C.Limborg-Deprey ERL Workshop, Jefferson [email protected] March 20th 2005 Optimum electron distribution for space charge dominated beams

C.Limborg-Deprey

ERL Workshop , Jefferson Laboratory [email protected]

March 20th 2005

Optimum electron distribution for space charge dominated beams

C.Limborg-Deprey

Minimum emittance Ellipsoidal electron bunch

Comparison with “Beer Can” nominal case Optimization for S-Band and L-Band guns Sensitivity

Generation of 3D-ellipsoidal laser pulseTolerances on “stacker”Simulation

ConclusionsIs the production of such a pulse realistic?

C.Limborg-Deprey


March 20th 2005

Minimum emittance: Intrinsic limits

Intrinsic emittance for metal cathodefor copper measured 0.6 mm.mrad per mm [1,2,3]

theoretical is 0.3 mm.mrad per mm

Space Charge Limit Minimum radius or electrons cannot leave cathode for metal cathodes

rminimum = 0.82/0.26 mm at 54 MV/m for a 1/0.1nCrminimum = 1.34/0.42 mm at 20 MV/m for a 1/0.1nC

RF emittance 10 degrees acceptable for small RF , gives 0.15 mm.mrad for S-BandFor a single slice out of 100, it reduces to nearly 0

Space charge Strong non-linear effects if local charge density varies

Ideal Emitted pulse = Uniform charge density inside 3D-Ellipsoid volumeCharge density remains constant as the space charge force is linear Perfect emittance compensation is achieved with linear optics elements space charge ==0

sin

2 peakoo

Er

QE

2arg

22echspaceRFcathodetot

??22 roughnessthermalcathode

cathodetot

C.Limborg-Deprey


March 20th 2005

Ellipsoidal Emission pulse

Beer Can shape is not the optimum

Ideal Emitted pulse = Ellipsoid Ideally differs from Laser pulse by Shottky effect Electrons are uniformly distributed inside a 3D ellipsoid volume

22

2

2

2

2

2

Ac

z

b

y

a

x .const

dzdydx

N

rmax = 1.2 mm

Pulse length

Radius

fwhm = 10 ps

Pulse length

Line

Density

C.Limborg-Deprey


March 20th 2005

Gun S1 S2 L0-119.8MV/m

L0-224 MV/m

‘Laser Heater’

‘RF Deflecting cavity’ TCAV1

3 screen emittance measurement

6 MeV = 1.6 m ,un. = 3keV

63 MeV = 1.08 m ,un. = 3keV

135 MeV = 1.07 m ,un. = 3keV

DL1

135 MeV = 1.07 m ,un. = 40keV

Spectrometer

Lina

c tu

nnel

UV Laser 200 J, = 255 nm, 10ps, r = 1.2 mm

Spec

trom

eter

S-Band Gun

Epeak~120MV/m

S1L0-1~20 MV/m

6 MeV

63 MeV

C.Limborg-Deprey


March 20th 2005

Comparison between“beer can” &“3D ellipsoid”

rmax = 1.2mm

r= 1.2mm

C.Limborg-Deprey


March 20th 2005

Comparison between“beer can” &“3D ellipsoid”

= 1.02 mm.mrad; 80% = 0.95 mm.mrad, r = 1.2mm

= 0.71 mm.mrad ; 80% = 0.71 mm.mrad; r = 1mm

3D ellipsoid is even better optimized with rmax = 1mm

Larger slice emittance for beer can with r = 1mm

C.Limborg-Deprey


March 20th 2005

Gaussian

Square pulse

Ellipsoid

with thermal

= 1.16 mm.mrad

= 2.34 mm.mrad

= 0.75 mm.mrad

= 0.15 mm.mrad

no thermal

C.Limborg-Deprey


March 20th 2005

Linear longitudinal Phase Space Beer can

3D-ellipsoid

Exit gun Entrance L01

Exit L01

Longitudinal Phase Space

Ek [MeV] vs T [ps]

• The longitudinal phase space gets linear

• Unfortunately, does not prevent the production of large spikes after bunch compressor

those spikes come from wakefield which follow’

☺☼ lower current density on head and tail might help

☼ LCLS will benefit from lower slice emittance anyway, and better match

C.Limborg-Deprey


March 20th 2005

Optimization

= ½(o-2o+o)

Smaller r more mismatch

Too short bunch large mismatch

C.Limborg-Deprey


March 20th 2005

Optimization vs pulse length and radius

Vs laser pulse length Vs laser spot size radius

• Increasing pulse length reduces emittances

suggests running 12ps , but too long in LCLS later pulse compression

• Optimum radius would be between 0.8 and 1mm

unfortunately at 0.8 mm , too strong image charge distorts too much the bunch

C.Limborg-Deprey


March 20th 2005

Much less sensitive !!

Solenoid 1 0.3%

gun 2.5

Solenoid 2%

“Beer can”

> 7

Ellipsoid

how much distorsion on that perfect shape until we start losing this low sensitivity ?

Very low sensitivity to Shottky – Anyway can be compensated for as pulse generated

C.Limborg-Deprey


March 20th 2005

Optimization for L-Band Gun1nC, with little effort in optimizing/retuning

=1.42 mm.mrad; 80% = 1.34 mm.mrad

= 0.93 mm.mrad ; 80% = 0.96 mm.mrad

= 1.02 mm.mrad; 80% = 1.03 mm.mrad

L-Band gun 40MV/m, = 33,

at 140 MeV

C.Limborg-Deprey


March 20th 2005

Stacking pulses

6+6 beamlets of different radii

Gaussians Wash out discrete steps of rms value

Interferences

C.Limborg-Deprey


March 20th 2005

Fighting interferences in Stacker

Alternating polarization + appropriate choice of , interference effect is minimized

No interference Interferences random phases

+/- 15 %

i

i

i

i

tt

ip eeAE 242

2

22

i

i

i

i

tt

is eeAE 2412

2

212

sp III

*. ppp EEI *. sss EEI

C.Limborg-Deprey


March 20th 2005

PARMELA simulations using stacker distributions

Beer Can

Direct beer can

Ellipsoid ideal

50 Beamlets no interferenceStacker

12 Beamlets and random phase

= 1.02 mm.mrad; 80% = 0.95 mm.mrad

= 0.71 mm.mrad ; 80% = 0.71 mm.mrad

= 0.80 mm.mrad; 80% = 0.80 mm.mrad

IDEAL

NOT IDEAL

IDEAL

C.Limborg-Deprey


March 20th 2005

Stacker Layout

Profile shaper

pulse energy control

delayline

imaging optics

collimator-magnifier

delayslide

gratinggrating

spectralfilters

photocathode

halfwaveplate

polarizing cube

launch mirror

To the Courtesy of P.Bolton

“what to try to avoid…” from P.Bolton

C.Limborg-Deprey


March 20th 2005

Production of the 3D ellipsoidal pulseTwo solutions proposed

Pulse StackerToo complexToo lossy Uses too much space Technically feasible with many $$$$$$$ for

controls, to achieve alignment , timingmeasurement to adjust amplitude coefficient

Spectral Control technique UV shaping using Four-gratings with masking array in dispersive environment

Principle : for highly chirp beam

projects (t,x) into a 2D surface Use masking matrix (2D) Projects back in (t,x)

A second pair of gratings : same for (t,y)masking technology for UV needs to be developed (transmissive or reflective scheme)fluence limits on optics (even worse upstream)efficiency lowprobably better for space and money than previous solution

C.Limborg-Deprey


March 20th 2005

Spectral Control

z

yx

X mask y mask

Chirped input,

temporally

t

x

y

t

To cathode

In z,y plane

In z,x plane

C.Limborg-Deprey


March 20th 2005

ConclusionIdeal emission pulse = “ellipsoid” not “beer can”

Perfect emittance compensation in high charge regimeWorks better at high gradient Impressively less sensitive to tuning parameter

tolerances are 1 order of magnitude above those defined for “beer can” pulse even using “stacker pulse”

More exploration required for L-Band gun

Ellipsoidal Laser pulse is aTechnical challenge maybe not worse than “beer can” generation? if direct UV shaping has to considered anyway for “beer can”, the ellipsoid generation shares many of the same difficulties

C.Limborg-Deprey


March 20th 2005

References

[1] , Sumitomo Industries

[2] B.Graves, DUVFEL

[3] J.Schmerge, GTF

[4] O.J.Luiten, et al. “How to realize uniform 3-dimensional ellipsoidal electron bunches”, Phys.Rev. August 2004

[5 ]

C.Limborg-Deprey


March 20th 2005

Computation of of stacker


No interference

Interferences assuming random phases

+/- 15 %

C.Limborg-Deprey


March 20th 2005

S-Band Gun

Epeak~120MV/m

S1L0-1~20 MV/m

6 MeV

63 MeV

C.Limborg-Deprey


March 20th 2005

Computation using stackerDistributions with 12 Gaussians run and random phase with PARMELA for the

LCLS set-up

r = 0.8 mm

C.Limborg-Deprey


March 20th 2005

Computation using stackerDistributions with 12 Gaussians run and random phase with PARMELA for the

LCLS set-up

= 1.02 mm.mrad; 80% = 0.95 mm.mrad

= 0.71 mm.mrad ; 80% = 0.71 mm.mrad

= 0.80 mm.mrad; 80% = 0.80 mm.mrad

= 1.02 mm.mrad; 80% = 0.95 mm.mrad

= 0.69 mm.mrad ; 80% = 0.69 mm.mrad

= 0.79 mm.mrad; 80% = 0.79 mm.mrad

r = 1mm r = 0.9 mm

C.Limborg-Deprey


March 20th 2005

Production of the 3D ellipsoidal pulseTwo solutions proposed

pulse stackerToo complexToo lossy Uses too much space Technically feasible with many $$$$$$$

For controls, to achieve alignment , timingFor measurement to adjust coefficient

UV shaping using Four-gratings with masking array in dispersive environment ELL_Shaper

Principle First pair of gratings :

projects (t,x) into a 2D surface Use LCD matrix (2D) for partially masking Projects back in (t,x)

A second pair of gratings : same for (t,y)

Requires high input power (as low efficiency)

C.Limborg-Deprey


March 20th 2005

Stacking pulses


No interference Interferences random phases

+/- 15 %

i

i

i

i

tt

ip eeAE 242

2

22

i

i

i

i

tt

is eeAE 2412

2

212

sp III

*. ppp EEI

*. sss EEI

12 beamlets

Gaussians

Wash out discrete

steps

Documents

C.Limborg-Deprey ERL Workshop, Jefferson [email protected] March 20th 2005 Optimum electron distribution for space charge dominated beams