X-ray free-electron lasers: from dreams to reality

Transcription

1 Physica Scripta PAPER X-ray free-electron lasers: from dreams to reality To cite this article: 016 Phys. Scr View the article online for updates and enhancements. Related content - Short-wavelength free-electron laser sources and science: a review E A Seddon, J A Clarke, D J Dunning et al. - Current status and future perspectives of accelerator-based x-ray light sources Takashi Tanaka - X-ray free-electron lasers J Feldhaus, J Arthur and J B Hastings Recent citations - The effect of electron transport on the characterization of x-ray free-electron laser pulses via ablation Stefan P. Hau-Riege and Tom Pardini This content was downloaded from IP address on 3/08/018 at 04:54

2 Royal Swedish Academy of Sciences Physica Scripta Phys. Scr. T169 (016) (pp) X-ray free-electron lasers: from dreams to reality 1, 1 Department of Physics and Astronomy, niversity of California at Los Angeles, Los Angeles, CA 90095, nited States of America SLAC National Accelerator Laboratory, Menlo Park, CA 9405, nited States of America claudiop@slac.stanford.edu Received 8 September 016, revised 14 November 016 Accepted for publication 8 December 016 Published 7 February 017 Abstract The brightness of x-ray sources has been increased one to ten billion times by x-ray free-electron lasers (XFELs) that generate high intensity coherent photon pulses at wavelengths from nanometers to less than one angstrom and a duration of a few to 100 femtoseconds. For the first time XFELs allow for experimental exploration of the structure and dynamics of atomic and molecular systems at the angstrom-femtosecond space and time scale, creating new opportunities for scientific research in physics, chemistry, biology, material science and high energy density physics. This paper reviews the history of this development, concentrating on the Linac Coherent Light Source (LCLS),theworld s first hard x-ray XFEL. It also presents the physical principles on which XFELs are based, their present status and future developments, together with some recent experimental results in physics, chemistry and biology. LCLS success has spurred the worldwide construction of more XFELs; SACLA in Japan, XFEL and FLASH in Germany, Swiss FEL, Korean XFEL, Fermi in Italy. The characteristics of these other sources are also discussed. Keywords: free electron lasers, x-ray lasers, synchrotron radiation sources (Some figures may appear in colour only in the online journal) 1. Introduction: early work on x-ray lasers Infrared and visible lasers were initially developed in the 1960s [1, ]. Since that time there has been a continued effort to extend the generation of coherent electromagnetic radiation to shorter and shorter wavelengths, with the ultimate goal of reaching the x-ray region. An important reason for these efforts is that an x-ray laser, generating a beam of coherent light at angstrom wavelength, would open a new window on the exploration of matter at a scale length, the Bohr radius, corresponding to the atom size and would make it possible to explore in great detail the structure of simple and complex molecules. If at the same time the x-ray pulse length could be reduced to a few femtoseconds, the Bohr time, the revolution time of a valence electron around the nucleus, one could also explore the dynamics of atomic and molecular process on their own time scale. The dream of exploring atomic/molecular processes on their own space and time scale would for the first time become a reality, opening the exploration of new science for physics, chemistry and biology, such as the imaging of periodic and non periodic systems, non crystalline states, studies of dynamical processes in systems far from equilibrium, nonlinear science, material science and high energy density phenomena. The main impediment in the search for an x-ray laser based on inner level atomic transition is the very short lifetimes of excited atom-core quantum energy levels and the larger energy required to excite electrons in the inner core levels. George Chapline and Lowell Wood [3] of the Lawrence Livermore National Laboratory, one of the most active centers for the development of x-ray lasers in the 1970s, estimated the radiative lifetime of an x-ray laser transition to be about 1 fs times the square of the wavelength in angstroms, making the pumping of the inner level in an atom practically impossible. Livermore scientists proposed using a nuclear weapon to drive a single pass x-ray laser. They tried the idea in the Dauphin experiment, apparently with success, in The experiment was part of the Star Wars Defense Initiative: generate an x-ray beam in space, exploding an atomic bomb, to kill incoming missiles. The program was terminated at the end of Star Wars [4] /16/ $ The Royal Swedish Academy of Sciences Printed in the K

3 Figure 1. Schematic arrangement of undulator magnets. Reprinted from [15], with the permission of AIP Publishing. The development of high peak power, short pulse, visible light lasers made another approach possible: pumping cylindrical plasmas, in some cases also confining the plasma with magnetic fields. These experiments led to x-ray lasing around 18 nm with a gain of about 100 in 1985 [5, 6]. More work has been done from that time and lasing has been demonstrated at several wavelengths in the soft x-ray region, however with limited peak power and tunability. A review of the most recent work and developments with this approach is given in [7]. A solution to this difficult situation is offered by the generation of electromagnetic waves from relativistic electron beams and by the Self Amplified Spontaneous Emission (SASE) x-ray free-electron laser [8 10]. Claudio Pellegrini proposed in 199 to build a SASE XFEL in the wavelength range 0.1 to 4 nm [11] using one third of the 40 GeV, two miles long, linear accelerator of the SLAC National Accelerator Laboratory [1]. The proposal was based on the emission of radiation from relativistic electron beams in a periodically alternating magnetic field: an undulator magnet. It has been shown [13] that an accelerated electron beam constitutes an inverted population medium. When the beam traverses a wiggler or a slow-wave structure it radiates electromagnetic waves and the radiative transitions in the FEL can be described in terms of conventional laser physics. However, in the case of interest to us, the SASE XFEL operates in the classical regime where a large number of photons are emitted before the electron energy changes significantly. A history of x-ray FEL development is found in reference [14]. Here we summarize some of the steps that lead in recent years to the successful construction and operation of the SLAC XFEL, LCLS, for experimental research in physics, chemistry and biology. In section 15 we discuss some recent results obtained in these fields at LCLS using its unique properties of coherence, high intensity and short pulse duration. An important step on the way to the x-ray FEL was Hans Motz s concept [15] of obtaining nearly monochromatic coherent radiation from relativistic electrons moving through a periodic magnetic array, that he called an undulator magnet, shown in figure 1. Motz evaluated the wavelength of the radiation emitted, at an angle q with respect to the undulator axis, by a relativistic electron moving along the axis. For the case of a helical undulator the wavelength is given by where l = l ( 1 + K + gq) g, ( 1.1) K = eb l pmc, ( 1.) is called the undulator parameter, l is the undulator period, typically a few centimeters, B the undulator magnetic field on axis, g the electron energy in units of the rest energy mc. The undulator parameter is the normalized vector potential and is typically of the order 1 to 3. The radiation wavelength can be easily tuned using the quadratic dependence on the electron energy and the undulator parameter. In 1953 Motz and coworkers observed coherent radiation at Stanford at millimeter wavelength using a planar undulator with 4 cm period and 3 to 5 MeV electron beam, generated by a linear accelerator, with a bunch length shorter than the radiation wavelength [16]. Raising the beam energy to 100 MeV they observed incoherent radiation. sing Motz s words: the mm wave generation might have some practical importance. In this case it is possible to bunch the electron beam so that groups of electrons radiate coherently. It was shown that the power level may be higher by a factor of the order of a million compared to non coherent radiation K [16]. Can we do the same at wavelength of about 1 Å? The answer is no, we do not know how to generate an electron beam with all electrons squeezed within one tenth of the wavelength and separated by one wavelength at 1 Å. But in this case nature is kind to us. nder proper conditions, using an FEL, as shown in figure, the electron beam can go through a self-organization process and do just that, as we will see later.. ndulator radiation characteristics There are two main types of undulators used to generate radiation, helical and planar. A detailed description of electron trajectories and of the emitted radiation can be found in [17]. Here we consider for simplicity only the case of a helical undulator. Assume a reference frame with z along the undulator axis and x, y in the transverse directions. Consider a relativistic electron with energy E = mc g, longitudinal velocity b z near to one and small transverse velocities bx, by 1. In the case of a helical undulator with period l, wave number k = p l, magnetic field on axis B 0, the field near the axis is approximated to lowest order by Bx =- B0 sin ( kz), By = B0 cos ( kz), Bz = 0. The transverse and longitudinal velocities are [17] b () z = x c = -( K g) sin ( k z), ( 1.3) x0 0 / b ( z) = y c = ( K g) cos ( k z), ( 1.4) y0 0 / b = { 1 - ( 1 + K) g} 1/ 1 - ( 1 + K) g, ( 1.5) z0 where K is given by (1.), and having assumed the relativistic factor g 1. Notice that in this case the longitudinal velocity is a constant. The trajectory is a helix

4 Figure. FEL schematic, showing an electron beam propagating through an undulator and the emitted radiation. Reproduced with permission from [17]. Copyright American Physical Society 016. of radius a = K k g. ( 1.6) To understand the FEL physics it is important to characterize the radiation emitted by one electron as it traverses an undulator magnet on a trajectory near to the magnet axis. From (1.1) the radiation on axis, q = 0, is peaked at a wavelength l = l ( 1 - b ) b» l ( 1 + K ) g, ( 1.7) R z z and consists of a wave train with a number of wave fronts equal to the number of periods, N in the undulator. Its length is N l. For a helical undulator the radiation is circularly polarized. Only the fundamental, at the wavelength (1.7), is present on axis and harmonics appear off axis. The undulator parameter is typically of the order of 1 to 3. For a case like LCLS the beam energy is about 15 GeV, the undulator period is 3 cm, the undulator parameter is 3, the number of periods in the undulator is 3500, giving a wavelength l» 0.1 nm, a line width D l/ l» , a radiation pulse length and duration, for a single electron, N l» 0.3 mm and 1 fs. The spectrum of the energy, di, radiated in a frequency interval dw and solid angle dw by one electron moving along the undulator is a sum of harmonics of the fundamental. However on axis, θ = 0, only the fundamental is present and the spectrum is given by di g w W = r mc K e N d d c ( 1 + K ) where r e is the classical electron radius and sin D D, ( 1.8) D= w p ( ) w - N The spectrum is dominated by the resonance at w = wr, allowing us to approximate a factor w w R with 1 when deriving (1.8). The FWHM width of the radiation line on axis, obtained from (1.8), (1.9), is Dw w R.8. ( 1.10 ) pn We use now a semi-classical approach to look at the coherence properties of undulator radiation [18], describing it as waves of wavelength l or photons of energy and momentum p c/ l, p / l. We first consider the radiation energy emitted in the minimum phase space defined by the conditions DxD px = /, DyD py = /, DED t = /. For radiation emitted near the axis at a small angle q and during the time duration D t = ln c these conditions can be written as sr q = l/ 4 p, D E/ E = 1 / N, where we assumed for simplicity D x =D y = sr. The coherent line width, 1 / N, is smaller by about a factor of two compared with the line width for the spectral width given by (1.10). Since the frequency depends on the emission angle according to (1.1), to remain within the line width 1 N the emission angle must be limited to the coherent angle q = ( 1 + K) gn = l l N, ( 1.11) c corresponding to a solid angle c DW = pq = pl l N. ( 1.1) It is interesting to notice that the coherent angle is quite small. In the LCLS case of interest to us, with 1.5 A wavelength, 3 cm period and 3000 periods, we have q» 10-6 c, a very small angle. The coherent undulator radiation energy, emitted by one electron within the solid angle (1.1) and the line width 1 N, evaluated from (1.8), is I = p mc r K c l 1 + K e. ( 1.13) The corresponding number of coherent photons, obtained by dividing (1.13) by the photon energy at resonance, is K Nph, c = pa, ( 1.14) 1 + K depending only on the undulator parameter and the fine structure constant, a» 1/ 137. For typical values of the undulator parameter, 1 to 3, the number of coherent photons emitted by one electron in crossing an undulator is of the order of 0.01, a value much smaller than one. This quantity, obtained from a classical treatment of the radiation, gives in a quantum description the probability that one electron will emit one photon within the assumed minimum phase space assumed here. 3

5 For coherent photons, within the minimum possible phase space area srqc = l/ 4 p, the source radius is given, using (1.11), by s = ll N 4 p. ( 1.15) r For the LCLS case already considered before we have s» 10-5 r m. ntil now we have considered the undulator radiation generated by one electron. We discuss now the case of an electron bunch with a large number, N e, of electrons in it, typically in the range 10 7 to If, as in the case of Motz s experiment at millimeter wavelength, the electrons are in a length much shorter than the wavelength, the radiation they emit adds coherently and the intensity is proportional to the square of the number of electrons, N e. The same conclusion applies also to the case when the electron beam consists of micro-bunches, each much shorter than the wavelength, separated by the wavelength. In the case when the electrons are distributed over a length much larger than the radiation wavelength and their distribution is a uniform random distribution. For an observer at some distance from the undulator axis, the electric fields of the waves generated by each electron are superimposed at random. The resulting intensity is then proportional to the number of electrons, N e [19]. For electron bunches generated in linear accelerators the number of electrons is typically in the range , and the difference between the two cases is rather large. For planar undulators only one of two transverse components of the magnetic field is present. The electron trajectory is a sinusoid of period l in the plane perpendicular to the magnetic field. The radiation is plane polarized instead of circularly polarized. The longitudinal velocity is not a constant as in the helical case, and oscillates at twice the undulator period, leading to the presence of harmonic on axis [17]. The resonant wavelength is still given by (1.7) if we make the substitution of the undulator parameter with K = eb l pmc. 3. The free-electron laser concept The next step is the introduction by John Madey, in 1971, of the free-electron laser concept [0]. Other authors [1 5] have also developed similar ideas. In an FEL an electromagnetic wave, co-propagating with the electron beam, is added to the electron beam-undulator magnet studied by Motz, opening new possibilities to generate very high brightness, coherent electromagnetic radiation. Madey used the Weizsacker Williams [6, 7] method to calculate the small signal, low gain due to the induced emission of radiation into a single electromagnetic wave propagating in the same direction of a relativistic electron through a periodic transverse magnetic field. He showed that it is possible to have gain from the far infrared through the visible region. However the gain decreases at shorter wavelengths. Considering an extension to the x-ray regions and beyond 10 kev Madey noted in his paper: The dependence of the gain on the Figure 3. Schematic of the FEL amplifier experiment at Stanford. Reproduced with permission from [8]. Copyright American Physical Society Figure 4. Madey s FEL oscillator configuration. Reproduced with permission from [9]. Copyright American Physical Society square of the final state wavelength probably precludes the development of steady-state oscillations in the region beyond the ultraviolet. K [0]. Madey s group demonstrated the feasibility of the FEL concept in two experiments. The first, shown in figure 3, isan FEL amplifier at 10.6 μm [8], using a 4 MeV electron beam from a Stanford superconducting linear accelerator, with current of 5 to 70 ma. The undulator is helical, with a period of 3. cm and a length of 5. m. The single pass gain is as large as 7%. The second, shown in figure 4, is an oscillator operating at a wavelength of 3.4 μm, beam energy of 43 MeV, using the same helical undulator and an optical cavity 1.7 m long [9]. Madey s FEL stimulated bremsstrahlung quantum theory, valid only for small changes in the electromagnetic wave intensity, the small signal low gain regime, was used to analyze these experiments. However, Madey s small signal low gain formula does not depend on Planck s constant, indicating that the FEL is essentially a classical system. A classical small signal low gain theory, based on non-quantized Maxwell equations for the field and Lorentz equation for the electrons, was developed by several authors [30, 31], and gives the same gain value as Madey s quantum theory. The low gain, small signal theory shows that the FEL single pass gain depends on the electron beam 6-dimensional phase space density. The scaling with wavelength of the required beam characteristics, as the electron bunch length, transverse phase space density and peak current, together with the lack of good optical cavities in the x-rays spectral region, precludes the possibility of pushing FELs to x-ray wavelengths, as already mentioned. This situation changed with the development, by many authors, of the classical high gain theory in the 70s and 80s, removing the condition of a small change in the 4

6 electromagnetic wave intensity, and using the full dynamics of the electron beam-radiation field interaction [3, 33, 8, 34 36, 9, 37 4]. An important contribution was the paper by Saldin and Kondratenko [8] that considered the possibility of using the high gain regime, starting from spontaneous radiation, to reach saturation in a single pass infrared FEL, using low energy electron beams (a few to 10 MeV). This approach eliminates the need of an optical cavity. In a second paper [43] they considered the possibility of increasing the beam energy to about 1 GeV, using a storage ring, to produce soft x-rays. 4. FEL physics as collective instability Another important contribution is that by Bonifacio, Pellegrini and Narducci [9], analyzing the FEL physics as a collective instability, the FEL collective instability, and showing that, in the 1-dimensional limit, the FEL equations can be written, by proper variables transformation, in a universal form, depending only on one parameter, r, the FEL parameter. This quantity is a function of the undulator and electron beam characteristics and does not depend explicitly on the radiation wavelength. In the paper the authors show and analyze the possibility of starting from noise, in the Self Amplified Spontaneous Emission (SASE) mode, and reaching saturation in a single undulator pass, avoiding the need of an optical cavity. Since in the 1-dimensional limit all main quantities characterizing an FEL depends only on one parameter, r, it is easy to compare with the theory experiments at different wavelengths. However, when operating the FEL as an oscillator, with the optical cavity mirrors reflectivity depending strongly on wavelength, or when 3-dimensional effects are important, a more extensive analysis is required. The instability works as follows (we consider again the helical undulator case but the same results apply with minor changes to the planar case): 1. The electron beam interacts with the circularly polarized electric field of the radiation, with components E x = E cos [ kr ( z - ct) + y], Ey = E sin [ kr( z - ct) + y], propagating along the undulator axis; the quantities E, y are the amplitude and phase of the electromagnetic wave; the transverse velocity of the electrons produced by the undulator magnet have components given by (1.3), (1.4); the interaction produces an electron energy modulation of the nth electron in the beam, on the scale l, given by where g mc d n dt ecke = sin [ F n + y], ( 1.16) g n F = k ( z - ct) + k z ( 1.17) n r n n is the relative phase of the radiation and the electron oscillation.. The electron trajectory depends on the electron energy. The oscillation amplitude in the transverse directions around the undulator axis, (1.6), is smaller for highenergy electrons than for low-energy electrons. The high-energy electrons path length is shorter than that of low-energy electrons, as shown in figure 5. Hence the energy modulation on the wavelength scale generates bunching on the same scale. 3. Electrons bunched within a wavelength emit radiation in phase, generating a large radiation field intensity. 4. Going back to step 1 closes the loop. The larger intensity leads to more energy modulation and more bunching, leading to exponential growth of the radiation intensity. The intensity can reach the limit I ~ N e for the case of extreme bunching. To complete the description of the FEL dynamics we must add two equations to (1.16), for the change in time of the phase (1.17) and of the wave phase and amplitude. To simplify the discussion we use an approximate form of the equations, neglecting 3-dimensional effects and other small terms. For a more complete form of the equations we refer the reader to two review papers [17, 44]. The equation describing the change of the phase F n of the nth electron, obtained taking the derivative of (1.17), is[17, 44] where F d g n = - R k c 1, ( 1.18) dt g R u n Figure 5. The figure shows two electrons of different energies oscillating around the undulator axis, z. The low-energy electron, continuous curve, has larger oscillation amplitude and longer path length than the high-energy electron, dashed curve. g = l ( 1 + K ) l ( 1.19) is the resonant energy. This relation is the same as (1.7), defining the wavelength of the spontaneous radiation peak. In this case we assume a wavelength and evaluate the corresponding electron energy. The electron energy change given by (1.16) is fast oscillating and averages out to zero except when gn gr and the phase changes slowly or remains constant. The wave amplitude and phase are combined in one complex quantity a =-iee iy. From Maxwell equations, using the slowly varying amplitude and phase approximation, ( l pa)( a z) 1, ( l pca)( a t) 1 one has 5

7 [9, 17, 44] a p å ( ) g ( ) + Ne 1 = enek exp -ifn n, 1.0 z c t N e n= 1 where n e is the electron bunch density. The quantity N e 1 B = å exp (-ifn), ( 1.1) N e n= 1 coupling the electrons to the radiation wave, is called the bunching factor. A simple analytical solution of the system of equations (1.16), (1.18), (1.0), does not exist. However, the main physical properties of the system can be understood starting from the existence of an equilibrium point corresponding to a = 0, gn = gr, B = 0 [9]. The behavior of the FEL near the equilibrium point can be studied linearizing the equations, assuming hn = ( gn - gr) gr 1, F n = F 0n + qn with F 0n = pn Ne, qn 1, a small. nder these conditions the system of Ne + equations (1.16), (1.18), (1.0), can be reduced to an analytically solvable system of 4 differential equations for the field and the collective variables B and Ne P = å h e-f i 0 n N n= 1 n e [9]. The last is called the energy modulation variable. If we further simplify the system assuming that the electron bunch length is much longer than each wave train emitted in the undulator, LB N l, and that the radiation electric field does not change along the bunch length, the 4 equations become ordinary differential equations and the solution is of the form [9, 17, 44] where a, B, P µ exp{ - i( m + d g ) 4 prz l), ( 1.) Kl W r = 8pc P / 3 is the elec- p is called the FEL parameter, W = 4 rcn e e P g3 tron beam plasma frequency, 0 R, ( 1.3) 0 1 / dg = ( g - g ) rg ( 1.4) is the detuning parameter. The detuning describes the effect of the difference between the average initial electron beam energy,g 0, and the resonant energy (1.19) defined by the radiation field wavelength. sing (1.19) we can also rewrite the detuning as dg = ( l - lr) rl, changing the beam energy is equivalent to changing the system wavelength. The other quantity appearing in (1.), m, is the solution of a dispersion relation that depends on the initial electron energy distribution. In the case of a monoenergetic beam the dispersion relation is m ( m + d) - 1 = 0, ( 1.5) a cubic equation with three real or 1 real and two complex conjugate solutions. The case of interest to us is that with complex solutions, when the equilibrium point is unstable and the field and the bunching will grow exponentially. For zero detuning the solution of (1.5) is m = (-1 i 3), m = 1 ( 1.6) 1, 3 The system is unstable and the radiation field amplitude grows like E µ e z/ L G, with L, the gain length, given by G L = l 3 pr ( 1.7) G Figure 6. Imaginary part of the root of the dispersion relation for different values of the ratio, D, of the electron relative energy spread to the FEL parameter r. Reproduced with permission from [17]. Copyright American Physical Society 016. The typical value of the FEL parameter for x-ray FELs like LCLS and SACLA is about 0.001, giving a gain length of the order of magnitude of meters. The imaginary part of m changes with detuning and with the beam energy spread, as shown in figure 6. It has a maximum for zero detuning and a monoenergetic electron beam and decreases for detuning values different from zero, and when the beam energy spread becomes of the order of the FEL parameter. The general solution of the FEL equations is a combination of the modes corresponding to the three roots of the dispersion relation, with initial condition given by the three initial values a0, B0, P0. For an undulator shorter or of the order of the gain length, all three modes are equally important. In this limit one can recover the small signal low gain results [45]. For an undulator length much larger than the gain length, the mode corresponding to the unstable root dominates. This is the case of interest to us for x-ray FELs. When the initial field is different from zero and the initial values of the bunching and energy modulation are zero or small, the FEL acts as seeded amplifier, as shown in figure 3. If the initial field is zero and B 0 and/or P 0 are different from zero the system acts as a Self Amplified Spontaneous Emission FEL (SASE FEL). For nearly monoenergetic electron beams used in x-ray FELs like LCLS, the term B 0 is larger than P o. The initial value of the bunching factor depends on the initial electron distribution along the z-axis. For a uniform electron distribution, for instance assuming F n = pn Ne, the bunching factor is zero, B = 0. For a random distribution the value is much smaller then one, B 1, and depends 6

8 on the number of electrons in one radiation wavelength [9, 17, 19, 44]. If all electrons are in one or more microbunches, each smaller than the wavelength and separated by a distance equal to the wavelength, the bunching factor is nearly one, B 1. For wavelengths much longer than the bunch length, the initial bunching factor is large, it ca be near to one. At wavelengths much shorter than the bunch length, a random distribution of the longitudinal electron position at the undulator entrance gives an initial value of the bunching factor that is small, has zero average value but not zero root mean square value, and depends on the number of electrons in a radiation wavelength [19]. In particular for the case of x-rays with wavelengths in the sub-nanometer range, where there are no practical laser sources to generate an initial value of the field different from zero, starting the instability from the initial bunching factor due to the randomness of the longitudinal electron distribution on the scale of the radiation wavelength is the only practical way to operate an FEL. This mode of operation an FEL, a SASE FEL is used for LCLS and SACLA. In addition to the gain length, all other important properties of the FEL are obtained, in the 1-dimensional limit, from the FEL parameter, r [9]. The system saturates when the bunching factors becomes near to one. The saturation power is a fraction r of the beam power P rp, ( 1.8) sat beam where the beam power, Pbeam = EbeamIbeam e, is the product of the beam current and energy. Hence the FEL parameter is the efficiency of energy transfer from electrons to the radiation field. The saturation length is about ten times the radiation electric field gain length, L sat 10 L. ( 1.9) The gain bandwidth is about equal to the FEL parameter [40] Dw w G r. ( 1.30) The number of coherent photons per electron is given by the simple formula N re w, ( 1.31) ph beam the ratio of the beam energy to the photon energy, times the FEL parameter. Consider a SASE x-ray FEL similar to LCLS: g = , l = 3cm, K = 3, N = In this case we obtain l = 0.1nm. Near saturation, assuming the FEL parameter to be 10 3, a typical value for existing x-ray FELs, we obtain from (1.31) 10 3 coherent photons per electron. Comparing this number with the spontaneous radiation case, (1.14), we see the large gain obtained from the FEL amplification effect. For the 1-dimensional approximation of the FEL dynamics to be valid some condition must be satisfied [10]: a. Matching of the electron beam and radiation transverse phase space requires that the beam emittance be smaller or of the order than the radiation wavelength: e < l 4 p; ( 1.3) r b. For the collective instability to develop the undulator length must be longer than the gain length: N l > L ; ( 1.33) G c. To avoid large loss of radiation from the electron beam volume requires the gain length to be shorter than the radiation Rayleigh range: L Z < 1; ( 1.34) G R where the Rayleigh range is defined using the minimum waist of a Gaussian radiation beam pwo = lrz R. d. Quantum recoil parameter, the ratio of emitted photon energy to the gain bandwidth must be small: q = w mcgr 1. ( 1.35) r This condition requires that the change in electron energy due to a single photon emission be small enough to avoid moving the electron out of the FEL gain bandwidth (1.30). 5. Time dependent and 3D effects The variation of the field amplitude, bunching factor, B, and energy modulation, P, along the bunch, for the case when the long bunch approximation, used in the previous section analysis of the FEL collective instability, is not satisfied, was studied in [46]. Electrons are slower than the electromagnetic wave and the radiation one of them generates moves ahead by one wavelength for undulator period [45]. The total advance along the undulator is called the slippage, S = ln. Electrons can interact with other electrons, through their emitted radiation, only if their distance is smaller than the slippage. For SASE FEL dynamics the important quantity characterizing this effect is the cooperation length, the slippage in one gain length [46] L = ( l l ) L. ( 1.36) c G If the bunch length is much longer than the cooperation length, LB L C, the temporal profile evolves along the undulator, as shown in figure 7. The initial profile consists of many spikes of fluctuating intensity, reflecting the random longitudinal distribution of the electron on the wavelength scale. As the electron and the radiation pulse propagate along the undulator, and slippage becomes important, a correlation is established between the spikes and their width grows. Near saturation the length of each spike is about plc [46], as shown in figure 7. The spikes are uncorrelated in phase and their amplitude fluctuates for each FEL pulse. 7

9 Figure 7. Evolution of the temporal profile of the radiation pulse of a SASE FEL. The coordinate z 1 gives the position along the electron bunch in units of the cooperation length and a is proportional to the wave electric field amplitude. Reproduced with permission from [17]. Copyright American Physical Society 016. Because the FEL starts from noise the spikes intensity measured foe each FEL pulse fluctuates according to a Gamma function distribution [47] - MM M 1 W pw ( ) = - á ñ e MW W, ( 1.37) G ( M) á W ñ á W ñ where M is the number of spikes, given at saturation by the ratio of the bunch length to the cooperation length, and áwñ is the average intensity. The 1-dimensional theory was extended to the 3-dimensional case in the 1980s, including diffraction effects and establishing radiation focusing by a microbunched electron beam [48 53]. A new parameter, the Fresnel parameter, FD = r0 kr LG for a cylindrical beam of radius r 0, is needed to describe the FEL physics when diffraction and 3-dimensional effects are considered. The beam radius is assumed to be the effective radiation source size given in (1.15). When FD 1 diffraction effects are small and the 1-dimensional model is a good approximation. This condition is similar to what we discussed before in section 4, equation (1.34). The set of 3-dimensional FEL equations has been solved, and the problem has been analyzed in terms of normal modes of the electromagnetic fields [17, 44]. The FEL eigenmodes are constant in shape and size, but grow in amplitude, differing from the propagation of a Gaussian beam in vacuum. The radiation propagation is similar to that in an optical fiber with an index of refraction [49] depending on the real part of the bunching factor. This guiding effect is called gain guiding. The gain is associated to the imaginary part of the index of refraction. The difference respect to a truly guided mode, such as optical modes in fibers, is that the guiding exists only because the energy flowing in the transverse direction by diffraction is overcompensated by the field amplification within the electron beam. 6. The experimental development of the SASE FEL The theoretical work on the FEL collective instability opened the way to consider the possibility of an x-ray FEL reaching the angstrom wavelength region. It was clear from the beginning that the beam characteristics, current, emittance and energy spread, played a critical role to achieve this goal. All these characteristics can be summarized in the electron beam 6-dimensional, positions and momenta, phase space 8

10 density. Condition (1.3) requires a smaller electron beam emittance as the wavelength decreases. Since the beam energy spread generates a frequency spread in the emitted radiation, according to (1.7), and the gain bandwidth is given by the FEL parameter, (1.30), the beam energy spread must be smaller than r. To make the undulator length practical the value of the FEL parameter cannot be much smaller than As the FEL lasing wavelength is decreased and the electron beam energy is increased it follows from the definition of the FEL parameter, (1.3), that a larger 6-dimensional density is required. The electron source and the type of accelerators chosen to generate the electron beam determine the density. In the early 1980 s the accelerators providing the best beams, larger 6-dimensional density, were electron storage rings. What could be obtained with these accelerators was studied in [54], showing that the FEL properties depend strongly on the electron beam transverse emittance and on the storage ring coupling impedance, the factor giving the strength of collective instabilities determining the electron beam relative energy spread. Even under the somewhat optimistic assumption of 1 Ω, the FEL shorter wavelength and power are limited to unsatisfactory values. The conclusion of this work is: The storage ring needed to operate the system is characterized by a small transverse emittance. The other important ring parameter is the longitudinal coupling impedance. For a value of the order of 1 Ω, one can obtain peak power of the order of 500 MW down to wavelengths of about 500 A and peak powers of 50 MW down to wavelengths of 80 A; the power decreases sharply at lower wavelengths. If it should become possible to reduce the longitudinal coupling impedance to 0.1 Ω, one could get peak powers of the order of 0 MW down to wavelengths of 30 A [54]. The way out of this situation is to generate the electron beam with a new electron source developed at Los Alamos as part of the Star Wars program, the radio-frequency (RF) photo-injector [55], and subsequently accelerate it in a linac. The RF photo-injector can generate beams with 100 times better emittance and ten times smaller energy spread that the sources used before, based on thermal emission from a heated gun. The analysis of this case [10] shows much more interesting results and the possibility of reaching the Å level with a large peak power. The analysis is based on Amplified Spontaneous Emission, lasing in a single pass starting from noise, without using optical cavities. The system scaling laws for this case show that, for given beam characteristics, the FEL parameter scales like the square root of the wavelength, r µ l 1 /. The conclusion is that using a photoinjector developed at Brookhaven National Laboratory and 1.5 GeV beam energy it is possible to reach the nm region with about 6mJ/pulse starting from noise in an 11 m long undulator. 7. Photo-injector development An S-band version of the Los Alamos photoinjector gun, optimized for peak current and small emittance, was designed Figure 8. A cross section of the BNL/SLAC/CLA 1.6 cell cavity gun. It operates in S-band, at a frequency near 3 GHz. The RF mode has an axial electric field. When V photons hit the copper cathode the emitted electrons are accelerated in the RF field, with a peak accelerating field larger than 100 MV m 1. The gun consists of one full-length Radio-frequency cavity, about 10 cm long along the axis, and part of another cavity, where the photo cathode is located near the point of maximum electric field. The power is fed in the full cell and the laser illuminates the cathode at approximately 70 from the normal through two laser ports in the 6/10 cell in a plane perpendicular to the drawing. The cathode plate is removable to allow the use of different materials. Reproduced with permission from [60]. Copyright IOP Publishing 008. and built at Brookhaven National Laboratory [56], to be used at the Accelerator Test Facility of the Center for Accelerator Physics. The main advantage of this source is the large value, 100 MV m 1 or more, of the accelerating electric field. By synchronizing the laser and the RF field the electrons are emitted when the accelerating field is at its peak value and reach relativistic velocities before they leave the first half cavity (see figure 8). The brightness reducing space charge forces decrease like the cube of the electron relativistic factor and become small before the electrons leave the gun [57]. The resulting final beam phase space density is much larger than in other designs, where the accelerating field is much smaller. Further development of the RF photoinjector and its technology followed the 199 proposal to build an XFEL at SLAC [68]. The CLA group built an S-band gun that was used in the early SASE FEL experiments. Herman Winick proposed, as part of the collaboration studying LCLS, to build a Gun Test Facility (GTF) at SLAC. The GTF was located in an existing vault at SLAC, next to the electron storage ring SPEAR, and used a 3 m S-band linac section [58]. An improved photoinjector design, called the Next Generation 9

11 Figure 10. The CLA S-band photonjector, operating at nearly 3 GHz, and driven by a V laser beam. The finger in the figure defines the scale of the system. Photograph credit: Pellegrini. Figure 9. Amplified signal output as a function of length along the undulator. The FEL operates at a frequency of 34.6 GHz, and the input signal, provided by a magnetron, is about 50 kw. Reproduced with permission from [61]. Copyright American Physical Society Photoinjector, was developed and built [59] by a BNL-SLAC- CLA collaboration. Four copies of this gun, shown in figure 8, were fabricated. Two were used at Brookhaven National Laboratory, a third went to CLA, and the fourth was characterized in detail at the GTF. The measured normalized emittance was about 10 6 m. The next generation gun generated beams with a smaller emittance than the original S band Brookhaven gun. Even if it did not achieve the beam quality needed for a 1 angstrom FEL, it was instrumental in showing how to design and build the LCLS photoinjector, which reached the desired emittance values, and allowed to successfully generate coherent hard x-ray photons. The results obtained at the GTF and the development of the LCLS photoinjector are reviewed and summarized in reference [60]. 8. Early experiments on high gain FELs and SASE theory A Lawrence Berkeley Laboratory-Livermore National Laboratory group operated a high-gain FEL experiment, as an amplifier and starting from noise, at Livermore in 1985 [61]. The FEL operated at about one cm wavelength using a 5 MeV, 10 ka induction linac and an electromagnetic planar undulator. Because of the low beam energy and high current the FEL operates in a regime where space charge forces are important, establishing an interaction between electrons additional to that generated through the electromagnetic Figure 11. The Kurchatov undulator [6] used for the first SASE experiment at CLA. Photograph credit: Pellegrini. waves they emit. The main results for the SASE experiment are shown in figure 9, and are compared with results of simulations based on the information available on the 6-dimensional electron beam phase space density distribution, that was again dominated by space charge forces. In 1989 a program to verify the SASE theory at infrared to visible wavelength was started by a CLA group led by Claudio Pellegrini. Since the collective instability theory [9] depends only on the FEL parameter and there is no explicit dependence on wavelength, verification in the infrared to visible would be meaningful to establish the case for shorter wavelengths, down to x-rays. James Rosenzweig led the construction at CLA of an S-band photoinjector, shown in figure 10, and of a small, <1 m long, 15 MeV linac. Alexander Varfolomeev, from the Kurchatov Institute in Moscow, built a 60 cm long, 1.5 cm period undulator [6], shown in figure 11. Graduate students and one post-doc did most of the work to setup the new laboratory, build the linac and associated hardware. Chan Joshi and his students built a V laser to illuminate a copper photocathode. The first experiment was done at a wavelength of 16 μm and reached a gain of about a factor of ten over the spontaneous radiation signal [63]. In addition to establish gain the experiment did a detailed study of the intensity fluctuations due to the statistical properties of the initial noise signal starting the amplification process, described by (1.37). The 10

12 Figure 1. Left. Measured coherent IR intensity as a function of electron charge. The vertical bars are the standard deviation for the intensity fluctuations. Beam charge and radius uncertainties are 9%, a standard deviation of 4 mv at 0.56 nc. Straight line: calculated spontaneous emission intensity. Curved line: data fit I = 1.85Qexp(4.4Q 1/3 ), and Ginger simulations. Right. Intensity distribution of the IR and background signals for a mean charge Q = 0.56 nc, standard deviation of nc, IR mean = 78 mv, standard deviation = 14.3 mv; background mean = 18.7 mv, standard deviation = 9.1 mv. Reproduced with permission from [63]. Copyright American Physical Society Figure 13. Left. Measurement of the photon pulse intensity as a function of peak current. Right. Measurements of the intensity fluctuations for individual nc micropulses compared with theory. Reproduced with permission from [65]. Copyright American Physical Society results are shown in figure 1. Since the undulator has a fixed length the experiment is performed changing the electron bunch charge, thus changing the current and the gain length. A change in gain length is equivalent to an effective undulator length change. The results on the FEL intensity are in in agreement with theoretical prediction within the statistical errors. The simulations were done using the numerical code Ginger developed at Berkeley [64]. The measurements on the intensity fluctuations are a good test of the theoretical model and give information on the number of amplified modes, again in agreement with the expectations. A much larger gain, , near to the saturation value, was obtained in the following experiment done using a linac at Los Alamos and a two-meter long planar, permanent magnet undulator [65]. The results are shown in figure 13 and are again in agreement with the simulation model, Ginger [66], based on the FEL theory, including 3-dimensional effect. 9. The beginning of the LCLS project In February 199 Max Cornacchia and Herman Winick organized a workshop on Fourth Generation Light Sources at SLAC [67]. Most of the work at the workshop was dedicated to storage ring based synchrotron radiation sources. However a proposal to use the High Gain SASE approach to build an x-ray FEL operating in the wavelength region 4 to 0.1 nm was presented by Claudio Pellegrini [68]. The proposal raised the interest of a group of accelerator and FEL scientists, in particular Herman Winick, who, after the workshop, organized a study group that he led from 199 to The study group established the feasibility of the project and defined the main challenges for success. First among them was the development of an electron source capable of providing the required electron beam properties to lase at 0.1 nm. To reduce the problem the initial work was dedicated to an FEL operating in the water window, to 4 nm, and a series of papers on it were published, [69 71]. Another workshop on 11

13 Scientific Applications of Coherent x-rays was organized in 1994, chaired by Arthur, Materlik and Winick, and it provided much needed scientific support for the an x-ray FEL at SLAC [7]. A Design Group, led by Massimo Cornacchia, was established at SLAC in 1996, with collaborators from CLA, Berkeley, Argonne National Laboratory, Livermore National Laboratory and other institutions. It published a Design Study Report in 1998 [73], for an x-ray FEL operating in the range 1.5 to 0.15 nm. The emphasis was again on reaching the shorter wavelength, because of the much larger area of scientific applications, in particular structural biology. All the work done at SLAC during this time, in collaboration with CLA and other national laboratories, was done without direct financial support from the Department of Energy (DOE). DOE had called two panels, in 1994 [74] and 1997 [75], to advise them on free-electron lasers. The first expressed a negative opinion on x-ray FEL development, while the second recommended continuing research, but did not support funding for the project. A new panel, led by Stephen Leone, was organized in 1999 [76]. The results of the high gain, , experiment [65] were reported to the panel, together with the Design Study Report. The new results and design led the panel to recommend initial funding for the x-ray FEL project at SLAC, called LCLS, and DOE funded the project with $1.5 M/year over 4 years. This was the effective beginning of the LCLS project, which led to first lasing in 009. John Galayda left Argonne to join SLAC and manage the construction of LCLS. The LCLS Conceptual Design Report was completed in 00 [77]. After its approval DOE provided funding for engineering and construction. The design of the experimental halls for all the areas of research covered by LCLS was studied and discussed in a report published in 003, on the first experiments [78]. An additional important development was the beginning of interest in x-ray FELs at the DESY laboratory, in Hamburg. Bjorn Wiik was on sabbatical at SLAC, just before becoming the Director of DESY, during 199. During his stay at SLAC he was informed by Herman Winick of the work being done on LCLS, and was present at the first LCLS review in November 199. After the review he went back to DESY and became the laboratory director in January Later Wiik and scientists at the DESY synchrotron radiation laboratory (HASYLAB), like Gerhard Materlik, became interested in the possibility of building an x-ray FEL as part of the electron-positron linear collider project, TESLA, being developed at DESY, using superconducting linear accelerators. A 1 GeV superconducting linac, the TESLA Test Facility (TTF), was being built at DESY to develop superconducting radio frequency technology and could be also used for a soft x-ray FEL. Joerg Rossbach was asked to lead the design and development of a VV FEL [79, 80], a project that led eventually to the FLASH Soft x-ray FEL. Figure 14. Intensity as a function of undulator length, under various electron beam conditions. (A) 530 nm saturated conditions. (B) 530 nm unsaturated conditions. (C) 385 nm saturated conditions. Solid curves: GINGER simulation results. Reproduced with permission from [81]. Copyright The American Association for the Advancement of Science Other experiments at shorter wavelengths: LETL, VV FEL, VISA at 800 nm Additional experiments to test the SASE theory and extend the verification to shorter wavelengths and reaching saturation were undertaken at Argonne National Laboratory with LETL FEL, at DESY with Flash and by a SLAC-CLA- Livermore-Brookhaven collaboration with the VISA FEL. These experiments used longer undulators, higher beam energies and existing accelerators. The results obtained in the Argonne experiments [81], called LETL and using a 5 meters long undulator, are shown in figure 14. These experiments were done at wavelengths of 50 nm and 385 nm and in both cases reached saturation and were again in good agreement with theory. An even shorter wavelength, 98 nm, was obtained at the VV- FEL experiment at DESY, reaching saturation in about 14 m of undulator length [8], as shown in figure 15. The results of the VISA experiment, reaching saturation in a 4 m long undulator at a wavelength of 840 nm, are shown in figure 16 [83, 84]. The same experimental setup was also 1

14 Figure 15. Average radiation pulse energy (solid circles) and rms energy fluctuations in the radiation pulse (empty circles) as a function of the active undulator length. The wavelength is 98 nm. Circles: experimental results. Curves: numerical simulations. Reproduced with permission from [8]. Copyright American Physical Society 00. Figure 16. Measured SASE intensity evolution along the undulator length and numerical simulations (gray lines are the rms boundaries of the set of GENESIS runs). The amplification curve yields a power gain length of 17.9 cm and saturates near the undulator exit. Reproduced with permission from [84]. Copyright American Physical Society 003. used to measure the predicted electron bunching at the lasing radiation wavelength [85] and the nonlinear harmonic generation [86]. 11. Where are we today? Following the initial experiments, the progress toward short wavelength continued. In 005 the VV-FEL at DESY now called FLASH- lased at a wavelength of 3 nm [87] and later at 4. nm [88]. Two seeded FELs, Fermi@Elettra, using the high gain harmonic generation mode, were built at Trieste: FEL-1, lasing in the wavelength range 65 to 9 nm [89] and FEL- reaching 4 nm [90]. SACLA in Japan [91] also obtained lasing at wavelengths as short as 0.6 A. An important milestone in the development of x-ray FELs is the initial operation of LCLS at 1.5 Å wavelength in 009 [9]. The measured FEL power growth along the undulator corresponds to a power gain length of 3.5 m, in good agreement with the high gain SASE theory simulations, including 3-dimensional and time dependent effects. The LCLS x-ray pulse duration can be changed from about 100 to a few femtosecond, by varying the electron bunch charge from 50 to 0 pc over the full wavelength range of. to 0.1 nm [93]. The brightness of LCLS, SACLA and FLASH is about nine orders of magnitudes higher than that of any other existing x-ray sources [94], an impressive step forward. X-ray FELs provide, for the first time, high brightness, coherent radiation pulses at a wavelength and time scale as short as 1 Å and few femtoseconds, typical of atomic phenomena, a breakthrough making possible the scientific exploration of the structure and dynamics of atomic and molecular processes. No other electromagnetic radiation source can do this. Another x-ray FEL, PAL XFEL, is being commissioned in Korea [95]. Two more are completing construction in Switzerland, SWISS-FEL [96], and the European nion, European XFEL [97]. Two soft x-ray FELs, FLASH [98] and Fermi [99] are in operation at DESY and Sincrotrone Trieste. LCLS is being upgraded to LCLS-II, covering both the soft and hard x-rays regions [93]. Their main characteristics are given in tables 1 and for FELs with wavelength shorter or longer than 1 nm [17] and can be summarized as follows: 1. Pulse energy: hundreds of μj to few mj;. Line width: in SASE mode about 10 3, the order of magnitude of the FEL parameter r; about ten times smaller when using self-seeding; 3. Pulse duration: from few to about 100 fs. In summary, Flash, Fermi, SACLA and LCLS have demonstrated outstanding capabilities, increasing by 7 to 9 orders of magnitude the photon peak brightness. The LCLS x-ray pulse duration and intensity can be changed from about 100 to a few femtosecond and to photons/pulse, over the wavelength range of 4 to 0.1 nm, by varying the electron bunch charge from 50 to 0 pc. The x-ray pulse wavelength, intensity and duration can be optimized for each experiment, something not possible in storage ring sources. 1. XFELs transverse and longitudinal coherence The spatial and temporal coherence of the LCLS x-ray beam has been measured [100] and is nearly diffraction limited as predicted by theory. The results of the double pinholes experiment are shown in figure 17. This is an important result because the spatial coherence is essential for applications like coherent diffraction imaging, x-ray holography and x-ray photon correlation spectroscopy. Presently SASE is the operating mode of all hard x-ray FELs. In SASE the line width is the FEL parameter r [9], of the order of 10 3 for all systems being considered. The x-ray pulse is spiky, as shown in figure 7, and its frequency width is larger than the minimum phase space value for the given pulse duration, DED t = /. Several methods to reduce the 13

15 14 Electron energy, GeV Wavelength range, nm X-ray pulse energy, mj Pulse duration, rms, fs Line width, rms, %, SASE Line width, rms,% seeded Table 1. Characteristics of hard x-ray FEL in operation or under construction (identified by the * sign). From [91 93, 95 97]. LCLS SACLA European XFEL * Korean X-FEL Swiss X-FEL * LCLS-II Cu RF * for 0.1 < λ < for 0.08 < λ < for 0.04 < λ < for 4.3 for 0.08 < λ < for 0.1 < λ < < λ < for for for 0.1 < λ < < λ < < λ < for * for 0.1 < λ < < λ < < λ < for 0.1 < λ < 0.6 nm for 0.1 < λ < for 0.1, λ < 0.6 nm 0 for 0.1 < λ < for < λ < 0.6 nm for 0.1 < λ < for < λ < 0.6 nm for 0.1 < λ < for 0.05 < λ < Phys. Scr. T169 (016)

16 15 Table. Characteristics of Soft x-ray FELs operating and under construction. LCLS-II has two undulators, SXR and HXR. From [93, 98, 99]. FLASH Fermi FEL-1 Fermi FEL- LCLS-II SXR nd * LCLS-II HXR nd * Electron energy, GeV Wavelength range, nm X-ray pulse energy, mj λ Max, λ min λ Max, λ min 10.8 nm, λ min λ max, λ min λ max, λ min Pulse duration, rms, fs 15 λ Max,15 min Depending on seed pulse duration and harmonic order, typically Line width, rms, % SASE λ Max, min Line width, rms, % seeded Max, λ min 0.06@10.8 nm,0.0@5.4 nm,0.04@λ Min 0.0 Phys. Scr. T169 (016)

17 Figure 17. Double pinholes measurement of LCLS spatial and temporal coherence at 780 ev photon energy. Measured diffraction patterns. Left column: Interference fringes from pinholes separated by (a),8(d), and 15 μm (g), each exposed to a single shot of the LCLS beam as a function of the transverse momentum transfer qx, qy. The area used for the analysis of the transverse coherence is shown by the dashed black rectangle close to the center of the patterns. Middle column: Line scans of the interference fringes on the right edge of the marked region, experimental data (red dots), and results of the theoretical fit (black lines). Right column: Enlarged regions of the line scans shown in the middle column. From [100]. Figure 18. Soft x-ray self-seeding schematic at LCLS. The first part of the undulator generates a SASE x-ray pulse, filtered by the monochromator and used to seed the electron bunch in the second part of the undulator. Reproduced with permission from [10]. Copyright American Physical Society 015. line width, and increase the longitudinal coherence, have been proposed. Self-seeding [101] has been successfully implemented at LCLS in the soft x-ray region [10], using the configuration shown in figure 18 and a somewhat different configuration, using the forward Bragg radiation with a single crystal [103], in the hard x-ray region [104]. As one can see from figure 19 the reduction in line width, and the improvement in longitudinal coherence, is quite substantial. A different approach has been used in the Fermi FEL. Running at longer wavelengths than LCLS it can use the High Gain Harmonic Generation method to seed the FEL and obtain a stable wavelength and a small line width [105]. The 16

18 Figure 19. Comparison of seeded (solid red line) and SASE (dashed blue line) spectra at 930 ev for shot averages, and seeded simulation (sim.) averaged over 30 shots (dotted-dashed black line). Inset shows the fraction of FEL energy contained within an integrated bandwidth when seeding. Reproduced with permission [10]. Copyright American Physical Society 015. Figure 0. Schematic for two color x-ray FELs. The two pulses have a tunable energy difference and tunable arrival time. system has been successfully demonstrated using a two step cascaded HGHG down to wavelength of 10.8 and 5.4 nm [105]. 13. Some recent developments of x-ray FELs The flexibility of XFELs and the possibility of further improving their characteristics is shown by many recent experiments [ ] that have generated two pulses of the same or different colors that can be separated by a variable delay in the range 0 to 100 fs, as shown in figure 0. These results open new areas of exploration of molecular systems and are very important for pump-probe experiments. I will mention just a few of these recent results. Two colors can be obtained by splitting the undulator in two parts with different values of the undulator parameters. The delay between the two pulses is obtained by a magnetic chicane. They can also be obtained by a periodic modulation of the undulator magnetic field [107], as shown in figure 1 and. Self-seeding for two colors with a single electron bunch and a single crystal has been demonstrated recently at LCLS [111]. By rotating the single diamond crystal used in the self seeding systems, it is possible to transmit two narrow lines which are both amplified by the electron bunch. The color separation is limited by the FEL bandwidth, which however can be increased by energy chirping the electron beam to obtain a larger bandwidth and a larger color separation. The results are shown in figure 3. Another two colors approach is the twin bunch FEL [110], starting with a double laser pulse on the injector photocathode to generate two electron bunches with variable delay and different energies. The two bunches are accelerated in the LCLS linac and compressed by two magnetic chicanes. Finally, they are sent to an undulator for the emission of two x-ray FEL pulses with tunable energy difference, in the range of a few percent, and a variable time delay of tens of fs. Selfseeding has been applied successfully to this case to obtain a bandwidth smaller than in the SASE case. The double-electron bunch method demonstrated in this work [110] allows for the generation of mj-level, two-color x-ray pulses with tunable energy separation and time delay. This performance improves the intensity of two-color XFELs by over an order of magnitude respect to other methods. In addition to the larger peak power, the double-bunch mode presents several other advantages over single-bunch methods. First, the two x-ray pulses have the same source point, improving their focusing properties at the down-stream experimental stations. Second, the radiation pulses can be diagnosed independently and non-destructively using longitudinal phase-space diagnostics on the dumped electrons, unlike single-bunch methods, where this diagnostic would only reconstruct the projection of both pulses. ntil now all existing x-ray FELs are based on SASE or HGHG and high gain single undulator pass of the electron beam. An oscillator configuration would provide the possibility of a much smaller relative line width than the values, about 10 3 to 10 4, obtained presently and would thus open additional research opportunities. Kwang-Je Kim and coworkers [11] have studied an x-ray oscillator, called XFELO, that would provide pulses, temporally and spatially coherent, of about 10 9 photons at very high repetition rate, 1 to 100 MHz, mev band-width and pulse length of about 1 ps. The proposed system is based on a super conducting linac to generate the electron pulses and a low loss, crystal, optical cavity. An example of XFELO s application is the generation of an x-ray comb for fundamental physics and metrology experiments [113]. 14. Some recent work at LCLS A review of the results obtained in the first five years of operation at LCLS in physics, chemistry, biology and material sciences has been published recently in Review of Modern Physics [114]. In this section we discuss three examples of LCLS recent experiments, one in physics, one in chemistry and one in biology. For physics we consider the observation of anomalous nonlinear x-ray Compton scattering [115]. The experiment is aimed at the observation of one of the most 17

19 Figure 1. Gain modulated x-ray FELs schematic. A periodic variation of the undulator magnetic field generates two or more lasing lines, depending on the ratio of the periodicity length and the gain length. Reproduced with permission from [107]. Copyright American Physical Society 013. Figure. Gain modulated x-ray FELs. Experimental results obtained at LCLS. Average spectrum (black line) and single-shot spectrum (dashed blue line) for a beam energy of 4.3 GeV. For comparison, the spectrum predicted from the linear theory is plotted as a red line. Reproduced with permission from [107]. Copyright American Physical Society 013. Figure 4. Schematic of the pump-probe experiment to image a chemical reaction. A V pump pulse excites a reaction in the 1,3- Cyclohexadiene molecule leading to transition to 1,3,5-hexatriene. The two different molecular structures, hexagonal and linear, are shown on the left. Reproduced with permission from [117]. Copyright American Physical Society 015. Figure 3. Two-color self-seeded spectrum using ( 113 ) and ( 113 ) diamond crystal reflections. Single shot (black), 100 shots average (red). The two color lines separation is 43 ev ( 0.6%), wider than the SASE bandwidth for normal LCLS operation. The shot pulse energy is 10 μj. Reproduced with permission from [111]. Copyright American Physical Society 014. fundamental nonlinear x-ray matter interactions: the concerted nonlinear Compton scattering of two identical hard x-ray photons producing a single higher-energy photon. In the experiment the x-ray pulse is focused to a spot of 100 nm radius where the power density reaches the value Wcm, corresponding to an electric field, Vm 1, well above the atomic unit of strength and within almost four orders of magnitude of the quantum electrodynamics Schwinger critical field [116] of about Vm 1. The incoming photon energy is 9 kev, the energy in the pulse 1.5 mj and the pulse duration 50 fs. The results show the generation of 18 kev photons, with their largest number obtained when the target is positioned at the focal spot, where the power density has a maximum. The molecular motion in an electrocyclic chemical reaction, on a 30 fs time scale, has been observed in a pump probe experiment at LCLS [117]. The schematic of the experiment is shown in figure 4, showing the initial and final molecular configuration. Mapping nuclear motions using femtosecond x-ray pulses creates real-space representations of the dynamical process, showing a series of time-sorted structural snapshots that have been used to make movies showing the motion of atoms on 30 fs time scale. The movies are available in the Supplemental material of [117] and are also discussed in a Physics Viewpoint paper [118]. The importance of the XFELS for structural biology has been discussed in a review paper, Biophysical Highlights from 54 Years of Macromolecular Crystallography [119]. For 18

20 electron energy near and after saturation, thus maintaining the synchronism condition and increasing the energy transfer from the electron beam to the x-ray pulse. More recent studies [15] show the way to increase the XFEL efficiency from 1/ 1000 to about 0.1. The number of pulses per second delivered to the experimental areas will increase from about 100 Hz to 100 khz or more using superconducting linacs, as in the European XFEL and LCLS-II. The detectors and optical system for fully using XFELs capabilities are being rapidly developed, and our knowledge of x-ray/matter interaction at the high field intensity generated by these lasers is also improving. All this progress will lead, in the coming years to enhanced possibilities to explore atomic and molecular science, physics, chemistry, biology and materials science. Acknowledgments Figure 5. Schematic of the experiment to determine the Angiotensin Receptor (AT1R) structure with.9 A resolution. Reproduced with permission from [14]. Copyright Elsevier 015. the year 014 they write: Free-electron laser crystallography is without question the most spectacular new technical development in the field. A jet of droplets with nanocrystals is sent past a beam of femtosecond x-ray laser pulses, and diffraction is recorded the crystal ahs time to explode. This has the potential for determining otherwise intractable molecular structures and for accessing rapid time steps. The many challenging problems with data and analysis appear to be solvable. After demonstration structures of photosystems and lysozyme (e.g. PDB:3PQC [10], PDB;4FBY [11] PDB:4ET8 [1]) there is now a novel structure of propeptide-inhibited trypanosomal cathespin B (PDB:4HWY [13]) potentially useful for drug design. Another recent experiment, shown schematically in figure 5, allowed the determination of the crystal structure of the human Angiotensin receptor [14], a primary regulator for blood pressure maintenance, with a resolution of.9 A, offering insight into the design of blood pressure modulators. 15. Conclusions XFELs give us an unprecedented view of the structure and dynamics of matter at the angstrom, femtosecond space and time scale, giving new exciting possibilities to expand our knowledge of physics, chemistry, biology and material science. The flexibility of the system allows optimization of the x-ray pulse intensity, time duration and spectral properties for the experiments being done. From 009, LCLS first lasing, XFELs spectral properties and intensity have been improved. Additional possibilities have been added with the development of two colors pulses. The peak power has been increased by adjusting the undulator magnetic field to the decreasing Transforming the x-ray FEL from a dream to a powerful tool for the study of nature required the contribution and work of many scientists, students and engineers from many countries, universities and laboratories, too many to name. My gratitude goes to them all. References [1] Bertolotti M 005 History of the Laser (Bristol: Institute of Physics Publishing) [] Zinth W, Laubereau A and Kaiser W 011 The long journey to the laser and its rapid development after 1960 Eur. Physics J. H [3] Chapline G and Wood L 1975 X-ray lasers Phys. Today 8 8 [4] Hecht J 008 The history of the x-ray laser Optics and Photonics News 19 6 [5] Matthews D L et al 1985 Demonstration of a soft x-ray amplifier Phys. Rev. Lett [6] Suckewer S et al 1985 Amplification of stimulated soft x-ray emission in a confined plasma column Phys. Rev. Lett [7] Suckewer S and Jaeglé P 009 X-ray laser: past, present, and future Laser Physics Lett [8] Kondratenko A M and Saldin E L 1980 Generation of coherent radiation by a relativistic electron beam in an undulator Part. Accel [9] Bonifacio R, Pellegrini C and Narducci L 1984 Collective instabilities and high-gain regime in a free electron laser Opt. Commun [10] Pellegrini C 1988 Progress toward a soft x-ray FEL Nucl. Instrum. Methods A [11] Pellegrini C 199 Proc. of the Workshop on 4th Generation Light Sources ed M Cornacchia and H Winick Stanford Synchrotron Radiation Laboratory report 9-0 p 341 [1] Neal R B (ed) 1967 The Stanford Two-Mile Accelerator (New York: W. A. Benjamin Inc.) available on line ( stanford.edu/library/mileaccelerator/mile.htm) [13] Friedman A, Gover A, Kurizki G, Ruschin S and Yariv A 1988 Spontaneous and stimulated emission from quasifree electrons Rev. Mod. Phys [14] Pellegrini C 01 History of the x-ray free-electron laser European Physics Journal H