BROOKHAVEN SCIENCE ASSOCIATES BIW ’ 06 Lepton Beam Emittance Instrumentation Igor Pinayev National Synchrotron Light Source BNL, Upton, NY

BROOKHAVEN SCIENCE ASSOCIATES

BIW’06

Lepton Beam Emittance Instrumentation

Igor PinayevNational Synchrotron Light Source

BNL, Upton, NY

2 BROOKHAVEN SCIENCE ASSOCIATES

Outline

• Motivation and Definitions• Invasive methods

• Three screens• Wire scan• Quadrupole and solenoid scan

• Non-invasive methods• Visible light imaging• Pinhole camera• Imaging with zone plate• Interferometric method• Undulator radiation• Optical diffraction radiation

• Conclusions


Emittance Definition

• Emittance is a measure of area occupied by a beam in phase space

• It affects major operational parameter: brightness, luminosity, gain length, coherency, etc.

222 '' xxxxx

x’

Area =

For uncoupled beam

maxx

x

max'x

slope

The invariant emittance ellipse is given by

)(

)(1)(

2

(s)'-(s)

where

')(')(2)(

2

22

s

ss

xsxxsxs


Matrix Gymnastics

0

0

1

1

x

x

SC

SC

x

x

0

0

1

1

10

1

x

xL

x

x

0

0

11

1

1

01

x

x

x

x

f

0

22

22

12

2

SSCC

SSCSSCCC

SCSC

Particle propagating from point to another

can be described by the transport matrix

Twiss parameters transform as follows

For drift space with length L

For thin lens


Three Screens Method

2

22

1

21

0

20

11

11

SC

SC

22

22

SC

SC

•Requires long drift space•Sensitive to optical magnification errors•Space charge effects can be significant•Shot-to-shot variations

S0 S1S2

2211

2221

222

2

2222,1

220

2222,1

20

1

1

2

2

0

1

0

2

2,1

2,1

2,1

2,1

0

2,1

2,1

2,1

2,1

2,1

0

2,1

where

4

4

1

SCSC

SS

S

S

SC

SC

SC

SC

SC

SC


Wire Scan


Factors Affecting Accuracy of Wire Scan

22

4

wire

beammeas

d• tilt angle of wire• dispersion in transfer line• beam jitter• scan non-uniformity

2

EE

xxxx


Quadrupole Scan

• Beam parameters are extracted from the dependence of observed beam size vs. quadrupole strength

• Change in the upstream quadrupoles strength may be required because quadrupole focuses in one plane and defocuses in another

Quadrupole (0, 0, 0)

beam

Screen (S)


Extracting Data from the Quadrupole Scan

For the thin quadrupole and drift with length L transport matrix is

0

0

1

1

11

1

x

x

f

LfL

x

x

L

aaaε

afLafLa

LLfLfL

LLfLfLS

4

is emittance the

)1()1(

fitparabolicthefrom

)1(2)1(

and

)1(2)1(

2120

012

22S

02

0022

S

02

002


Solenoid Scan

• Similar to the quadrupole scan• Solenoid introduces beam rotation

(coupling)• Low energy• Radial symmetry can be usedGun Solenoid

Screen

2

01

cos0sin0

0cos0sin

sin0cos0

0sin0cos

T

where

done becan decoupling

mc

eBL

TRR

T

RR T


Imaging with Visible Radiation

• Used mostly for storage rings with well known -functions• Versatile and easily realized• Can be used for real-time beam measurements

Synchrotron radiation

Iris Lens Bandpass

filter

Neutral

filter

CameraMirror

10025

540022.122.1

mm

mnm

D

LL phres

•Source length should be accounted for

•Mirror should provide minimal distortion under the heat load


Pinhole Camera

2122222pinholendiffractiocamerascreenx

wD

ddDw

ndiffractio

pinhole

412

1221

21

At ESRF 10 μ pinhole provides resolution of 13 μ for beam size


Imaging with Fresnel Zone Plate

source

double crystal monochromator

zone plate screen

• Monochromator is required due to the strong chromatic aberrations of zone plate

• SPring-8 achieved 4 μ resolution for beam size with the help of X-ray zooming tube

• Observed transient in the beam size during top-off operation


Laser “Wire”

• Replaces solid “wire” with laser beam• Can reach micron level resolution (waist 12 μ)


Laser “Harp”

• Standing wave interference pattern is generated by two crossing laser beams

• Electron beam is moved across the pattern and modulation in the intensity of Compton scattered photons is observed

2

2expcos2sin2 dNN

NNd


Interference Method

• Similar to Michelson stellar interferometer• Measures dependence of contrast of interference

fringes on slit separation

2

minmax

minmax 2expL

D

II

II x

For Gaussian beam


Set-up KEK-ATF


Undulator Radiation

222

2 212

KnU

n][][934.0 TBcmK U

222

222

unde

unde

ph

ph

screen

The nth harmonic wavelength

Uund

Uund L

L

24

2

2

2222

l

lundscrl

Emittance of 0.2 nm was measured with 30 keV X-ray photons

lUndulator (LU)


Undulator Spectrum

RMS

E

Energy

FWHM

x

Emittance

FWHMUNat

EnergyEmittanceDetectorNat

E

K

nN

2

21

1

2

22

2222


Calculated vs. Measured

200x109

150

100

50

Phot

/s/0.

1%bw

5800eV5600540052005000480046004400

Photon Energy

120x109

100

80

60

40

20

0Ph

ot/s/

0.1%

bw

7800eV760074007200700068006600

Photon Energy

100x109

80

60

40

20

Phot

/s/0.

1%bw

9500eV90008500

Photon Energy

SRW

Cal

cula

tions

Mea

sure

d

780 800 820 840 860 880

50

100

150

200

250

300

350

400

450

Flux from X25 through 30x50 um at 26.1 for diff. coupling

1

00.5

520 540 560 580 600 620 640 660 680

100

200

300

400

500

600

700


1

00.5

360 380 400 420 440 460 480 500

50

100

150

200

250

300

350

400

450


1

00.5

34 5


Optical Diffraction Radiation

2

h

=2500 y=0, 30 μm

Dependence of contrast

vs. beam size at different

wavelengths


Conclusions

• The emittance measurement technique became state-of-the-art capable to satisfy most requirements

• Wide variety of methods is used• Some methods require thorough theoretical

consideration• Some has experimental complexity• New methods will appear as improvements in beam

quality will require more precise instrumentation


mrad = meter·radian


Optical Klystron Spectrum

• Spectrum is interference of two wave packets

• Fringes visibility is defined by energy spread

• Only longer wavelength part of the spectrum is affected by non-zero emittance

• Horizontal emittance is obtained

Undulator 1 Undulator 2Buncher



wire

beam scan

bend

beam

detector

WS

a) b)

S0 S1 S2

x’

Area =

maxx

x

max'x

slope

source

screenmask

L

Documents

BROOKHAVEN SCIENCE ASSOCIATES BIW ’ 06 Lepton Beam Emittance Instrumentation Igor Pinayev National Synchrotron Light Source BNL, Upton, NY