Laser-Driven Table-Top X-Ray FEL

Synchrotron radiation sources nowadays benefit a wide range of fundamental sciences from physics and chemistry to material science and life sciences as a result of a dramatic increase in the brilliance of photons emitted by relativistic electrons when bent in the magnetic field of synchrotron accelerators. A trend will tend toward the X-ray free electron laser (FEL) that will produce high-intensity ultrashort coherent X-ray radiations with unprecedented brilliance as kilometer-scale linear accelerator-based FELs are being commissioned to explore new research area that is inaccessible to date, for instance femtosecond dynamic process of chemical reactions, materials and biomolecules at the atomic level (Gerstner, 2011). Such large-scale tool could be built on a table top if highquality electrons with small energy spread and divergence are accelerated up to the GeV range in a centimetre-scale length (Gruner et al., 2007; Nakajima et al., 1996; Nakajima, 2008, 2011). It is prospectively conceived that a compact source producing high-energy highquality electron beams from laser plasma accelerators (LPAs) will provide an essential tool for many applications, such as THz and X-ray synchrotron radiation sources and a unique medical therapy as well as inherent high-energy accelerators for fundamental sciences (Malka et al., 2008).


Introduction
Synchrotron radiation sources nowadays benefit a wide range of fundamental sciencesfrom physics and chemistry to material science and life sciences as a result of a dramatic increase in the brilliance of photons emitted by relativistic electrons when bent in the magnetic field of synchrotron accelerators. A trend will tend toward the X-ray free electron laser (FEL) that will produce high-intensity ultrashort coherent X-ray radiations with unprecedented brilliance as kilometer-scale linear accelerator-based FELs are being commissioned to explore new research area that is inaccessible to date, for instance femtosecond dynamic process of chemical reactions, materials and biomolecules at the atomic level (Gerstner, 2011). Such large-scale tool could be built on a table top if highquality electrons with small energy spread and divergence are accelerated up to the GeV range in a centimetre-scale length Nakajima et al., 1996;Nakajima, 2008Nakajima, , 2011. It is prospectively conceived that a compact source producing high-energy highquality electron beams from laser plasma accelerators (LPAs) will provide an essential tool for many applications, such as THz and X-ray synchrotron radiation sources and a unique medical therapy as well as inherent high-energy accelerators for fundamental sciences (Malka et al., 2008).
The present achievements of the laser wakefield accelerator performance on the beam properties such as GeV-class energy Clayton et al., 2010;Lu et al., 2011), 1%-level energy spread (Kameshima et al., 2008;Rechatin et al., 2009), a few mm-mrad emittance (Karsch et al., 2007), 1-fs-level bunch with a 3-4 kA peak current (Lundh et al., 2011), and good stability and controllability (Hafz et al., 2008;Osterhoff et al., 2008) of the beam production allow us to downsize a large-scale X-ray synchrotron radiation source and FEL to a table-top scale including laser drivers and radiation shields. The undulator radiation from laser-plasma accelerated electron beams has been first demonstrated at the wavelength of rad 740 nm   and the estimated peak brilliance of the order of 16 6.5 10  photons/s/mrad 2 /mm 2 /0.1% bandwidth driven by the electron beam from a 2-mm-gas jet with the beam energy 64 MeV b E  , the relative energy spread /5 . 5 % b EE   (FWHM) and total charge 28 pC b Q  , which is produced by a 5 TW 85 fs laser pulse at the plasma density 19 3 21 0 c m p n   (Schlenvoigt, 2008). The soft X-ray undulator radiation has been also successfully demonstrated at the wavelength rad 18 nm   and the estimated peak brilliance of the order of  (Fuchs, 2009). With extremely small energy spread and peak current high enough to generate selfamplified spontaneous emission so-called SASE (Bonifacio, 1984), a photon flux of the undulator radiation can be amplified by several orders of magnitude to levels of brilliance comparable to current large-scale X-ray FELs (Nakajima, 2008).
Here we consider feasibility of a compact hard X-ray FEL capable of reaching a wavelength of 0.1 nm X   , which requires the electron beam energy of the multi-GeV range in case of a modest undulator period of the order of a few centimeters. One of prominent features of laser-plasma accelerators is to produce 1-fs-level bunch duration, which is unreachable by means of the conventional accelerator technologies. The X-ray FELs rely on SASE, where the coherent radiation builds up in a single pass from the spontaneous (incoherent) undulator radiation. In an undulator the radiation field interacts with electrons snaking their way when overtaking them so that electrons are resonantly modulated into small groups (microbunches) separated by a radiation wavelength and emit coherent radiation with a wavelength equal to the micro-bunch period length. This process requires an extremely high-current beam with small energy spread and emittance in addition to a long precisely manufactured undulator. Therefore the conventional accelerator-based FELs need a long section of the multi-stage bunch compressor called as a 'chicane' that compresses a bunch from an initial bunch length of a few picoseconds to the order of 100 fs to increase the current density of the electron beam up to the order of kilo-ampere level before injected to the undulator, whereas the laser-plasma accelerator based FELs would have no need of any bunch compressor. Although the present LPAs need further improvements in the beam properties such as energy, current, qualities and operating stability, the beam current of 100 kA level (i.e. 100 pC electron charge within 1 fs bunch duration) allows a drastic reduction to the undulator length of several meters for reaching the saturation of the FEL amplification. In addition to inherently compact laser and plasma accelerator, a whole FEL system will be operational on the table-top scale. The realization of laser-driven compact table-top X-ray FELs will benefit science and industry over a broad range by providing new tools enabling the leading-edge research in small facilities, such as universities and hospitals.

Laser wakefields in the linear regime
In underdense plasma an ultraintense laser pulse excites a large-amplitude plasma wave with frequency for the electron rest energy 2 mc and plasma density p n due to the ponderomotive force expelling plasma electrons out of the laser pulse and the space charge force of immovable plasma ions restoring expelled electrons on the back of the ion column remaining behind the laser pulse. Since the phase velocity of the plasma wave is approximately equal to the group velocity of the laser pulse for the laser frequency L  and the accelerating field of ~ 100 GV/m for the plasma density ~ 10 18 cm -3 , electrons trapped into the plasma wave are likely to be accelerated up to ~ 1 GeV energy in a 1-cm plasma. In the linear and quasilinear regime with the normalized laser intensity   where L I is the laser intensity and 2 LL c    is the laser wavelength, the wake potential  is obtained from a simple-harmonic equation (Esarey et al., 1996)   and  erf 2 respectively, and is the complex error function. Using Eq. (7) For the Gaussian mode, the axial and radial fields Eq. (15) and (16) Consider the radial potential profile described by super-Gaussian functions as where 2 n  (Sverto, 1998). A Gaussian profile corresponds to 2 n  . Substituting Eq. (25) into Eq. (15) and (16) and for a super-Gaussian pulse 4 n  , the peak power is In this condition, the laser pulse length is shorter enough than a half plasma wavelength so that a transverse field at the tail of the laser pulse is negligible in the accelerating phase of the first wakefield. The net accelerating field z E that accelerates the bunch containing the charge bb Qe N  , where b N is the number of electrons in the bunch, is determined by the beam loading that means the energy absorbed per unit length, k   . Since the loaded charge depends on the accelerating field and the bunch radius, it will be determined by considering the required accelerating gradient and the transverse beam dynamics.

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The electron linac with 10 GeV-class beam energy can be composed of a high-quality beam injection stage with beam energy of the order of 100 MeV in a mm-scale length and a highgradient acceleration stage with meter-scale length. Ideally, the stage length stage L is limited by the pump depletion length pd L for which the total field energy is equal to half the initial laser energy. For a Gaussian laser pulse with the pulse length 1 pL k   , the pump depletion length is given by In laser wakefield accelerators, accelerated electrons eventually overrun the acceleration phase to the deceleration phase, of which the velocity is roughly equal to the group velocity of the laser pulse. In the linear wakefield regime, the dephasing length dp L where the electrons undergo both focusing and acceleration is approximately given by In the condition for the dephasing length less than the pump depletion length dp pd LL  , the normalized vector potential should be 0 1.
Here we assume the accelerating field z E keeps constant over the whole stage length . In fact the 2D particle-in-cell simulation shows that the laser pulse undergoes self-focusing at the entrance of the plasma channel and propagates over the stage length with the energy depletion, leading the average amplitude to be 0 /1 aa  . The plasma density will be determined by setting the required beam energy b E for the FEL injector linac as In the operation of the staged LPA, self-focusing of the drive laser and self-injection of plasma electrons should be suppressed to prevent the beam quality from deterioration as much as possible. These requirements can be accomplished by the LPA operation in the quasilinear regime, where the laser spot size is bounded by conditions for avoiding bubble formation, and strong self-focusing,

Betatron oscillation
Beams that undergo strong transverse focusing forces 22 Fm c K x   i n p l a s m a w a v e s exhibit the betatron oscillation, where x is the transverse amplitude of the betatron oscillation. From the axial and radial fields, Eqs. (21) and (22), driven by the Gaussian pulse , the focusing constant K is given by where 0 n  is the initial normalized emittance (Schachter, 2011). Assuming the beam energy  is constant, this equation is rewritten as Consider the betatron oscillation in the wakefields given by Eqs. (26) and (27), driven by the super-Gaussian pulse. The focusing force is written as where z E is the peak amplitude of the accelerating field. For L rr  , the equation of betatron oscillation is given by where the focusing constant 2 K is 2 0 2 sin The envelope equation of the rms beam radius r  is given by Assuming the beam energy  is constant, Eq. (60) leads to

Betatron radiation and radiative damping
The synchrotron radiation causes the energy loss of beams and affects the energy spread and transverse emittance via the radiation reaction force. The motion of an electron traveling along z-axis in the accelerating force z eE and the radial force r eE from the plasma wave evolves according to where RAD F is the radiation reaction force and / e mc  up is the normalized electron momentum. The classical radiation reaction force (Jackson, 1999) is given by Since the scale length of the radiation reaction R c is much smaller than that of the betatron motion, assumming that the radiation reaction force is a perturbation and zx uu  . the equations of motion Eqs. (65) are approximately written as Finally the particle dynamics is obtained from the following coupled equations, The particle orbit and the energy are obtained from the coupled equations, Eqs. (69) and (70), describing the single particle dynamics, which can be solved numerically for specified focusing and accelerating fields.
For the betatron oscillation of a matched beam in the plasma wave, the damping rate is given by is an average over the beam particles. Assuming the damping time is slow compared to the betatron oscillation Assuming the first term that means an adiabatic decrease of the energy spread is neglected in comparison with a radiative increase given by the second term, the energy spread leads to

Design considerations on a laser-plasma X-ray FEL
4.1 A design example for 6 GeV LPA-driven X-ray FEL

Requirements for emittance and energy spread
The SASE FEL driven by an electron beam with energy  requires the transverse normalized emittance where X  is a FEL wavelength of radiation from the undulator with period u  , . In addition , it is essential for SASE FELs to inject electron beams with a very high peak current of the order of 100 kA. This requirement imposes a charge of ~ 200 pC on the LPA design in the case of accelerated bunch length of 2 fs. Eq. (36) where i E is the injection energy.  , which will lead to decoherence that is a slippage of the particles with respect to each other, and then to emittance growth until the emittance reaches the matched value. This emittance growth rate (Michel et al., 2006) is given by The super-Gaussian wakefields mitigate the emittance growth due to mismatching of the injected beam.
In order to reach the X-ray wavelength 0.
Scanning the electron beam energy in the range from 1.2 GeV to 6 GeV can allow the FEL to cover the X-ray wavelengths 0.1 nm 2.5 nm The FEL operation is characterized by the FEL Pierce parameter (Bonifacio, 1984), The gain length gain L that is the e-folding length of the exponential amplification of the and the relative energy spread requirement for the SASE FEL is given as

Numerical studies of betatron radiation effects
According to Eq. (80), we estimate the energy spread growth due to the betatron radiation from the electron beam accelerated in the wakefields from the injection energy 100 MeV The degradation of the energy spread and the emittance due to betatron radiation effects is investigated by solving the coupled equations, Eqs. (69) and (70), describing the single particle dynamics. We have solved them numerically for the case of the aforementioned 6 GeV LPA. Using the numerical results for a set of test particles that can be solved for the initial conditions corresponding to the initial energy, energy spread and transverse emittance, an estimate of the underlying beam parameter can be calculated as an ensemble average over test particles; for example, the mean energy is given by where i  is the energy of the i th particle and p N is the number of test particles, and the energy spread is defined as The normalized transverse emittance is calculated as where / 1.2 10  for both the analytical and the numerical calculations after the LPA stage, which corresponds to an electron energy of 6 GeV. Since the radiative effects are negligibly small as estimated from Eq. (105), the emittance is well conserved over the LPA stage, where the matched beam is injected. In Fig. 1, an

Attainable peak brilliance of the laser-driven X-ray FEL
In the saturation regime, the photons flux of X-ray radiation is This peak brilliance is comparable to large-scale X-ray FELs based on the conventional linacs (Ackermann et al., 2007).
The parameters of the required drive laser pulse can be obtained from Eq.  is the critical channel depth (Sprangle, 1992).
The design parameters of a

M o s t o f L P A e x p e r i m e n t s t h a t s u c c e s s f u l l y d e m o n s t r a t e d t h e p r o d u c t i o n o f q u a s i -
monoenergetic electron beams with narrow energy spread have been elucidated in terms of self-injection and acceleration mechanism in the bubble regime (Kostyukov et al. 2004;Lu et al., 2006). In these experiments, electrons are self-injected into a nonlinear wake, often referred to as a bubble, i.e. a cavity void of plasma electrons consisting of a spherical ion column surrounded with a narrow electron sheath, formed behind the laser pulse instead of a periodic plasma wave in the linear regime. Plasma electrons radially expelled by the radiation pressure of the laser form a sheath with thickness of the order of the plasma skin depth / p c  outside the ion sphere remaining unshielded behind the laser pulse moving at relativistic velocity so that the cavity shape should be determined by balancing the Lorentz force of the ion sphere exerted on the electron sheath with the ponderomotive force of the laser pulse. This estimates the bubble radius B R matched to the laser spot radius L r , approximately as for which a spherical shape of the bubble is created. This condition is reformulated as where 22 0 17( / ) GW cp P   is the critical power for the relativistic self-focusing (Lu et al., 2006). The electromagnetic fields inside the bubble is obtained from the wake potential of the ion sphere moving at the velocity B v as where B zv t

 
is the coordinate in the moving frame of the bubble and r the radial coordinate with respect to the laser propagation axis (Kostyukov et al. 2004). One can see that the maximum accelerating field is given by at the back of the bubble and the focusing force is acting on an electron inside the bubble. Assuming the bubble phase velocity is given by where 25 2 /8 . 7 2 G W r Pm c e  (Lu et al., 2007).
The 2D and 3D particle-in-cell simulations confirm that quasi-monoenergetic electron beams are produced due to self-injection of plasma electrons at the back of the bubble from the electron sheath outside the ion sphere as the laser intensity increases to the injection threshold. As expelled electrons flowing the sheath are initially decelerated backward in a front half of the bubble and then accelerated in a back half of it toward the propagation axis by the accelerating and focusing forces of the bubble ions, their trajectories concentrate at the back of the bubble to form a strong local density peak in the electron sheath and a spiky accelerating field. Eventually the electron is trapped into the bubble when its velocity reaches the group velocity g v of the laser pulse. The trapping cross section (Kostyukov et al. 2004 with the sheath width d imposes 0 28 pB kR a  , i.e. 0 2 a  for the matched bubble radius. Once an electron bunch is trapped in the bubble, loading of trapped electrons reduces the wakefield amplitude below the trapping threshold and stops further injection. Consequently the trapped electrons undergo acceleration and bunching process within a separatrix on the phase space of the bubble wakefield. This is a simple scenario for producing high-quality monoenergetic electron beams in the bubble regime.
However, in most of laser-plasma experiments aforementioned conditions and scenarios are not always fulfilled. In the experiment for the plasma density 19 3 (1 2) 10 cm p n   , observation of the self-injection threshold on the normalized laser intensity gives 0th 3.2 a  after accounting for self-focusing and self-compression that occur during laser pulse propagation in the plasma. In terms of the laser peak power the self-injection threshold for the power ( / ) 12.6 ct h PP  as the laser spot size reduces to the plasma wavelength due to the relativistic self-focusing (Mangles et. al, 2007). In the www.intechopen.com corresponding to 0th 1.6 a  (Froula et al., 2009).

A design example of self-injection bubble-regime LPA
We study the production of high-quality electron beams by means of the particle-in-cell (PIC) simulations for the self-injection. We have confirmed the qualities of accelerated electron beams with the r.m.s. energy spread less than 1%, the normalized transverse emittance of the order of a few mm mrad  and the r.m.s. bunch duration of the order of 1 fs. These parameters can satisfy the criteria of the electron beam injector that are required for X-ray FELs.
The self-injection electron beam production has been investigated by the 2D PIC simulation code VORPAL (Nieter et al., 2004), using the 2D moving window, of which the size is . For each pulse duration, two bunches are trapped and accelerated as follows: the higher energy bunch with narrow energy spread is trapped and accelerated in the first bucket of the wake, while the lower energy bunch with large energy spread is trapped to the second bucket of the wake. Figure 2 shows the energy spectrum of accelerated electron bunch for 38 fs L   at 2.9 mm z  , where the first bunch reaches the maximum energy and the minimum energy spread. The beam parameters such as the bunch energy, the energy spread, the charge, the normalized emittance and the bunch length of the first bucket are investigated as a function of the laser pulse duration, when the bunch energy reaches the maximum value, for which the bunch has travelled approximately the dephasing length. For the optimum pulse duration, we obtains the best beam parameters characterized by the energy 283  . These electron beam parameters satisfy requirements for the table-top soft X-ray FEL capable of generating a 10 GW-class saturation power at the radiation wavelength of 13.5 nm (92 eV photon energy) using a 1.1-m long undulator with 5-mm period and the 1-Tesla magnetic field that give the undulator parameter 0.465 u K  ( Nakajima, 2011).
In practical applications, high-quality beams from laser-plasma injectors are transported and injected to the undulator or the next LPA stage through a beam transport system. We consider the compact beam transport system for focusing the above-mentioned accelerated electron beam into the next accelerator stage or the miniature undulator for the soft X-ray FEL. The design has been studied using TRACE3D (Crandall & Rusthoi, 1997), which is an envelope code based on a first-order matrix description of the transport. The focus system consists of four permanent-magnet-based quadrupoles (PMQs), arranged in the defocusdefocus-focus-focus lattice configuration. The simulation results of TRACE3D are shown in Fig. 3, where the electron bunch is transported from the left to the right for the aforementioned beam parameters. The field gradient of the two dimensional Halbach-type PMQ (Lim et al., 2005) is given by . Hence, we can tune the beam energy of the focus system so as to discriminate the first bunch with high energy and high qualities from the second bunch with low energy and less qualities.

Stability control of laser-plasma acceleration
Many of applications require the stability of the beam parameters as well as their qualities. In particular, the stability issue is crucial for the X-ray FEL relying on the SASE mechanism. The stability of the laser system itself is very important for achieving stable LPAs (Hafz et al., 2008). However, up to date there is no conclusive proposal for stabilizing the production of electron beams from LPAs at the low plasma densities which are relevant to GeV energies. Here we show the effect of laser pulse skewness (asymmetry) on minimizing the electron beam pointing angle in the weakly-nonlinear laser wakefield accelerator operating at the low densities in a gas jet target.

Setup and parameters
The experimental setup is described as follows. A laser beam from a titanium sapphire system had, after compressor, the energy of ~ 0.9 J per pulse. The laser pulses are delivered to a target chamber and focused above a 4-mm long supersonic helium gas jet by using a focusing optic having F-number of 22 that focuses the laser pulse on the FWHM spot size 0 23 1 m w   in vacuum. The gas jet stagnation pressure is ~ 1 bar and the laser is focused at the height of a few millimeters above the nozzle, where the gas density is in the range of 17 18 3 10 10 cm   . Therefore the expected wavelength of the wakefield is in the range 30 100 m p    . The electron beam pointing angle is detected by using a LANEX Kodak phosphor screen which is located at the distance of 78.5 cm from the gas jet. The LANEX is imaged onto an intensified charge-coupled device located near the interaction chamber in a radiation shielded area (Hafz et al., 2008). In order to obtain temporally-asymmetric laser pulses, the distance between two gratings of the pulse compressor is detuned from its optimum value which produces the shortest (37 fs) and symmetric pulses. The temporal pulse shape is measured by using a spectral phase interferometer for direct electric field reconstruction (SPIDER) device. Of interest is the negative detuning (positive chirp) which produces fast rise time laser pulses. Through negative detuning values from 0 to 250 µm, the laser pulse asymmetry increases and its length increases from 37 fs to 74 fs. In this range, the laser intensity is in the range 17 18 2 7.5 10 1.46 10 W/cm  , corresponding to the normalized vector potential of the laser pulse in the range 0 0.59 0.83 a . Therefore, this experiment is characterized roughly with the parameters 0 1 a  and www.intechopen.com

Results
In the following, the reference direction for the electron beam pointing angle is the laser beam direction itself. At first, we set the laser compression to optimum (no detuning), so that the laser intensity is 18 2 1.46 10 W/cm  . The helium gas jet backing pressure is 1 bar and the interaction point is located at 1 mm height to the nozzle. At this height the gas density is 18 3 1 10 cm   . With those interaction conditions, the probability of observing an electron beam is as low as 1% or lower. However, the situation dramatically changes by detuning the compressor grating distance toward negative values. At a detuning distance of -100 µm the electron beam started to appear, however, the beam pointing angle is as large as ± 40 mrad. (The ± sign here means the direction of deflection angle with respect to the laser reference. In what follows we will remove the ± sign for simplicity). By changing the detuning distance to -200 µm the electron beam pointing angle is improved to 25 mrad and to 15 mrad at the detuning of -300 µm. Then the electron beam pointing angle has increased again to 25 mrad by increasing the detuning to -500 µm. In this experiment, the electron beam pointing in the vertical direction is smaller than that in the horizontal one. At laser height of 1.75 mm to the nozzle position, we notice that the electron beam pointing angle is improved to 8.5 and 10 mrad for the detuning distances of -200 and -400 µm. The electron beam pointing angle (horizontally and vertically) has been dramatically reduced to 2 mrad at a laser height of 3.25 mm where the gas density is in the range of 17 3 10 cm  . Each data point is an average of 10 successive shots. From these data we can conclude that a detuning distance of -200 through -250 µm and the height of 3.25 mm are almost the optimum conditions for producing the smallest electron beam pointing angles. It should be noted that for this detuning range the laser intensity is in the range of 17 2 7.5 9 10 W/cm   . More precise scanning for the grating detuning distance at a fixed laser height of 3.25 mm shows an interesting result as illustrated in Fig. 4. For this height and at zero detuning, the electron beam pointing angle is severely large ~100 mrad and the beam generation reproducibility is ~50%. Again, within the grating detuning range from -200 to -300 µm the electron beam pointing angle reaches its minimum value at 2 mrad. In addition, the electron generation reproducibility is almost 100%, and the electron beam charge is ~30 ±10 pC as measured by an integrating current transformer. The data points of Fig. 4 are averages over hundreds of successive laser shots except for those at 0 or positive detuning values where the electron beam production is null or extremely rare.
Finally, we measured the electron beam energy by using a bending dipole magnet (Hshaped) which had a uniform magnetic field intensity of 0.94 Tesla and a longitudinal length of 20 cm (Hafz et al., 2008). The distance from the gas jet to the magnet entrance is ~1.5 m and the LANEX is located at 25 cm from the end of the magnet. Between the gas jet and magnet we installed 1-m long helical undulator with 0.5 T magnetic field and 2.4 cm period for generating a synchrotron radiation. The distance from the gas jet to the undulator is 30 cm, and the inner diameter of the undulator tube is 9 mm. Thus an electron beam from the gas jet must enter the undulator, propagate through it and then enter the dipole magnet region which bends the beam into the LANEX screen. The measured electron beam have a quasi-monoenergetic energy peak at ~ 165 MeV. This article is focused on minimizing the fluctuation of the electron beam pointing angle, thus our results are crucial for on-going world-wide experiments on compact free-electron laser and undulator radiation using intense laser irradiated gas jets as a compact electron beam accelerator (Hafz et al., 2010;Nakajima, 2008). Fig. 4. Electron beam pointing angle versus detuning distance at the optimum height of 3.25 mm above the gas jet nozzle.

Conclusion
We have worked out the design considerations of a compact X-ray FEL that can reach the wavelength of 0.1 nm corresponding to the hard X-ray with photon energy of 12 keV. The system consists of a cm-scale 100 MeV-class electron beam injector, a 0.4-m long PMQ-based transport beam line , a 0.4-m long 6 GeV LPA linac and a 8-m long undulator. Including a 100 TW-class table-top laser system and an application space for the coherent X-ray research, main system can be installed within a 10-m long, 2-m wide space. The present considerations are based on the current achievements of laser-plasma accelerators and currently available technologies on drive lasers and undulators, for which we have not assumed new technologies and developments as well as new physics concepts on FEL. In this context, the present design of the hard X-ray FEL would be rather conventional and therefore it may be materialized in a near term at a reasonably low cost, guaranteeing the performance comparable to large-scale X-ray FELs. Harnessing miniature undulators with period of 5 mm u   Eichner et al., 2007) may make the required saturation length shorter by a factor of 3, i.e. a 2.5-m long undulator, and the required electron beam energy becomes approximately half, i.e.
3 GeV b E  , for a 0.1 nm X-ray wavelength, assuming the saturation length scales as 56 sat u L   with 12 u    and the LPA is operated at the same plasma density. This option may turn out a whole system to be on a 3-m long table top under the condition of trading off requirements for further high-quality, high-stability electron beam production from the LPAs.
Another way to build X-ray FELs on a table top is to produce the interaction between an electron beam and a laser pulse via coherent Thomson scattering or Compton scattering www.intechopen.com Free Electron Lasers consists of 10 chapters, which refer to fundamentals and design of various free electron laser systems, from the infrared to the xuv wavelength regimes. In addition to making a comparison with conventional lasers, a couple of special topics concerning near-field and cavity electrodynamics, compact and table-top arrangements and strong radiation induced exotic states of matter are analyzed as well. The control and diagnostics of such devices and radiation safety issues are also discussed. Free Electron Lasers provides a selection of research results on these special sources of radiation, concerning basic principles, applications and some interesting new ideas of current interest.