Transcript Single pass FEL

A.3 FEL basics
A.3 FEL basics
A.3.1 Low- and high-gain FELs
X-ray wavelength
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Beam wiggles with undulator wavelength λu:
with
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Due to relativistic Doppler shift (next page), the X-ray wavelength λl is compressed longitudinally
with
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Due to the wiggle motion
famous formula
. Using the correct expression for
(see exercise) leads to the
Parameter choice:
1. K has to be around 1 for undulator radiation
2. λu as small as technology allows.
3. Beam energy γ as high as necessary to reach
targeted X-ray wavelength λl.
Relativistic Doppler shift
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Electron emits one wavefront F each
wiggler period.
In wiggler period N, FN is emitted.
In wiggler period N+1, FN+1 is emitted.
But light has moved only a little bit faster
than beam and FN is spatially very closely
emitted to FN+1.
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Time light and particle need for λu
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Time difference between wavefronts
corresponds to a wave length via
X-ray power
Small gain regime
High gain regime
Saturation regime
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Power gain length: length for X-ray power
increase by e.
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FEL parameter: allows estimates for many
important properties: Psat, Δω/ω0, ηe
Two types of FELs
FEL oscillators
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Produced light is trapped between mirrors
(in pulsed form).
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At every beam passage, light is amplified
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Part of the light is coupled out through a
semi-permeable mirror.
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Very weak micro-bunching (small gain
regime).
Single pass FEL
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Light is produced in one long undulator.
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Strong micro-bunching (high-gain regime).
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LSAT has to be small to be able to build
undulator short enough (beam quality).
FEL oscillators (FELO)
Saturation power:
• In each passage the light power P is
amplified by a small amount G << 1
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Light reaches after some time a high
power between the mirrors.
The light power reaches saturation
when
Advantages:
• Very high spectral purity
• High repetition rate
• High average power
• Energy efficiency several beam
passages
Application:
• Can be driven by beam from
synchrotron, energy recovery linac, or
linac.
• Used wherever possible, but …
• There are only mirrors available below
the X-ray regime (IR, optical, UV).
XFELO (not achieved):
• In the X-ray regime, normal mirrors
cannot withstand the photon power.
• Crystals, e.g. diamond, are tested as
Bragg reflectors (crystal lattice).
• Reflection only at certain angles.
Single pass FELs (high-gain FELs)
For X-rays, light has to be created in a single pass. Since FEL power grows exponentially, the goal
is to reach saturation.
Hence, the main design goals for a single-pass FEL are (typical values for hard X-ray facilities)
• Small X-ray wavelength λl (0.1nm)
• High PSAT (< 1GW)
• Small saturation length LSAT ≈ 22 Lg ( 60-100 m)
• Also short beams are advantageous for the photon science.
1.
X-ray wavelength: Given by the undulator parameters K, λu and the beam energy γ.
– The undulator with the smallest possible λu (about 1.5cm) is chosen that still has a large
enough K≈1.
– Then the beam energy (typically 6-15GeV) is chosen to reach λl as
Electron beam and undulator parameter choice
for a single-pass FEL
2. Saturation power: mainly determined by the beam current (order of 1-5 kA)
3. Saturation length:
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The basic gain length (1D gain length Lg0) is fixed by the already determined parameters
and cannot be reduced (order of (50-100m)/22 ≈ 2-4m).
But it is at least possible to increase Lg0 not too much if also the effects of beam
emittances εx, εy and energy spread ση are taken into account (3D gain length Lg).
This implies very small values for ε (< 1μm) and ση (order of 10-4)
Linac vs storage ring:
• The necessary high beam current I and the low emittances correspond to a high beam
brilliance
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The needed values for Be cannot be achieved in a storage ring, but in a linac.
A.3 FEL basics
A.3.2 High-gain FEL facilities
Typical high-gain FEL layout
Electron Gun
• creates low εx, εy beam.
• Relatively high charge.
Linac
• Bring beam to γr.
• Preserve ε and ση.
Bunch compressors
• Reduce bunch length.
• Increase of I0.
• Shortening of X-ray pulse.
Photon beam lines
• Transport and
focusing.
• Steering to different
experiments
Experiment
Undulators
• Several
• Creation of X-ray
experimental
pulses.
rooms to house
• Dogleg to distribute to
photon science.
several undualators.
Electron gun
Goal: beam of highest brightness:
- High charge and low ε.
- Two counteracting wishes, since high
charge creates high space charge fields
which increase the emittance.
Cathodes:
– Thermal cathodes:
• Heating of metallic cathode increases energy if unbound electrons.
• Part of the electrons can escape cathode into vacuum due to their thermal energy.
– Photo cathodes:
• Short laser shot on cathode.
• Electrons are ejected from cathode due to photo-electric effect.
• Higher beam brightness compared to thermal cathodes.
Acceleration:
– Beam has to be accelerated as fast as possible, since SC effects reduce with increasing γ.
– Guns with RF acceleration field produce higher gradients than DC guns.
– Transverse focusing with solenoid magnets.
RF acceleration
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Several RF structures mounted on
one module and are powered by
one RF station.
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NC and SC structures in use. Choice
impacts e--bunch structure and RF
and linac design.
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The RF station consists of an
klystron (RF source) and its power
supply called modulator.
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Depicted case: power of two
klystrons combined with hybrid
coupler to power 10 structures.
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EM waves are transported with
waveguides (cooper pipe).
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RF bunch compressor shortens and intensifies
the RF pulse.
RF system of the X-band XFEL collaboration
Linac
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Beam focusing:
– Usually FODO lattice.
– Quadrupoles in the gaps between RF
structure modules.
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Main target is to preserve the small ε and
ση from gun. Some aspects:
– Longitudinal wakefields cause energy
chirp. Can be compensated with offcrest acceleration.
– Mechanical element offsets can cause
the beam oscillations and dispersion.
Can be compensated with beam-based
alignment (BBA) techniques.
Linac of PAL-XFEL (Korea)
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Many other interesting beam
physics topics:
- Micro-bunching instability and
laser heating.
- Transverse wakefields
- Sensitivity studies of element
parameter.
Bunch compressors
Principle (linear dynamics):
Complications (non-linear dynamics and collective effects):
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Energy chirp is not perfectly linear (sinusoidal RF wave).
The magnets of the chicane have non-linear components.
In the dipoles, CSR is emitted and can increase projected ε.
Small charge variations in combination with long. SC can create
energy modulation that can result in unwanted micro-bunching.
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Acceleration of bunch
off-crest to create
energy chirp.
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Chirped beam is send
through chicane.
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Particles in bunch head
have less energy and
have longer path
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Particles in particle tail
vice versa.
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This leads to reduction
of beam size.
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Two stage compression
is easier for
“complications”.
Undulator magnets
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In XFEL facilities permanent magnet (PM)
undulators are used (best suited up today).
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High precision element:
– To keep K in tolerances, the mechanical
tolerances are very stringent.
– In operation, temperature in hall must be
constant to about +/- 0.1 degree.
– During whole life time, temperature must
stay within +/- 1 degree. Otherwise
irreversible deformations.
– https://www.youtube.com/watch?v=7Fk1A
ysFkUg
LCLS undulator
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In- and Out- of vacuum undulators:
- LCLS vs SACLA
- In-vacuum undulator has better
performance but causes problems.
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Fixed and variable gap undulators
- No variable gap in-vacuum (too
complicated).
Undulator section
Structure
Beam guidance
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Undulators only fabricated to a length
of 4-5 m, several undulator modules
are added.
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Beam has to be steered to centres of
the undulators: use of BPMs and
either steering dipoles or QP movers.
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About 12-20 modules: 60 to 120m
length.
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Gaps between undulators house:
- Quadrupole magnets.
- Beam position monitors (BPMs).
- Phase shifters.
- Beam loss monitors.
The beam is focused with quadrupole
magnets that form a strongly focusing
FODO lattice.
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But weak focusing of the undulator
has to be taken into account.
Phase shifters
Taken from: “A PERMANENT MAGNET PHASE SHIFTER FOR THE
EUROPEAN X-RAY FREE ELECTRON LASER” by H. H. Lu et al.
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Phase shift between beam and
X-rays in gaps is unavoidable:
360o = 1 Å.
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Phase shifters (magnetic
chicane) are used to shifty
beam.
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Sometimes there are individual
magnet designs, sometimes
they are based on the magnets
of the undulators.
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First and second field integral
determine properties of phase
shifter.
Photon beam lines and experimental area
To supply several
(usually 3)
experimental
rooms, X-rays have
to be steered with
deflector mirror.
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Only crystal mirrors (Bragg reflection) can be used, but only small angle are possible (13 deg. soft X-rays; 0.1 deg. hard X-rays). This causes long photon beam lines.
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Still directly after the undulator, the X-ray intensity is too large for any material to
withstand it. Therefore the X-ray beam is widened by its natural opening angle.
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After 50m (SwissFEL), X-rays can be used on first steering mirror.
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Shortly before experiment there is a second mirror to focus the X-rays again.
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More complex optics exist for soft X-rays (including monochromator), but more
elements reduce X-ray coherence.