Post on 31-Mar-2021
EM Structures EM Structures &&
Laser Acceleration Laser Acceleration
Levi Schächter
Department of Electrical EngineeringDepartment of Electrical EngineeringTechnion Technion -- Israel Institute of TechnologyIsrael Institute of Technology
Haifa 32000, ISRAELHaifa 32000, ISRAEL
OutlineOutline
Constraints on optical structuresOptical structuresFour acceleration configurationsComments on luminosity & power
Constraints Constraints
GradientGradient: order of 1[GV/m] or higher.EfficiencyEfficiency: limited by radiation source and acceleration scheme
# Lasers anticipated efficiency of wall-plug to light 10% → 30%?!
# Efficiency of acceleration scheme – major difficultydifficulty
BreakdownBreakdown: at optical wavelengths dielectricsdielectrics sustain higherfields comparing to metals.
ManufacturingManufacturing constraints favor planar structures – consistentwith luminosity constraints.
Single ModeSingle Mode: width of vacuum tunnel 0.3λ - 0.8λMachining toleranceMachining tolerance: 1µm at 3 cm wavelength. Four orders ofmagnitude difference difficult to be preserved at λ=1µm (poster).
Optical structuresOptical structures
Planar Bragg StructurePlanar Bragg StructureCylindrical Bragg StructureCylindrical Bragg Structure
Longitudinal PBGLongitudinal PBGTransverse PBGTransverse PBG
int 19.5 @ 1Z mµ= Ω
E. Lin, PR STAB, 2000 B. Cowan, PR STAB, 2003
A. Mizrahi & L. Schachter, Phys. Rev. E, 2004
Talk in EM structures WG
Structure parameters Structure parameters
Planar Bragg StructurePlanar Bragg StructureCylindrical Bragg StructureCylindrical Bragg Structure
Longitudinal PBGLongitudinal PBGTransverse PBGTransverse PBG
int
intgr
acc
max
2.1, 1.5[ ]
250 20[ ]
0.55 1.25 0.2 0.6
0.35 0.15
y
m
ZD
EE
ε λ µ
λβ
λ=
∆÷ Ω
= ÷ ⇒ ÷ ÷
E. Lin, PR STAB, 2000 B. Cowan, PR STAB, 2003
A. Mizrahi & L. Schachter, Phys. Rev. E, 2004
intint
acc
max1 22.1, 4, 1[ ]
268 37[ ]0.3 0.8 0.41 0.48
0.73 0.37
gr
m
ZR
EE
ε ε λ µ
βλ
= = =
÷ Ω÷ ⇒ ÷ ÷
int
intgr
acc
max1 22.1, 4, 1[ ]
147 25.7[ ]
0.3 0.8 0.42 0.53
0.47 0.20
y
m
ZD
EE
ε ε λ µ
λβ
λ= = =
∆÷ Ω
= ÷ ⇒ ÷ ÷
intint
acc
max
2.1, 1[µm]
19.5[ ]0.68 0.58
0.5
gr
ZR
EE
ε λ
βλ=
Ω⇒
ConfigurationsConfigurations
Active Medium
Active Medium
Traveling-wave Acceleration
Module
Active Medium
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
Active Medium
Active Medium
Traveling-wave Acceleration
Module
Active Medium
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
• High efficiency
• Low # of electrons
• High efficiency
• Large # of electrons
Train of microTrain of micro--bunches & feedbackSingle bunch & feedback
Train of microTrain of micro--bunches & no feedbackSingle bunch & no feedback
Traveling-wave Acceleration
Module
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
External Laser
Traveling-wave Acceleration
Module
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
• Low efficiency
• Low # of electrons
• Moderate efficiency
• Large # of electrons
bunches & no feedbackSingle bunch & no feedback
Single bunch & feedback bunches & feedback
••Wake parameter:Wake parameter:
Decelerating field for a given charge …………
••BeamBeam--loading parameterloading parameter:
Beam-loading of the accelerating mode ……….. ( )dec 1
FE qκ≡
decE qκ≡
( ) ( )1
1
( 0, / ) cos 2
1
z n nn
nn
E r t z c q W h
W
τ κ ω τ τ∞
=
∞
=
= = −
=
∑
∑1 1Wκ κ≡
gr int1 2
gr 00 01 4/Zβ πκ
β πε λµ ε=
−
Traveling-wave Acceleration
Module
External Laser
022 / 4 Rκ πε=
Single bunch & no feedback Single bunch & no feedback
Contribution of the fundamental Contribution of the fundamental to the total deceleration Stupakov & Bane, PR STAB, 2003to the total deceleration
Acc. Structure
d
c
EMτ
Traveling-wave Acceleration
Module
External Laser Single bunch & no feedbackSingle bunch & no feedback
Acc. Structure
c
grcβ
EMτ
Laser pulse length for full overlap
dTime it takes the micro-bunch to traverse thestructure
1 1EM grEM
gr gr
d cd dc c c
τ βτ
β β −
= ⇒ = −
( )0KIN accmax opt 02
EM 0
1 12
42
qU Eq qU q
q qη η
κ−∆
≡ = ⇒ = ≡
1max
κηκ
=
eff acc dec accE E E E qκ≡ − = −
Traveling-wave Acceleration
Module
External Laser
Single bunch & no feedback Single bunch & no feedback
• Loaded gradient:
• Kinetic energy:
• EM energy:
KIN effU qE d∆ ≡
EM Laser grgr
(1 / )dU P V cV
≡ −
Zero force chargeZero force charge
Maximum efficiency is set by the projection of the Maximum efficiency is set by the projection of the total deceleration on the fundamental !!total deceleration on the fundamental !!
Planar Bragg StructurePlanar Bragg StructureCylindrical Bragg StructureCylindrical Bragg Structure
Longitudinal PBGLongitudinal PBGTransverse PBGTransverse PBG
[ ]
[ ]
int
Laser
int4
opt
max acc
0.682.1, 1.0[µm] 50 kW
19.5[ ] 6%0.58 7 102[GV/m] 1 GV/m
gr
RP
Zq e
E E
λε λ
ηβ
= Ω ⇒ ×
[ ]
[ ][ ]
int
Laser
int 4opt
accmax
0.552.1
2.3 kW/ m1.5[µm]36%/ 250[ ]5 10 /µm0.20.6 GV/m2[GV/m]
y
gr
D
P
Zq e
EE
λε
µληλ
β
= ⇒∆ Ω ×
[ ]
[ ]
int
1 2Laser
int 4opt
accmax
0.682.1, 4
18 kW1[µm]
9%56.4[ ]
7 100.581 GV/m2[GV/m]
gr
R
P
Zq e
EE
λε ελ
η
β
= = ⇒Ω ×
[ ]
[ ]
int
1 2Laser
int 4opt
accmax
0.552.1, 4
5.3 kW/ m1[µm]8%/ 57[ ]3.3 10 [ / m]0.480.56 GV/m2[GV/m]
y
gr
D
P
Zq e
EE
λε ε
µληλ
µβ
= = ⇒∆ Ω ×
E. Lin, PR STAB, 2000 B. Cowan, PR STAB, 2003
A. Mizrahi & L. Schachter, Phys. Rev. E, 2004
Single bunch & no feedback Single bunch & no feedback
Traveling-wave Acceleration
Module
External Laser
Single bunch & no feedback Single bunch & no feedback Maximum efficiency is set by the Maximum efficiency is set by the
projection of the total deceleration on projection of the total deceleration on the the fundamental
1max
κηκ
=
fundamental
By By splitting the bunchsplitting the bunch into a train of microinto a train of micro--bunches, the projection bunches, the projection of the wake on the fundamental remains the same, but of the wake on the fundamental remains the same, but higher higher frequencies arefrequencies are suppressedsuppressed
12 2
1
1
2
sinc( ) ( )
sinc
nM
nn n
MP M q c W q c M
ωπω
κ κωπω
=
= =
∑
1 1max
1 2( ) ( ) ....M Mκ κη
κ κ κ= =
+ +
??0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20
Nor
mal
ized
Coe
ffic
ient
M
Rb / R
ext= 0.7
Rb / R
ext= 0.5
Rb / R
ext= 0.3
Train of bunches & no feedbackTrain of bunches & no feedback
What is the efficiency in case of a train of microWhat is the efficiency in case of a train of micro--bunches? bunches?
For an answer, one needs to make two observations:For an answer, one needs to make two observations:
a) The laser pulse duration ought to be a) The laser pulse duration ought to be longer longer in order to in order to account for the macroaccount for the macro--bunch length.bunch length.
b) The envelope of the laser pulse must be b) The envelope of the laser pulse must be tapered, tapered, in order to in order to compensate for beam loading.
Traveling-wave Acceleration
Module
External Laser
compensate for beam loading.
Still we have a problem: wake propagates at cwhereas laser’s envelope propagates at cβgr.
Solution: Mλ=d
Uniform laser pulse Uniform & loading Tapered laser pulse Tapered & loading
⇒ ⇒ ⇒
Tapered laser pulseTapered laser pulse
Traveling-wave Acceleration
Module
External Laser Train of bunches & no feedbackTrain of bunches & no feedback
Laser tapered pulse tapered pulse necessary to compensatecompensate for the beam loading in order to ensure uniformuniform acceleration of allall micro-bunches
1000 200 300 400 5000.0
0.2
0.4
0.6
0.8
1.0
Norm
alize
d Env
elope
of th
e Wak
e
dM =λ
dM <λ
dM >λ
λτ /c
1M
( ) ( )
( ) ( )
1gr 0
221 1
0gr
02gr gr 2 2 2
0 gr
12 1
1 13 1
12 1 .3
q q q
q q q qM
q q qq q
κβκη
κ κκ β κ
β ββ
− − = − + + +
−−
+
20 02
13 1 13opt gr
gr
q q qβ ξβ
+ − ≡
( ) ( )2max 2 2
112 1
3gr grgr
ξ ξη β β
ξ β−
−+
Traveling-wave Acceleration
Module
External Laser Train of bunches & no feedbackTrain of bunches & no feedback
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
0.0
0.1
0.2
0.3
0.4
0.5
Max
imum
Eff
icie
ncy
grβ
0/q
q opt
»1M11, 1M κκ
In spite of splitting the macro-bunch, there still is 50% waste of the laser energy feedback loop.
Traveling-wave Acceleration
Module
Active Medium
External Laser
• External laser field: EL
• Input to acceleration module : Ein=EL+EFB
• Output of the acceleration module : Eout=Ein – Ew
Single bunch & feedbackSingle bunch & feedbackFundamental
mode
2κ1q
• Feedback loop: EFB= Γ Eout
• Dynamics:
( ) ( ) ( )( )out out gr gr( ) / /F
rr L WE t E t T E t d c E t d cβ β=Γ − + − − −
overall gain loss coefficientgain
21 1/
g e
e Q
ψ
ψ
−
−
Γ =
− =
Acceleration Module
FBE
outE
Active Medium&
Loss
LE
( )FWE
( )HWE
e- e-inE
• External energy injected into the system:( ) ( ) ( ) ( ) 22
acc 12 2Laser EM ACTIVE OUT EM
int int
2, 1 1L E qE
U U g U gZ Z
λ κλτ τ
− = = − = −
Traveling-wave Acceleration
Module
Active Medium
External Laser
Single bunch & feedbackSingle bunch & feedback
• In steady state it compensates energy which leaves: ∆UKIN and ULOSS=UOUT/Q 1
11
KIN KIN
OUTLASER ACTIVE KIN LOSS
KIN
U UUU U U U
Q U
η ∆ ∆= = =
+ ∆ + +∆
opt 0 max 1
1
1 11 1, 12 11
Qq q
Q
Q
η κκκ
κ
=
→+
High efficiency but,
small number of electrons train of bunches and feedback loop
Train of bunches & feedbackTrain of bunches & feedback
Traveling-wave Acceleration
Module
Active Medium
External Laser
Traveling-wave Acceleration
Module
Active Medium
External Laser
⇒
Ensure that output & feedback are consistent with the necessary input !!
Traveling-wave Acceleration
Module
Active Medium
External Laser
output2.0=αcvgr 4.0=
input
laser
EMt τ/
Nor
mal
ized
Fie
ld
output
input
laser
output
input
laser
2.0=αcvgr 5.0=
2.0=αcvgr 6.0=
-1.0 0.0 1.0 2.0 3.0-0.2
0.0
0.2
0.4
0.6
0.8
1.0
EMt τ/-1.0 0.0 1.0 2.0 3.0
EMt τ/-1.0 0.0 1.0 2.0 3.0
M dλ =
Active enhancement of the quality factor
Train of bunches & feedbackTrain of bunches & feedback
Laser pulse shapingLaser pulse shaping
Talk in Exotic schemes WG
Conditions for self-consistent field:
(I) Amplifier compensates for all radiation lossradiation loss
(II) External laser compensates for beambeam--loadingloading
111
KIN
OUTLASER ACTIVE
KIN
UUU U
Q U
η ∆= =
+ +∆
Traveling-wave Acceleration
Module
Active Medium
External Laser
0.2
0.4
0.6
0.8
1.0
0/ qq
5.0=grβ( ) 0.1/ =κκ F25=Q
5=Q
1=Q
Effic
ienc
y
0.00.0 0.2 0.4 0.6 0.8 1.0
0/ qq0.0 0.2 0.4 0.6 0.8 1.0
0/ qq0.0 0.2 0.4 0.6 0.8 1.0
9.0=grβ
5.0=grβ5=Q
.5.0=grβ5=Q
1.0=grβ
( ) 0.1/ =κκ F
( ) 5.0/ =κκ F
( ) 0.1/ =κκ F
( ) 1.0/ =κκ F
High Q: (I) High efficiency (II) Reduced sensitivity
- Peak efficiency independent of κ1/κ
- Sensitivity
- Peak efficiency dependent on βgr
- Sensitivity
Train of bunches & feedbackTrain of bunches & feedback
frr
Nel
microNzσ
,x yσ
NLC:
el posrr micro 4 D
x y
N NL f N H
πσ σ=
Luminosity Luminosity
microN
Optical Acc.:
Nel
( )( )el micro pos microrr 4
1x y
N N N NL f
πσ σ= × ×
frr Assumption:
Ignore structure of the macro-bunch
Luminosity Luminosity
80808080444(4(--3)3)13.713.7Beam power [MW]
1.2(36)1.2(36)1.2(34)1.2(34)3(30)3(30)3(25)3(25)2(34)2(34)L[cm-2sec-1]
1.01.01.01.01.4HD
4
24.5
0.27
0.3
4
245
2.7
1.4
4
24.5
0.27
0.8
4
245
2.7
3.8
0.11(6)
245
2.7
2.1
σz [nm]σx [nm] σy [nm]n-1/3 [Å]
1(6)
1(3)
1(6)
Train & FB
1(6)5(4)5(4)0.75(10)Nel
1(3)11190Nmicro
1(6)1(9)1(6)120frr [Hz]
Train & FB
Single no FB
Single no FB
NLC
Fluence
Density !
Summary: Dielectric StructuresSummary: Dielectric Structures
Planar Bragg StructurePlanar Bragg StructureCylindrical Bragg StructureCylindrical Bragg Structure
Longitudinal PBGLongitudinal PBGTransverse PBGTransverse PBG
int 19.5 @ 1Z mµ= Ω
Dielectric periodic structures may confine an accelerating mode and allow high order modes to leak out.
Train of micro-bunches contributes to suppression of high frequency wakes.
Summary: ConfigurationsSummary: Configurations
Active Medium
Active Medium
Traveling-wave Acceleration
Module
Active Medium
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
Active Medium
Active Medium
Traveling-wave Acceleration
Module
Active Medium
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
• High efficiency
• Low # of electrons
• High efficiency
• Large # of electrons
Train of microTrain of micro--bunches & feedbackSingle bunch & feedback
Train of microTrain of micro--bunches & no feedbackSingle bunch & no feedback
Traveling-wave Acceleration
Module
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
External Laser
Traveling-wave Acceleration
Module
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
• Low efficiency
• Low # of electrons
• Moderate efficiency
• Large # of electrons
bunches & no feedbackSingle bunch & no feedback
Single bunch & feedback bunches & feedback
Summary: Efficiency & LuminositySummary: Efficiency & Luminosity
Active Medium
Active Medium
Traveling-wave Acceleration
Module
Active Medium
External Laser
External Laser
External Laser
Traveling-wave Acceleration
Module
Traveling-wave Acceleration
Module
(I) Amplifier compensates for all radiation loss radiation loss (active enhancement of the Q—factor) facilitated by the wake being “quasi-coherent”
(II) External laser compensates for beambeam--loading loading (tapered pulse)
(III) Luminosity
Talk in Exotic schemes WG