FREE ELECTRON LASERS
Giuseppe Dattoli and Alberto Renieri
ENEA, Divisione Fisica Applicata, Centro Ricerche Frascati, CP. 65, 00044 Frascati,Rome (Italy)
Abstract
We review the main aspects of Free Electron Laser Physics and the relevant
state of art, describe the operating principle of the device and discuss the role
of some key parameters. We specify different operating regimes, with
particular emphasis on devices operating in the high gain self amplified
single pass regime, owing to its perspective importance as fourth generation
sources of synchrotron radiation.
1.
INTRODUCTION
More than 40 years ago the first coherent red light has been generated by a ruby laser [1]. From that
time an impressive scientific and technological development transformed a laboratory experiment in a
pervasive device, widely utilized in all field of science and technique and in everyday life. More than
20 years ago the first coherent infrared light has been generated by a quite exotic new laser developed
at the Stanford University (USA), this laser was named FREE ELECTRON LASER (FEL) [2].
Many review articles and books have been dedicated to theoretical and experimental aspects of
Free-Electron Lasers and a non exhaustive bibliography can be found in [3-8].
2.
FREE-ELECTRON LASER OPERATING PRINCIPLE
This new type of coherent radiation source appeared from the very beginning to be quite promising.
The reasons of this fact lies on the peculiarity of its operating principles. In a FEL the active medium
is not made of atoms or molecules, it consists of a beam of free electrons, propagating at relativistic
velocities in a spatially periodic magnet (undulator), where the electrons experience the Lorentz force,
execute transverse oscillations and emit synchrotron radiation in the forward direction (see Fig. 1).
The wavelength λ of the emitted radiation depends on the electron energy E, on the period of the
undulator magnet λu and on its magnetic field B,
λ = ( 1 / 2 λ) u (1+ K2 )(mc 2 / E)2 ,
K=eBλu/(2π mc2)=pitch parameter
Fig. 1 Synchrotron emission in Undulator Magnet
(1)
This relationship can be easily derived by taking into account the synchronism condition, i.e. the
request that the electron, which is oscillating with a spatial period λu and it is moving with at a
longitudinal speed v, maintains, oscillation after oscillation, the same phase relation with respect to the
emitted electromagnetic wave of wavelength λ, running along the same direction at the speed c. This
condition reads:
v = cλ u /(λ u + λ)
(2)
Equation (1) is therefore a consequence of Eq. (2), if we take into account the relationship
between electron energy and relativistic velocities.
The process described so far can be viewed as a kind of spontaneous emission by electrons
propagating in an undulator magnet. By spontaneous we mean that the emission occurs in absence of a
field quasi resonant with the emitted radiation and co-propagating with the electrons.
The possibility of realizing a stimulated process is quite natural and suggested by conventional
Laser Physics. If the photons emitted along the passage through the undulator are trapped in an optical
cavity and than interact again with a fresh electron beam (see Fig. 2), these electrons are forced to emit
stimulated synchrotron radiation. We can associate to this process a gain and if the gain is larger than
the cavity losses, we have the onset of the laser action and, in full analogy with conventional lasers,
when saturation is reached highly coherent (transverse and longitudinal) radiation can be extracted
from the optical cavity.
In the suggested references [3-8] it is possible to find a complete treatment of the FEL theory, in
particular a quantity of paramount importance is the so called small signal gain coefficient which
characterize the gain of the device be it operating in low or high gain regime
g = (16 /
) [m] N 2L u [m] j[ A/ m2 ] f b ( ) 2 /1.7 ×104
(3)
Where it has been defined,
γ = /(mc2)= relativistic factor
N = number of undulator periods
Lu= undulator length, j= electron current density
ξ=(K/2)2/(1+K2/2), fb(ξ) = J0(ξ) – J1(ξ),
Jn≡nth order Bessel function
From Eq. (3) it is possible to derive that the gain decreases drastically at short wavelength. The
gain decreases indeed with the wavelength and, in the meantime, with the increasing of the electron
energy, which is needed in order to go to shorter wavelengths (Eq. (1)). In this region (typically up to
the VUV) the operation of FEL oscillator requires very high brilliant electron beams (high j) that can
be obtained in high quality linac accelerators or in Storage Rings.
Fig. 2 Typical FEL layout (single passage)
In the spectral region where the mirror reflectivity is too small (typically in the VUV-X) a
different operation scheme, based on single passage self amplified spontaneous emission (SASE), is
possible if the electron beam brightness is good enough (high peak current, small emittance) to have
very high gain. In this operation mode the electron beam interacts with its own spontaneous radiation
and an unstable wave is excitated. The radiation intensity I growths exponentially along the undulator:
I = (I0 /9)exp(2z/ LG )
(4)
where I 0 is the starting e.m. intensity (spontaneous radiation emitted in an undulator of length
LG) and LG is the so-called gain length:
LG = λ u /2
( 3) πρ
(5)
ρ (FEL parameter) is the key dimensionless parameter which characterizes the performance of a
SASE device:
ρ ∝g1 / 3∝ γ−1 j1 / 3K 2 / 3
(6)
Saturation length ≈ λu /r
(7)
Saturation power ≈ ρ ×e.beam power
(8)
Gain bandwidth ∆λ/λ ≈ ρ
(9)
Namely we have:
The quality of the e-beam strongly influence the performance of a SASE device:
1) Emittance ε must be small enough in order to enhance the current density j and than enhance ρ
2) Emittance ε must be small enough in order to match a diffraction limited photon beam of
wavelength λ to ensure large output brightness
ε ≤λ /4 π
(10)
3) In order to avoid gain degradation, the e-beam energy spread must be smaller than the gain
bandwidth ρ, i.e.
∆E /E ≤ ρ/ 2
(11)
Typical values of ρ ranges around 10-3. According to Eq. (7) the number of undulator periods
can be fixed around 103. Namely the length of the undulator must be of the order of the saturation
length (Eq. (7)), which cannot exceed, for practical reasons, the order of hundreds of meters (with
undulator periods of the order of some centimeters). In addition it would be very difficult to produce
electron beam with energy spread (Eq. (11)) much smaller than a fraction of 10-3.
It must be underlined, finally, that in this configuration the FEL radiation will be only partially
coherent (only transverse). In order to overcome this problem many different schemes have been
proposed, like, e.g., seed injection from an external laser and self filtering techniques.
3.
FEL: STATUS OF THE ART
The most interesting features of FELs are:
•
tunability: λ can be easily tuned by varying electron energy, period and amplitude of magnetic
field; in addition harmonic generation can provide even shorter λ
• time structure: depending on the e.beam time structure it ranges from c.w. to ultrashort pulsed
regime (fraction of ps)
• coherence: transverse and longitudinal for oscillators and coherent seed amplifiers, only transverse
for SASE
• brilliance: depending on the status of the art of the electron beam technology, the FEL brilliance
can be larger, in some spectral regions (in particular in VUV-X), by many order of magnitude than
the brilliance of the existing sources (lasers and synchrotron radiation).
Due to the peculiarities of these features, many laboratories have been involved from the very
beginning in the FEL R&D, in spite of the considerable complexity (e.g. remote operation) and cost.
The family of devices based on the FEL operating principles is now a well established technological
field. In the present time there are many FEL devices in operation around the world ranging from
millimeter waves to UV. A non exhaustive list of the existing devices is reported in the following
tables 1 (single passage FEL devices) and 2 (recirculated FEL devices). The performance and the
reliability of these sources increased steadily in a significant way in these last years. Namely many of
the devices reported in tables 1 and 2 are now currently utilized for applications in many scientific and
technological fields (e.g. Physics, Material Science, Biology, Medicine. etc.).
Table 1
Single passage FEL devices (not exhaustive).
(collection of data from FEL Conferences, private communications and Research Center web sites)
Accell.
AFEL (USA)
CEBAF (USA)
CLIO (F)
Darmstadt (D)
Duke Mk III (USA)
F-CUBE (I)
FELI (J)
FELIX (NL)
Standord (USA)
UCSB (USA)
Vanderbilt (USA)
Linac
Linac
Linac
Sc/linac
linac
µtron
linac
linac
Sc/linac
e.static
linac
λ(µm)
E(MeV)
14-20
48
21-50
30
26-45
2-5
20-165
15-50
15-40
2-6
24-45
4-20
3-6.2
3-50
7
2-9
2-3.5×103
0.28-40
5-100
4-100
63-2500
2-9.4
∆t(ps)
10
0.5-2
0.5-6
2
0.5-3
50
2-3
0.3-3
2×107
0.75
P(MW)
50
100
50
1000
0.01
10
100
1
0.006
6
Pav(W)
1
1720
1
0.15
1
0.06
0.3-1
0.3
1
0.1
1.5-3
Table 2
Recirculated FEL devices (not exhaustive)
(collection of data from FEL Conferences, private communications and Research Center web sites)
DELTA (D)
Duke OK-4 (USA)
ELETTRA (I)
S-ACO (F)
UVSOR (J)
Accell
s.ring
s.ring
s.ring
s.ring
s.ring
E(GeV)
0.45
0.2-1.1
1
0.6-0.8
0.6
λ(nm)
420-470
217-413
189.7-350
300-vis
270-vis
∆t(ps)
30
<50
8
20-60
10
Pav(W)
150
10-200
300
15
4.
SELF AMPLIFIED SPONTANEOUS EMISSION (SASE) FEL DEVICES AS A
FOURTH GENERATION SYNCHROTRON RADIATION SOURCE
Synchrotron Radiation is now a well established powerful tool for research in a large variety of
scientific and technological fields (material science, spectroscopy, biology…).
Starting from the first pioneering activities performed by using the light generated in the
bending magnets of synchrotrons devoted to elementary particles research, in about three decades the
field developed in a terrific way, evolving itself through three generations of Synchrotron Radiation
Sources.
In spite of the excellent performances of the existing sources, there is an increasing demand of
more advanced radiation quality in the X-ray spectral region (between about 10 nm and 1 Å) in terms
of brilliance (peak and average), coherence (transverse, longitudinal) and time structure (pulse
duration well below the picosecond).
• higher brilliance will allow to increase spatial resolution without loosing spectral resolution, to
utilize one shot techniques in order to avoid to damage samples quite sensible to the radiation, to
make nanoimaging experiments in an acceptable long acquisition time.
• coherence (at least transverse) will be of crucial importance for diffraction and interference
techniques and, in addition, the signal content is substantially richer, because the image will
contain the phase information
• ultrashort radiation pulses (on the order of 100 fs) will allow real time measurements which,
together with the high peak and average brilliance, will make possible, e.g., to be faster than the
damage process and, eventually, to investigate the damage dynamics itself.
FELs driven by Linac electron beams in SASE configuration are foreseen to meet the
challenging requests for the new generation synchrotron radiation sources (4th generation). Namely,
For undulator periods of some centimeters, K of the order of 1 and electron energy spanning from 1 to
10 GeV, the FEL wavelength ranges from tens of nm to some Å. With electron bunches of about 1 nC
of charge, 1mmxmrad of normalized slice emittance and energy spread less than 0.1%, traveling along
long undulator (of the order of hundreds of meters) the peak brilliance will exceed of about 10 order of
magnitude that produced by the undulators of the 3 rd generation sources, while the average one will be
Table 3
SASE FEL technology: Status of the art and experiments under development
e-beam energy
Current [A]
Energy spread
[%]
Emittance
[mm×mrad]
Slice emittance
[mm×mrad]
Wavelength
[mm]
UCLA-LANL
VISA
LEUTL
TTF I
TTF II TESLA FEL
Los Angeles Brookhaven Argonne Hamburg Hamburg Hamburg
(USA)
(USA)
(USA)
(D)
(D
(D)
Exp. results Exp. results Exp.
Exp.
Design
Design
results
results
values
values
18 MeV
71 MeV 217 MeV 233 MeV
1 GeV
25 GeV
167
85
150
400
2500
5000
(0.2 nC)
0.25
0.1
0.13
0.1
0.02
1.5
12000
830
5
530
380
265
8
108.5
LCLS
Stanford
(USA)
Design
values
15 GeV
3400
0.02
2
2.6
1.5
1
1
1
6.3
0.1
0.15
larger by a factor 103–104 (depending on the duty cycle of the accelerator). In addition the pulse
duration could be quite short (of the order of 100 fs) with respect to what is attainable with storage
ring based radiation source (many ps).
The extension of FEL devices to shorter wavelengths (VUV-X) is foreseen in the frame of quite
ambitious projects based on SASE technology. In Table 3 are reported the main characteristics of the
sources presently under development
New projects have been proposed in Italy too, in the frame of the Italian National Research
Plan (PNR), aimed at realizing a 4th generation X-ray synchrotron radiation source based on SASE
FEL technology.
REFERENCES
[1]
T.H. Maiman, Nature 187, (1960) 493
[2]
D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman and T. Smith,
Phys. Rev. Lett. 38, (1977) 892.
[3]
G. Dattoli and A. Renieri, Experimental and theoretical aspects of Free-Electron Lasers, Laser
Handbook Vol. 4, ed by M.L. Stich and M.S. Bass, North Holland, Amsterdam (1984)
[4]
J.C. Marshall, Free Electron Lasers, Mac Millan Publishing Company, New York (1985)
[5]
P.Luchini and H. Motz, Undulators and Free-Electron Lasers, Claredon Press, Oxford (1990)
[6]
Laser Handbook Vol. 6, Free-Electron Lasers, ed. by W.B. Colson, C. Pellegrini and A.
Renieri, North Holland, Amsterdam (1990)
[7]
C.A. Brau, Free-Electron Lasers, Academic Press, Oxford (1990)
[8]
G. Dattoli, A. Renieri and A. Torre, Lectures in Free-Electron Laser theory and related topics,
World Scientific, Singapore (1995)