An Ultra-Compact X-Ray Free-Electron Laser

In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV/m. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 meters. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by ~50 nm-rad normalized emittances. These beams, when injected into innovative, short-period (1-10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine which may profit from this new model of performing XFEL science.


Introduction
The x-ray free electron laser (XFEL) is a transformative instrument, producing coherent x-ray pulses with peak brightness 10 orders of magnitude greater than preceding approaches [1]. The existence of a coherentÅ-wavelength source with femtosecond pulses has changed the landscape of science. After only a decade of operation of the first hard x-ray FEL, the LCLS at SLAC, its unprecedented source parameters and associated instruments have combined to form an invaluable tool for research in chemistry, biology, materials science, medicine, and physics [2]. As such, XFELs are laboratories with an inherent and deep multi-disciplinary flavor. The LCLS and the other hard xray FELs [3,4] worldwide are based on two enabling technologies: conventional or superconducting RF accelerating structures and multi-cm period magnetic undulators. These each contribute to the footprint (∼km scale) and cost of all existing XFELs. This combination of unique research significance and high cost means user demand significantly outstrips supply. As a concrete example there exists only a single XFEL facility in the US, the LCLS, which is able to satisfy the beam-time requests of less than 20% of the proposed experiments. The types of science that can be engaged in this constrained model are limited there can be little cross-checking and iteration based on empirical feedback. There are also few opportunities for translational research in industry, medicine and other applied fields.
The first generation of XFELs has greatly exceeded performance expectations. The success of the LCLS and other XFELs has made a case that next-generation FELs are essential. This interest in expansion is manifested in the soft x-ray regime by LCLS-II, a billion-dollar-class facility aimed at exploitation of coherent, ultra-fast photons at longer wavelength, where new opportunities in spectroscopy await. There is also compelling interest in harder x-rays, above 40 keV, to perform imaging in dense, high-Z, mesoscale systems, such as the MaRIE XFEL proposed at LANL [5,6,7]. While x-ray free-electron lasers have attracted multiple billions of dollars in cumulative investment, they still number only a handful worldwide [8,9]. Despite the scientific success and tremendous demand from the user community, the XFEL in its present configuration, due to its expense and limitations, has stimulated competitive approaches to appear. These seek to preserve the extraordinary flexibility and temporal advantages of an XFEL while dramatically reducing the size and cost of the instrument. An XFEL that is both highly capable and miniaturized has the power to resolve the issue of access that is currently constraining scientific discovery. To develop an ultracompact XFEL, however, one must reinvent the approach to creating x-rays using the free-electron laser mechanism. Given this history and current status, it is notable that the birth of the XFEL was based on proof-of-principle physics experiments in previous decades that were carried out by small research teams working in an innovative, exploratory fashion [10]. To reinvent the XFEL we seek to profit from the same approach.
Previous proposals on realizing very compact XFELs have concentrated on the use of advanced accelerator techniques [11,12] to minimize the length of the accelerator, thus achieving 10 GeV-class beams in a length in the 10s of meter range or below. This class of instrument is seen as a step beyond the XFEL, which is termed a 4 th generation light source -thus the miniaturization of the XFEL with an advanced accelerator is termed a 5 th generation light source. These proposals, at present emphasizing a range of techniques from existing high gradient radio-frequency linear accelerators (linacs), to plasma-based acceleration, have not profited from potentially transformative changes in magnetic undulator design. As we shall see in the following, this is due, particularly in the case of plasma acceleration, to the lack of advances in beam quality needed to use accelerators with lower energy, employed in tandem with advanced, short-period undulator methods.
In this paper, we will present the details of a new approach that exploits multiple scientific advances to realize the design of an ultra-compact XFEL (UC-XFEL). We emphasize first the fundamental performance aspects of the XFEL, to approach an optimized design. Instead of adapting the FEL to the acceleration technique used, we employ a comprehensive design philosophy that is derived from simultaneously examining multiple aspects of the FEL system. Given the decade of dedicated research relevant to components of the 5th generation light source, this integrated approach can now be crystallized; the concept for an ultra-compact x-ray FEL presented here utilizes a recipe based on dramatic advances in the critical component ingredients of the FEL, with the key enabling aspect being the use of an electron beam with very high six-dimensional brightness.
On this basis, we propose here a new class of UC-XFEL sources that can be implemented at the university level, at size and cost diminished by more than tenfold. Despite this down-scaling, we project that this type of UC-XFEL may produce photon fluxes per pulse that yield several percent of existing full-scale XFELs, in both the soft and hard x-ray regions. This model of affordable, distributed x-ray lasers will make intense, coherent, ultra-fast sources available to the broad scientific community in a ubiquitous way, similar to the optical lasers now employed at university labs in many diverse fields. Present XFEL experiments, by their nature, have a certain metric for success, which is found in producing one-of-a-kind results in a short period of running on the scale of days. Relaxing this constraint will inevitably lead to new scientific results, much like the explosion of scientific activity in the early days of synchrotron radiation sources, with the subsequent, rapid development of hundreds of beamlines worldwide [13]. It is similarly envisioned that the UC-XFEL, which has a predicted cost that is similarly less than five percent of existing XFELs, will permit wide availability of coherent x-rays to a significantly broadened user community.
We discuss below a recipe for taking the km-scale XFEL and miniaturizing it to fit inside the footprint of a university building. To inform the discussion that follows, and to aid in visualization, we show in Figure 1 a conceptual layout of the UC-XFEL, including its major components at scale. It can be appreciated that the total footprint of the instrument is near 40 m. The rationale for the choices made in the UC-XFEL are motivated in what follows. The discussion in this paper is quite detailed, examining many aspects of the UC-XFEL's physical and technological properties. Through this discussion it is shown that a highly credible path to realizing this paradigm-changing instrument exists.

A Recipe for an Ultra-Compact XFEL
There are a number of relations that one should introduce to quantify the challenge of realizing the ultra-compact XFEL. The most important gives the dependence of the resonant, on-axis lasing wavelength, λ r , on the beam and magnetic undulator parameters: Here γ = U e /m e c 2 is the beam energy, U e , normalized to the rest energy, m e c 2 , and the planar undulator parameter where the magnetic field in the undulator's symmetry plane is taken to be of the form For present-day undulators, with period λ u = 2π/k u of a few cm, the parameter K u slightly exceeds unity in most devices. The physical significance of K u is that it is the vector potential amplitude, normalized to the measure of relativistic momentum, m e c. Further, one may note that it also measures the coupling of the electromagnetic wave in the FEL to the electron's undulating motion, as the maximum angle found in the oscillating design trajectory is θ max = K u /γ. This angle measures the degree with which the electrons can exchange energy with the FEL light. The present authors have examined in some detail the mitigation of beam energy demands in the XFEL through a significant shortening of the undulator period from λ u,> to λ u,< , to the millimeter level or below [14]. This period-shortening has the effect of reducing the beam energy demanded, γ < , from a reference design, γ > , by a factor With peak fields B 0 near the 1 T level, scaling to mm-period reduces K u,< to below unity. This reduction factor in the beam energy demanded is significant; it is approximately λu,> λu,< K u,> . It is clear from this relation that one may decrease the energy needs of the FEL in this manner by as much as an order of magnitude, dependent on the details of the undulator parameters chosen. We will in this paper discuss various options for employing short-period undulators, and progress in their realization. The examples chosen will have energies in the 1 to 1.6 GeV range, to be compared with 4.3 GeV and 14 GeV in the cases of LCLS-II and LCLS, respectively.
We note that the use of shorter undulator period also inherently shortens the undulator length required to achieve FEL saturation. This is explicitly seen through the expression for the exponential gain length of the FEL instability [15], A typical SASE FEL proceeds to saturation within 20L g , and so this indicates that the undulator length is shortened proportionally to λ u , without consideration of the variation of other parameters. This expression also introduces the Pierce parameter, given by where [JJ] 2 (K 2 u ) is a Bessel-function dependent parameter that is near unity for K 2 u < 1, I is the beam current, I A is the Alfvén current, I A = ec/r e ≈ 17,045 A, where r e is the classical electron radius, k r = 2π/λ r and the transverse beam rms spot size is σ x . It can be seen that ρ 3 ∝ I/σ 2 x , the current density. Its maximization, or alternatively the minimization of the gain length, is accomplished through high currents (kA-level), small emittance, n , and tight focusing of the beam. It is often stated that the ρ 3 is proportional to the five-dimensional beam electron brightness, B 5D ≡ 2I/ 2 n . We will, in the following section, give a more direct, quantified analysis of the dependence of the gain parameter on beam quality, using the six-dimensional beam brightness where σ γ = σ Ue /m e c 2 is the electron beam's normalized rms energy spread. We note that this energy spread also is directly related to ρ, in that we require σ γ /γ < ρ in order achieve lasing -larger energy spreads cause Landau damping to extinguish the FEL instability. Further, one may relate the efficiency of beam energy extraction to FEL radiation with the Pierce parameter, η FEL = N γh ω r /N b U e ρ.
One may also note that the gain parameter is dependent on the efficacy of the focusing applied to the beam. Innovative approaches to this focusing, using advanced high field quadrupoles, may be needed to provide an optimal spot size σ x ; these methods are discussed in this paper. This spot size is limited from below by diffraction effects, which require that the radiation Rayleigh range as approximated by Z r = 4πσ 2 x /λ r is notably larger than L g . For XFELs, this effect is often ignorable due to the short wavelength of the lasing photons. Finally, the emittance should also be small to obey the coherence requirement termed the Pellegrini criterion, n < γλ r /4π, which guarantees the overlap of the radiation of individual electrons in the beam with each other to coherently add and create the lasing mode [16]. Quantitatively, as we are attempting to strongly lower the beam energy by the use of short period undulators, a very low normalized emittance is demanded.
Much recent progress has been made in understanding how to improve the emittance and attendant brightness of electron beams. The introduction of the high field RF photoinjector approximately 30 years ago was a critical step forward in this regard, an advance that yielded an order of magnitude increase in beam brightness. This improvement, which was based on the use of large accelerating fields and optimized beam optics (emittance compensation) techniques was a key element in the realization of the SASE FEL [17]. Recently, it has been shown by a SLAC-UCLA collaboration that one may strongly increase the peak operating surface field in copper RF cavities from the nominal current value of E 0 =120 MV/m by a factor of 2.5 to 4. This is accomplished by cryogenically cooling the copper, to enter into the anomalous skin effect (ASE) regime [18]. The combination of resulting lower dissipation due to diminished surface resistivity with increased material yield strength and mitigation of thermal expansion are the physical effects underpinning this remarkable advance. Applying increased fields in the photoinjector should have profound implications for beam brightness, which stands to be increased 50-fold over the original LCLS design [19,20,21], and similarly advance the recent state-of-the-art [22]. We discuss the expected performance of such a high field photoinjector, operated at E 0 = 240 MV/m below.
This new approach to high field RF acceleration also permits a dramatic reduction in length of the accelerator needed for the UC-XFEL. A cryogenically-cooled C-band linear accelerator structure is now being developed for linear collider applications at SLAC and UCLA [19,20], with operation at an average accelerating gradient of eE acc = 125 MeV/m; this entails using a peak field nearly identical to that of the photoinjector. To put this gradient in perspective, it is over a factor of six larger than that employed at LCLS [3] and LCLS-II. To reach U e =1 GeV (for our soft x-ray example) one would need eight meters of active length with this approach. Between the reduction in energy needed and enhanced gradient employed, the accelerator is shortened by a factor of over 25. The proposed accelerator sections are of an innovative design where the coupling is achieved independently through a guide manifold; there is negligible cell-to-cell coupling in this standing wave design. As such, the accelerating structure may be optimized to have a very high power efficiency [23], as measured by the shunt impedance.
The approach described above yields, in simulation, a beam from the photoinjector having 20 A peak current and n = 50 nm-rad. This extremely low emittance must be preserved during both high field acceleration and pulse compression, which entails enhancing the current to several kA to achieve strong XFEL gain. We explore this process in detail, identifying a compact (total length <10 m) two-stage compression scheme: the first is a compact chicane that yields I = 400 A [24]; the second is an optical micro-bunching technique that utilizes the inverse free-electron laser (IFEL) mechanism [25,26]. The advantages of such an approach, which have been discussed in several recent works [24,27], are manifold. If one does not attempt to compress the beam into a single pulse, but instead organizes the beam into a pulse train on the scale of a laser wavelength λ L , then the bending and accompanying longitudinal motion is limited. This approach suppresses collective effects which can increase the emittance.
The IFEL produced micro-bunch train, may produce a laser-synchronized train of x-ray FEL pulses [25]. To permit robust lasing performance in this system, the micro-bunches cannot be too short, as the radiation slippage over a gain length z s = L g (λ r /λ u ) needs to be limited to a fraction of a micro-bunch length [15,25]. Operation at short λ r aids in satisfying this condition, but one must also have robust gain, which in turn is a function of beam brightness, as discussed below. Assuming micro-bunch lasing is achieved, the x-ray pulse train obtained presents distinct advantages in pump-probe experimental applications, as has been noted in other laser-synchronized systems such as high harmonic generation [28] and Compton scattering sources based on IFEL [29].
Finally, a micro-bunched format for achieving the needed peak current serves to ameliorate a problem that particularly afflicts short period undulators. As the gap used in the undulator scales with λ u , the material boundaries in mm-period undulators are only 100's of µm away, and serious issues may arise from resistive wall wakefields. Use of micro-bunches can strongly mitigate this issue [30,27,26], and this aspect of XFEL design is therefore attractive in our case.
With the above-listed ingredients, a beam capable of using 1 to 10 mm period undulators, reaching hard and soft x-ray FEL operation, may be envisioned. In this context, we discuss the present state-of-the-art in sub-cm period undulators, and identify paths to extend current designs (existing down to λ u = 7 mm) to the 1 mm level. We show through start-to-end simulation analysis, that the saturation length for producing multi-10's of gigawatt XFEL power is 4 m at 1 nm, and 6 m at 1.5Å operation, respectively. The per-pulse photon flux predicted is nearly five percent of current LCLS operations, in an instrument with a footprint below 30 m in length. Such a compact system demands, for consistency, x-ray optics and experimental end stations which are scaled down in size in a similar fashion. We discuss approaches to such optics which take advantage of several notable differences between the UC-XFEL and current generation full-scale XFELs: the reduction in peak power and integrated fluence, and increased divergence in the radiation. This analysis is informed by a discussion of a variety of experimental opportunities opened by the realization of an ultra-compact XFEL based on these emergent technologies discussed above, and associated advances in physics design principles.

Six-dimensional Brightness Scaling in SASE FELs
While the recipe introduced above explains the conceptual dependencies connecting the suite of ideas introduced that enable the UC-XFEL, it is more direct to describe the XFEL in the order in which one encounters the component systems. This begins with the electron source, which plays a central role in enabling the needed performance of the UC-XFEL.
Arguments in favor of the advantages of high brightness beams for driving SASE FELs have traditionally been based on the 5D brightness, B 5D . This viewpoint is problematic, however, as B 5D is not a conserved quantity. On the other hand, the Liouville theorem indicates that the six-dimensional brightness B 6D is conserved in a local sense. We thus present here an analysis of the Pierce gain parameter, ρ, that seeks to reveal its dependence on B 6D . Here we assume that there are no correlations in the 6D phase space after the beam is prepared for lasing, and that dilution of B 6D (a measure based on rms quantities) may be ignored.
We begin by noting that for values of the undulator strength parameter K u < 1 as encountered in the UC-XFEL, the expression for the Pierce parameter can be simplified to read approximately We have written ρ in terms of the radiation wavenumber, as we will aim to reveal scaling of parameters while holding the FEL wavelength fixed.
To relate the gain to the beam brightness, we first write the emittance in terms of the Pellegrini criterion x n /γ = η /2k r , i.e., where η is less than or equal to unity. When it takes the value 1, the electron and photon beam emittances are equal. Additionally, we will assume the peak undulator fields to be fixed by design limits at B 0 1 T and thereby rewrite the undulator parameter in the following way where this parameter r B = 1.7 mm can be understood as the radius of curvature of the trajectory an electron having momentum m e c follows in a uniform field of strength 1 T. In the last equality we have approximated the FEL resonance condition valid to lowest-order in K u , k u = k r /2γ 2 .
To optimize the focusing of the electron beam, we additionally take the average Twiss β-function of the electron beam to scale to be near the FEL gain length, where we have introduced another factor, η β . This tuning factor is near to unity and generally a slightly smaller, depending on final FEL optimization. We insert scaling relations into the expression for ρ 3 , eliminating one power of ρ, In this last equality the 5D brightness is used. We now pass to a description of the scaling which employs the six-dimensional rms brightness which, in the absence of transverse and longitudinal emittance growth or beam loss, may be conserved. We relate the 5D and 6D brightness by introducing the normalized rms energy spread σ γ , and indicate the familiar scaling relationship, where η γ is another optimization factor, similarly limited above by unity. In this case we can rewrite the expression for ρ utilize the 6D beam brightness, to obtain From this analysis we see that the Pierce parameter, which dictates the gain length and efficiency characteristics of the XFEL, has linear scaling with the six-dimensional electron beam brightness. This is much more striking than the commonly quoted dependence on 5D brightness ρ ∝ B 1/3 5D . The scaling with energy also appears as quite strong, depending as γ 6 . Conversely, if one includes the implicit variation of k r (γ), holding the undulator period constant (as is more often the case in FEL design strategies), this reverses, and ρ ∝ γ −2 . However, in the UC-XFEL, we are concerned with achieving a certain k r = 2π/λ r through increasing k u and thus using smaller γ. This strong energy dependence indicates that we must, in order to operate at smaller γ, dramatically increase the electron beam 6D brightness. The approach to the electron source yielding this advance is discussed in the next section.
Before introducing the approach to the initial production of high beam brightness, we note that the factors η , η β ,and η γ can be analyzed with sophisticated optimization procedures. These procedures are aided by theoretical work that has been based, as is presented here, on an analysis based on 6D brightness [31]. Similarly, design tradeoffs are necessary to include the effects of non-one-dimensional phenomena such as diffraction. This type of optimization has been studied in the context of the well-known Xie analysis, found in Refs. [32,33], and extended to include space-charge in Ref. [34].

High Gradient Cryogenic Photoinjector
The photoinjector for UC-XFEL has been chosen on the basis of several studies of the potential use of cryogenic cooling of the RF cavities [19,20]. These studies, along with experimental investigations of the breakdown and dark-current emission performance of cryogenic cavities [35], have yielded an optimized surface electric field on the photocathode E 0 = 240 MV/m. This field, obtained in a high shunt-impedance RF structure, is a factor of two below the measured breakdown limit in cryogenic copper [36], and also well below the threshold (300 MV/m) of large dark current emission. The geometry of the structure is indicated in Figure 2. Even with derating of the maximum field, the brightness obtained by this new generation of RF photoinjector should increase over current values significantly, by a factor of between six and sixteen. This is due to, above all, the increased beam density at emission. As discussed in Ref. [20], the fivedimensional brightness is expected to scale as B 5D ∝ E n i , where E i is the amplitude of the initial launch field, and the exponent n is between 1.5 and 2, depending on the beam shape. The six-dimensional brightness, including the effect of space-charge on slice energy spread scales similarly [37,38], as B 6D ∝ E 2 i . The proposed high field cryogenic C-band RF photoinjector source takes advantage of this scaling. We will see that this step forward must also be accompanied by innovative approaches to brightness preservation during beam manipulations after the injector. Overlaid with the longitudinal electric field, illustrating significant higher spatial harmonics.
As illustrated, the proposed photoinjector RF structure is a 1.6 cell C-band gun that is optimized in shape to minimize the magnetic field on the surfaces. This permits lower input power and mitigates dissipation at cryogenic temperatures. With an expected overall repetition rate of 100 Hz, and nominal 300 nsec RF pulses, at the foreseen operating temperature of 27 K this dissipation is 11 W, requiring over 0.5 kW cooling power. This design is functionally similar to a less sophisticated structure without reentrant nose cones studied in detail in Ref. [19]. It is chosen, in part, to take advantage of the faster response times and associated mitigation of power considerations in the UC-XFEL, as well as its possible utility for application in the MaRIE XFEL. This optimized RF structure has several potentially important impacts on the performance of the photoemitted beam. The significant higher spatial harmonics (see Figure 2) in the RF profile arising from optimizing shunt impedance provides a beneficial effect: enhancement of the second-order RF transverse focusing experienced by the electrons [39]. These spatial harmonics may also introduce a nonlinear radial dependence of the focusing and defocusing fields in the gun cavity which could, for beams with non-trivial radial extent, lead to rms emittance growth. This is not the case for the parameters of the UC-XFEL photoinjector. Indeed, these effects have been studied along with the overall performance of the photoinjector, and found to yield enhanced brightness over that reported in Ref. [19]. This scenario includes solenoid focusing similar to that of a scaled LCLS gun with a 1.05 meter drift to the first post-acceleration linac (described in the next section). Designs of the compact, cryogenic high field (B peak =0.55 T) solenoid have been employed in the beam dynamics simulations. Results from these studies include the evolution of the rms emittance and beam size during the focusing and accelerating process, yielding emittance compensation, as shown in Figure 3. The final emittance after acceleration to U e = 153 MeV is excellent: n = 55 nm-rad. This is achieved with Q b =100 pC charge, and 5 psec FWHM pulse length, with peak current I p = 20 A. As we are interested in the 6D brightness of the source, it is important to point out that the longitudinal slice energy spread is at or below 0.55 keV. In this case, the achieved 6D brightness is B 6D = 6.1 × 10 18 A/(m-rad) 2 . This can be compared to the value associated with the LCLS design, at B 6D = 1 × 10 17 A/(m-rad) 2 ; the improvement in this parameterization of beam quality is a factor 60.
The characteristics of the beam longitudinal phase space at the injector exit are shown in the GPT [40] simulation results displayed in Figure 4. Use of a stronger solenoid (0.64 T) can result in a beam with lower emittance, ( n = 50 nm-rad) through control of the transverse beam oscillation amplitudes. The decrease in beam size, however, yields some pulse length expansion from longitudinal space-charge effects, to 6.2 psec. For the remainder of this paper, we utilize the shorter beam option, as it stresses the sensitive downstream compression processes less.  We note that the beam dynamics and emittance compensation process have been optimized in this case considering a copper photocathode with nominal "thermal" rms normalized emittance [41] given by 0.5 mm-mrad/mm. This can be improved upon in principle by using advanced methods involving novel cathode materials, or by taking advantage of the cryogenic state of the emitting surface [42]. This approach permits the maintenance of a small emittance at larger emitting spot sizes, while giving shorter pulses and higher peak current. Studies of this optimization path in the zero-thermalemittance limit have shown higher brightness. While this potentially advantageous approach remains under study, the predicted performance of the UC-XFEL as presented here does not depend on its implementation. In this regard, it should be stated that introduction of novel photocathodes would also have an effect on the challenge of operating in a large field-emission (dark current) environment [35], which remains a key issue in the experimental realization of this high field, high brightness photoinjector. Similarly, potential problems in managing emission characteristics are found in a large laser fluence environment [43], as may be necessary in the high-field photoinjector.
The photoinjector functionally consists of a very high field RF gun, focusing optics, and post-acceleration cryogenic linacs operated at an average acceleration gradient of 125 MeV/m. A first version of both the cryogenic C-band RF gun and linear accelerator (linac) structures are now under development by a UCLA-Stanford-LANL-INFN collaboration, with an initial emphasis on linear collider applications [44]. In this experimental work the RF gun beam dynamics concentrate on the case of a magnetized photocathode, which is used with skew quadrupoles after post-acceleration in the linac to produce highly asymmetric emittances after removal of the angular momentum in the beam [45]. The design of the linac structure used in these tests, and in the UC-XFEL, are described in the next section.

Linear Accelerating Structure
The linac structures proposed for the UC-XFEL, as noted, also rely on use of cryogenic C-band copper cavities. Their design is based on a similar philosophy as the RF gun cavities, with a highly optimized shape. At cryogenic temperatures, this optimized structure yields a shunt impedance of 460 MΩ/m. This quite high value is obtained by eliminating cell-to-cell coupling through the irises, in favor of a re-entrant geometry. In applications such as the linear collider or XFEL, this geometry has notable advantages over previous generations of X-band linacs, where such a re-entrant structure would provoke transverse wakefields that are very challenging to manage. As the re-entrant design isolates each cavity, the linac section design thus exploits a new coupling scheme, with independent coupling from a wave-guide manifold to each individual cell. The resulting form of the linac structure is shown in Figure 5. These structures are now under development and initial testing at SLAC and UCLA. The initial goal of these studies is the integrated investigation, introduced above, into the production of linear collider-quality, asymmetric emittance beams through the use of a magnetized photocathode [45], and the demonstration of robust high gradient acceleration, at both 27 K and 77 K operating temperatures. While the design and innovative realization of these cryogenic structures is rapidly maturing, there are compelling issues left to address. Prominent among these topics is the control of multibunch beam break-up (BBU) through damping of higher order modes (HOM) [46]; simulation and optimization studies are now underway to consider the addition of mode dampers in this novel geometry. Experimentally, peak accelerating gradients of up to 140 MeV/m, consistent with the design parameters demanded here, have been demonstrated in linac prototypes based on this design [23]. It should also be noted that multi-cell cryogenic copper accelerating sections are now being fabricated by creating two pieces split along the midplane, and then joining these pieces using innovative techniques such as electron-beam welding. In such a way, one may create intricately shaped cavities for optimizing the shunt impedance as well as HOM damping effectively and at lower cost.
It should be noted that the essential advantage of using high gradient cryogenic RF linacs is to produce the beam energy needed for UC-XFEL on a 10 m length scale. This serves the goal of making a compact system in its own right. The compactness of the linac (as well as the unique approach to final beam compression) also yields a secondary, but critically important advantage: it suppresses the micro-bunching instability. As this instability is particularly worrisome for high brightness beams, its mitigation, discussed further below, is essential for the UC-XFEL.
In the longer term, research and development into cryogenic RF acceleration has other fundamental subjects to address. First, one should understand the dramatic increase in breakdown fields in more detail, to push demonstrated, useful performance of cryogenic RF cavities to >500 MV/m surface fields. To do so, it is essential to understand the dynamics of surface breakdown, and field emission currents, as well as their mitigation. These investigations have been initiated, and are enabled through a first-principles simulation effort using molecular dynamics codes developed at LANL [47] for advanced materials investigations. These studies should permit an understanding of the potential role of copper alloys and other materials in extending breakdown towards the theoretical limit dictated by material stress. Further, the use of coatings such as graphene and silicon oxynitride [48] is now under study for mitigation of field emission. These efforts, while not critical to the vision of the UC-XFEL presented here, are directed towards large long-term projects such as compact linear colliders [44,49] and next generation full-scale XFELs such as MaRIE [27].

Alternative Approaches for High Brightness Beam Production
The push towards an ultra-compact XFEL using advanced accelerators has taken place predominantly in the context of plasma accelerators. Particularly, laser-plasma accelerators (LPAs) that can produce, by injection of electrons from the background plasma, a beam that is accelerated up to multi-GeV [50,51] energies in a few cm distance, are very attractive to apply in the XFEL context. Indeed, due to this fortuitous energy reach, LPAs have been vigorously examined as candidates for ultra-compact FELs [52]. Further, the beams produced by LPAs possess parameters that are competitive with certain classes of present day injectors. As such, much research has been focused recently on radiation production by LPA-produced beams, not only from FELs [53,54], but also including hard photon emission from Compton scattering sources [55], and from betatron radiation [56].
Progress, while notable, has been incremental in the field of LPA-based XFELs. As a concrete example of the level of beam quality presently achievable by LPAs, consider the parameters reported in Ref. [57], which explicitly cites the 6D brightness achieved. It is given, in the units of this current paper, by B 6D 1 × 10 15 A/(m-rad) 2 . This is a surprisingly small value, but one must keep in mind that, for similar charge, while the pulse length is notably shorter in the LPA, the beam emittance is an order of magnitude larger, and energy spread exceeds that of the photoinjector by two orders of magnitude. Thus one can see from the scaling given by Equation 14, that use of lower energy beams and/or short FEL wavelengths will be very challenging with such a source.
There are two possible paths forward that arise from current research trends. The first is that one may utilize beams that are stretched either transversely, using a transverse gradient undulator [58], or longitudinally through a chicane transformation [59], to mitigate the influence of energy spread on the gain of the FEL. These approaches produce modest advantages [60]. A more definitive solution is found in changing the approach to particle injection, to emphasize the creation of a much higher 6D-brightness beam. For example, one may employ the plasma photocathode (or "Trojan Horse") ionization scheme, to produce beams with much lower emittance, and improved energy spread [61]. Studies have shown [62] that the 6D brightness obtained from this scheme is at the level of B 6D 3.6×10 18 A/(m-rad) 2 . This value is superior to that found in the current case of a high field cryogenic photoinjector, and points to the critical role of the injection field; E 0 10 GV/m in this case, and very small source size. This promising approach to very high brightness beam production is in its experimental infancy, with beams near in quality to the LPA-based injectors achieved in first tests [63].
One may also examine the possibility of using a high brightness beam obtained from an RF photoinjector that is externally injected into a plasma accelerator. While this solution is not as compact as a plasma-based injection scheme, with an optimized approach to matching the beam transverse dynamics to the strong plasma focusing, the brightness needed for driving an FEL may be reached. This is one of the central goals of the EuPRAXIA project, which has reached the conceptual design phase [64].

Electron Beam Acceleration and Compression
The electron beam is foreseen to be accelerated in the high gradient linac from 153 MeV to full 1 GeV (soft x-ray, or SXR, FEL) or 1.6 GeV energy (hard x-ray, HXR, FEL) with two stages of compression taking the 20 A beams obtained at the photoinjector exit to I p = 4 kA. The first stage uses a standard chicane, albeit with a higher harmonic RF linearization scheme [65] operating in Ka-band [66]. The second stage employs inverse free-electron laser bunching, in a scheme known as ESASE [25]. We discuss the physics performance of each of these steps below. This discussion is guided by simulations of the beam performance using the beam dynamics code Elegant [67], using the beam produced by the photoinjector as input for the acceleration and compression stages.

Acceleration to the First Bunch Compressor
The first compression occurs at 400 MeV to balance the competing scaling of longitudinal space-charge and coherent synchrotron radiation (CSR). After the gun, the beam is accelerated in three linac sections up to 416 MeV then decelerated in a sixth harmonic 34.272 GHz RF cavity [68] to 400 MeV to mitigate the second-order variation in the beam longitudinal phase space due to RF and wakefield effects. In this way, one may cancel the effects of the second-order momentum compaction in the chicane. The sixth harmonic was chosen over a more conventional 11.424 GHz cavity due to RF voltage considerations; the required energy drop in the harmonic cavity scales with the inverse square of the harmonic number, resulting in a needed > 100 MeV energy loss using 11.424 GHz. In Table 2 Table 2. Parameters for the first linac section and linearizing cavity.

Dynamics in the Compressor
In the interest of maintaining a compact design, only 5.5 m of the beamline is allocated to the first compressor. Additionally, to preserve as well as possible the beam's 55 nm-rad emittance, we make use of two consecutive smaller chicanes arrayed such that the second chicane mitigates the CSR effects induced by the first chicane [69,70] . The relevant parameters for the two chicanes are reported in Table 3. The parameter is the momentum compaction, i.e. the final final longitudinal position ζ f to the initial fraction momentum deviation from nominal δp i /p 0 .
The projected normalized emittance grows to 80 nm-rad after the first chicane but is brought back down to the 65 nm-rad level by the end of the second. The projected emittance computed only for particles within the full-width at half-maximum of the current distribution is yet smaller, at n = 60 nm-rad, indicating only 5 nm-rad projected emittance growth in the region of interest. As expected, the vertical emittance is largely unaffected by the compressor. The slice emittance in both planes is nearly unchanged  Table 3. Parameters for the chicanes of the first bunch compressor.
by the first bunch compressor, with all growth resulting from misalignment of the x' centroids of the longitudinal slices of the beam. To conclude the description of the first compressor we plot in Figure 6 the longitudinal phase space, current, and energy spread profile of the beam immediately following the chicane. There is a ∼40 µm longitudinal region in which the current lies between 400 and 500 A. The energy spread in this region is approximately 12 keV; very little dilution of B 6D is observed.

Second Bunch Compressor
Immediately following the first bunch compressor a passive dechirping cavity [71] is employed to remove the remaining energy chirp from the beam. The longitudinal phase space following this dechirping cavity is shown in Figure 7.

Overview of IFEL Compression
In order to avoid deleterious collective effects while reaching a peak current of I p = 4 kA, as well as logistical issues, the second compressor does not employ an RF and chicane-based transformation. Instead, it utilizes IFEL compression, introduced by Zholents and also known as the method of enhanced self-amplified spontaneous emission (ESASE) [25]. The conventional compressor approach would specifically introduce several complications: first, the downstream linac would have to preserve an energy chirp on the beam which would require space after the compressor to remove. Further, the compressor would have to be quite large at the higher 1 GeV energy. With ESASE, 4 kA current can be achieved with only a mm-scale momentum compaction, and there is no need for a dechirper afterwards, as we demonstrate below. This small momentum compaction physically entails much less bending, and the attendant severe challenges in brightness preservation due to CSR are significantly reduced.
For an ESASE compressor scheme, one first modulates the electron beam energy as a function of time using an infrared laser, in our case. with wavelength of λ L = 10 µm, which co-propagates with the electron beam inside of a short planar undulator. Once this modulation is compressed in a chicane, the beam is micro-bunched into a train of current spikes, each of which lases independently of the others in the final undulator. We describe the process using a sequence of two transformations. Let p = (γ − γ 0 )/σ γ and θ = k L s where γ 0 is the mean beam energy, σ γ is the initial uncorrelated beam energy spread, and k L = 2π/λ L . Then the ESASE process is described by where A = ∆γ L /σ γ is the modulation amplitude normalized to the uncorrelated energy spread and B = R 56 k L σ γ /γ 0 is the normalized compression strength. The final longitudinal particle coordinates are then related to the initial coordinates by The resulting periodic current profile can be written [25,27,72] where J n is the nth-order Bessel function of the first kind. For our design a factor of ten compression is required in the center of the current spikes. With the compression occurring at the relatively low energy of 1 GeV (in the SXR FEL case), the beam is particularly susceptible to energy loss and subsequent slice emittance growth from CSR. To counteract this concern, we choose a large modulation amplitude: A = 100, which allows for a small compression strength B = 0.0097, corresponding to an R 56 = 1.29 mm in the final chicane. Similarly, we utilize only 10 cm length dipole magnets to minimize the amount of beam-radiation interaction in the bend magnets.

Dynamics in the Modulator and Second Linac
The electron beam must satisfy the resonance condition with the λ L = 10 µm laser inside of the modulator, where γ 0 is the average beam energy. The practicalities of dealing with the 1/γ 2 0 scaling, causes us to choose to energy-modulate immediately after the first compressor. Further, we note that in order to wavelength-tune an XFEL with a low-K u undulator, it is necessary to change the final beam energy. As we are employing a resonant interaction in the IFEL modulator, it is convenient to use a fixed energy after the first compressor. The parameters for the modulator are reported in Table 4, and the modulated phase space is plotted in Figure 8. We note that the momentum compaction in the modulator begins the development of the current spikes. The modulated beam is then accelerated on-crest through five one-meter linac sections to its final energy, in the current case of interest, of 1 GeV.

Dynamics in the Second Compressor Chicane
The second compressor chicane is extremely compact, occupying a length of only 2.6 meters. The chicane design is specified in Table 5, and an image of the longitudinal phase space after the chicane is shown in Figure 9. Although the ESASE method allows for smaller momentum compaction, CSR can still present a non-negligible problem, as discussed briefly in [24]. Due to the extremely short length scales present at relatively  low energy, the energy loss induced by CSR effects in the compressor chicane is nonnegligible. By shortening the magnet lengths, however, this loss may be diminished to the point where it does not disrupt the formation of the current spikes, incur notable slice emittance growth, or otherwise strongly impact XFEL performance. The structure of the five current spikes is explored further in Figure 10. We have taken a 1 µm window around each spike and plotted them directly next to each other showing the current profile, emittance, and energy spread inside of each spike. The spikes have a FWHM length of approximately 200 nm, which is ∼200 SXR wavelengths. As discussed below, it can be seen that the slice emittance has been well-preserved, remaining at the 70 nm level for most of the spikes. The relative energy spread obtained is just under 10 −3 , yielding the desired parameters for the UC-XFEL.

Micro-bunching Instability Considerations
Conventional XFELs are plagued by the so-called micro-bunching instability (MBI), whereby a very low energy spread beam from the photoinjector has induced energy modulations that are amplified by collective effects. Specifically, a combination of longitudinal space charge (LSC) forces during acceleration, CSR in the bunch compressors, and the added longitudinal rearrangements due to the momentum compaction of the compressor bends, act together to produce unstable growth of the energy modulations. The typical sequence of events is that, first, LSC forces coupled with beam shot noise lead to high-frequency modulation of the beam energy. This is followed by the initial bends in the compressor which convert this energy modulation into density modulation. The bends contribute further energy modulation due to enhanced CSR. This amplified density modulation drives an even stronger LSC-induced energy modulation in the next linac.
The gain resulting purely from LSC and geometric wakefields in a linac section followed by a chicane has been calculated in Ref. [73], where I 0 is the current of the beam in the linac, γ b is the energy of the beam at the chicane, I A ≈ 17 kA is the Alfvén current, k 0 is the wave-number of the bunching factor before compression, and here R 56 is the chicane momentum compaction. Further, σ δ is the relative energy spread at the entrance of the chicane, k f = Ck 0 is the final wave- number of the bunching factor with C the compression factor in the chicane, Z 0 is the free space impedance, and Z(k 0 ; s) is the system impedance, Here K 1 is the first-order modified Bessel function of the second kind, r b is the beam radius, and a is the average iris radius of the linac. This first-pass design for the UC-XFEL beamline does not display any indication that MBI will be a large problem, as evidenced by the results shown in the previous section. We do see evidence for MBI in Figure 9, however it is not strong enough to disrupt the bunching or cause appreciable emittance growth. This result can be understood using the expression for the gain given above. Although the photoinjector beam produces an exceedingly low energy spread, which leads to significant susceptibility to MBI if not increased with a laser heater, the very high accelerating gradients employed in the linac, combined with the relatively low final beam energy, yield a very short total linac length -between 8 and 13 m active length. This short interaction distance does not permit LSC energy modulation to develop to the same extent it can in other instruments such as the LCLS, which has a total linac length nearly two orders of magnitude larger than the UC-XFEL. The mitigation of MBI is yet further aided by the small momentum compaction associated with the IFEL-based bunch compressor. The near-elimination of MBI in a very high brightness beam-based XFEL is a key advantage of the UC-XFEL approach.

Short-period Undulators
We consider here two different beam energies and two different undulator designs for the SXR and HXR examples discussed. The SXR case operates near 10Å using a U e = 1 GeV electron beam and conservative undulator parameters: a B 0 = 1 T peak field with a λ u = 6.5 mm period. This is comparable to previously demonstrated hybrid Halbach undulators [74], which have measured a B 0 = 1.1 T peak field within a 2 mm gap for a 7 mm period undulator at room temperature, expected to increase to 1.33 T when cryogenically cooled to 30 K, e.g. [75]. This technology, based on Pr or Dy material, is by now well-diffused and mature [76,75,77]. The HXR case examines the generation of x-rays near 1.6Å using a U e = 1.6 GeV electron beam and a more ambitious undulator design; combining the concepts of cryogenically cooled, hybrid Halbach undulators with comb fabrication [78] to produce a 1 T peak field in a 3 mm period undulator. Below this period, the feasibility of the undulator faces challenges attendant with use of MEMS fabrication techniques [14,79]. A rendered schematic indicating a proposed Halbach geometry is shown in Figure 11. While these undulators have not yet been realized, they have been studied in detail, and at the periods under discussion, the challenges of fabrication and tuning should be met. Such undulators (Table 6) have notable systematic issues to address in implementation. The undulator parameter is naturally low, and while the loss is mitigated somewhat in the scaling of the coupling parameter θ max = K u /γ, the

Parameter
Units Soft x-ray Hard x-ray Undulator period, λ u mm 6.5 3.0 Peak undulator field, B 0 T 1.0 1.0 Undulator parameter, K u 0.60 0.28 Table 6. Summary of undulator specifications for soft and hard x-ray UC-XFEL simulations.
electron-radiation coupling can be impacted, particularly at very low K u . Further, short-period undulators are compact and have narrow gaps, which requires that the beam be well-focused during traversal of the undulator. Small focused spot sizes also will yield high beam density, potentially improving XFEL gain. Several innovative approaches enable the use of very strong (up to 3 kT/m gradient) focusing quadrupoles in micro electro-mechanical systems (MEMS) structures integrated with the undulator [80]. Recently, this work has concentrated on a modified Panofsky quadrupole geometry, which naturally may be placed inside the gap of the cryogenic undulator, and operated cryogenically to obtain up to 500 T/m gradient. A simulation of this device, which is currently under development at UCLA, is shown in Figure 12. Note the major simplifying modification of this miniaturized device is the lack of current layers on vertically oriented side walls. As will be seen through discussion of the FEL simulations, the optimized β-function needed for this system is in the range of 60-80 cm. For the 1 GeV beam in the SXR case, this can be accomplished by focusing with an intra-undulator 40 cm-period focusdefocus (FD) quadrupole lattice. The peak field gradient in this case is B =375 T/m, which is within the capability of the modified Panofsky quadrupole introduced above. One may also consider a VISA-style focusing schemes [81], with a pair of (opposing) vertically polarized permanent magnets placed inside the Halbach array, to arrive at a field gradient of B > 150 T/m. Lengthening the lattice period would enable focusing adequate to optimize the XFEL performance.
We note that for sub-cm λ u undulators the narrow, mm-scale gap (including possible focusing elements) produces an effect that can have large impact on the UC-XFEL: resistive wall wakefields. With the low energy scale of the instrument, energy loss due to these wakefields, which is enhanced by the nearness of the material boundaries, can be a serious issue. It is fortunate that the bunch-train format associated with the ESASE method serves to mitigate these wakefields, as discussed in the following section.

Resistive Wall Wakefields
Resistive wall wakefields are an important consideration for these high current beams in an undulator and, as such, have been investigated in some detail. Here we review the salient parts of resistive wall wakefield theory to show that the use of a micro-bunch train strongly mitigates the effects of these wakes. A recent article [82] discusses a regime of resistive wall wakes particularly relevant the UC-XFEL parameter space: a cryogenic, flat wall geometry with ultra-short beams. In instances where the mean free path of electrons in the resistive material, l, is not much larger than the classical skin depth, δ NSE , the anomalous skin effect (ASE) must be considered to calculate the wakes. The classical skin depth is defined as: where Z 0 is the free space impedance, and σ c is the conductivity of the material, and ω. At cryogenic temperatures σ c increases, and use of short beams extends the relevant range of ω: both of these serve to reduce δ NSE , causing the classical model to break down [83,84]. Using the Drude model where ω p is the plasma frequency and v f is the Fermi velocity, relating l and σ c . Finally, the effect on conductivity at cryogenic temperatures is encapsulated by the residual resistivity ratio, RRR, defined as: Copper is considered as the resistive material which has relevant constants [85]: n = 8.5 × 10 28 m −3 , v f = 1.2 × 10 6 m/s, ω p = 1.7 × 10 16 rad/s, and σ c (293 K) = 5.7 × 10 7 (Ω · m) −1 . The complex conjugate of the ASE surface impedance [83,84] is: with u defined as 1 + iωl/v f . The beam impedance of a resistive flat wall is given as [86]: where the wave-number, k = ω/c, and a is the half-gap between the two flat surfaces. The wake, w(ζ), at a position ζ behind the driving electron, is given by The spatial wakes converted from the beam impedances are given in Figure 13. By convolving the wake function with the beam profile, the wake induced relative energy variation η = ∆E/E is calculated at a point along the bunch ζ: where e is the electron charge, L is the length of the parallel plates, U e is the initial beam energy, and I(ζ) is the bunch's current profile. An example of the energy losses induced by the resistive wakefields is shown in Figure 14. A train of six gaussian micro-bunches with 10 µm interbunch spacing passes through the cryogenic (RRR = 100) copper flat wall structure with gap size of 2 mm and an overall length of one meter. Each micro-bunch has σ z = 424 nm, particle energy U e = 1 GeV, and a peak current of 4 kA. We compare this result to that obtained from examining a beam with the same total charge in a single, longer pulse, also with a peak current of 4 kA. It can be seen that the resistive wall wake amplitude is strongly suppressed by the use of a micro-bunch train instead of a single, fully compressed spike. This is because the wake is notably dissipated in the time between micro-bunches. This damping does not strongly assert itself, however, during the passage of the single, full charge bunch. For the micro-bunched case, as we will see in the following section, the energy spread induced by these wakes does not significantly impact the XFEL performance. Figure 14. The relative energy loss for micro-bunch train (solid) and a single bunch (dashed) as they transit a cryogenic (RRR = 100) copper flat wall structure with gap size of 2 mm and an overall length of one meter. Both beams have an energy of 1 GeV, total charge of 85 pC and peak current of 4 kA, but the train splits the charge over 6 micro-bunches with 10 µm inter-bunch spacing. The energy loss as a percent is in blue and the beam current is in red.

Soft X-ray FEL Performance
Two representative cases of the UC-XFEL are considered in detail using the 3D, timedependent FEL simulation code, GENESIS 1.3 [87]. The first is the SXR case, where the performance of the system is based on self-consistent simulations of the component parts of the XFEL system, i.e. the GPT and Elegant simulation suite output. The second is the HXR scenario, which requires some improvements in both the undulator and beam performance over those demonstrated either in simulation or in experiment, or both. We begin with the detailed discussion of the SXR case.
The beam and undulator parameters used in the XFEL simulations, as well as other performance characteristics, are summarized in Tables 6 and 7 for a single ESASE micro-bunch. In both cases, uncorrelated longitudinally gaussian beams were generated based on the moments expected from the accelerator and beamline simulations discussed above. Due to the large inter-bunch spacing (10 µm) relative to the slippage length (100's of nm), each micro-bunch can be treated as independent in the simulations. The final results presented in Table 7 and in Figure 15 are each based on 16 time dependent, SASE averaged GENESIS runs. The SXR case presented here is thus a result of a complete simulation of the subcomponents of the system.
The spatial characteristics of the beam critically include both its longitudinal and transverse properties. We have discussed the approach to transverse focusing above; this produces a beam with small spot size (< 5 µm), presenting challenges in measurement that may be overcome using novel optical methods [88,89] as well as coherent imaging [90]. The methods employed in coherent imaging used to reconstruct the spatial profile are borrowed from those used in x-ray science. In order to employ them in beam diagnosis, one should imprint coherence onto the emission process (coherent transition radiation in [90]). This is accomplished naturally in the UC-XFEL, through the tight micro-bunching imposed in the ESASE section. With each micro-bunch having rms length of 0.42 µm, transition radiation emission on harmonics of the ESASE laser frequency up to λ TR = 2πσ z 2.5 µm (4th harmonic of λ L for the SXR case) are coherently emitted. By observing the diffractive far-field intensity of the CTR at this wavelength, one may robustly reconstruct the beam spot profile.
For the longitudinal diagnostics, one may extend the range of existing RF deflectorbased methods [91] straightforwardly by using the same Ka-band (34.27 GHz) multi-MW source available for the longitudinal phase space linearizer to create a sweeping measurement that can reach femtosecond resolution. In addition, to see the details of the micro-bunches at a finer length scale, a hybrid IFEL/deflector-based approach termed attosweeper can be employed [92], Finally, we note that by direct observation of the form of the CTR spectrum over a range of wavelengths from ∼ λ L down to partially coherent harmonics, one may reconstruct the form of the micro-bunch train [93,94].
The value of ρ calculated from Equation 6 is derived from one-dimensional, idealized theory. We have optimized through simulation the various values of emittance, energy spread and focusing β-function. It is instructive to revisit the definitions introduced concerning this optimization procedure in light of the final scenario identified through simulation. We have, for the case discussed: η = 0.45, η γ = 0.31 η β = 0.35. These tuning parameters indicate the complex trade-offs that one must make when optimizing an FEL design. The value of the gain parameter which is instead deduced empirically from simulation or experiment through determination of the observed gain length L g,3D = (d(ln P )/dz) −1 , quantitatively takes into account all effects contributing to its value not included in the 1D theoretical value. This parameter is often termed ρ 3D , and it is compared to ρ in Table 7. These effects include energy spread, finite emittance, radiation and diffraction, and space-charge, as discussed in Refs. [ 1D 2. 2   Table 7. Summary of parameters and results for soft x-ray UC-XFEL simulations.
[33]; for completeness we note that in our simulation analysis the effects of slippage are also included. The value of ρ 3D , obtained through examination of simulation data shown in Figure 15 (via use of the relation L g,3D = λ u /4π √ 3ρ 3D ) is compared to the calculated ρ in Table 7. It is decreased by a factor of 2.2. Of the increase in gain length, approximately fifty percent is due to diffraction.
With all of these effects included, the overall performance of the SXR case for the UC-XFEL is quite robust, producing the desired few percent of energy obtainable from present km-scale instruments. The SXR FEL proceeds to saturation in a remarkable 4 m of undulator length, with three-dimensional gain length L g,3D also predicted well by the scaling laws given in Ref. [34]. It should be noted in this regard that the observed cooperation length determined by L c = λ r /4π √ 3ρ 3D is, at 33 nm, smaller than the rms electron micro-bunch length. It is known that if the micro-bunch length approaches 2πL c (and up to 4πL c ) in single-spike mode [95], that the output fluctuations of the FEL are stabilized above multi-mode long-pulse SASE [96], diminishing to ∼20 percent. The slippage inherent in the cooperation length also has a slight suppressing effect on the final SXR photon output and associated value of ρ 3D . This micro-bunch-derived effect is less important in a HXR FEL case, as discussed in the following section.
As we operate with a relatively low electron energy, U e , and high value of ρ 3D in this case, the efficiency of converting beam energy to photon energy is quite high, which is nearly identical to ρ 3D , as one might expect. The electron beam energy needed  Table 7. The shaded area corresponds to one standard deviation based on 16 SASE averaged runs.
to create one photon of 1.2 keV is, with this efficiency, 890 keV. By comparison, one needs over 7 MeV of energy in an LCLS-based scenario to create an equal-energy photon. In order to compare wall-plug power needs for the UC-XFEL with those of existing sources, one must specify the beam loading level utilized; however, in the linear collider study of Ref. [44], it is found that a highly efficient system based on cryogenic RF acceleration is possible. Thus one may see that the energetic cost of x-ray photons in the UC-XFEL may be notably smaller than in existing full-scale sources. The model used for evaluating the SXR case is also useful in exploring the wavelength tunability of this UC-XFEL system, As noted above, the energy of the beam at the undulator can be shifted by changing the acceleration downstream of the IFEL modulator, as well as the settings of the final chicane. The performance of the SXR over the relevant tuning range is shown in Figure 16. It can be seen that one may access wavelengths up to ∼4 nm before there is a significant loss of power. This power loss is driven in the example SXR scenario by diffraction and slippage effects.  Table 7. The electron energy range scales from the minimum constrained by the bunching process to the full, 1 GeV energy. With the exception of energy and matched spot size, parameters are otherwise held constant. Each instance shown gives the mean peak power and one standard deviation error bars from 16 SASE averaged GENESIS simulations.

Extending UC-XFEL to Hard X-ray Lasing
A detailed analysis of the SXR case was made possible by the fact that the sub-components needed have been identified through design and simulation work. Simulations of the injector have already produced the emittance and beam brightness needed for the case summarized in Table 8, at n = 50 nm. However, for hard x-ray lasing, some progress in downstream systems must be made. Critically, the emittance of the beam after compression must be improved; this implies a renewed emphasis on the performance of the compression system. Further, the undulator performance with λ u = 3 mm must be improved to reach the level needed for HXR lasing. This awaits further development of concepts such as the comb Halbach array.
Returning to the issue of optimized compression, with a radiation wavelength shorter by a factor of 6.5, the HXR case can utilize a beam with notably smaller microbunch length. As such, we examine a case where the ESASE laser system operates at λ L = 3.2 µm, thus lowering the micro-bunch charge (the peak current remaining at I p = 4 kA) and mitigating collective effects in compression as well as those due to the resistive wall wakes. We note that for the HXR case that the beam energy is also increased to 1. 10 −3 0.42 L g,3D /L g,1D 1.9 Table 8. Summary of parameters and results for hard x-ray UC-XFEL simulations.
The beam and undulator parameters used in this study are shown in Table 8, along with a summary of the results obtained from GENESIS. The simulation output is given graphically in Figure 17, which shows robust predicted performance for the case under study. The gain length is near 30 cm, with attendant saturation, at 8.3 GW (15 µJ/pulse train), obtained in less than 6 m. It can be seen that the slippage is well controlled despite the reduction of the micro-bunch length.
This study, as introduced above, does not yet correspond to a self-consistent parameter set obtained from simulation of all component parameters. Small improvements in the injector 6D brightness performance are needed, and these have already been obtained in simulation [20]. A path to the undulator design, utilizing the comb Halbach approach, is also outlined above, but has yet to be realized. The major advances needed to reach the performance outlined here are found in the compression system, with a particular challenge found in the first compressor. Design studies to mitigate emittance growth in the compressors is ongoing.  Table 8. The shaded area corresponds to one standard deviation based on 16 SASE averaged runs.

X-ray Optics
While the downstream x-ray optics of a XFEL might experience nonlinear effects due to the enormous peak power density, the dominant factor for damage is the peak energy density [21]. This concern drives many of the design considerations for the UC-XFEL x-ray optics. It is instructive to review some of the historical record as well as the current state-of-the-art in this area. The x-ray optic transport system for an XFEL faces some extra challenges with respect to those encountered in the field of synchrotron radiation. As the beam is almost fully coherent, as well as possessing a high energy density, two major problems have to be well controlled: wavefront preservation and surface damage. If one needs to further monochromatize the radiation, especially in the SXR spectral region, the beam stretching effect caused by a grating monochromator should be minimized to preserve a transform limited pulse. Non-ideal effects can be mitigated by designing a monochromator in which the dominant effect limiting the resolving power is the number of illuminated lines on the grating.
The main problem to confront in avoidance of deterioration of the x-ray beam quality is the degradation of the wavefront due to mirror imperfections. To quantify this effect, the Strehl ratio (SR) [97], is often used. The SR represents the ratio between the obtained or simulated peak intensity and what is available from a perfect optical system. It therefore may take on values between 0 and 1. The SR can be expressed as: Here φ is the λ r -dependent phase error introduced by the non-ideal optics on the wavefront. In the case of a grazing incidence mirror, with rms shape deviation from the desired profile δh and grazing angle-of-incidence θ, this phase error can be expressed as From the equations above, one can calculate the maximum tolerable shape error to achieve a given SR. For a general system with N separate optics this shape error is: One must next examine restrictions on the optics' shape errors. The Marchal criterion [98], is often used to assess the quality of an optical system. It states that an adequate optical system must possess SR ≥ 0.8, e.g. 80 percent of the available photons are actually focused within the ideal spot. This is a useful criterion if the optical system is employed to deliver light at a focus. Away from the focus, one needs a more rigorous criterion. It has been demonstrated, during the studies for the upgrade of LCLS, that a SR ≥ 0.97 is required to maintain the beam uniformity out of focus.
These concepts permit us to consider a possible scenario for the UC-XFEL. The limited available space for the optics, while posing a potential problem for optical damage, as described below, may be advantageous in limiting the effect of the shape errors on the wavefront. In fact, the low divergence of the beam and the vicinity of the mirrors to the source, allows the use of very shallow grazing incidence angle on relatively short mirrors. From the above discussion, it is evident that this permits relaxed requirements on the shape error needed to achieve a SR in excess of 0.97. As an example, a mirror located 5 m from the end of the undulators, mirrors having angles as shown in Table 10, require the rms shape errors shown for Strehl ratios of 0.97 and 0.8. The angles of incidence in this example are chosen to maintain the requirements for shape errors to an achievable value with the current state of the art mirror polishing capabilities, while keeping the x-ray flux below the damage threshold and avoiding excessive optical system lengths, as described below.
The mirrors envisioned for this optical system are pre-shaped plane elliptical mirrors mounted in the so-called Kirkpatrick-Baez configuration [99]. Each mirror focuses along its tangential direction and the two mirrors are installed one after the other at respective 90 degree angles. The mirrors are installed on a two-actuator bender to preserve the elliptical profile over various focal distances. For such short mirrors and these types of elliptical profiles, shape errors of 1 nm rms are achievable with state-of-the-art polishing. Further, bending mechanisms able to maintain this mirror quality have been designed at  Table 9.
Overview of x-ray optics design requirements. both the LCLS or ESRF. With 5 m focal length mirrors as described here, the expected beam profiles, both in and out of focus, are shown in Figure 18. The other major potential problem related to optical transport of ultra-intense and ultra-short-pulse x-ray sources is damage to the optical surface. All the energy absorbed by the mirror in the short time of a pulse length cannot be thermally dissipated. Therefore, the material on the surface should be able to dissipate the energy in the crystalline atomic structure, without breaking of bonds or reaching the instantaneous melting temperature. To address these concerns, the LCLS utilizes two optics hutches, indicated as A and B, at distances of 50 and 400 m downstream of the undulator [21]. The x-ray pulse carried 3 mJ of FEL fundamental radiation at 0.8 keV in the LCLS SXR configuration and 2.5 mJ of 8.3 keV photons in the corresponding HXR configuration, resulting in peak energy densities of 0.59 and 11.9 J/cm 2 in hutch A and 0.01 and 0.57 J/cm 2 in hutch B for SXR and HXR respectively. Comparing these values with the results obtained from GENESIS simulations, and summarized in Tables 7 and 8, the peak energy as a function of distance has been plotted for the UC-XFEL SXR and HXR cases, and compared with the values calculated for the LCLS case ( Figure 19). In each case, the energy of the full pulse train has been used since the inter-pulse timing is short compared to typical electronic thermalization times [100]. Also plotted are the energy densities for the four LCLS scenarios discussed above. The plot illustrates that both UC-XFEL cases drop to energy density levels below those in LCLS hutch A in less than 5 meters, facilitating the use of focusing optics and harmonic rejection on an unattenuated beam in a very compact footprint.  The energy density delivered to an optical surface is responsible for the potential damage of the optical element. Several completed and ongoing studies on damage have been performed. These results are not conclusive, in the sense not all the mechanisms involved in the deterioration of the optical properties are fully understood. However, for low repetition rate machines such as the UC-XFEL, a conservative approach is to consider 1 eV/atom as the damage threshold for most materials, with a a safe limit for operation being 0.1 eV/atom. Details on how to calculate the adsorbed dose can be found in the LCLS conceptual design report [21] and in [101]. For the present discussion, we have calculated the absorbed dose for some optics that may be envisioned to be used with the UC-XFEL. For simplicity, and to consider a conservative case, all the optics are located at 5 m downstream of the source. The optics considered are: the K-B focusing mirrors for the SXR range with two potential coatings: a harmonic rejection system Figure 19. Plot of the peak energy density of the fundamental radiation produced by the SXR and HXR UC-XFEL configurations as a function of distance downstream from the undulator. Also shown are the peak energy densities experienced by optics at the LCLS hutches A and B for their SXR and HXR configurations.
composed of 4 mirrors to reduce, by 6 orders of magnitude, the contamination of the third harmonic at 400 eV; a diffraction grating with blaze profile and blaze angle of 0.40; a K-B mirror system for hard x-ray; a Si(111) crystal monochromator; and a zone plate for HXR nano-focusing. Table 10, gives the values calculated using the maximum power per bunch of 0.114 mJ for the SXR at 1200 eV and 0.039 mJ at 7800 eV. One can immediately see that in almost all cases the optical components operate at safe levels. The only exception is the Au zone plate. This is because high-Z materials tend to absorb the radiation within a few nm of the surface, depositing all the energy within a few atomic layers. Tests carried out at the LCLS [102] have confirmed that Au-based zone plates do not survive the FEL radiation, while a diamond-based zone plate does. Fortunately, the technology for developing diamond zone plates has advanced notably and it is now possible to obtain small spots (near to 100 nm) without compromising flux or wavefront requirements. Diamond-based solutions operating in cryogenically cooled conditions are also favored for x-ray optics thanks to an exceptionally high thermal conductivity and a very small coefficient of thermal expansion for temperatures T ≤ 100 deg K [103,104]. Current work in these areas at UC-Merced is based on in-house developed heat transfer, dynamic diffraction and thermo-mechanical analysis codes that are now being integrated to form a complete tool for systematic photothermal-mechanical characterization and analysis of thermal loading effects on crystal optics.

Brief Survey of UC-XFEL Applications
We have introduced above a new design paradigm for an affordable x-ray free-electron laser that will make available coherent, ultra-fast sources to the broad scientific community in a ubiquitous fashion, similar to the way that optical lasers are currently employed routinely in laboratories. The dominance of present XFELs in single-shot HXR imaging is not in doubt; this is an important but relatively small subset of possible applications. However, as dictated by operational limitations, current XFELs tend to produce one-of-a-kind results in a short period of running on the scale of a few days. Relaxing these restrictions to make coherent x-ray sources widely distributed will give a new, open path to significant results in x-ray-based science and applications. This is particularly true in the SXR regime, where the demand for photon flux is lessened. The model we envision is that the UC-XFEL becomes a ubiquitous technology, with many such instruments available to the user community. We now proceed to give examples of the promise brought by the flexibility of use of the proposed instrument; these applications represent a small sample of those enabled by a UC-XFEL.

Physics Applications
The UC-XFEL has a unique temporal format that naturally permits attosecond-level synchronization of the x-ray pulses with the phase of an infrared laser. This opens new possibilities in experiments involving coherent x-rays and IR light as both pump and probe [105] well beyond the capabilities of high harmonic generation sources [28]. With such sub-cycle synchronization, one may be able to obtain dynamical information with unprecedented resolution, as recently demonstrated in the XLEAP experiment at SLAC [106], which was also a first test of the ESASE scheme for XFEL use. Further, the compactness of the XFEL and the high gain predicted from the presented UC-XFEL approach may enable a new frontier in recirculating FEL systems such as regenerative amplifiers. Such an x-ray FEL could produce very large fluxes of x-rays with highly monochromatic radiation in the ∼4 keV range, a spectral region ideal for performing pump-probe condensed matter investigations, including THz excitation [107] derived from the electron beam itself [108]. Systems and behaviors under study could include ferro-and anti-ferromagnetism, multi-ferroics, charge and spin density waves, high T c superconductors, and topological insulators. As the properties listed are sensitive to a wide variety of parameters (temperature, pressure, doping, external fields), comprehensive and time-intensive studies would represent a critical advantage in their success.
As a relevant example from condensed matter physics, soft x-rays can resonantly excite core electrons to valence levels in both oxygen and transition metals, which makes them an ideal probe to investigate, among other materials, transition metal oxides. Transition metal oxide materials continue to play an outsized role in condensed matter research as they exhibit high temperature superconductivity, multi-ferroicity, and colossal magneto-resistance among other high-impact phenomena. Because it is largely the valence electrons in these materials that are responsible for their behavior, resonant soft x-ray scattering has become a necessary tool to investigate ordering phenomena that are too subtle to be detected by other means. For example, soft x-rays have played a major role in identifying stripe and charge order in the copper-oxide superconductors and orbital order in magneto-resistive manganites [109].
The UC-XFEL may offer a next generation of experiments, where these orders can not only be detected, but manipulated with light. One of the major goals in this line of research is to disentangle the roles of different degrees of freedom in a strongly correlated system that give rise to several coexisting orders. In many of these compounds, it is not known whether orders coexist due to cooperation between the two (or more) orders or whether they are in competition. For instance, in copper-oxide superconductors, one can use an incident pump pulse to melt the sample and monitor the charge order response with soft x-rays to observe enhanced or diminished behavior, or changes in resonance frequency or wavelength. This would yield crucial information about proposed competition/cooperation scenarios. Furthermore, one can coherently drive a particular vibration or spin mode by tuning the incident energy of the pump laser pulse and use this excitation to coherently control the charge or orbital order. These kinds of experiments tend to be extremely challenging at present due to the large amount of experimental preparation needed during allocated beam time, a constraint mitigated by the UC-XFEL.
It should also be noted that through tuning the energy chirp of the electron beam through linac phase and tunable wakefield effects [110,111] before the IFEL modulator, that one may obtain a single attosecond pulse of x-rays from the UC-XFEL. A variant of this approach also utilizing beam self-fields for micro-bunching was shown in the XLEAP experiments at the LCLS recently [106]. This capability will be exploited in a wide variety of scientific applications. Indeed, as the micro-bunch current and charge in the UC-XFEL are foreseen to be similar to that shown in XLEAP, the obtainable pulse energy should be similar (∼10 µJ [106]). One may also produce two pulses in this manner, with x-rays obtained that enable nonlinear scenarios such as attosecond pumpattosecond probe experiments [112], with time scales shorter than the Auger recombination permitting the study of ultrafast phase transition dynamics. Finally, we note that flexibility in the ESASE modulating laser wavelength is desirable, as one may adjust the timing between x-ray pulses, and thus stroboscopically probe different periodic processes.
The UC-XFEL has a number of particular properties that can be exploited to push the frontiers of XFEL physics per se. In the SXR spectral region, each micro-bunch in the electron beam train may reach single spike lasing, and will thus display a high level of first order coherence. Further, the train could be used to increase the coherence even at higher orders [113] (e.g. fluctuation suppression in second order) by coupling the emission of the different micro-bunches. This may be realised by splitting the amplifier into sections and inserting at the end of each section, a long-period undulator segment being resonant at a wavelength comparable to the micro-bunch separation. The light from previous micro-bunches seeds the following, a process which may be repeated until the final spike is seeded in all the amplifier sections. The second-order coherence should be greatly improved by this coupling, as shown recently in a seeded XFEL [114].
A new frontier in the HXR regime has been recently observed in the stimulated emission of x-rays in Mn-based systems pumped by XFEL pulses [115]. This mechanism has produced very narrow line widths starting from an initial population inversion on a 6.6 keV transition. Recently, it has been proposed to utilize this effect in creating an x-ray laser oscillator [116]. Such an experimental program, given its multiple layers of complexity, would be an excellent candidate for development at an HXR UC-XFEL, where iterative experimentation is permitted.
Finally, we note that as a complex large instrument, the XFEL has required significant human resources to operate and optimize in use. Recent trends in machine learning have had a notable, positive impact on the needs for expert operators [117,118]. The UC-XFEL may serve as a platform form exploring advanced methods in machine learning for free-electron laser [119] and associated acceleration and beam transport systems [120]. Conversely, the refinement of such methods should permit much smaller teams of expert personnel to operate the UC-XFEL.

Chemistry
The introduction of such an operational mode in the soft x-ray spectral region may open the way to exploratory investigations of the basic underpinnings of chemistry. With liberal access to a soft x-ray FEL, allowing exploitation of absorption edges in oxygen and nitrogen, experiments may be performed that drive theoretical and simulation efforts for comprehensive understanding of the electron dynamics involved in chemical reaction [121], relying on the ultra-short x-ray pulse duration to create "molecular movies". Resolving the dynamics of charge transfer processes illuminates the making and breaking of chemical bonds and, by tuning the x-ray energy to be resonant with the target atom, molecular dynamics can be revealed [122,123]. This element-targeted approach can even be used to probe the spin dynamics of excited states [124]. Such techniques are useful in the study of systems relevant to solar cells, batteries, and photocatalysts [125]. The unique pump-probe synchronization characteristics of a UC-XFEL may be used to directly observe photoexcited electronic states, as recently demonstrated with XFEL-derived soft x-rays for both x-ray absorption spectroscopy and resonant inelastic scattering methods [126].

Biology
The possibilities associated with an on-campus coherent hard x-rays with high availability likewise promise high impact in biological and biomedical research [127], as evidenced by the work of the UCLA DOE Imaging Institute [128], which was an early adopter of the XFEL in biology. In addition, the availability of highly increased access would permit the promising start to coherent imaging of cell structures in bacterial [129] and cancer studies begun at the LCLS to proceed to a mature level of success that has not been possible with the current generation of XFELs. The "diffractionbefore-destruction" method leverages the enormous peak power of the XFEL pulses to extract a useful diffraction pattern before the sample is destroyed by the deposited energy. The speed with which this occurs allows samples to be studied in more natural conditions, e.g. not requiring cryo-cooling. A further application of the UC-XFEL is to crystallography of "nanocrystals", comprised of only a few unit cells. This technique was demonstrated by [130] using nanocrystals as small as 200 nm, even facilitating in vivo crystallography of naturally occurring nanocrystals within their originating cells [131]. This is also a particular advantage for many medically relevant structures which are difficult to crystallize; obviating the need for large crystals opens the door to structuredriven drug design [132,133]. Also, as with the chemistry application, "molecular movies" of biological systems can also elucidate their operation [134].

Ultrafast Imaging
As a further example, from the hard x-ray regime, one may envision introducing entirely new techniques in coherent diffraction imaging (CDI) [135], but these must be developed through dedicated, time-intensive experiments. Realization of these initiatives are not possible without lengthy delays with the limited beamtime now available at XFELs. As a current example, we can point to x-ray ptychography, which enables diffractive imaging of extended samples by raster-scanning across the illuminating x-ray beam, permitting more general application of CDI techniques. As this is a time-intensive technique, a migration towards table-top sources such as HHG has recently been noted [136,137,138,139]. The availability of a UC-XFEL source would give essential advantages in the time needed for employing this technique in scientific applications.
Another application of UC-XFEL is based on its emerging ability to produce attosecond x-ray pulses, as recently experimentally demonstrated [140]. Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules and solids [141,142,143]. However, to date, almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically broad spectra due to the uncertainty principle, and are incompatible with conventional imaging systems. Recently, a novel CDI method has been proposed to overcome this major obstacle [144]. Using simulated attosecond pulses, it has demonstrated that the spectrum, probes and spectral images of extended objects can be simultaneously reconstructed from a set of ptychographic diffraction patterns. This method was recently experimentally validated by successful reconstruction of the spectrum, 17 probes and 17 spectral images using a broad spectrum optical source [144]. The combination of this powerful method with the UC-XFEL may significantly reduce the data acquisition time for spectro-imaging experiments by harnessing the considerable x-ray flux available. Potentially enabled applications range from visualizing attosecond electron dynamics to imaging materials and biological samples at the nanometer scale.

Industrial Applications
One may also consider advanced industrial uses for the UC-XFEL. In applications of x-rays to modern nano-electronic devices, the objects being imaged have reached the point where it is no longer possible to image entire devices with their intricated interconnections non-destructively. This is due to the small feature sizes and the complex three-dimensional structures present on a chip. This unmet need in metrology represents a serious problem for device production and quality control. It has been recently demonstrated, however, that with a coherent source one may employ x-ray ptychography to create three-dimensional images of integrated circuits with a lateral resolution in all directions as low as 14.6 nm [145]. This method relies on x-ray fluxes that are notably smaller than the maximum available at existing XFELS, and thus the availability and lower intensity of the UC-XFEL would represent a significant step forward in widespread adoption of this technique. This application would advance the state-of-the-art in chip inspection and also permit reverse engineering and inspection, opening the door to use in device security.

Conclusions and Future Directions
The principles behind an ultra-compact XFEL have been presented here, as well as the details of how these principles are manifested in the beam and radiation physics involved, and the advanced technologies and methods -such as machine learningemployed. With the vision of realizing this potentially paradigm shifting instrument stated, it is useful to discuss the near-future research directions that are needed to permit progress towards the goal of the UC-XFEL. It is important to note that this research impacts not only the outlook for the UC-XFEL, but also the future plans for more traditional free-electron lasers. We review these research areas by subject, as with the preceding discussions.
As noted, the production of very high brightness electron beams is the linchpin of the UC-XFEL recipe presented. The development of the critical component, that of the cryogenic RF photoinjector, is presently underway at UCLA, in an effort undertaken by a UCLA-SLAC-INFN-LANL collaboration with wide-ranging interests in high gradient acceleration [44]. This experimental effort is aimed primarily at demonstrating the operation of the C-band cryogenic photoinjector discussed above, operated at 27 deg K, and testing the production and diagnosis (particularly the measurement of very low emittances [146]) of high brightness beams. This program has many relevant technical challenges such as the integration of a cryogenic solenoid. Further, issues such as dark current emission and control using coatings and active sweeping are being examined experimentally. Cryogenic cathode operation, using a dedicated 0.5 cell source with cathode load-lock, is being investigated in the context of this program. As noted previously, this new approach to photoinjectors can enhance the outlook for linear collider sources, and may also be utilized for larger scale XFELs, for wakefield acceleration experiments, and for next generation relativistic electron microscopy and diffraction instruments [20,147]. The development of this generation of sources is of strong interest to the NSF Science and Technology Center known as the Center for Bright Beams.
The experimental development of linear accelerator structures is proceeding at SLAC, with notable experimental activity performed in parallel at LANL and UCLA. This work is presently concentrated on cryogenic operation at 77 K. The linac structures constructed for current experiments employ novel brazeless joining techniques. Efforts are underway in support of the development of the independent manifold coupling and, importantly, to implement transverse higher order mode damping in the linac cells. This initiative is aimed at three applications that utilize multiple bunches per RF pulse: the linear collider; a MaRIE-class XFEL [148]; and a high averarge flux inverse Compton scattering (ICS) source. Transverse damping in these cases is needed to avoid multi-bunch BBU. Once developed, a BBU-stabilized linac may also be applied the UC-XFEL, potentially enabling kHz average repetition rate, thus giving over 10 13 HXR photons/second, enabling many high average flux applications. The advantages conferred on these applications include a much diminished spatial footprint, and associated mitigation of instabilities such as MBI and also BBU.
Along with beam production and acceleration, advanced work on pulse compression is now being performed. The immediate challenge in this work is to further optimize the performance of the first UC-XFEL compressor, to bring down the emittance to near the 50 nm-rad level. These investigations entail a more detailed understanding, using advanced computational models, of shielding to mitigate CSR effects. This is accompanied by a renewed emphasis on the ESASE analysis of the second compressor, where by taking into account finite-laser spot size effects, one may increase the brightness of the electron beam micro-bunches, at a cost of some efficiency in the bunching process. Advanced work on the ESASE technique is being applied to exploratory research on MaRIE-class XFELs; the current work here also has potential impact on XLEAP-like scenarios for existing XFELs [106]. Finally, we note that optically bunched high-peakcurrent beams may be effectively used to excite TV/m-amplitude wakefield acceleration waves in plasma [149].
The development of cryogenic, sub-cm-to-cm period undulators has continued in recent years, with notable progress reported at a number of laboratories [75,150,151]. This technology is by now mature enough to be applied in a UC-XFEL. Other standard approaches to undulator development may include superconducting undulators, where designs with periods nearing those needed have been studied [152]. At few-mm period length, development work on novel variations on short period Halbach arrays is being pursued [59]. At the mm-to-sub-mm scale, there has been progress reported on mesoscale machined undulators [153,79]; designs so far do not reach the peak fields needed, and the innovations introduced at the few mm-period may be necessary in this scaled down device. MEMS fabricated systems applied to the UC-XFEL now concentrate mainly on microquadruple development, with microundulators less emphasized, due to their impracticality in scaling to mesoscale. Successful development of shorter period undulators may extend the wavelength reach of XFELs. Finally, we note that for many applications, a helically-polarized, very short-period undulator would be advantageous. Research efforts into this option are in their early stages [154].
The performance of the XFEL remains the subject of further refinement and optimization. The parameter sets employed here were driven by the current availability of beam sources, compression schemes, instability theory, and advanced undulators. As these evolve, the UC-XFEL will also be re-evaluated. This evolution is ongoing in the present development of the HXR case, where emphasis is being placed on studies of the compressor systems. It is also desirable to examine in further detail both space-charge [155] and quantum mechanical [156] effects on XFEL performance, as well as two-color schemes. In addition to single operating point optimizations, one must explore further the reproducibility and wavelength tunability of the UC-XFEL. The applications of xray pulse trains and the FEL physics associated with this format, concentrating on the production of low-fluctuation, single-spike-per-micro-bunch operation, are of interest. Further, the suitability of the x-ray pulse trains in pump-probe experiments [112] must be investigated. These issues are central to UC-XFEL development, as well as systems with shared emphasis on this format (MaRIE, XLEAP).
The problems of designing appropriately compact x-ray optical systems at relevant SXR and HXR wavelengths are under study by the current collaboration, with work ongoing at UC-Merced and UC-Berkeley as well as connected institutions. This activity is performed in tandem with LCLS-II-directed research and development, and thus is synergistic with current efforts on large-scale XFELs. Based on the model of the UC-XFEL photon output in both soft and hard x-ray cases, this effort seeks to confront the design challenge of creating an x-ray optics system to deliver the photons to experimental users that is commensurately as compact as the UC-XFEL. With the photon flux per pulse, and repetition rate (up to 120 Hz) of the UC-XFEL may have problems in thermal loading similar to those of existing XFELs, due to absorption of x-rays on crystal optics [157]. There are issues that are specific to the UC-XFEL as well. These include the effects of the pulse-train format on x-ray optics, which also are of concern for two-pulse x-ray pump-probe experiments.
Investigations of applications of the UC-XFEL in advanced scientific, medical and industrial applications are still in the early phase of development. The survey of such applications given above illustrates the central theme of these investigations well -to identify uses of the UC-XFEL that would benefit from a much more liberal availability of the instrument, or by the unique aspects of the UC-XFEL, or both. These motivations are also present in other projects, such as EuPRAXIA, or by the emerging proposed x-ray sources, based on super-radiant emission from nano-bunching of low charge, low energy beams, at Arizona State University [158]. The ASU initiative involves a series of workshops [159] on the use of the source. Despite notable differences in approach, these discussions aid the maturation of the science program outlined here.
The initiative described in this article is now beginning its path to realization.
The beam, FEL physics, accelerator and x-ray experimental technology development efforts are centered at UCLA, with research efforts taking place at the SAMURAI Laboratory. The suite of initiatives reviewed in the above discussion, encompassing high brightness electron beam production and measurements, high gradient acceleration, beam compression (particularly emphasizing ESASE and coherent radiation-based beam diagnosis), and initial FEL and ICS radiation production are to take place in a large (18 m length) bunker that is now nearing completion. SAMURAI has the radio-frequency, laser, vacuum, and ultra-fast experimental measurement infrastructure for proceeding to the next steps in making the vision of the UC-XFEL a reality. The first UC-XFEL, upon realization, is envisioned to serve as a template for the diffusion of such instruments to many universities, industrial laboratories, and medical research facilities.