high brightness electron beams - desy · focusing an electron beam with a solenoid 0 0.05 0.1 0.15...
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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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 3
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 4
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∝
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 5
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).
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 6
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 7
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 ==′
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 8
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 9
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 10
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 11
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 12
LINAC based FELs: generic layout
high energy
low emittance
high currentshort
small energy spread
stable
e-source
linac (booster)
bunch
compressors
linacs
undulator
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 13
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 14
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 15
Photo Injector: RF Gun
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 16
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 17
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!
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 18
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.
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 19
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 20
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 21
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 22
Emittance compensation with a solenoid
x
x’
x
x’
Beam phase space in a drift with space charge
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 23
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!
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 24
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 25
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 26
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 27
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 28
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 29
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
??
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 30
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?
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 31
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 32
Bunch Compression (Chicane BC)
tail
Δz
Δpzhead
RF
D1BC1
D2BC1 D3BC1
D4BC1
head particles, less energy
tail particles, more energy
15 - 21 deg
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 33
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 34
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
Mikhail Krasilnikov, PITZ physics lecture for summer students, August 11, 2009 35
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