Pub 00028

PBPL Publications: 2009-00028

PUBLICATION NOVEL RADIO-FREQUENCY GUN STRUCTURES FOR ULTRAFAST RELATIVISTIC ELECTRON DIFFRACTION P. Musumeci, L. Faillace, A. Fukasawa, J.T. Moody, B. O’Shea, J.B. Rosenzweig, C.M. Scoby Abstract Radio-frequency (RF) photoinjector-based relativistic ultrafast electron diffraction (UED) is a promising new technique that has the potential to probe structural changes at the atomic scale with sub-100 fs temporal resolution in a single shot. We analyze the limitations on the temporal and spatial resolution of this technique considering the operating parameters of a standard 1.6 cell RF gun (which is the RF photoinjector used for the first experimental tests of relativistic UED at Stanford Linear Accelerator Center; University of California, Los Angeles; Brookhaven National Laboratory), and study the possibility of employing novel RF structures to circumvent some of these limits.

Microscopy Microanalysis

Microsc. Microanal. 15, 290–297, 2009 doi:10.1017/S1431927609090412

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© MICROSCOPY SOCIETY OF AMERICA 2009

Novel Radio-Frequency Gun Structures for Ultrafast Relativistic Electron Diffraction P. Musumeci,* L. Faillace, A. Fukasawa, J.T. Moody, B. O’Shea, J.B. Rosenzweig, and C.M. Scoby University of California, Los Angeles, Department of Physics and Astronomy, 475 Portola Plaza, Los Angeles, CA 90095-1547

Abstract: Radio-frequency ~RF! photoinjector-based relativistic ultrafast electron diffraction ~UED! is a promising new technique that has the potential to probe structural changes at the atomic scale with sub-100 fs temporal resolution in a single shot. We analyze the limitations on the temporal and spatial resolution of this technique considering the operating parameters of a standard 1.6 cell RF gun ~which is the RF photoinjector used for the first experimental tests of relativistic UED at Stanford Linear Accelerator Center; University of California, Los Angeles; Brookhaven National Laboratory!, and study the possibility of employing novel RF structures to circumvent some of these limits. Key words: ultrafast, RF photoinjectors, relativistic electron diffraction, electron sources

I NTR ODUCTION Ultrafast electron diffraction ~UED! investigates ultrafast structural changes at atomic scale with sub-ps temporal resolution ~Dwyer et al., 2006; Zewail, 2006! by recording the change in the characteristics of electron diffraction peaks ~position, intensity, width! when varying the time delay between an excitation pulse ~typically a sub-50 fs infrared laser pulse! and a probing electron bunch. A large number of important results ~Dudek & Weber, 2001; Ihee et al., 2001; Siwick et al., 2003; Ruan et al., 2004; Nie et al., 2006; Gedik et al., 2007! have already been obtained by UED, which has the key advantage with respect to X-ray diffraction of a much larger interaction cross section, making it an ideal technique to study thin crystals and gas phase samples. The temporal resolution of the technique depends on the length of the pump and probe pulses, and on the synchronization of their time-of-arrival on the sample. The latter can vary either shot-to-shot ~timing jitter! or in a systematic way ~velocity mismatch!. A tilted laser pulse front scheme has been successfully employed in reflection mode diffraction to eliminate the velocity mismatch ~Baum et al., 2007!. Very fast excitations are provided using ultrashort laser pulses, and the length of the pump pulse has typically the smallest contribution on the final time resolution. The problems relative to the time jitter and velocity mismatch in transmission mode should not be underestimated, but they go beyond the subject of this article. UnReceived December 17, 2008; accepted March 30, 2009 *Corresponding author. E-mail: [email protected]

doubtedly the limiting effect in time resolution so far has been the duration of the probing electron pulses. The difficulties of creating very short electron bunches are due to the strong space-charge forces that lengthen charged particle bunches during propagation. In recent years, due to a better understanding and an improved control of the propagation dynamics in the nonrelativistic electron guns used for UED experiments, the temporal resolution of this technique has improved to the sub-ps level ~Siwick et al., 2002; Reed, 2006!. This has been accomplished by placing the sample in close proximity of the electron source to minimize the propagation distance and by decreasing the number of particles in the beam to avoid excessive bunch lengthening due to space-charge forces. For reversible processes, the space-charge pulse broadening, in principle, can be completely eliminated as shown in Lobastov et al. ~2005! using single electron pulses to obtain images and diffraction patterns with temporal resolution limited only by the duration of the laser pulse used to generate the electrons. More advanced methods to compensate for the bunch lengthening, involving the use of a properly phased radio-frequency ~RF! cavity ~Van Oudheudsen et al., 2007! or even a magnetic compressor, have been proposed, but yet lack experimental validation. In the quest for sub-100 fs temporal resolution, a drastically different approach is constituted by the use of relativistic electrons. At relativistic energies the space-charge forces that cause the beam debunching are strongly suppressed. A much larger number of particles ~10 7 –10 8 ! can be packed in a single ;100 fs long bunch, allowing single shot diffraction patterns and enabling the study of irreversible ultrafast processes that are currently out of the reach of present UED machines.

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For this reason, the application of the brightest source of relativistic electrons available to date—the RF photoinjector—as a possible electron source for UED has recently stirred a lot of interest, bringing together the efforts of both the accelerator and microscopy/electron diffraction communities ~Wang et al., 2003, 2006; King et al., 2005!. RF photoinjectors have definitely been a fundamental technological breakthrough in the last 20 years as relativistic electron sources and are in fact the preferred electron source for advanced accelerator and free electron laser ~FEL! applications ~ICFA, 2008!. Taking advantage of accelerating gradients—that can be larger than 100 MV/m—these devices accelerate the photo-emitted electrons to relativistic energies in few cms of propagation distance. In other words, the beam exits very quickly the region close to the cathode where most of the bunch lengthening happens. Outside the gun, as the bunch is much longer in its own rest frame due to relativistic dilation, the space-charge forces are greatly suppressed. First experimental tests of RF photoinjector-based electron diffraction at Stanford Linear Accelerator Center ~SLAC! and the University of California, Los Angeles ~UCLA! have been successful ~Hastings et al., 2006; Musumeci et al., 2008b! and a temporally-resolved study obtained with relativistic electrons is soon expected. In the first section of this article, we review the limitations due to the relativistic energy of the electrons and the RF photoinjector source. We will first establish the beam parameters required to obtain a high quality diffraction pattern and then show how a beam satisfying these parameters can be generated with a 1.6 cell RF gun. This is the most common kind of RF photoinjector, and the one employed in all the preliminary relativistic electron diffraction experiments at SLAC, UCLA and also for the proposed Brookhaven National Laboratory beamline. It will be apparent though that using the current RF photoinjector design is necessary to find a compromise between spatial and temporal resolution. In the second section of this article, we analyze possible solutions to this problem in the form of two new RF gun structures. These structures are being developed for THz generation and FEL applications, but could very well offer a solution to the problems of relativistic UED as they aim at the generation of shorter, higher brightness electron beams.

L IMITATIONS OF C URR ENT RF P HOTOINJECTOR UED S ETUPS It has been recently demonstrated that RF photoinjector can generate sub-100 fs beams with more than 10 7 particles per bunch suitable for electron diffraction. Many of the concerns related to using a relativistic electron source like an RF photoinjector for UED arise when considering the spatial quality of the patterns. The De Broglie wavelength

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associated with the beam ~l ⫽ h/p, where h is the Planck constant and p is the beam momentum! is 0.3 pm for 4 MeV beam. For a typical interatomic distance d ⫽ 2 Å, the Bragg scattering angle is ub ⫽ 1.6 mrad. In comparison, for a 30 keV beam, l ⫽ 7 pm and ub ⫽ 35 mrad. To be able to distinguish the scattered particles from the undiffracted beam core, ub has to be much larger than the intrinsic root-mean-square ~rms! spread in beam divergence angles su , i.e., su ⬍ ub ⫽ l/d. An equivalent way of formulating the problem is by introducing the concept of the transverse coherence length. Transverse coherence length is defined as L c ⫽ l/2psu and it has to be compared with the structure interplanar distance d. If the beam is not coherent over few unit cells of the observed structure ~i.e., L c ⬎ d !, then no constructive interference can be obtained and the visibility of the diffraction peaks is strongly reduced ~Born & Wolf, 1975!. We can quantify these statements calculating the resolving power of the diffraction camera ~Grivet, 1965!. This quantity can be defined as R ⫽ R/DR, where R is the radius of the diffraction rings on the detector screen and DR is the smallest distance between two neighboring rings that can be barely discriminated. A typical electron microscope diffraction camera for static images has R ⫽ 10 3 or more. For UED, a resolving power of R . 10 guarantees a good quality diffraction pattern and provides enough spatial resolution to adequately resolve typical ultrafast structural rearrangement. The limiting distance between two rings that can just be separated is DR ; 2sx , where sx is the radius of the undiffracted beam size at the detector. There are many contributions to the ring thicknesses ~beam optics, beam energy spread, sample thickness!, but let us consider first the one arising from the beam emittance. The diffraction camera electron optics is set to image the angular distribution of the beam onto the detector screen. That can be expressed requiring that the matrix element M0,0 of the optical transport line between the diffraction and the detector screen be equal to 0. In this case the beam spot at the detector will be equal to sx ⫽ M0,1 su . At the same time, the radius of the diffraction ring is R ⫽ lM0,1 /d, and hence R ⫽ R/2sx ⫽ l/~2dsu !. Note that even though the De Broglie wavelength of 4 MeV electrons is more than 20 times shorter than the one for nonrelativistic particles, the coherence length and therefore the resolving power of the diffraction camera depend only on the normalized emittance of the source and are in fact independent of the beam momentum. This is because both the beam rms angle spread and the scattering angle scale inversely with the beam momentum, holding «n and sx constant. In symbols, since su ⫽ «n /bgsx , we have R ⫽ ~h/2m 0 cd !~sx /«n ! ~Van Oudheudsen et al., 2007!. To keep R . 10 with a wavelength l ⫽ 0.3 pm and d ⫽ 2 Å, it is necessary to have at the target su , 80 mrad. For relativistic electron diffraction, the limiting effect to the diffraction camera resolving power is the intrinsic spread in beam angles due to the beam emittance. To make

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a comparison, the contribution from the rms beam energy spread Dg/g—typically smaller than 1%—would give R ⫽ R/DR ⫽ g/Dg . 100. This small spread in divergence angle has to be obtained in conjunction with the requirements on the transverse beam size. For a time-resolved study, one wants to focus down the pump laser to excite a fast response in the diffraction target using a typical fluence ~energy per unit area! on the order of hundreds of mJ/cm 2 ~Siwick et al., 2003!. With a 1 mJ energy per pulse available on the pump arm of the setup, the largest sample area that can be uniformly excited is ;1 mm 2. Finally, the beam charge is set by the requirement of having enough scattered electrons to be able to detect the Bragg peaks. The milestone results on Al melting have been obtained using 150 shots of 6,000 electrons each, that is, a total of 1 million electrons per image. In the relativistic case, the detectors have not been fully developed yet to yield single-electron detection, and some improvements should be expected from further research in this direction. Nevertheless, that limit is not very far and as an example at the UCLA Pegasus Laboratory diffraction images with ,5 ⫻ 10 6 electrons have been recorded ~Musumeci et al., 2008b, 2009!. Assuming then 5 ⫻ 10 6 electron in an rms bunch length of 100 fs, an angular divergence of 0.08 mrad, and an rms beam size of 0.4 mm at 4 MeV energy, the source has to be able to generate a beam with normalized brightness of B ⫽ 2I/«n2 ⫽ 1 ⫻ 10 14 A/m 2, which is at the limit of what state-of-the-art RF photoinjectors can produce. To give a sense for the order of magnitude of state-of-the-art beam brightness, the RF photoinjector source for the Linac Coherent Light Source X-ray FEL reportedly generated beams of 20 pC, 0.13 mm-mrad emittance and 5 ps bunch length with brightness ;4.5 ⫻ 10 14 A/m 2 ~Akre et al., 2008!. Theoretically, the maximum brightness in RF photoinjector is limited by the photocathode temperature and the so-called “thermal” or intrinisic emittance. When the electrons are emitted from the photocathode, they have an angular spread due to the excess kinetic energy Ek arising from the difference between the energy of the driver laser photon energy and the cathode work function. The thermal emittance is proportional to this angular spread and to the rms laser spot size slaser . In other words, any photogenerated beam has an initial normalized rms emittance given by «n ⬵ slaser ~Ek /mc 2 !1/2. Because of the Liouville theorem, an optimum accelerator design can only preserve the cathode emittance avoiding its growth. This is far from being straightforward to achieve and requires fully linear transport and space-charge forces. A recent development in high brightness beam research is the demonstration of the feasibility of a scheme to create an ideal uniformly filled ellipsoidal beam based on a space-charge driven rearrangement of the beam distribution from an initial pancake shape ~blowout regime in RF photoinjector! ~Luiten et al., 2004; Musumeci et al.,

2008a!. Such distribution is characterized by space-charge forces fully linear in the coordinate offsets and by transverse emittances at the intrinsic “thermal” level. As discussed in Musumeci et al. ~2008a! in order for the scheme to properly work, avoiding the degradation effects due the image charge at the cathode, it is necessary that the initial charge density generates a longitudinal electric field smaller 2 than 10% of the accelerating field ~i.e., Q/2pslaser ⱕ 0.1«0 E0 !. In a one-dimensional ~1D! model, which assumes that the beam remains a pancake in its rest frame during propagation, the final bunch length can be analytically calculated and it is equal to t ⫽ mcs/«0 eE02 ~Luiten et al., 2004!. Putting everything together, we have for the beam brightness B ⫽ 2I/«n2 ⬵ 4p«0 ecE02 /Ek depending only on the cathode temperature and the accelerating electric field. For a copper cathode illuminated by a 266 nm ultraviolet laser pulse ~~Ek /mc 2 !1/2 ; 0.8 mrad! in a 100 MV/m field the calculated value for B is 1 ⫻ 10 15 A/m 2. The assumptions of the 1D calculation, in fact, are not valid as the beam quickly reaches a point in its evolution where its rest frame longitudinal size becomes comparable with the transverse dimensions. At this point the spacecharge driven expansion ceases to be only longitudinal and the model assumptions break. The results from threedimensional simulations with Astra ~Flottman, 2000! are reported in Figure 1, where the evolution of the beam parameters for the first 1.5 m of propagation is shown. The beam charge in the simulation is 3 pC and the rms laser spot on the cathode is 100 mm. At a distance z ⫽ 1.0 m from the cathode, the beam rms size is 600 mm, the rms divergence is 25 mrad ~beam emittance 0.12 mm-mrad!, and the rms bunch length is 240 fs. The beam brightness is B ⫽ 1 ⫻ 10 15 A/m 2, and in fact such a beam would be perfectly suitable for ultrafast electron diffraction. To improve the temporal resolution, the length of the beam could be reduced, for example, by increasing the laser spot size at the cathode, but only at the expenses of beam emittance and hence spatial resolution. In Figure 2 we report the simulation results where we changed the initial rms laser spot size on the cathode to 600 mm. The beam at the target is now more than a factor of 2 shorter, but the rms beam size and spread in divergence angles have increased to 1 mm and 65 mrad, respectively, resulting in a decreased quality of the diffraction patterns.

N EW D IR ECTIONS

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R ELATIVISTIC UED

It is important to remember at this point that the standard 1.6 cell gun was not designed as an optimized source for relativistic UED. The main problem with the existing RF gun design is that to maintain a short beam, one is required to keep under control the longitudinal space-charge field and so make the laser larger at the cathode at the expense of transverse beam quality. The 1.6 cell gun beam

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Figure 1. Simulation results from Astra using a 100 mm laser spot size and 3 pC beam charge in a standard 1.6 cell gun operated at 100 MV/m accelerating gradient. The laser pulse length on the cathode is 50 fs rms.

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Figure 2. Simulation results from Astra using a 600 mm laser spot size and 3 pC beam charge in a standard 1.6 cell gun operated at 100 MV/m accelerating gradient. The laser pulse length on the cathode is 50 fs rms.

Figure 3. ~a! Guncher stucture HFSS model and ~b! on-axis electric field profile.

dynamics is such that, as the beam goes out of the gun, it always has a positive energy chirp that tends to elongate it in the propagation drift at the gun exit. A significant improvement could come from a different RF design that would incorporate some longitudinal bunching in the beam dynamics. Other groups have proposed different methods to compensate for the bunch lengthening suggesting the use of an external properly phased RF cavity, or even of a magnetic compressor. These approaches are all in the direction of reversing the energy chirp ~or its effect! to shorten the beam and introduce some longitudinal focusing to counteract the space-charge-induced debunching. In the following we discuss two RF structures that could potentially offer an elegant solution for the introduc-

tion of RF longitudinal focusing. These are being developed at UCLA in conjunction with international collaborators ~Tel Aviv University and University of Rome La Sapienza/ INFN! for other applications like FEL injection and THz generation. The optimization of the various RF photoinjector parameters will be obviously different depending on the final application ~relativistic UED, THz generation, or FEL injection!, but a common theme is the quest for shorter and higher brightness beams. The first one—the “guncher”—is a relatively simple modification to the existing design obtained by adding a 0.5 cell at the end of a 1.5 cell gun. Note that the initial cell should also be shorter, as this mitigates the longitudinal defocusing present in the 1.6 cell gun. The second one—the “hybrid”—is a more drastic change in which a 908 phase-

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shifted traveling wave section is attached at the exit of the gun. The underlying philosophy for both structures is similar, that is, to compensate for the space-chargeinduced chirp with an opposite chirp coming from the RF fields. In the next two sections of this article, we discuss the application of these structures to relativistic UED, comparing their performances with the results that can be achieved with the standard 1.6 cell gun outlined in the previous section.

G UNCHER Perhaps the simplest solution to the problem of introducing longitudinal focusing in the beam dynamics is obtained by adding a half-cell cavity at the exit of a 1.5 cell gun. In this case the beam during the propagation in the extra length of the accelerating structure acquires an RF-induced energy chirp that effectively compensates the space-charge-induced energy spread. One requires a short final cell, as this effectively pushes the bunch forward in RF phase, allowing focusing. For relatively low beam charges, this gun acts like a longitudinal lens with a net bunching effect on the beam. The “guncher” is being developed at UCLA in collaboration with Tel Aviv University for FEL and THz generation application. The High Frequency Structure Simulator ~HFSS! model of the structure is shown in Figure 3a. With an input power of 10 MW, the field gradient at the cathode is 100 MV/m. The mode field profile on axis is also shown in Figure 3b. For the energy chirp compensation to take place, we observe that the beam cannot be ultrashort at the cathode in order for the RF to impart a significant chirp on it. Because of this, illuminating the cathode with an ,100 fs laser pulse, which corresponds to ,0.18 of RF wavelength, is not the optimum scenario in this case. One obtains much better results starting with a longer beam at the cathode and then letting the compression reduce the bunch length to sub-100 fs level. In Figure 4 the Astra simulation results are reported. The beam at the cathode is 3 pC, the laser pulse has a Gaussian distribution in the longitudinal dimension with an rms length of 600 fs and a flat-top distribution in the transverse dimension with rms size of 100 mm. The beam at 1.5 m downstream of the cathode is 60 fs rms long, 500 mm in rms transverse size, and 45 mrad rms beam divergence with a peak brightness of 1.2 ⫻ 10 15 A/m 2. When comparing these results with those obtained in the 1.6 cell case, we observe that the need to maintain the beam large at the cathode in order to obtain an ultrashort beam at the sample is relaxed when using the guncher. The emittance compensation, on the other hand, is still not ideal due to the fact that the beam distribution is no longer a uniformly filled ellipsoid and some space-charge-induced emittance growth is observed. Nevertheless, such a beam could

very well be used for electron diffraction and has the potential to break the 100 fs barrier for time resolution in ultrafast pump-probe studies.

H YBRID P HOTOINJECTOR Another structure that could possibly alleviate some of the problems encountered with the standard 1.6 cell design is the hybrid RF photoinjector. This is a standing wave/ traveling wave structure being developed jointly by a UCLA/ INFN/University of Rome collaboration ~O’Shea et al., 2008!. As conceived, the hybrid should produce an ultrashort bunch by strong velocity bunching due to the inherent dephasing between the standing and the traveling wave parts of the structure. From the point of view of RF system input, the hybrid is near a traveling wave structure, and there is almost no reflection at the input port. This enables one to remove the RF isolator, which is usually required with standing wave structures to protect the RF system from the reflected RF. This is very important when one considers scaling the photoinjector to higher frequency, such as X-band, where no high power isolator is available. For the details of the hybrid design and construction and many beam dynamics issues, we refer the reader to the recent articles on the subject ~Fukasawa et al., 2008!. The important point to emphasize here is that there is a 908 phase shift that occurs naturally between the “gun” section and the downstream traveling wave section of the device. This scenario introduces very strong longitudinal focusing. We analyze here the possible application of this device for the relativistic UED technique. A cutaway of the technical design of the RF structure is shown in Figure 5a. The accelerating electric field profile on axis and the magnetic field are reported in Figure 5b. A strong solenoid around the first cells is required to keep the beam size under control as it undergoes strong RF bunching inside the structure. The results of the beam dynamics from the Astra simulations are reported in Figure 6. The laser pulse illuminating the cathode in this structure is quite long—a Gaussian distribution with rms length of 1.2 ps rms—to increase the RF-induced bunching effect, and the laser spot size is a flat-top 50 mm rms. At z ⫽ 1.5 m from the cathode a diffraction target would be illuminated by an electron beam that is ,50 fs long, 400 mm in rms transverse size, and 45 mrad in rms divergence with a peak brightness of .1.5 ⫻ 10 15 A/m 2.

C ONCLUSIONS In Table 1 we report the performances obtained with the various RF photoinjector designs analyzed in this article. In

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Figure 4. Beam dynamics in the guncher structure. The longitudinal and transverse focus are obtained at the same distance from the cathode z ⫽ 1.2 m.

Figure 6. Astra simulation results for hybrid photoinjector structure.

Figure 5. ~a! Technical design of RF hybrid photoinjector and ~b! electric and magnetic field profiles on axis.

Table 1.

Summary of Simulation Results for All the Various RF Photoinjector Structures Considered.

Beam charge Pulse length rms beam size rms beam divergence Peak brightness rms normalized emittance Laser rms spot size Laser rms pulse length

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1.6 Cell

1.6 Cell ~Short!

Guncher

3 pC 240 fs 600 mm 25 mrad 1.0 ⫻ 10 15 A/m 2 0.12 mm 100 mm 50 fs

3 pC 90 fs 1 mm 65 mrad 1.0 ⫻ 10 15 A/m 2 0.5 mm 600 mm 50 fs

3 pC 60 fs 500 mm 45 mrad 1.2 ⫻ 10 15 A/m 2 0.18 mm 100 mm 600 fs

Hybrid 3 pC ,50 fs 400 mm 45 mrad 1.5 ⫻ 10 15 A/m 2 0.14 mm 50 mm 1.2 ps

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particular it is evident that, for the two cases of 1.6 cell gun, a compromise between temporal resolution fixed by the bunch length and spatial resolution ~determined by the beam transverse parameters! has to be found. The two new proposed structures analyzed here, the “guncher” and the “hybrid,” should markedly improve the situation by adding external RF focusing to counteract the effect of the longitudinal space-charge field. The simulation results obtained from a first optimization pass on the two new considered structures are very promising and assuredly deserve further investigation and refinement. A new simulation tool to fully model the dynamics of the beam and the diffraction from a target with known properties ~as for example a thin Al foil! is being developed to allow a direct comparison of the diffraction patterns. Furthermore, considering different magnetic field configurations and exploring the best compromise between quantum efficiency and thermal emittance for the cathode/ laser wavelength choice ~Schmerge et al., 2007! could bring other significant improvements. In short, the outlook for photoinjector based relativistic UED application is very promising because this technique can greatly benefit from the contemporaneous development of advanced structures for other applications such as THz and FEL, which share with UED the need for shorter, higher brightness electron beams.

A CKNOWLEDGMENTS We acknowledge the group at the University of Rome “La Sapienza” and Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati for the development of the mechanical design of the hybrid photoinjector, in particular, D. Alesini, B. Spataro, and V. Lollo.

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