Lasers, Free-Electron

Claudio Pellegrini and Sven Reiche • Q1 University of California, Los Angeles, CA 90095-1547, USA e-mail: [email protected]; [email protected]

Abstract Free-electron lasers are radiation sources, based on the coherent emission of synchrotron radiation of relativistic electrons within an undulator or wiggler. The resonant radiation wavelength depends on the electron beam energy and can be tuned over the entire spectrum from micrometer to X-ray radiation. The emission level of free-electron lasers is several orders of magnitude larger than the emission level of spontaneous synchrotron radiation, because the interaction between the electron beam and the radiation ﬁeld modulates the beam current with the periodicity of the resonant radiation wavelength. The high brightness and the spectral range of this kind of radiation source allows studying physical and chemical processes on a femtosecond scale with angstrom resolution.

Keywords free-electron laser; undulator; microbunching; SASE FEL; FEL oscillator; FEL ampliﬁer; FEL parameter; gain length.

1 Introduction 2 2 Physical and Technical Principles 5 2.1 Undulator Spontaneous Radiation 6 2.2 The FEL Ampliﬁcation 7 2.3 The Small-signal Gain Regime 10 2.4 High-gain Regime and Electron Beam Requirement 11 2.5 Three-dimensional Effects 13 OE038

2 Lasers, Free-Electron

2.6 Longitudinal Effects, Starting from Noise 14 2.7 Storage Ring–based FEL Oscillators 16 3 Present Status 17 3.1 Single-pass Free-electron Lasers 17 3.2 Free-electron Laser Oscillators 18 4 Future Development 20 Glossary 21 References 23 Further Reading 24

1 accelerator and can be used to accelerate Introduction the electron beam to higher energies. The energy transfer can take place only A free-electron laser (FEL) [1] transforms if a condition of synchronism between the the kinetic energy of a relativistic electron wave and the beam oscillations is satisfied beam produced by a particle accelerator (Sect. 2.2). This condition gives a relation- like a microtron, storage ring, or radio ship between the radiation wavelength λ, • Q2 frequency (RF) linear accelerator into the electron beam velocity βz along the un- electromagnetic (EM) radiation. The trans- dulator axis (measured in units of the light formation occurs when the beam goes velocity c), and the undulator period λ0: through an alternating magnetic field, pro- λ (1 − β ) duced by a magnet called an undulator [2], λ = 0 z (1) that forces the electrons to move in an βz oscillatory trajectory about the axis of the For relativistic electrons, this condition can system, as shown in Fig. 1. An electromag- alsobewritteninanapproximate,but netic wave propagates together with the more convenient, form using the beam electron beam along the undulator axis, energy γ (measured in the rest energy and interacts with the electrons. units E = mc2γ ): The undulator magnet is a periodic structure in which the field alternates λ λ = 0 (1 + a2 ). (2) between positive and negative values and 2γ 2 w has zero average value. It produces an electron trajectory having a transverse The dimensionless quantity velocity component perpendicular to the eB0λ0 axis and parallel to the electric field of the aw = (3) 2πmc wave, thus allowing an energy exchange between the two to take place. One can is the undulator vector potential normal- either transfer energy from the beam to the ized to the electron rest mass mc2; e is the wave, in which case the device is an FEL, or electron charge and B0 is the undulator from the wave to the beam, in which case it peak magnetic field. (Here, and in the rest is an inverse FEL (IFEL) [3]. In the second ofthepaper,weuseMKSunits.)Thequan- case, the system is acting like a particle tity aw is called the undulator parameter, OE038

Lasers, Free-Electron 3

Undulator

Electron Outcoupled beam field

Optical cavity mirror Radiation field Partial mirror Fig. 1 Schematic representation of an FEL oscillator, showing its main component: the electron beam, undulator magnet, and optical cavity. The undulator shown is a permanent-magnet planar undulator. The arrows indicate the magnetic field direction. In an FEL amplifier of SASE FEL setup the optical cavity is omitted. The FEL amplifier is seeded by an external radiation field which is the normalized vector potential of fact suggests that high- to average-power the undulator field. The undulator can be FELs can be designed without the problem, of two types: helical and planar (Sect. 2). common in atomic and molecular lasers, Equation 2 is valid for a helical undulator. of heating the lasing medium. In the case of a planar undulator, Eq. 2 The time structure of the laser beam is still valid if we replace the undulator√ mirrors that of the electron beam. De- parameter with its rms value aw/ 2. pending on the accelerator used, one can Because of the dependence of the radi- design systems that are continuous-wave ation wavelength on the undulator period, (cw) or with pulses as short as picoseconds magnetic field, and electron-beam en- or subpicoseconds. ergy – quantities that can be easily and Tunability, high efficiency, and time continuously changed – the FEL is a tun- structure make the FEL a very attractive able device that can be operated over a source of coherent EM power. In some very large frequency range. At present, the wavelength regions, like the X-ray, the range extends from the microwave to the FEL is unique. Its applications range from UV [4]. A new FEL is now under construc- purely scientific research in physics, chem- tion in the United States [5] to reach the istry, and biology to military, medical, and X-ray region, about 0.1 nm. A similar pro- industrial applications. gram is being developed in Germany [6], FELs originate in the work carried out and other FEL to cover the intermediate in the 1950s and 1960s on the generation region between 0.1 nm and the UV [7] are of coherent EM radiation from electron also being considered by several countries. beams in the microwave region [2, 8]. The efficiency of the energy transfer As scientists tried to push power sources from the beam kinetic energy to the EM to shorter and shorter wavelengths, it wave is between 0.1 to a few percent for became apparent that the efficiency of most FELs, but it can be quite large, up to the microwave tubes, and the power about 40%, for specially designed systems. they produced, dropped rapidly in the The beam energy not transferred to the millimeter region. It was then realized that EM wave remains in the beam and can this problem could be overcome by using be easily taken out of the system, to be an undulator magnet to modify the beam disposed of, or recovered elsewhere. This trajectory [1], making it possible for the OE038

4 Lasers, Free-Electron

beam to interact with a wave, away from 1. portions of the EM spectrum, like the any metallic boundary. Two pioneering far infrared (FIR), or the soft and experiments at the Stanford University [9, hard X-ray region, where atomic or 10] proved that the FEL is a useful source molecular lasers are not available or of coherent radiation. are limited in power and tunability; The current disadvantage of FELs is the 2. large-average power, high-efﬁciency greater complexity and cost associated with system. the use of a particle accelerator. For this reason, the use and development of FELs An order-of-magnitude comparison of are mainly oriented to the following: the peak brightness obtained or expected

1035

TESLA SASE FELs 1033

DESY TTF-FEL LCLS (seeded) 1031

Spontaneous spectrum SASE FEL 1 0.1% bandw.)] 29 DESY 2 10 TTF-FEL 30 GeV

mm 15 GeV 2 Spontaneous spectrum TESLA SASE FEL 4 spontaneous undulator 1027

SPring8 undulator 25 10 (30m in vacuum) ESRF-undulator TTF-FEL (ID23) spontan

1023 Peak brilliance [Phot./(sec mrad Peak BESSY-II APS U-49 undulator BESSY-II (Typ A) 21 U-125 10 PETRA undulator ALS U5.0

1019 101 102 103 104 105 106 Energy (eV) Fig. 2 Peak brightness of free-electron lasers in the VUV and X-ray regime, compared to 3rd generation light sources [11] OE038

Lasers, Free-Electron 5 for the FEL, compared to other sources of The accelerators used to provide the elec- EM radiation, is given in Fig. 2, pointing tron beam are of many types: electrostatic, out again the interest for FELs in the soft- induction line, radio-frequency (rf) linear to-hard X-ray regions. accelerator, pulsed diode, or storage rings. In Sect. 2 of this article, we discuss Some of their basic characteristics, their the general physical principles of FELs energy ranges, and the FEL wavelengths and the properties and characteristics of for which they are more commonly used their main components, that is, the un- are given in Table 1. dulator magnets, electron beams, and Undulator magnets are of two main optical systems. We also describe the types: helical or planar. In the first case, main properties of the spontaneous ra- the magnetic field vector rotates around diation from an undulator, the process the axis as a function of axial distance; leading to the amplification of radia- in the second case, its direction is fixed, tion, the high-gain and small-signal-gain and its amplitude oscillates along the axis. regimes, diffraction effects, saturation These magnets can be, and have been, effects, the limits on the system effi- built using a wide variety of technologies: ciency, the dependence of gain on beam pulsed or DC electromagnets, permanent parameters. magnets, and superconducting magnets. In Sect. 3, we give a short review of the The field amplitude can vary from a experimental results obtained to date for fraction of a tesla to over 1 T, and the various FELs. The future development of period from 1 cm to many centimeters. FELs is described in Sect. 4. A great effort is under way to develop undulators with periods in the millimeter range; these would allow a reduction of 2 the beam energy for a given radiation Physical and Technical Principles wavelength, thus reducing the cost and complexity of the FEL. A helical undulator An FEL has three fundamental compo- was used by Madey and coworkers [9] nents: an electron beam of given energy in the first FEL. This undulator was a and intensity and the associated accelerator superconducting magnet, built with two used to produce it; the undulator magnet; helical windings with current flowing in and the EM wave and the associated optical opposing directions. components controlling its propagation. TheFELcanbeoperatedasanoscillator, A schematic representation of an FEL is using an optical cavity to confine the radi- given in Fig. 1. ationintheundulatorregion,asshownin

Tab. 1 Particle accelerators for FELs

Energy Peak current Pulse length FEL wavelength

Electrostatic 1–10 MeV 1–5 A 1–20 µsmmto0.1mm Induction linear 1–50 MeV 1–10 kA 10–100 ns cmto µm accelerator Storage ring 0.1–10 GeV 1–1000 A 30 ps–1 ns 1 µmtonm RF linear accelerator 0.01–25 GeV 100–5000 A 0.1–30 ps 100 µmto0.1nm OE038

6 Lasers, Free-Electron

Fig.1,oritcanbeusedasanamplifier. this case, the longitudinal velocity is not Oscillator–amplifier combinations [mas- constant; in fact, it can be written as the ter oscillator, power amplifier (MOPA)], sum of a constant term plus one oscillating as well as systems in which one amplifies at twice the undulator period. The electron the electron spontaneous radiation emitted trajectory in a helical undulator is a helix of in traversing the undulator [self-amplified radius awλ0/2πγβz and period equal to the spontaneous radiation (SASE) [12]], have undulator period. For a planar undulator, been used. it is a sinusoid in the plane perpendicular The performance characteristics of some to the magnetic field. of the existing FELs are discussed in detail When traversing the undulator, the elec- in Sect. 3. trons are subject to an acceleration and radiate EM waves. This spontaneous emis- 2.1 sion is fundamental to the operation of Undulator Spontaneous Radiation an FEL. One relativistic electron traversing an undulator magnet emits radiation in a For this discussion, we use a reference narrow cone, with an angular aperture of frame with z along the undulator axis γ and x and y perpendicular to z.Fora order 1/ [13]. The radiation spectrum is a helical undulator, the field near the axis z superposition of the synchrotron radiation is given by emitted when the electron trajectory is bent in the undulator field, a narrow line intro- z duced by the periodic nature of the motion B = B0 ex cos 2π λ inthesamefield,anditsharmonics.The 0 z wavelength of the fundamental line is of + π ,() 2 ey sin 2 4 the order of λ0/2γ , which can be inter- λ0 preted as the undulator period λ0 doubly where ex, ey,andez are unit vectors along Doppler shifted by the electron motion. the x, y,andz axes. The electron velocity The aperture 1/γ of the synchrotron in this field, in units of c,is radiation cone can be compared with a z the angle between the electron trajectory β = w π ex sin 2 and the undulator axis, aw/γ .Ifaw is γ λ0 smaller than 1, the emitted radiation is z + ey cos 2π + ezβz.(5) contained within the synchrotron radiation λ0 cone, and the emission is predominantly The amplitude of the transverse velocity in a single line. If aw is larger than 1, the synchrotron radiation cone sweeps an is aw/γ . This quantity also represents the maximum angle between the electron angle larger than its aperture. In this trajectory and the undulator axis. For case, the spectrum is rich in harmonics relativistic beams, this quantity is much and approaches the synchrotron radiation less than 1, and the longitudinal velocity is spectrum when aw is very large. When near 1. Notice that in the case of a helical aw 1, the magnet is usually referred to undulator, the axial component of the as a wiggler, reserving the name undulator velocity, βz, remains constant. For a planar for the case aw less than or on the order undulator, only one of the two transverse of one. In this article, we use the generic components in Eqs. 4 and 5 is nonzero. In term ‘‘undulator’’ to describe a magnet OE038

Lasers, Free-Electron 7 with a periodic transverse field described spread is larger than 1/2Nw,thesingle by Eq. 4. electron width. Similarly, the effective The fundamental wavelength seen by an source radius and angular distribution can observer looking at an angle θ to the undu- be increased by the electron beam. This = 2 + 2 + 2 2 lator axis is λ (λ0/2γ )(1 aw γ θ ), effect can reduce the FEL gain, as we will and is the wavelength at which there is discuss in the next section. positive interference between the radiation emitted in two undulator periods. This is 2.2 also, when θ = 0, the wavelength corre- The FEL Amplification sponding to the ‘‘synchronism condition’’ Eq. 1. Undulators are widely used in storage In a planar undulator, the magnetic rings as brilliant sources of synchrotron field has only one component, say along radiation. In this case, the superposition of y. Then the velocity has components in spontaneous radiation of many electrons the x and z directions. The wavelength of has no phase correlation, so that the total the spontaneous radiation is the same as intensity is proportional to the electron that for a helical undulator if the vector number Ne.InanFEL,asinanatomic potential√ aw is replaced by its rms value, laser, there is a phase correlation between aw/ 2. emitting electrons. This correlation is In a helical undulator, the radiation obtained by modulating the longitudinal on axis contains only the fundamental beam density on the scale of the radiation harmonic given by Eq. 1. In a planar wavelength, a process called bunching. undulator, the longitudinal velocity is When electrons are bunched together in • modulated twice at the undulator period. a distance that is short compared to the Q3 This leads to a richer spectrum: all the wavelength of the radiation, they emit in odd harmonics of Eq. 1 appear on axis. phase, thus increasing the intensity in the For both type of undulators, even and odd emitted line and simultaneously reducing harmonics appear off axis. its width. The linewidth of the radiation is deter- The formation of bunching is caused by mined by the number Nw of undulator the interaction between the electrons and periods; the total length of the pulse emit- the radiation field. It can be summarized ted by one electron is that of a wave train by three actions, fundamental to any FEL with a number of periods equal to Nw,the process: number of undulator periods. The corre- sponding linewidth of the fundamental is 1. the modulation of the electron energy ω 1 due to the interaction with the radiation = .(6) field, ω 2N w 2. the change in the longitudinal position When more than one electron is producing of the electrons owing to the path length the radiation, the pulse length and angular difference of the trajectories within the distribution can be affected by the electron- undulator of electrons with different beam characteristic. The pulse length is energies, increased by the electron bunch length 3. the emission of radiation by the elec- when this is larger than Nwλ.Theradiation trons and, thus, growth in the radiation linewidth is increased if the beam energy field amplitude. OE038

8 Lasers, Free-Electron

Each point will be explained in detail be- as given by Eq. 5. An energy transfer low. The FEL amplification couples these between the EM field and the electron basic processes and exploits the inherent beam can take place. Using Eqs. 5 and 7, instability of this system. A stronger mod- one finds ulation in the electron density increases 2 dγ aw the emission level of the radiation, which, mc = eE0 sin ( + ) ,(8) dt γ in return, enhances the energy modulation within the electron bunch. With stronger where the phase is energy modulation, the formation of the bunching (modulation in the electron po- 1 1 = 2π + z − ωt + 0.(9) sitions) becomes even faster. The FEL λ λ0 amplification is stopped, when the electron This quantity is called the ponderomotive density modulation has reached a maxi- force phase [14] and plays a key role in FEL mum. At this point, all electrons have the physics. The ponderomotive force phase same phase of emission and the radiation has terms changing at the ‘‘fast’’ EM field is fully coherent. The free-electron laser frequency and terms changing with the has reached saturation. ‘‘slow’’ undulator period. The time-average TheFELprocessiseitherinitiatedbya value of the electron energy change (8), seeding radiation field or by the inherent averaged over a few radiation periods, fluctuation in the electron position at the is 0 unless we satisfy a ‘‘synchronism undulator entrance. The first classifies the condition’’ d / dt = 0. This condition free-electron laser as an FEL amplifier, canbewrittenasλ = λ (1 − βˆ )/βˆ with while the latter is called a self-amplifying 0 z z βˆ as the ‘‘resonant’’ velocity for a spontaneous radiation (SASE) FEL, where z given undulator period and radiation field the initial radiation level is produced by wavelength. In the case of relativistic the spontaneous radiation, as described in ˆ particles, using the relationship βz = Q4 Sect. 2.1•. (1 − 1/γ 2 − β2 − β2)1/2, and assuming In the following, we describe the basic x y γ 1, β ,β 1, this condition can FEL process. We start with a simplified z y be approximately written as λ = λ (1 + model, where transverse effects such 0 a2 )/2γ 2. These are Eqs. 1 and 2, given as the diffraction of the radiation field w in the introduction. If the synchronism due to its finite size is ignored. The condition is satisfied, the ponderomotive discussion of these three-dimensional force phase is constant, and the electron effects is postponed till Sect. 2.5. Let beam, oscillating at the slow undulator z frequency, can exchange energy with the E = E e cos 2π − ωt + 0 x λ fast oscillating EM wave. + z − + If the longitudinal velocity βz differs ey sin 2π ωt (7) ˆ λ from the resonant velocity βz, the electron slips in the ponderomotive force phase as be the electric field of a plane wave propagating along the undulator axis. The d 2πc β = z − 1 .(10) initial phase of the radiation field at t, dt λ βˆ z = 0is. This field is transverse to the z undulator axis, and thus has components If the electron moves with the resonant parallel to the transverse electron velocity, velocity, its ponderomotive force phase is OE038

Lasers, Free-Electron 9 constant according to the synchronism phase interval [, + π], gain energy condition. Particles with higher energy and become faster ( d /dt > 0), while move forward with respect to the initial electrons in the interval [ + π, + 2π] phase 0, while particles with lower energy are slowed down ( d /dt < 0). As a result, fall back. all electrons tend to drift toward the The distribution of the initial position phase + π and become bunched with of the electrons within the bunch is de- the periodicity of the radiation field. The termined by the electron source and the electrons emit in phase and the radiation acceleration process. If the electron beam is coherent. is produced by an accelerator using RF The radiation emitted by the electrons cavities to accelerate the beam, the dis- adds up to the interacting EM wave. The tribution is characterized by two scale amplitude E0 and the phase of the EM lengths. One is the RF wavelength; the field change with the ongoing interaction other is the radiation wavelength. In an between radiation field and electron beam. FEL, the first is much larger than the sec- This is apparent because the electrons ond. The wavelengths used in RF cavities tend to bunch at a phase different to vary from a minimum of about 10 cm the radiation field. The radiation phase is foranRFlinearacceleratortoinfinityfor slowly adapting to the new phase defined an electrostatic accelerator. At the scale by the bunching phase of the electrons. length defined by the RF system, the elec- For a self-consistent description of the trons are distributed longitudinally into FEL interaction, the Maxwell equation bunches separated by one RF wavelength. for the EM wave has to be solved as The length of these bunches is a frac- well. If the fast oscillation of the EM tion of the wavelength of the accelerating wave exp[i(2π/λ)z − iωt]issplitfrom RF and varies from about 1 mm for the the amplitude and phase information, = ≡ case of a 3-GHz (λrf 10 cm) RF linear the complex amplitude E E0 exp[i] accelerator to a continuous beam for the changes slower than the ‘‘slow’’, transverse electrostatic case. oscillation of the electrons (Eq. 5). The At the scale length of the radiation wave- change is given by [15]: length, the electron distribution is in good −i approximation uniform; there is no cor- ∂ ∂ µ0 e j + E = i aw (11) c∂t ∂z 2 γj relation between the longitudinal electron j positions at the scale of the radiation wavelength λ except for a residual, but small with µ0 as the magnetic permeability and bunching owing to the finite number of the sum over all electrons. Equations 8, electrons per radiation wavelength. It rep- 10, and 11 are the mathematical represen- resents the spontaneous radiation level at tation of the three basic processes, listed at the given wavelength λ, which is amplified the beginning of this chapter. Note that the in an SASE FEL. Section 2.6 discusses in right-hand side of Eq. 11 is determined by detail the properties of this device. the degree of bunching in the electron den- If the electrons have the resonant sity and is at maximum when all electron velocity or are close to it, the interaction phases j are identical. It is also clear from with the radiation field results in a the same equation that if more electrons sinusoidal modulation of the electron are contributing to the FEL process, the energy (Eq. 9). Electrons, lying within the growth in the radiation field is stronger. OE038

10 Lasers, Free-Electron

The strength of this coupling scales with amplification of the seeding field is called the FEL parameter [16] lethargy regime [16]. The growth in the radiation field am- 2 a ωp 3 plitude stops at saturation, when the ρ = w ,(12) 4γ ω0 modulation in the electron distribution has reached a maximum. At this point, 2 1/2 where ωp = (4πrec n0/γ ) is the beam the bunch is broken up into multiple plasma frequency, n0 is the electron-beam microbunches. The spacing of the mi- density, and ω0 = 2πc/λ0.Typicalvalues crobunches is the radiation wavelength. − of ρ vary from 10 2 for a millimeter FEL Because the wavelength is tunable with −3 to 10 or less for a visible or UV FEL. the electron beam energy, the free-electron The solutions for Eqs. 9, 10, and 11 laser is also a device to modulate the cur- ∝ are of type E exp[i 2ω0ρt], where the rent of a long pulse with free control on growth rate depends on the electron the periodicity. This property is useful for distribution in energy and the deviation some experiments on plasma-beam inter- of the mean energy from the resonance action [19]. = · + 2 energy γR (λ0/2λ) (1 aw).Forthe simplest case of a mono-energetic beam 2.3 with <γ > = γR, is the solution of The Small-signal Gain Regime the dispersion equation 3 =−1 [17]. Although energy deviation or finite energy The first FEL experiments had an enhance- spread adds additional terms, the resulting ment of a few percent of the seeding dispersion equation is always cubic for this radiation field. In this low-gain regime, one-dimensional model. the undulator length is shorter than the Of particular interest for the FEL process gain length. All modes – growing, decay- is the solution of the dispersion equation, ing, and oscillating – have approximately which has a negative imaginary part. It the same amplitude and the radiation corresponds to an exponentially growing power at the end of undulator as a result mode. The maximum growth rate in of the interference of these modes. If the this√ one-dimensional model is −e(i ) = wavelength of the seeding radiation field • Q28 3/2. Inserted into the ansatz for the fulfills the synchronism condition, the in- radiation field amplitude E,thee-folding terference is completely destructive and length of the amplification is thegain–therelativechangeintheradi- ation field intensity – is zero. The growth λ0 Lg = √ ,(13) rate of each mode depends differently on 2π 3ρ the deviation from the synchronism con- whichisalsoreferredtoasthegain dition (Eq. 1) and a slight deviation ω length [18]. Besides the exponentially results in an enhancement of the EM growing mode, the other modes are either field. oscillating or decaying. In the beginning of The small-signal gain was first evalu- the free-electron laser, all modes are of the ated by Madey [1]. Although his original same magnitude and it requires a few gain theoretical discussion of the FEL used a lengths before the exponentially growing quantum-mechanical description, it was mode dominates. This retardation in the soon realized that under most conditions, OE038

Lasers, Free-Electron 11 a classical description is sufficient to de- 2.4 scribe the system, since the most relevant High-gain Regime and Electron Beam quantities, such as gain, Eq. 14, are inde- Requirement pendent of the Planck constant. When the initial EM field amplitude The FEL saturates when the electron is small – and the relative change in the bunch has achieved maximum modula- intensity is also small – the gain is called tion and all electrons radiate coherently. the small-signal gain. For an initially mono- Early free-electron lasers could not reach energetic electron beam, the small-signal saturation with a single pass through an gain, calculated by Madey, is undulator. The gain can be accumulated √ when the undulator is enclosed by an opti- √ 2 λλ0 aw Ip 3 cal cavity and the radiation field is reflected Gs = 4 2π N 2 + 2 3 w w0 (1 aw) IA back to seed the FEL for succeeding electron bunches. On the other hand, optical d sin2(x/2) × ,() cavities restrict the FEL to radiation wave- 2 14 d(x/2) (x/2) length where the losses of the cavity are where x = 2πNwω/ω, Nw is the number smaller than the gain per single pass. To of undulator periods, Ip is the beam avoid this restriction, the undulator length current, IA = ec/re is the Alfven´ current has to be several gain lengths long to obtain (about 17 kA), re is the classical electron a large gain and to reach saturation [18]. ≈ × −15 2 To reduce the overall undulator length, radius (re 2.8 10 m), and πw0 is the transverse cross section of the EM the gain length (Eq. 13) must be made as wave (assumed to be larger than that of the short as possible. The undulator period electron beam). length is typically limited to a few The gain curve in Eq. 14 is proportional centimeters and found by optimization to the derivative of the spectrum of the of the gain length. Shorter values would spontaneous radiation. The gain is zero for reduce the undulator parameter and, thus, x = 0, at synchronism, and is maximum the coupling of the electron beam to the for x 2.6. The linewidth is on the order radiation field, while longer values would of 1/Nw, the inverse of the number of increase the resonant wavelength (Eq. 2). periods in the undulator. The energy has to be increased to keep Since the EM radiation frequency and the radiation wavelength constant, which the electron energy are related by the reduces the ρ-parameter. synchronism condition, Eq. 2, we can The gain length depends on the electron also redefine x,forafixedfrequency, beam parameters as well. The gain length as x = 4πNwγ /γ .Thegainlinewidth is reduced for a higher electron density, then corresponds to an energy change although there are limits on this, given γ /γ on the order of 1/2Nw.When by the transverse velocity spread in the the radiation field increases, the beam electron beam. We discuss this and kinetic energy decreases; and when the other three-dimensional effects in the next change is about 1/2Nw, the gain becomes section. 0. Hence the maximum FEL efficiency, The gain length of Eq. 13 is based defined as ratio of the laser intensity to the on a beam with no energy spread. initial beam kinetic energy, is on the order Energy spread prevents bunching of all of 1/2Nw. electrons at the same ponderomotive force OE038

12 Lasers, Free-Electron

phase, because the electrons have different Note that in the high-gain regime, the longitudinal velocities and the bunching gain is the largest if the beam energy is is smeared out. The bandwidth in energy, on resonance, as shown in Fig. 3. This is which contributes to the FEL performance, opposite to the small-signal gain regime is given by the ρ-parameter. A larger with no gain at <γ > = γR. value means that the energy exchange Only electrons that lie within the en- between radiation field and electron beam ergy acceptance bandwidth of the FEL is stronger. The undulator length, over around γR contribute to the FEL inter- which the synchronism condition must be action. The relative width is approximately fulfilled, is shorter. This allows a larger ρ. During the FEL amplification, energy tolerance in the spread of the longitudinal is transferred from the electron beam to velocity and thus, in energy. To keep the the radiation field. The amplification stops increase in the gain length reasonable, the whenmostoftheelectronsaredropped initial rms energy spread σγ must be out of the bandwidth. After that the interaction with the radiation field is negligible σγ ρ. (15) because the synchronism condition is no γR longer satisfied. Thus, the efficiency of the FEL, which is the relative amount of en- Following the same argument, the devia- ergy transferred from the electron beam tion of the mean energy from the resonant to the radiation field, is ρ.Thesatura- energy is limited to tion power of the radiation field [20] is given by − <γ > γR ρ. (16) = γR Psat ρPb,(17)

1.0

0.8

0.6 ) Λ Re(i − 0.4

0.2

0.0 −8 −6 −4 −2 0 2 4 (<γ> − γ /ρ<γ> R) Fig. 3 Growth rate of the FEL ampliﬁcation as a function of the detuning–the deviation of the mean energy of the electron beam from the resonant energy OE038

Lasers, Free-Electron 13

= 2 where Pb <γ >Ipmc /e is the electron FEL process, which are beam power and Ip is the peak current. 1. the spread in the transverse velocity of Because of this scaling, it is of interest the electron beam and to maximize the ρ-parameter not only 2. the diffraction of the radiation field. for reducing the needed undulator length for saturation but also for increasing the A measure for the transverse spread output power level of the FEL. in the electron beam is the normalized Because the FEL amplification is an emittance εn [22], which is the area covered exponential process, the major change by the electron beam distribution in in the electron energy occurs close to transverse phase space. It is an invariant saturation, when the electrons are pushed in linear beam optics. If the beam is out of the FEL bandwidth. Although the more focused, the spread in the transverse FEL amplification stops at saturation, momenta is increased. Focusing along further energy can be extracted from the the undulator is necessary to prevent electron beam. For this, the synchronism the growth of the transverse electron condition has to be extended beyond beam size, reducing the electron density saturation. The radiation wavelength is and decreasing the gain. Electrons that fixed, so the undulator field or period drift away from the axis are deflected has to be reduced to compensate for the back to the undulator axis. As a result, beam energy, which has been lost due electrons perform an additional oscillation to the FEL interaction. This process to even slower than the ‘‘slow’’ oscillation gradually reduce the undulator field or due to the periodic magnetic field of period is called tapering. Although the the undulator (Eq. 5). Because part of energy transfer during tapering is slow the electron energy goes into this so- compared to the exponential regime of called betatron oscillation, the electron is the FEL, the process has no fundamental slower in the longitudinal direction than an limits beside the given length of the electron without a betatron oscillation. The undulator. Experiments have shown that a spread in the betatron oscillation, which tapered system can enhance the efficiency scales with the normalized emittance, has up to 40% [21]. a similar impact as an energy spread. Thus, the requirement for the transverse 2.5 emittance is Three-dimensional Effects 4λβ<γ > ε ρ, (18) n λ The basic FEL process, as described in 0 Sect. 2.2, remains the same when three- where the beta-function β [22] is a measure dimensional effects are included in the for the beam size of the electron beam. discussion, although the one-dimensional Stronger focusing would increase the FEL parameter ρ (Eq. 12) might not electron density (β becomes smaller) and be valid anymore. However, an effective consequently, the ρ parameter. But at the three-dimensional FEL parameter can be same time, the impact of the emittance found, which satisfies Eqs. 13, and 15 effect is enhanced, reducing the amount to 17. of electrons that can stay in phase with the Two major effects contribute to the radiation field. It requires the optimization extended, three-dimensional model of the of the focusing strength to obtain the OE038

14 Lasers, Free-Electron

shortest possible gain length. A rough rate or gain length. That mode, which has estimate for the optimum β-function the largest growth rate, dominates after is β ≈ Lg ≈ λ0/4πρ. Inserting this into several gain lengths and the radiation field Eq. 18 shows that the beam emittance becomes transversely coherent. = • ε εn/γ has to be smaller than the photon At saturation gain, guiding vanishes Q5 beam ‘‘emittance’’ λ/4π. If this condition and the electron beams radiate into mul- is fulfilled, the electron beam does not tiplemodes.Typically,thefundamental diverge faster than the radiation field and FEL-eigenmode is similar to that of free- all electrons stay within the radiation field. space propagation and the resulting reduc- The diffraction of the radiation field tion in transverse coherence at saturation transports the phase information of the is negligible. radiation field and the bunching of the The characteristic measures for diffrac- electron beam in the transverse direction. tion and FEL amplification are the Rayleigh This is essential to achieve transverse co- length zR and gain length Lg.Tocalculate herence of the radiation field, in particular, zR, we approximate the radiation size at if the FEL starts from the spontaneous ra- its waist by the transverse electron beam diation (SASE FEL). SASE FELs do not size as the effective size of the radiation guarantee the transverse coherence as a source, resulting in zR = k/2. For zR seeding laser signal of an FEL amplifier Lg, the FEL amplification is diffraction- would do. The betatron oscillation, which limited with a gain length significantly yields a change in the transverse position larger than that in the one-dimensional of the electron, contributes to the growth model (Eq. 13). In the opposite limit of transverse coherence as well. (zR Lg), the one-dimensional model be- As a degrading effect, the radiation field comes valid. escapes from the electron beam in the transverse direction. The field intensity 2.6 at the location of the electron beam is Longitudinal Effects, Starting from Noise reduced and the FEL amplification is in- hibited. The compensation for field losses The radiation field propagates faster than due to diffraction is the FEL amplifica- the electron beam and advances one ra- tion itself. After the lethargy regime, the diation wavelength per undulator period. FEL achieves equilibrium between diffrac- Thus, information cannot propagate fur- tion and amplification. The transverse ther than the slippage length Nwλ,where radiation profile becomes constant and Nw is the total number of undulator pe- the amplitude grows exponentially. This riods. If the bunch is longer than the ‘‘quasi-focusing’’ of the radiation beam is slippage length, parts of the bunch amplify called gain guiding [23] and the constant the radiation independently. While an FEL profile of the radiation field is an eigen- amplifier is seeded by a longitudinal co- mode of the FEL amplification. herent signal, this is not the case for an Similar to the eigenmodes of the free- FEL, starting from the spontaneous emis- space propagation of a radiation field sion (SASE FEL). SASE FELs with electron (e.g., Gauss–Hermite modes), there are an bunches longer than the slippage length infinite number of FEL eigenmodes [24]. generate longitudinally incoherent signals. Each couples differently to the electron Further processing, succeeding the FEL, is beam and thus has a different growth required for fully longitudinal coherence OE038

Lasers, Free-Electron 15

(e.g., it can be achieved with a monochro- lasers in the IR regime to a few kilo- mator with a bandwidth smaller than the watts for FELs in the VUV and X-ray Fourier limit of the electron bunch length). regime. An FEL amplifier has a coherent seeding When the electron bunch length is signal and the electron beam can be more longer than the slippage length, the ra- or less in resonance with it. The output diation profile contains many spikes. The power level depends on the deviation of spikes are also present in the frequency the mean energy of the electron beam from spectrum. The origin is the random the resonant energy γR.AnSASEFEL,on fluctuation in the beam density. The the other hand, uses the broadband signal shot-to-shot fluctuation in the radiation of the spontaneous emission to start the pulse energy follows a Gamma distri- • Q6 FEL amplification. Independent of the bution [26]. The only free parameter of beam energy, the resonance condition this distribution, M, can be interpreted is always fulfilled, but the SASE FEL as the number of the spikes in the amplifies all frequency components within radiation pulse. The√ relative width of the acceptance bandwidth of the FEL as the distribution is 1/ M.Thelengthof well. The relative width is ω/ω = ρ and the spikes is approximately (λ/λ0)Lg [27]. is typically much larger than the observed A shorter pulse would result in a width of an FEL amplifier. larger fluctuation of the radiation en- The initial emission level of the sponta- ergy. The fluctuation of the instantaneous neous radiation depends on the fluctuation power is given by a negative exponential in the electron density. Because there distribution. areonlyafinitenumberofelectrons From the optical point of view, the elec- per radiation wavelength and the initial tron beam acts as a dielectric, dispersive ponderomotive force phase is random, medium for the radiation field. The field electrons can cluster together at random. amplitude E evolves as exp[i 2ω ρt]. The The radiation from parts of the bunch with 0

a larger clustering will have larger inten- imaginary part of results in the growth of sity than that of other parts. The variation the radiation field and thus, gain guiding, in these clusters and, thus, the fluctua- while the real part adds a phase advance − tion in the beam current, depend on the to the fast oscillating wave exp[ikz iωt]. total number of electrons. Because of the The effective phase velocity differs from c, random nature of the electron positions, the speed of light. The electron beam is more electrons result in a smoother distri- dielectric and the radiation field is focused bution. The chances for large clusters are due to the same principle of fiber optic reduced. cables. In addition, depends on the de- The effective power level, emitted be- viation of the radiation frequency from cause of spontaneous radiation and then the frequency that fulfills the synchro- further amplified by the FEL interaction, nism condition in Eq. 1. This dispersion is called the shot noise power [25]. An reduces the group velocity below the speed FEL amplifier, seeded with a power sig- of light [28] and spikes advance less than nal smaller than the shot noise power one radiation wavelength per undulator pe- level does not operate as an FEL ampli- riod. Amplification stops at saturation and fier but as an SASE FEL instead. Typical the ‘‘dielectric’’ electron beam becomes values are a few watts for free-electron nondispersive. OE038

16 Lasers, Free-Electron

2.7 pass. Because the electron emission is fully Storage Ring–based FEL Oscillators coherent at saturation, the field cannot be further amplified. The oscillator reaches Free-electron lasers are mainly based upon an equilibrium between the losses of the linear accelerator and storage rings. Elec- optical cavity and the reduced gain is closed tron beams, provided by linear acceler- to saturation. ators, have the beam quality needed to When the FEL oscillator has reached sat- reach saturation in a single pass. Because uration, the power level within the optical this setup exhibits a strong amplification, cavity is small compared to that of a single- the single-pass FEL has properties that are pass FEL because the effective ρ parameter a disadvantage in comparison to quantum and beam power are lower (Eq. 17). In ad- lasers or storage ring–based FEL oscilla- dition, only a fraction can be coupled out tors. Radiation of a single-pass FEL suffers of the cavity for succeeding experiment be- from the inherent fluctuation of the beam cause the out-coupling contributes to the parameters such as energy and position net loss of the optical cavity. Higher, out- jitter. In addition, an SASE FEL does not coupled radiation power requires a higher necessarily provide longitudinal coherence gain to compensate for the losses. In the and has a spectral bandwidth, which is equilibrium state, the FEL oscillator’s tem- large compared to standard lasers. The poral and frequency stability, longitudinal average power is limited by the repetition coherence, and repetition rate are better rate of a linear accelerator, small compared than those of a linear accelerator–based to that of a storage ring. The single-pass FEL. However, the official quality of linear high-gain FEL is the only solution for a accelerator–based FELs can be improved high-brightness radiation source for wave- using optical instruments, like monochro- length regions, where an FEL oscillator mators. system will not work owing to the losses The radiation of an FEL oscillator is in the optical cavity. typically longitudinal coherent, because The limitations for storage ring–based the phase information of the radiation FEL are given by the instabilities that field is distributed over the entire electron occur in a storage ring. These instabilities bunch mainly due to two reasons. The yield an upper limit on the electron first reason is the same as for a single-pass beam current of typically a few hundred FEL, because the radiation field propagates amperes [29]. In addition, the energy faster than the electron beam. The second spread and normalized emittance are reason depends on the design of the optical large compared to those in a linear cavity. If the cavity is ‘‘detuned’’, the time accelerator [30]. of the radiation pulse to pass the cavity The FEL oscillator accumulates the is different from the arrival time of the single-pass gain of typically a few percent. next electron bunch. The radiation field As long as the amplitude of the EM field has a longitudinal offset with respect to is small, the gain per pass is constant the electron bunch. This offset allows a (small-signal gain) and the field grows faster buildup of coherence. exponentially with the number of passes. The FEL oscillator can start from the The oscillator reaches saturation when spontaneous radiation. If the gain is the FEL interaction is strong enough to larger than a few percent and the detun- induce complete bunching within a single ing is small, the random nature of the OE038

Lasers, Free-Electron 17 spontaneous emission phase can man- 3.1 ifest in the occurrence of superradiant Single-pass Free-electron Lasers spikes [31]. The peak power can be con- siderably larger than the power level of Single-pass free-electron lasers are fre- the fully coherent signal, while the spike quently based on linear accelerators. Be- length is shorter than the electron bunch cause the FEL does not rely on any optical length. The nature of these superradiant cavity to accumulate the gain, there is no spikes is the same as those occurring in restriction on the wavelength. A beam en- the temporal radiation profile of an SASE ergy of about 10 MeV corresponds to a FEL. resonant wavelength of about 10 microns, while a 10- to 25-GeV beam can drive an FEL in the VUV and X-ray region. The 3 energy of the electron beam is determined Present Status by the length of the linear accelerator. The requirements on the beam qual- The current status of the FEL research ity (Sect. 2.4 & 2.5) are more stringent program around the world can be clas- for FELs operating at shorter wavelength, sified into two groups with different and the first single-pass FELs started at objectives. The single-pass free-electron wavelengths in the millimeter or infrared laser is aiming toward shorter wave- regime [32]. The major motivation of the length, while storage ring–based FELs ongoing FEL research is to shorten the are developed to overcome the limita- wavelength down to the angstrom level, tion of the losses of the optical cavi- where no alternative radiation sources with ties. Free-electron lasers, which have fin- the same radiation properties exist. The to- ished their research program, are often tal number of single-pass FEL is numerous converted to user facilities, where re- and Table 2 lists a selection, namely, those searchers can use the unique properties with the shortest wavelength. The record of the FEL radiation for research in their for the shortest wavelength so far lies at field. around 80 nm [33]. The majority of future

Tab. 2 Linear accelerator–based free-electron lasers

FEL UCLA VISA LEUTL TTF-FEL I

Energy [MeV] 18 71 217/255 250 Energy 0.25 0.1 0.4/0.1 0.06 spread [%] Norm. emittance 5.3 2.3 8.5/7.1 6 [mm·mrad] Peak current [A] 170 250 630/180 1300 Wavelength [nm] 12 000 840 530/385 95 Peak 0.0001 15 500 1000 power [MW] Pulse length 5.5 0.3 0.2/0.7 0.02 [ps, RMS] Gain length [cm] 25 18.7 97/76 67 OE038

18 Lasers, Free-Electron

FELs will operate at shorter wavelengths energy variation along its length by the RF (Sect. 4). structure, so that electrons at the head of The FEL performance is limited by the bunch have lower energy than those the electron beam quality, the transverse inthetail.Thepath-lengthdifferencein emittance, the energy spread, and the the bunch compressor reduces the bunch beam current. The linear accelerators of length and increases the beam current. all the latest single-pass free-electron lasers The beam energy correlation is obtained are based on RF photoelectron guns [34]. when the RF field is still building up A conventional laser in the visible or UV (‘‘off-crest’’ injection). Electrons entering illuminates a cathode, embedded into an first see a lower accelerating gradient than RF cavity. The photo effect generates the those entering later. At the cavity exit, electrons and the RF field accelerates them the bunch has an energy correlation along to minimize the beam ‘‘blowup’’ due to bunch, needed to compress the bunch in the electric field of each electron (space the bunch compressor. charge field). The value of the transverse emittance arises mainly from this space 3.2 charge field at the cathode region [35]. Free-electron Laser Oscillators At higher energy, the electron beam is relativistic and is less sensitive to space Storage rings impose a limit on the charge effects. achievable electron beam quality. Because Becauseamoreintensepulseofthe bending magnets are required to trans- photo gun laser produces a higher electron port the electron bunches back to the density, the space charge field is stronger. undulator entrance, electrons emit sponta- As a consequence, there is a limit on the neous radiation. When an electron looses achievable emittance and current from the energy owing to the spontaneous radi- RF photoelectron gun [36]. Increasing the ation, its orbit shifts with respect to current would increase the emittance as the design orbit. The energy losses are well. Typical values are an emittance of not the same for every electron due around 2 mm·mrad at a current of about to quantum fluctuations of the emitted 50 A. The total charge of the electron photons. This results in a limitation of bunch is on the order of 1 nC. Single- the achievable transverse emittance [37]. pass free-electron lasers typically require To increase the performance of a stor- beam currents of 100 A and above to keep age ring–based FEL oscillator, this limit the saturation length within reasonable has to be reduced, which often requires limits. This is achieved by including bunch a special lattice of bending and fo- compressors in the beam line of the linear cusing magnets. Bends with more, but accelerator. shorter, bending magnets alternating with A bunch compressor consists of bending quadrupole magnets, perform better than magnets, which deflect the beam off the those with less magnets. This approach is axis of the linear accelerator and then bend not only used for storage ring–based FEL it back to the axis. Because the bend angle but also for most third-generation light depends on the electron energy, electrons sources [38]. with a lower energy have a stronger Since electron bunches are kept in a distortion and, thus, a longer path length. storage ring for minutes or hours, even The electron bunch is given a correlated small effects can be accumulated and can OE038

Lasers, Free-Electron 19

degrade the beam quality. One effect is 1. the extension of the wavelength range intrabeam scattering, in which, due to intheVUVrangebynovelcoatingor Coulomb collision electrons are gradu- material, ally kicked out of the orbit and lost in 2. increasing average power by improved the storage ring aperture [39]. Another power handling. effect is the ‘‘communication’’ between bunches by means of wakefields [40]. Each The shortest wavelength an FEL oscil- storage ring has RF cavities to com- lator is operating is around 100 nm [41] pensate energy losses, which occur be- with significant power emitted at higher cause of spontaneous radiation and the harmonics as well. The FEL oscillator at FEL interaction. The modes of the cav- Jefferson Lab achieved an average power ities are excited whenever an electron in the IR region above 2 kW [42]. In slight bunch passes the cavities. These higher contrast to the single-pass FEL, which modes are not damped quickly enough, are mostly FEL experiments to extend Q7 so that• the next bunch interacts with the wavelength range, storage ring–based them. The resulting energy modulation FELs mostly serve as a user facility, where is not constant over the entire bunch the radiation wavelength and power is and dispersion – energy dependence of tuned to the needs of experiments from the orbit – tears the bunch apart, spoil- all fields of science. ing the beam quality or even dumping The limitations in beam current and part of the beam in the vacuum cham- bunch length can be overcome in ber wall. an Energy Recovery Linear accelerator Besides an advanced lattice design of (ERL) [43], where the electron bunches are the storage ring to minimize the effects only kept for a few turns in the storage described above, storage ring limitation ring. The beam energy is extracted back can be diminished by improving the to the accelerating field prior to the ejec- optical cavity of the FEL oscillator. The tion and dumping of the bunch. Since the current research on oscillators is focused peak current in an ERL is higher than to improve the reflecting mirrors in two that in storage ring, the brightness and the areas such as saturation power is increased.

• Q8 Tab. 3 Free -electron laser oscillators

FEL Dukea Elletraa Cliob Felixc Jefferson Labd

Energy[MeV] 200–1200 1000 15–50 15–50 48 Avg. current [mA] 115 25 2–40 2.5–100 4.8 Bunch length [ps] <50 6.3 0.5–6 0.8 0.4 Rep. rate [MHz] 13.95 4.63 62 25/1000 74.8 Wavelength [µm] 0.19–0.4 0.19–0.20 3–90 4.5–250 3–6.2 Avg. power [W] 0.025 0.01 3 25–5000 2000

aStorage ring. b10 µs electron bunch train from thermionic gun at 25 Hz. c10 µs electron bunch train from thermionic gun at 10 Hz. dEnergy recovery linear accelerator. OE038

20 Lasers, Free-Electron

4 beginning of the beam line. It propagates Future Development to the accelerating cavities a second time, ◦ but with a 180 difference in the RF phase. All recent single-pass free-electron laser The residual kinetic energy of the bunch is experiments have not shown any fun- transferred back to the RF field, and thus damental limits that would prevent a is available for succeeding bunches. It re- resonant wavelength at the angstrom level. quires superconducting cavities; otherwise The typical beam energy would be around the stored energy will be lost by thermal 10 to 25 GeV. The required undulator losses before the next bunch enters the length would be around 100 m. Several beam line. Using this setup, the repetition projects have been proposed or are under rate of the electron bunches are not limited construction to have single-pass FELs op- by the RF system and FELs can be operated erating in the wavelength regime between in cw mode, similar to storage ring but with 1 and 1000 A˚ [5–7]. Table 4 lists a selec- the advantage that there are no limitations tion of them. All these FELs are planned on the beam current or emittance. to be user facilities. Most of them have The research in FEL physics is shifting several beam lines and undulators to serve from the proof of principle toward en- multiple users simultaneously. To reduce hancement of the radiation properties, in the limitation on the average brightness, particular, in the X-ray regime. SASE FELs most of the linear accelerators are based have an intrinsic instability in the output on superconducting technology. It allows energy of a few percent up to 100%. In ad- to lengthen the RF pulse and fill the beam dition, the operation of a linear accelerator line with multiple bunches per RF pulse, isnotasstableasthatofastoragering.The while operating on a lower power level of system fluctuation adds up to the intrin- the RF system. sic fluctuation of the SASE pulse. Another A combination of a storage ring with disadvantage is the reduced longitudinal alinearacceleratoristheEnergyRecov- coherence. Because of the short coopera- ery Linear accelerator (ERL) [43]. After the tion length of FELs in the VUV and X-ray electron bunch is accelerated and passes regime, part of the bunch amplifies the the undulator, it is transported back to the spontaneous radiation independently. The longitudinal coherence can be achieved by Tab. 4 VUV & X-ray free-electron lasers, a pulse stretcher, namely, monochroma- planned or under construction (∗) tor, with a bandwidth slightly smaller than the Fourier limit of the electron bunch FEL Wavelength [A]˚ Location length. All spikes are stretched to the bunch length and add up coherently. Each ∗ TESLA 1–50 Germany spike in the SASE pulse has 100% fluctu- SCSS 1–10 Japan ∗ ation, so has the resulting coherent pulse LCLS 1.5–15 USA MIT Bates FEL 5–1000 USA after the monochromator. Stability of the FERMI 12–100/400 Italy output power is achieved if the monochro- BESSY 12–1500 Germany mator is not placed after the SASE FEL but SPARX 15–140 Italy ∗ between, splitting the undulator in two TTF-FEL II 60–1200 Germany parts [44]. The second undulator is seeded 4GLS 120–4000 UK NSLS DUV-FEL 200–2000 USA by the output signal of the monochromator and operates as an FEL amplifier OE038

Lasers, Free-Electron 21 instead of an SASE FEL. Because the sat- present technology. It is desirable to re- uration power of an FEL amplifier does duce the size of the FEL facility or make not depend on the input signal, the output it even portable and robust. The FEL can power level in the deep saturation regime benefit from results of other branches in is stable despite the 100% fluctuation of the accelerator physics. Acceleration based the input signal. on plasmas are promising higher acceler- Another focus is on short radiation ation gradient and lower emittances [47], pulses. Standard methods are pulse com- thus shortening both the undulator and the pression and slicing, similar to conven- linear accelerator. The FEL physics is un- tional lasers. It requires an energy correla- changed, when the undulator is replaced tion along the electron bunch (‘‘chirp’’), by a device that also enforces a transverse driving an SASE FEL. Because of the oscillation of the electron bunch. A pos- square dependence of the resonant wave- sible solution would be a •high-intensity length on the energy (Eq. 1), the radia- Q9 optical laser pulse [48]. Because the pe- tion frequency chirp is twice as large. A riod length is several orders of magnitude monochromator selects only that part of smaller than that for an undulator, the FEL the pulse in which frequency components interaction requires less energy to obtain fall within the bandwidth. The monochro- the same wavelength. Other proposals are mator bandwidth has to be optimized in based on plasma columns [49], transverse order to avoid a pulse stretching for a wakefields [50] or crystal lattices [51]. too-small bandwidth or large chirps for a too-wide bandwidth. For X-ray FELs, a − monochromator bandwidth of 10 4,which is roughly a tenth of the intrinsic FEL band- Glossary width, and a frequency chirp of around 1%, 3rd Generation Light Sources: Spontane- results in a 10-fs slice [45]. ous emission from dipoles and undulator An alternative method for short bunches with radiation pulse lengths in the picosec- is to condition the driving electron bunch. A stronger compression spoils the emit- ond regime and recirculating electrons tance and energy spread by wakefields and with an energy between 3 and 10 GeV. coherent synchrotron radiation in the linear accelerator and bunch compressor, so Bending Magnet: see dipole magnet. that the electron pulse length is limited to roughly 200 fs FWHM for the shortest β-function: Characteristic function of the gain length. On top of that, the beam can focusing property of a given beam line. be conditioned by various methods (RF Depending on the initial values of the cavities, wakefields, external laser pulses) β-function and its derivative, it describes to keep the beam quality good over only a the evolution of the beam size along the short subsection of the bunch. Although beam line. theentirebunchemitsspontaneousradia- tion, only the preserved part of the bunch Bunch Compressor: A series of dipole mag- amplifies it and reaches saturation [46]. nets to deflect the electron beam from the A free-electron laser in the X-ray regime orbit and then back onto the orbit. The requires about 100 m of undulator and a resulting orbit and thus the path length of linear accelerator of about 1 km, using the this orbit bump depends on the electron OE038

22 Lasers, Free-Electron

energy. With a correlation between lon- Plasma Frequency: Measure for the gitudinal position and energy within an strength of the beam size growth due to the electron bunch, the path-length difference repulsive electrostatic field between each yields a reduction in the bunch length and electron. an increase in the beam current. Ponderomotive Phase: Phase of the elec- Bunching: Density modulation of the electron–radiation interaction due to the beat tron beam on a scale shorter than the wave of the transverse oscillation of the bunch length. Also called microbunching. electrons and the oscillation of the EM wave. Coherent Synchrotron Radiation: Strong enhancement of the synchrotron radiation Quadrupole Magnet: Magnet with a linear for wavelength longer than the bunch growing transverse magnetic field with length. The radiation can interact back respect to the orbit of the electron bunch. with the electron bunch and because of its The field configuration yields a focusing large amplitude alter the electron energy in one transverse plane but a defocusing and, thus, the orbit of the electron bunch. in the perpendicular transverse plane. A net focusing in both planes is achieved by Dipole Magnet: Magnet with a constant, a series of quadrupoles with alternating transverse magnet field to deflect electron polarity. and thus, cause a bend in the orbit of the electron bunch. Linac: linear accelerator, where the electron passes the beam line only once. Emittance: Phase space area, covered by In contrast to the storage ring, the lin- the electron bunch distribution. ear accelerator consists mainly of accelerating structures, such as RF cavities. Energy Recovery Linear Accelerator: Cir- Quadrupole magnets keep the transverse cular accelerator with continuous injection beam size within the acceptable limits. of electron bunches. After acceleration, each electron bunch passes each RF cavity Radiofrequency Cavity: Cavity, which res- ◦ again but with a 180 phase difference. onantly holds an oscillating EM field at The deceleration transfers back the kinetic well-defined frequencies. The fundamen- energy of the electron bunch to the RF tal mode has a longitudinal electric field field, which can be used to accelerate the component, which is used to accelerate an succeeding bunch. electron beam, passing the cavity.

Microbunching: See bunching. Shot noise Power: Power of the spontaneous radiation, which falls within the Photoelectron Gun: RF cavity with an bandwidth of the free-electron laser and embedded photo cathode. A UV laser pulse which is amplified in the SASE FEL con- illuminates the cathode and generates free figuration. electrons due to the photo effect. The RF field accelerates these electrons to Storage Ring: Circular accelerator to keep relativistic energies within the length of injected electron bunches on a closed orbit the RF gun. for many turns. RF cavities compensate OE038

Lasers, Free-Electron 23 the energy loss due to the spontaneous [2] Motz, H. (1951), J. Appl. Phys. 22, 527. radiation within the dipole magnets and [3] Palmer, R. B. (1972), J. Appl. Phys. 43, 3014. other transverse deflecting magnets (e.g., [4] Freund, H. P., Granatstein, V. L. (1999), Nucl. Inst. & Methods A429, 33; Col- undulators) son, W. B. (1999), Nucl. Inst. & Methods A429, 37; online at http://sbfel3.ucsb.edu/ Superconducting Magnet: Electromagnet, www/vl fel.html based solely on superconducting windings [5] Linac Coherent Light Source (LCLS), SLAC- to overcome saturation effects of any yoke R-521, UC-414 (1998). material. [6] TESLA - Technical Design Report, DESY 2001-011, ECFA 2001-209, TESLA Report 2001-23, TESLA-FEL 2001-05, Deutsches Undulator: Device with transverse, alter- Elektronen Synchrotron, Hamburg, Ger- • nating magnetic field on the main axis many (2001 ). Q10 in planar and helical configuration. In a [7] Various proposals are listed in the Proc. of planar undulator, the transverse magnetic the 24th Free-Electron Laser Conference, • field is oscillating within only one trans- Argonne, USA (2002 ). Q11 verse plane, while the magnetic field is [8] Phillips, R. M. (1960), IRE Trans. Electron Devices 7, 231. constant but rotates along the longitudinal • [9] Elias,R.L. et al. (1976), Phys. Rev. Lett. 36, Q12 axis for a helical undulator. 717. • [10] Deacon,D.A.G.etal. (1977), Phys. Rev. Q13 Undulator Parameter: Normalized ampli- Lett. 38, 892. tude of the vector potential of the undulator [11] Litvinenko, V. (1999), Storage Ring-based field. It is proportional to the product of Light Sources, Proc. of the 17th Advanced Beam Dynamics Workshop on Future Light peak undulator field and undulator period Sources, Argonne, USA. and can be regarded as the total deflection [12] Derbenev, Ya. S., Kondradenko, A. M., Sal- strength of the undulator field per half din, E. L. (1982), Nucl. Inst. & Methods 193, period. 415. [13] Nodvick, J., Saxon, D. Phys. Rev. (1954), 96, Undulator Taper: Variation of the undula- 180. [14] Dawson, J. M. (1989), Sci. Am. 260, 54. tor field and/or period along the longitudi- [15] Born, M., Wolf, E. (1980), Principles of nal axis of the undulator. • Optics.PergamonPress . Q14 [16] Bonifacio, R., Pellegrini, C., Narducci, L. M. Wakefield: Radiation, caused by the inter- (1984), Opt. Commun. 50, 373. action of the electric static field of an [17] Kim, K. -J. (1986), Nucl. Inst. & Methods electron with the vacuum chamber. The A250, 396. radiation can interact with succeeding elec- [18] Kondradenko, A. M., Saldin, E. L. (1980), Part. Accel. 10, 207. trons, changing the electron energy or [19] Ogata, A. (1992), in J. Wurtele (Ed.), Ad- transverse momentum. vanced Accelerator Concepts. Port Jefferson, New York, p. 420, AIP Conf. Proc. 279, New Wiggler: See undulator. York, 1993. [20] Bonifacio, B.,Pellegrini, C., Narducci, N. (1984), in J. M. J. Madey C. Pellegrini References (Eds), Free Electron Generation of Extreme Ultraviolet Coherent Radiation.NewYork: • American Institute of Physics, p. 236 . Q15 [1] Madey,J.M.J. (1971), J. Appl. Phys. 42, [21] Orzechowski, T. J. et al. (1985), Phys. Rev. 1906. Lett. 54•. Q16 OE038

24 Lasers, Free-Electron

• [22] Edwards, D. A., Syphers, M. J. (1992), In- [45] Schroeder, C. B. et al. (2002), J. Opt. Soc. Q25 troduction to the Physics of High Energy 19, 1782. • Q17 Accelerators. John Wiley & Sons . [46] Reiche, S., Emma, P. (2002), Proc. of the [23] Krinsky, S., Yu, L. H. (1987), Phys. Rev. A35, 24th Free-Electron Conference, Argonne, 3406. USA. [24] Moore, G. T. (1984), Opt. Commun. 52, 46. [47] Suk, H., Barov, N., Rosenzweig, J. B., [25] Kim, K. -J. (1986), Phys.Rev.Lett.57, 1871. Esarey,E.(2001), Phys. Rev. Lett. 86, 1011. [26] Goodman, J. (1985), Statistical Optics.New [48] Warren, B. (1969), X-Ray Diffraction. Addi- York: John Wiley & Sons. son-Wesley. • • Q18 [27] Bonifacio, R. et al. (1994), Phys.Rev.Lett. [49] Joshi, C. et al. (2002), Phys. Plasmas 9, Q26 73, 70. 1845. [28] Saldin, E. L., Schneidmiller, E. A., Yurkov, [50] Zhang, Y., Derbenev, Y. (2002), Proc. of the M. V. (1997), TESLA-FEL 1997-02, Deut- 24th Free-Electron Conference, Argonne, sches Elektronen Synchrotron, Hamburg, USA. • Germany. [51] Avakian, R. O. et al. (2001), Nucl. Inst. & Q27 [29] Chao, A. W. (1993), Physics of Collective Methods B173, 112. Instabilities in High Energy Accelerators.New York: John Wiley & Sons. [30] Renieri, A. (1979), Nuovo Cimento 53B, 160. Further Reading • Q19 [31] Jaroszynski, D. A. et al. (1997), Nucl. Inst. & Methods A393, 332. [32] Hogan, M. (1998), Phys. Rev. Lett. 81, 4867. A complete description of the FEL theory is • Q20 [33] Ayvazyan, V. et al. (2002), Phys. Rev. Lett. given in the books Thy Physics of Free Electron 88, 104802. Lasers by E. L. Saldin, E. A. Schneidmilller, • Q21 [34] Palmer, D. T. et al. (1997), Proc. of the M. V. Yurkov (Springer, Berlin, 2000) or Part. Accel. Conf., Vancouver, p. 2843. Free-Electron Lasers by C.A. Brau (Academic [35] Carlsten,B.E.(1989), Nucl. Inst. & Methods Press, Boston, 1990). A brief overview on the A285, 313; Seraﬁni, L., Rosenzweig, J. B. high gain FEL can be found in the paper (1997), Phys. Rev. E55, 7565. ‘‘Introduction to the Physics of the FEL’’ [36] Rosenzweig, J. B., Colby, E. (1995), Ad- by J.B. Murphy and C. Pellegrini (Proc. of vanced Accelerator Concepts.AIPConf.Proc. the South Padre Island Conference, Springer • Q22 335 , p. 724. (1986) 163). [37] Sands, M. (1955), Phys. Rev. 97, 470. The book An Introduction to the Physics of [38] Litvienko, V. (1999), Storage ring-based light High Energy Accelerators by D.A. Edwards and sources, Proc. of the 17th Advanced Beam M.J. Syphers (John Wiley and Sons, New Dynamics Workshop on Future Light York, 1993) covers the physics, needed to Sources, Argonne, USA. generate and accelerate an electron beam, [39] Bruck, H. Accel´ erateurs´ circulaires de par- driving the free-electron laser. A review of ticules, Paris. undulator design is given by J. Spencer and [40] Krinsky, S., Wang, J. M. (1985), Part. Accel. H. Winick in Synchrotron Radiation Research 17, 109. (eds. H. Winick and S. Doniach, Plenum • Q23 [41] Walker,R.P.etal. (2001), Nucl. Inst. & Press, New York, ch. 21, 1980). Methods A475, 20. The radiation process of relativistic particles • Q24 [42] Neil, G. R. et al. (2000), Phys.Rev.Lett.84, are covered in great detail by J.D. Jackson’s 662. Classical Electrodynamics (John Wiley and Sons, [43] Tigner, M. (1965), Nuovo Cimento 37, 1228. New York, 1975) while the description of the [44] Saldin, E. L., Schneidmilller, E. A., Yurkov, random nature of the SASE FEL follows the M. V. (2000), Nucl. Inst. & Methods A445, treatment of Statistical Optics by J. Goodman 178. (Wiley and Sons, New York, 1985).