AnalysisofBBUincompactstructure-basedacceleratorand

asuppressionmethodS.S.Baturin*

UniversityofChicagoA.Zholents

ArgonneNationalLaboratoryFACET-IIworkshop

10/18/2017

1

Outline

• Compactstructurebasedwakefield accelerator

• Introductiontodynamicsproblem

• Adaptivefocusing

• BNSdampingandstabilityanalysis

• ApplicationtoCollinearWakefieldAccelerator

2

Compactstructurebasedwakefield accelerator

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JointlypursuedbyArgonne'sAWAandAPSgroupsforacompactFELfacility

Introduction

• Initialstudy• A.W.Chao,B.RichterandC.Y.Yao,Nucl.Instr.andMeth.A,178(1980)

• ExtensiveanalysisandfullBBUtheoryforsmoothfocusingJ.R.Delayen

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Introduction

•Chao– limitedtosmallwakeamplitudes.

•Delayen – limitedtosmoothfocusing.

5

Canweapplyexistingtheorydirectlytoanalyse CWA?

Themodel

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Themodel

Equationsofmotion

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Adaptivefocusing

• Howwekeepconstantphaseadvance?

• Howtotweakmagneticsystemtomatchtheenergyofthefirstparticle?

• Weknowthattomitigatethewakefield weneedenergyspread. 8

Adaptiveenergy chirp

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Adaptiveenergy chirp

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Adaptiveenergy chirp

weintroducenewvariables

11

AdaptivelenslengthL

Periodicfunctionofu

!" #"" #!"

-$

-#

"

#

$

%(&'(')

!(")/!!

1(1 - αz)1/4

!" #"" #!"

-$

-#

"

#

$

%(&'(')

!(")/!!

11 - αz

z

g(z)

z

g(z)

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Adaptivefocusingsummary

• Adaptivechip

• Adaptivelenslengthvariation

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Wakefieldcancelation

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Wakefieldcancelation

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Vladimir I. Arnol’d, Ordinary Differential Equations, Springer-Verlag, Berlin (1992)

Wakefieldcancelation

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Wakefieldcancelation

GeneralideaofBNSdamping1fordeterminingf(s)

-! " !

-!

"

!

#($)

!"(#)

a)

-! " !

-!

"

!

#($)

!"(#)

b)

-! " !

-!

"

!

#($)

!"(#)

c)

-! " !

-!

"

!

#($)

!"(#)

d)

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1 V. Balakin, S. Novokhatsky, V. Smirnov, Transverse Beam Dynamics, Proc. 12th Int. Conf. on High Energy Acc., Batavia, Illinois, (1983) p.119- 120

Wakefieldcancelation.Stability.

!"!! !"!# !"$! !"$#%

&

'

(

$!

$%

)(*)/+

!/η

Φ1 0.1

Φ1 0.2π

Φ1 0.3πΦ1 0.4πΦ1 0.5π

!"!! !"!# !"$! !"$#

$"#

%"!

%"#

&"!

'(()/)

!/η

Φ1 0.6π

Φ1 0.74π

Φ1 0.4π

Φ1 0.5π

Unstable region

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StabilityconditionforCollinearWakefiledAccelerator

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StabilityconditionforCollinearWakefiledAccelerator

���� ���� ���� ����

���

���

���

���

�(�)/

�/η

Φ1=0.6π

Φ1=0.74π

Φ1=0.4π

Φ1=0.5π

Unstable region

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StabilityconditionforCollinearWakefiledAccelerator

Summary

• Adaptivechip

• Adaptivelenslengthvariation

• Restrictionsonchirp

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Numericexample

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Numericexample

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100MV/m

p g

Acknowledgments

• CenterforBrightBeamsandNSF

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Fullsimulationoftwoparticlemotion

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