High Brightness Electron Beams - DESY · Focusing an electron beam with a solenoid 0 0.05 0.1 0.15 0.2-0.2 0 0.2 0.4 0.6 z, m Bz, T In the first half of the solenoid, the field imparts

High Brightness Electron BeamsIntroduction to the physics of high-quality electron beams

Mikhail KrasilnikovPhoto Injector Test facility, Zeuthen (PITZ)

x

x’

Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 2

The plan for this morning

• Motivation for high-quality electron beams

• Description of beam quality– Beam brightness, peak current and emittance

• Evolution of beam quality in a linear accelerator– Emittance growth and compensation

– Emittance conservation

– Bunch compression


Motivation for high-quality electron beams

Beam quality from the point of view of twoimportant particle beam applications

Particle colliders X-ray free electron lasers

ILC LHC XFEL LCLS


Particle colliders high luminosityThe number of collisions at the interaction point depends on the density of particles there:

– beam current (number of particles)– beam focal spot size

Linear collider one shot at the interaction point (before the beam dumped)Circular machine considerations can be a little different

yx

NNLσσ

21∝


Free Electron LasersIn a free-electron laser (FEL), the magnetic field of the undulator magnet causes the electrons to oscillate transversely and at resonant wavelength λph

2

2

21γ

λλ Kwph

+=

wλ

γ

wHK ∝

These oscillations induce micro-bunching on a scale of λph,which causes electrons within the micro-bunch to radiate coherently at the resonant wavelength.

In the oscillator configuration, the laser light reflects back and forth between mirrors, gaining strength on each pass.

radiation

electr

on be

am

At ultra-short wavelength, less than 100 nm, mirrors are not available. In such a case, at high phase space density of an electron bunch the FEL instability develops in a single pass through the undulator, the process is referred to as self-amplified spontaneous emission (SASE).


Free Electron Lasers: beam brightnessHigh phase space density of an electron bunch high beam brightness

Beam brightness is a local property that measures the achievablecurrent density for a given angular acceptance

dAdIdB

Ω∝

2 beam current

divergence transverse area


Beam brightnessThe natural coordinates for looking at the beam brightness distribution are called the “trace space” e.g. (X, X’)

x

x’

x and y are the coordinates transverse to the beam motion (along z) and the primes indicate derivatives with respect to z

ydxddydxId

ddAIdB

′′=

Ω∝

42

differential intensity at a given point on this picture gives

xddxId′

2z

x

pp

dzdxx ==′


Peak and average brightness

x

x’

x

x’

For a given beam, we can define the peak brightness and the average brightness

to calculate it, we have to define the area in trace space


Beam emittance

222 xxxxx ′−′=εx

The area in trace space is called the emittance of the beam.

The area bounded by this dotted line is equivalent to the rms transverse emittance in x – it has units of length times angle mm mrad

2x

2x′

xx ′~

z

x

pp

dzdxx ==′

But acceleration! normalized phase space ),( xpx x ′= βγ

222 xxxxx ′−′=ε

222 xxxxnx ′−′= βγε :emittance beam Normalized


Why low emittance is so important for FEL

εn = 1 mm mrad

outp

utpe

akpo

wer

of t

heXF

EL S

ASE

2@

0.1

nm

(G

W)

path length in the undulator (m)

εn = 2 mm mrad

εn = 3 mm mrad

peak current: 5 kAenergy spread: 2.5 MeV


FEL requirements on electron beam parameters

• Energy

• Transverse emittance

• Peak current

• Energy spread

• Stability(charge, energy, timing jitter, …)

GeV nm 20...5.21.0...4.6,2

12

2

2 →≈=⎟⎟⎠

⎞⎜⎜⎝

⎛+= r

ur

K λγλλ

kA ...,Length Gain 3/12

→≈⎟⎟⎠

⎞⎜⎜⎝

⎛∝

IL N

gβεγ

310−≤E

Eσ

mrad mm 1≤nε

high energy

low emittance

high currentshort

small energy spread

stable


LINAC based FELs: generic layout

high energy

low emittance

high currentshort

small energy spread

stable

e-source

linac (booster)

bunch

compressors

linacs

undulator


Electron source: RF-GunRFgun:

L-band (1.3 GHz) nc (copper)

standing wave1½-cell cavity

Main solenoid,Bz_peak~0.2T

Bucking solenoid

Photo cathode (Cs2Te)

QE~0.5-5%

Coaxial RF coupler

Cathode laser262nm

20ps (FWHM)

Vacuum mirror

Electron bunch1nC, ~5-7MeV

UHV


RF phase of the gun

-7

-5

-3

-1

1

3

5

7

-180 -140 -100 -60 -20 20 60 100 140 180

RF phase, [deg]

Mom

entu

m, M

eV/c

-80

-60

-40

-20

0

20

40

60

80

E-fie

ld a

t cat

hode

, MV/

m

Mean momentum ofe-beam, MeV/c

Electric field atcathode, MV/m

Initial (launch) phase of RF-gun

• The electrons are emitted when the radio-frequency (RF) field is accelerating, and arrive at the next crest in time to get another push• Finite cathode laser pulse duration (~20ps FWHM) results in the energy spread within the electron bunch

laser

cathode the at fieldelectric - )sin( 00 φω +⋅= tEEz

0φ


Photo Injector: RF Gun


Space charge force

Forces acting on electron bunch

22)()(

RRpRRppqF

+⋅+⋅⋅

⋅= rr

rrrrr

γ

pr

prRr

Gyx

z

Vrr

GeQFrrr −

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛

+⋅=

σσσγ

γ2

2

Lorenz force ( )BvEqFrrrr

×+⋅=

External forces:

•RF cavity (e.g. RF-gun)

•Gun solenoids

{ }{ }0,,0),,(

,0,),,(

ϕBtzrB

EEtzrE zr

=

=r

r

{ }zr BBzrB ,0,),( =r


Focusing an electron beam with a solenoidHow does that work?

Electrons movingdown the axis of anideal solenoid havetheir velocityparallel to the field,so no force!


Focusing an electron beam with a solenoidIn a real solenoid, Maxwell doesn’t allow just this field along the axis

Gauss’ Law tells us thatwhen the magneticfield changes along z, itmust have a radialcomponent also.


Focusing an electron beam with a solenoid

0

0.05

0.1

0.15

0.2

-0.2 0 0.2 0.4 0.6z, m

Bz, T

In the first half ofthe solenoid, thefield imparts atwisting motion tothe electron beam

In the second half, theforce is in the oppositedirection, removing thebeam’s angularmomentum


Focusing an electron beam with a solenoidElectrons with angular momentum then feel a force from the main solenoid field

( )BvqFrrr

×⋅= This resulting force is always focusing

The focal length of the solenoid changes with the inverse of the B-field squared, because the fringe fields and the main field are both involved

Br

trv

z


Emittance compensation with a solenoidNow that we know how to focus the beam, what does the focal spot have to do with the emittance?

x

x’

x

x’

Beam phase space in a drift without space charge


Emittance compensation with a solenoid

x

x’

x

x’

Beam phase space in a drift with space charge


Emittance compensation with a solenoid

x

x’

0

0.05

0.1

0.15

0.2

-0.2 0 0.2 0.4 0.6z, m

Bz, T

Beam phase space in a solenoid with space charge

x

x’

x

x’

drift

In linear fields the ellipse area (beam emittance) remains constant!


Emittance compensation: slice and projected emittance

x

px

px

x

βγω B∝

With Solenoid

Electron bunch

px

x

Without SolenoidSpace-charge forces are stronger in the middle of the bunch, where the charge density is greater

z

Emittance compensation

We use the solenoid focusing to compensate the space-charge emittance growth


Thermal emittance sets a lower bound on the beam emittance

What is a lower limit for the emittance

Beam initial emittance depends on the nature of the source

Where does initial emittance come from?

In thermionicemission, the temperature of a filament is raised until electrons spill over the vacuum barrier

Transverse velocity is random, with rms value depending on temperature

In a photocathode, electrons are liberated by absorbing photons

Transverse velocity is also random, but the rms value depends on the energy difference between the photon and the work function


Space charge forces within a bunch

Short bunch nonlinear transverse space charge force nonlinear phase space

In statistical mechanics: microcanonical distribution = linear forces and the phase space remains const

1959: I.M. Kapchinsky and V.V. Vladimirsky

transverse beam dynamics of this distribution in linacs K-V distribution

y

x

x

Fxinv=ε

2D X-Y distribution“long” beams

x

Fxy

x

z

px

x

px

x


Space charge forces within a bunch

Flat-top temporal electron bunch

++ --• but during emission bunch is short

• beam peak current also reduced

• reduce space charge force nonlinearityreduced slice emittance

• space charge density reduced

-2

-1

0

1

2

3

4

-6 -4 -2 0 2 4 6Δz, m m

π m

m m

rd

Density (Gaussian) Slice Emit (Gaussian)

Density (Flat-top) Slice Emit (Flat-top)

Peak current ~ 50A


Laser

5-7 MeVSuperconducting TESLA

module (ACC1)3rd harmonic

section ACC39RF Gun

150-160 MeV

Photo injector concept: space charge effect reduction

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18z from cathode,m

XYrms, mm

Norm.emitXY / mm-mrad

Reduce space charge effect

on the cathode

Flat-top longitudinal laser profile

20ps

Longitudinal phase space

correction applying 3rd

harmonic (3.9GHz) cavity

Longitudinal Phase Space

-5 -4 -3 -2 -1 0 1 2 3 4 5

-150

-100

-50

0

50

100

Δz

Δpz

Longitudinal Phase Space

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

Δz

Δpz

0100200300400500600700

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18z from cathode,m

Ek, MeV

Long.emit / mm-keV


Laser

5-7 MeVSuperconducting TESLA

module (ACC1)3rd harmonic

section ACC39RF Gun

150-160 MeV

Photo injector concept: emittance conservation

Space charge compensating

scheme by applying solenoid field

Emittance conservation using booster with proper

position and gradient -matching conditions:

γσγ

032

II

w

=′

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 z from cathode,m

Xrms, mm

EmX, mm mrad

Xrms, mm (no booster)EmX, mm mrad (no booster)

Gyx

z

Vrr

GeQFrrr −

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛

+⋅=

σσσγ

γ2

2

??


Photo injector concept: beam peak current

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 z from cathode,m

Xrms, mm

EmX, mm mrad

Xrms, mm (no booster)EmX, mm mrad (no booster)

Transverse projected emittance compensated and conserved. How to increase the peak current of the beam?


Particle in a field of magnetic dipole

zpB

∝αBr

1zp

12 zz pp >

Electrons with higher longitudinal momentum (energy) are less bended by a dipole magnet

!But: Coherent Synchtotron Radiation (CSR) could delute transverse phase space


Bunch Compression (Chicane BC)

tail

Δz

Δpzhead

RF

D1BC1

D2BC1 D3BC1

D4BC1

head particles, less energy

tail particles, more energy

15 - 21 deg


Bunch Compression (Chicane BC)

tail

Δz

Δpzhead

RF

13.6 m

1.7 – 5.4 deg

D1BC1

D2BC1 D3BC1

D4BC1

head particles, less energy

tail particles, more energy

3.6 m

15 - 21 deg

CSR!

130 MeV 350 MeV


Conclusions

• FELs and linear colliders need particle beams that can be well-focused

• Overall quality of particle beams is described by average brightness or by emittance

• Linear accelerators are capable to produce high brightness electron beams:– Emittance compensation technique– Emittance conservation principle– Bunch compression


On 18.08.2009!Frank Stephan from PITZ, will tell you all about the actual machine that we use to create these electron beams and characterize electron guns

Documents

High Brightness Electron Beams - DESY · Focusing an electron beam with a solenoid 0 0.05 0.1 0.15 0.2-0.2 0 0.2 0.4 0.6 z, m Bz, T In the first half of the solenoid, the field imparts