Stanislav Baturin Euclid TechLabs 10/26/2016 · 2016. 10. 26. · • Wakefields are very important...
Transcript of Stanislav Baturin Euclid TechLabs 10/26/2016 · 2016. 10. 26. · • Wakefields are very important...
Stanislav BaturinEuclid TechLabs
10/26/2016
• Introduction to the wakefield concepts
• Simple calculation of the wakefields
• Wakefield based devices
Outline
Wakefield. Friend or foe?
• Beam energy spread
• Parasitic transverse momentum induction
• Negative effect on beam dynamics
Source of the wakefield
Disk loaded structureCollimators
and pipe transitionsStructures with
the “retarding” layer
Definition of the wakefield
Transverse wakefield potential
Longitudinal wakefield potential
Definition of the wakefield potential
1
1 ,z zz sW E z t dz
Q c
∞
−∞
+ = − = ∫
1
1 , z sW F z t dzQ c
∞
⊥−∞
+ = = ∫
1 2 ( )zE Q Q W s∆ = −Energy change of the test particle
Problem: How to calculate wakefield?
Finite differencemethods
Semi-analyticalmethods Pen and paper
What are the steps?
Pen and paper
The Idea
The Method
The Result
zW Ws⊥
⊥
∂= ∇
∂
(0 ) 2 (0)z zG G+ =
Panofsky-Wenzel theorem
Beam loadingtheorem
Important theorems
A. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley
and Sons, New York, 1993).
One more theorem
Relativistic Gauss Theorem
(0 ) 0D
Dz
S
E dS+ =∫∫
The Idea
Relativistic Gauss Theorem
z
S
DHdl qnV dSt
⊥
∂ = + ∂ ∫ ∫∫
0
0
(0 )V
Vz
S
qE dSε
+ = −∫∫1 ( )z
S
DHdl dS qc
δ ζζ
⊥
∂= +
∂∫ ∫∫
S.S. Baturin, A.D. Kanareykin. PRL113, 214801, 2014
0 0( ) (y ) (z )n x x y Vtδ δ δ= − − −
Vt zζ = −
(0 ) 0V
Vz
S
dH S+ =∫∫
The Method
Relativistic Gauss Theorem S.S. Baturin, A.D. Kanareykin. PR-AB19, 051001 (2016)
0zE⊥∆ =0zH⊥∆ =
Inside vacuum cannel
Relativistic Gauss TheoremThe Method
x iyω = +
x ye E iE= +
)( z zZg E iHχ ζ
∂−
∂=
∂ ∂
· 4 z zE Hi iπρζ ζ⊥ ⊥ ⊥ ⊥
∂ ∂∇ + ∇ × = + −
∂ ∂E E
· 4 z zE Hi i iπρζ ζ⊥ ⊥ ⊥ ⊥
∂ ∂∇ + ∇ × = + − ∂ ∂
H H
Maxwell equations in vacuum channel
x yh H iH= +
ct zζ = −
2 2 ( ) ( ) Zge Q x yδ δω ω
∂∂ ′ ′= +∂ ∂
Relativistic Gauss TheoremThe Method
*
2 2 ( ) ( ) Zge dQ x ydχ δ δ
χ ω χ∂∂ ′ ′= + ∂ ∂
0zH =zE const=
0Ze g− = 0Ze g− =
0
*
2(0 ) (0 ) 4z z
Q d dE iHa d d
ω ω
χ χω ω
+ +
=
− = −
0
*2
2 2( ) 4( )x yeQ d dF iF sa d
sd
sω ω
χ χω ω
=
=
+
Relativistic Gauss Theorem
Longitudinal electromagnetic field
Transverse Lorentz force
The Result
0s +→
The Result
Conformal mapping
2
20
(0 )16
Vz
c
qEa
ππε
+ = −2
0z
c
qEa
χ
πε= −
General formula
( ) tanh4
ia
π ωωχ = −
2dJdχω
=
(0 ) (0 )z zE J E χω + +=
0
*
2 20
2R) e(0zc
Q Q d dEa a d d
ω ω
χ χπε ω ω
+
=
= − −
Relativistic Gauss Theorem S.S. Baturin, A.D. Kanareykin. PR-AB19, 051001 (2016)
Conformal mapping
02
0
( ) cc
raa r
χ ωωω−
=−
40
320
0
2
1
( )r
c
c
rF eQa r
a
ss πε
= −
0
*2
2 20
( )
c
rF eQ d da d
ss d
ω ω
χ χπε ω ω
=
=
General formula
The Result
Relativistic Gauss Theorem
A. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (Wiley and Sons, New York, 1993).
S.S. Baturin, A.D. Kanareykin. PRL113, 214801, 2014
Cylinder Cylinderdisplaced
Planar Rectangular
The Result
Relativistic Gauss Theorem
1f =( ) 22
0
1(1 / )
dpc
fr a
=+
2
16plf π= 0.86sqf =
S.S. Baturin, A.D. Kanareykin. PRL113, 214801, 2014
0
*
2 20
2R) e(0zc
Q Q d dEa a d d
ω ω
χ χπε ω ω
+
=
= − −
Example of Dielectric Wakefield Accelerator:▫ Dielectrics: ε = 4.4 (cordierite-10 (alumina) – low-loss ceramic,
ε = 5.7 – diamond, ε = 3.7 - quartz▫ Electron beam parameter: σz = 20-30 um, Q = 1-3 nC, frequency 0.3-1.2 THz, ▫ Wakefield maximum 0.1-1.0 GV/m
Wakefield accelerator
W RW+ −∆ =
Transformer ratio
max
maxz
z
ER
E
+
−=
Now we define limits on wakefield maximum and transformer ratio.
Wakefield accelerator
The Idea
Limiting Gradient
( )z zE E E R+ + −→ →
( )z zE E R+ +→
max
maxz
z
ER
E
+
−=
0 0 00
( ) cos[ ( )] ( )s
zE s A k s s s dsρ− = −∫ 2
0
( ) ( )( )s
z zE s E ss k dsA A
ρ− −
= + ∫
The Method
Limiting Gradient
0 0 00
( ) cos[ ( )] ( )l
zE s A k s s s dsρ+ = −∫ ( )z zE E E+ + −→
STEP 1
STEP 2
Estimate the integrals in ( )zE E+ −
Limiting Gradient S.S. Baturin, A. Zholentsto be published
2 20
2max( )1z
Qf REa Rπε
+ ≤+
The Result
2 21R k l≤ +
The Result
Argonne studies of Wakefield Accelerator*
Driver charge
Aperture Driver energy
Desired energy gain
Transformer ratio
8nC 2 mm 400 MeV 1.6 Gev 5
max( ) 109zMVEm
=
*A. Zholents et al, Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment 829 February 2016
Now we will discuss wakefield application to the bunch
diagnostics.
30
Bunch diagnostics in principle
Slice Emittance Measurement
31
Retractable structure
Induced transversemomentum
Transverse wake
Quadruple
slice beam size
on Screen
Slice Emittance Measurement
S. Bettoni, P. Craievich, A. A. Lutman,2 and M. Pedrozzi1 PR-AB 19, 021304 (2016) Experimental results
Slice Emittance Measurement
[ ]8n A
p
Ismrad Iε
γ≈ 'n r rε γσ σ=
17.045AI kA=
Energy 140 MeV 1.4 GeV 14 GeV
bunch length 1 mm 100um 30 um
current 300 A 1 kA 3.5 kA
resolution 75 um 10 um 1.7 um
1n mm mradε = ×
There are more applications that may take advantage of controllable
wakefields.
1) S. Antipov, S. Baturin et al. PRL 112, 114801 (2014)Energy Spread Compensation2) P. Emma, M. Venturini, K. L. F. Bane, G. Stupakov et al. PRL 112, 034801
S. Antipov et al. PRL 108, 144801 (2012)
Subpicosecond Bunch Train Production
U=50 MVPh. -10 deg.
U=70 MVPh. 15 deg.
U=250 MVPh. 30.8 deg.
R56= 0 mm
Drive bunch In
R56= 20 mm
Drive bunch Out
Time reversible tracking
Includes:• Wakefields• Long. space charge• T566
CSR is next
Large energy chirp
~ 4 kA~ 200 A
Bunch Shaping
• Wakefields are very important part of accelerator science and technology
• Many novel ideas on how we can benefit from wakefieldsappeared and proved to be working during past years
• New tools for calculation of the wakefields and beam dynamics have been developed and more to come
• Analytical tools for the plasma wakefields
Conclusion