The good and bad situations

40A. Cianchi Particle Accelerators For Science And Interdisciplinary Applications

The good and bad situations


Overlap between photons and electrons

The amplification process in the high-gain FEL depends critically on a good transverse overlap between electron and photon beam

Transverse focusing is mandatory in the long undulator structures of high-gain FELs. The so-called “natural focusing” in an undulator is analogous to the “weak focusing” in circular accelerators.

A horizontally deflecting dipole magnet of rectangular shape exerts a weak vertical focusing which is caused by end field effects. A planar undulator is a sequence of short rectangular dipole magnets and provides thus weak focusing in vertical direction

This focusing acts only in the vertical plane, while the horizontal motion remains unfocused, and it is too weak for short wavelength FELs


Effect of betatron oscillation

The generally adopted solution is to apply the principle of “strong focusing” by augmenting the undulator system with a periodic lattice of quadrupole lenses of alternating polarity, a FODO lattice

This FODO lattice can be realized by placing electromagnetic quadrupoles between the segments of a long undulator structure

The horizontal and vertical betatron oscillations introduce additional transverse velocity components. The average longitudinal speed of a particle carrying out betatron oscillations in the undulator is lower than the speed vz


Energy spread

Concerning the FEL synchronization process, the reduction of the longitudinal speed is equivalent to a reduction of the mean electron beam energy

Owing to the fact that the particles in the beam have all different betatron oscillation amplitudes one obtains in fact not only a reduction in the longitudinal speed but in addition a smear which is equivalent to an energy spread of the incident beam

Limit of energy spread coming from theory

Energy spread coming from betatron motion

Limit of emittance due to energy spread consideration


Gaussian Beam

The field amplitude drops to 1/e of its peak value at a radius r = w(z).

The smallest width w0 is obtained at the waist at z = 0.

The phase factor exp i k r2/(2R(z)) implies that the wave fronts are curved and of nearly spherical shape.


Gaussian Beam

The beam width at position z is described by w(z) while R(z) is the radius of curvature of the wave front


TEM


TEM00

The fundamental Gaussian mode depends only the distance r from the axis and the longitudinal coordinate z

This mode has its highest intensity on the axis.

In an FEL there is optimum overlap between the TEM00mode and the electron beam, and for this reason this mode will be strongly amplified


TEM10

The higher modes with odd indices have vanishing intensity on the axis and can generally be neglected in the high-gain FEL while the modes with even indices have a finite size on the beam axis.

In the TEM10 mode the electric field Ex changes sign when going from positive to negative x.

This is because H1(x) is an odd function. Therefore this mode cannot couple to an electron beam with a charge distribution that is symmetric in x


Divergence

In vacuum n=1


Beam emittance

Quadratic term in the Gaussian


Rayleigh length for a FEL

Ideally the photon beam should have the same transverse size as the electron beam. However, like any electromagnetic wave, the FEL wave in the undulator undergoes optical diffraction.

Since FEL radiation has a lot of similarity with optical laser beams we use here the Gaussian beam description

A typical number is zR ≈ 1m for w0 ≈ 100 μm and λ=30 nm


Relation with radial beam size

In Gaussian laser beam optics it is convention to define the radial width by the condition that the intensity of a TEM00 beam drops to 1/e2 of its value at r = 0 (the electric field drops to 1/e).

From this definition follows that the rms radial width of the light beam intensity is


Gain Guiding

The FEL beam will also be subject to diffraction, and the resulting widening could readily spoil the good overlap with the electron beam and reduce the energy transfer from the electrons to the light wave

It exists an effect counteracting the widening of the FEL beam which is called gain guiding.

We consider an observation point z0 in the exponential gain region. Most of the FEL intensity at this point has been produced in the last

two or three gain lengths upstream of z0, and the width of this newly generated radiation is determined by the electron beam width.

The more distant contributions are widened by diffraction, however they play a minor role because they are much smaller in amplitude.

The overall result is an exponential growth of the central part of the light wave, and this part will retain its narrow width.

Nevertheless, diffraction losses will occur. Some field energy evades radially from the light beam.


Rule of thumb

To provide efficient gain guiding the FEL amplification has to be large enough so that the growth of the light intensity near the optical axis overcompensates the losses by diffraction.

A gain length shorter than the Rayleigh length appears thus desirable. This criterion, however, is not easy to fulfill because the gain length depends on the particle density and the rms electron beam radius as

A very short gain length requires a small transverse beam size, which in turn would lead to a short Rayleigh length if we want to keep the width of the photon beam equal to that of the electron beam.

A good compromise is to choose a Rayleigh length that is somewhat larger than the FEL field gain


Limit for the emittance

We request that the electron beam emittance does not exceed the light beam emittance.


SASE

For wavelengths in the ultraviolet and X-ray regime the start-up of the FEL process by seed radiation is not readily done due to the lack of suitable lasers.

The process of Self-Amplified Spontaneous Emission SASE permits the startup of lasing at an arbitrary wavelength, without the need of external radiation.

The electrons produce spontaneous undulator radiation in the first section of a long undulator magnet which serves then as seed radiation in the main part of the undulator.

The bunches coming from the accelerator do not possess such a modulation at the light wavelength. But due to the fact that they are composed of a large number of randomly distributed electrons a white noise spectrum is generated which has a spectral component within the FEL bandwidth


Layout of SASE FEL


Sase mechanism I

All particles emit radiation at every phase. All particles feel the radiation at every phase

φ1

E

φ2

φ3

φn


Sase mechanism II

The n-particle feel the fields 3E1+E2+E3+..En-1

At every oscillation, the phase φ1 is the leading phase and the other particles will start to bunch at this phase

The seed is inside the bunch

φ1

E1

φ2 φ3φn


Slippage

Narrow wave packets of the FEL field escape from the bunch and move away from the bunch head.

This is clear evidence for the slippage effect. When an FEL wave packet has slipped away from the

bunch it will move with the speed c of light in vacuum, and its magnitude will remain invariant because the overlap with the electron beam is no longer existent and the FEL gain process has come to an end.


Slippage

Due to resonant condition, light overtakes e-beam by one radiation wavelength per undulator period

Slippage length = λl×undulator period (100 m LCLS undulator has slippage length 1.5 fs, much less than 200-fs e-bunch length)


Cooperation length and spikes

Cooperation length (slippage in one gain length) Lc=λ/4πρ.

Number of “spikes”: bunch length/2πLc


Emission spectrum

The emission of spontaneous undulator radiation is a stochastic process, and as a consequence SASE FEL radiation, starting from shot noise, has the properties of chaotic light.

A characteristic feature are shot-to-shot fluctuations in wavelength. The averaged spectrum of many FEL pulses has a smooth lineshape


Developing of spatial coherence


Development of the Coherence in a FEL

Central mode TEM00 (Gaussian) has the best overlap with the electron beam⇝ fastest growth

⇝ increase of coherence

Saturation in the last part of the undulator⇝ other modes gain

importance⇝ decrease of coherence


Mode cleaning

The fundamental Gaussian mode TEM00 has its highest intensity on the beam axis while the higher TEMmnmodes extend to larger radial distances and some of them even vanish on the axis.

With increasing length in the undulator, the fundamental TEM00 mode will therefore grow faster than the other modes, owing to its superior overlap with the electron beam.

This process is called mode competition. When the saturation regime is approached the

fundamental mode will usually dominate (mode cleaning) and the FEL radiation will possess a high degree of transverse coherence in the end will nearly be Fourier transform limited


Movies FEL light


Movies FEL light 2


Seeding vs SASE


Our seeding @ 266 nm

the SASE FEL does not reach saturation and the output energy is about 12 nJ .

The FEL gain length LG=1.1m When the FEL amplifier is seeded, the output energy increases up to

2.6 µJ corresponding to an amplification factor of 20 (the seed energy at 266 nm, measured at the end of the undulator was 120 nJ) and more than 200 times the energy available in the SASE mode


Narrow Bandwidth FELs: Self-Seeding

SASE-FEL process in the first undulator is interrupted well below saturation SASE radiation from the first undulator is monochromatized and used as a

seed in the second undulator. Electron Beam is demodulated by the Magnetic Chicane

A. Cianchi Particle Accelerators For Science And Interdisciplinary Applications

Particle accelerators

Light Sources


Synchrotrons sources in the world


Impact of Synchrotron radiation

The x-rays from synchrotrons are being used by more than 20,000 researchers at 54 dedicated facilities in 19 different countries.

There are eight more facilities under construction, and eleven more in the design and planning stage.

Through the years, the intensity of x-ray beams has grown. Between 1960 and 2000 it first increased by a factor of a billion and then by a further factor of a million more.

In fact, this rate of growth was even more than that of computer performance, which is otherwise considered the most rapid the world has ever seen.

Studies with synchrotron radiation range over much of science. There have been 19 Nobel Prizes awarded for work related to x-rays: 9 in chemistry, 7 in physics and 3 in medicine.


Light sources vs computers


Increase in Brilliance

Every increment was due to a new technology


Life science examples: DNA and myoglobin

Franklin and Gosling used a X-ray tube: Brightness was 108 (ph/sec/mm2/mrad2/0.1BW) Exposure times of 1 day were typical (105 sec) e.g. Diamond provides a brightness of 1020

100 ns exposure would be sufficient Nowadays pump probe experiment in life science are

performed using 100 ps pulses from storage ring light sources: e.g. ESRF myoglobin in action

Photograph 51 Franklin-Gosling

DNA (form B)

1952


First light ever

1940: Kerst builds first 2.3-MeV betatron at University of Illinois. Followed by 20-MeV and 100-MeV machines by GE


But the book of history…

1947: Pollack builds 70-MeV synchro-cyclotron at GE, having transparent tube to observe HV sparking;

Instead, a bright arc of light from electrons was seen


1st Generation SR sources

Electron synchrotrons start to be built for high energy physics use (rapidly cycling accelerators not Storage Rings!)

There is interest from other physicists in using the “waste” SR

The first users were parasitic


2nd Generation SR sources

Purpose built accelerators start to be built –late 70’s First users ~1980 (at SRS, Daresbury) Based primarily upon bending magnet radiation

The VUV ring at Brookhaven in 1980 before the beamlines are fittedNot much room for undulators!


3rd Generation SR sources

Primary light source is now the undulator

First built in the late 80’s/early 90’s

First users ~1994 ESRF


Third generation light source


Monocromaticity


4th Generation SR sources

Now the primary light source is the single pass Free Electron Laser

First built ~2000 First users ~2006


Brilliance


Stability issue

2nd and 3rd Generation Sources: orbit position < 1-5 μm orbit angle < 1-10 μrad beam size < 0.1 % e- energy < 5 x 10-5

Improved 3rd and 4th Generation Sources: orbit position < 0.1-1 μm orbit angle < 0.05-0.5 μrad beam size < 0.01 % e- energy < 5 x 10-6

pump-probe timing synchronization for femtosecond sources < 100 fs


Interest in X-Ray FEL

The interest in X-ray FELs is motivated by their characteristics of tunability, coherence, high peak power, short pulse length. They can explore matter at the length and time scale typical of atomic and molecular phenomena

Peak power, about 10 Gigawatt or more Pulse length, about 100 femtosecond or shorter Transversely coherent, diffraction limited Line width < 0.001 Tunable from 15 to 0.5Å


A new world


New physics

The large number of photons per pulse allows to determine the structures of complex molecules or

nanosystems in a single shot; to study non linearphenomena;

to study high energy density systems. The transverse coherence gives new possibilities of

imaging at the nano and sub-nano scale. Using fast, single shot imaging, one can follow the

dynamics of these phenomena. Using all these properties we can explore matter

with unprecedented time-space resolution.


What we can do with a XFEL?


LCLS facts


Relation between 3rd and 4th generation

It is generally believed that 3rd generation light sources will not be replaced by SASE-FEL (4th generation light sources) but rather they can coexist.

3rd generation will remain unrivalled in terms of stability and cost effectiveness, and will still be competitive in terms of average brightness, tunability, reliability.

4-th generation light sources will be superior in their peak brightness and time structure, providing fs and sub-fs radiation pulses.

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The good and bad situations