipole beam excitation @(0,2mm)&(0mm,-2mm)



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.



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.


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



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



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.



探寻宇宙起源

Approaches to solve the problem

T junction like stop band filter

Disk like stop band filter


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


SPX beamline and new superconducting cavity

Approaches to produce Short Pulsed X-ray


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



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



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


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.



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



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



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



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


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

accelerator laboratory of tsinghua university research on deflecting cavities for spx project in aps...

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