technion - electrical engineering faculty - em structures laser … · 2008. 3. 9. · em...

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



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

= ÷ ⇒ ÷ ÷



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


Module


Module

Active Medium

Active Medium


Module

Active Medium

External Laser

External Laser

External Laser


Module


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


Module

External Laser

External Laser


Module


Module

External Laser


Module

External Laser

External Laser

External Laser


Module


Module

• Low efficiency


• Moderate efficiency


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=

−


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


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≡ − = −


Module

External Laser


• 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 !!



[ ]

[ ]

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 ×





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.


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


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−

−+


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.


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

− = = − = −


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


Module

Active Medium

External Laser


Module

Active Medium

External Laser

⇒

Ensure that output & feedback are consistent with the necessary input !!


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


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 ∆= =

+ +∆


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


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



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


Module

Active Medium

External Laser

External Laser

External Laser


Module


Module

Active Medium

Active Medium


Module

Active Medium

External Laser

External Laser

External Laser


Module


Module

• High efficiency


• High efficiency


Train of microTrain of micro--bunches & feedbackSingle bunch & feedback

Train of microTrain of micro--bunches & no feedbackSingle bunch & no feedback


Module

External Laser

External Laser


Module


Module

External Laser


Module

External Laser

External Laser

External Laser


Module


Module

• Low efficiency


• Moderate efficiency


bunches & no feedbackSingle bunch & no feedback

Single bunch & feedback bunches & feedback

Summary: Efficiency & LuminositySummary: Efficiency & Luminosity

Active Medium

Active Medium


Module

Active Medium

External Laser

External Laser

External Laser


Module


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

technion - electrical engineering faculty - em structures laser … · 2008. 3. 9. · em...

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