# Accelerating the future

## 1 Introduction

Advancement in particle physics has historically been linked with the availability of particle beams of ever increasing energy or intensity. For more than three decades the collision energy in particle colliders has increased exponentially in time as described by the so-called Livingston plot. A recent version of the Livingston plot is shown in fig. 1. It includes achievements with conventional and novel accelerators and indicates the present plans beyond 2014. It is seen that particle accelerators are a remarkable success story with beam energies having increased by 5 – 8 orders of magnitude since the first RF-based accelerators in the 1920s. However, it is also evident that the exponential increase of beam energy with time has levelled off in conventional accelerators since the 1980s. Limits in conventional accelerators arise from technical limitations (e.g. maximum fields in super-conducting magnets for hadron machines, synchrotron power losses in lepton machines, breakdown effects at metallic walls of RF cavities in linear machines) but also practical issues like size and cost. This limitation has serious implications for future scientific use of accelerators such as TeV colliders, as it implies machines that may reach many 10’s of km in length and cost in excess of €10 billion.

To overcome such limitations, a vigorous worldwide effort is on going aimed at the development of high field superconducting magnets, of muon colliders and of novel high-gradient acceleration techniques.

In order to afford the energy needed to excite high-gradient accelerators, their operating wavelength must be reduced, from the RF to the THz spectral range and even down to optical wavelength. This presents distinct challenges in power generation, requiring new paradigma in the excitation of accelerating waves and in the beam time structure.

In recent times a new technology emerged, based on the revolutionary proposal of plasma accelerators by Tajima and Dawson in 1979, and the invention of amplified chirped short ($\sim$ fs) optical pulses (CPA) by Mourou and Strickland in mid 1980s, both awarded the Nobel Prize in Physics in 2018 for the invention of CPA techniques. Plasma-based concepts presently offer not only the high beam energies shown in fig. 1, but also the highest accelerating gradient compared to other novel acceleration techniques like high-frequency metallic RF structures or dielectric structures. To proceed towards high-energy physics (HEP) applications, however, one must demonstrate progress in beam quality and control. Advances in understanding limitations on accelerating gradient go beyond linear colliders; compact and cost-effective accelerators can be used in applications such as inverse Compton scattering gamma-ray sources, free-electron lasers, medical linacs, all may benefit from larger accelerating gradients.

This paper will review the most promising developments in new high gradient acceleration methods for linear machines, namely high-frequency metallic RF structures, dielectric structures and plasma-based accelerating modules, and will present the status of on-going projects including the EU project EuPRAXIA.

## 2 Metallic structures

Conventional normal conducting RF particle accelerators consist of metallic (copper) corrugated waveguides that can support the propagation of an electromagnetic wave with a longitudinal (accelerating) field component. Charged particles, propagating on the axis of the RF structure and synchronous with the RF wave propagation, can gain kinetic energy at the expenses of the electromagnetic stored energy. RF structures are driven by high-power microwaves generators (Klystrons) and have recently shown the capability to achieve accelerating fields up to 120 MV/m at X-band frequency. A significant progress if compared to the long-lasting S-band SLAC type structure that is typically limited to 20 MV/m. To exploit this new technology, a European design study has been recently funded, the H2020 XLS-CompactLight Project, which aims at designing the next generation of compact X-rays free-electron lasers and to investigate all the possible applications of compact high-gradient X-band structures. The X-band successful progress has been achieved after an R&D effort performed mainly at SLAC and CERN towards the understanding of breakdown physics and improved fabrication processes. An electric breakdown event (or discharge) is in fact the main limitation in a metallic structure to achieve high gradient. The discharge event occurs from the surface melting over a macroscopic area in a high E-field region of the structure wall. A plasma forms over the molten area, bombarding the surface with an intense ion current producing consistent changes in the structure shape with crater formations in the copper surface and vacuum breakdown, thus limiting the maximum operating accelerating field.

The breakdown rate (BDR) is one of the main quantitative requirements characterizing high gradient performance of the linac. The CLIC linear collider requires RF breakdown probability to be less than $3\times 10^{–7}$/pulse/m for an accelerating gradient of 100 MV/m operating with a 180 ns long RF pulse. As a result of the R&D effort, 11.4 GHz Traveling Wave (TW) accelerating structures can today run at BDR of about $10^{–6}$ /pulse/m at gradients up to 120 MV/m and $\sim$ 200 ns pulse length. This result scaled to a 180 ns RF long pulse is consistent with the CLIC requirement.

The pulse length $\tau_{RF}$ is one of the key parameters to achieve high gradient. It has been experimentally demonstrated that the maximum achievable accelerating gradient for a fixed BDR scales like $\tau_{RF}^{–1/6}$. Beam time structure, accelerating structure length and filling time together with the available RF peak power set the minimal acceptable RF pulse length $\tau_{RF}$. One possibility to reduce the RF peak power is to lower the pulse energy required for the same E-field in the structure by adopting structures operating at higher RF frequency, hence with a reduced volume to fill with energy. In this way the stored energy scales with RF frequency like $f^{-3}$ leading to a considerable reduction of the required input peak power. On the other hand, one has to face additional limitations related to fabrication tolerances and beam instability due to enhanced wake fields effects in corrugated structures. In fact any discontinuity in the accelerating structure boundaries produces an electromagnetic disturbance induced by the beam current, called wake field. Wake fields can have both transverse and longitudinal field components that might back-interact with the beam itself causing energy spread and/or off-axis deflection and eventually beam loss. Nevertheless, corrugated structure boundaries are necessary to keep the phase velocity of the accelerating field synchronous with the speed of the particle beams, i.e. less than the speed of light, a condition that is impossible to satisfy in a smooth waveguide. Since the intensity of the transverse wake field is inversely proportional to the third power of the structure aperture and linearly increases with the beam offset with respect to the structure symmetry axis, higher RF frequency structures are more subject to beam instabilities than lower-frequency structures. The advantage of using high-frequency structures to achieve higher gradient is consequently limited by possible beam quality degradation due to wake field effects.

Nevertheless very promising results have been achieved in this direction at SLAC at the FACET facility where RF breakdown and beam deflection studies have been performed with a 140 GHz RF structure, see fig. 2. Since there was not access to RF generators at that frequency, the structure has been excited by an ultra-relativistic electron beam exciting a longitudinal wake field with a component at the frequency of the accelerating mode. The maximum achieved accelerating gradient was 300 MV/m with a peak surface electric field of 1.5 GV/m and a pulse length of about 2.4 ns.

Another interesting approach to increase electric fields in copper cavities is to cool them down to temperatures below 77 K, where the RF surface resistance, coefficient of thermal expansion and crystal mobility decrease, while the thermal conductivity and hardness increase, all of which can contribute to reduce the BDR. Recent studies show that an X-band structure can be conditioned up to an accelerating gradient of 250 MV/m at 45 K and a breakdown rate of $2\times 10^{-4}$/pulse/m. So far for this breakdown rate, the cryogenic structure has the largest reported accelerating gradient. A combination of short RF pulses, cryogenic and high-frequency operation will probably lead to additional significant progress of high-gradient RF metallic structure in the next decade. Nevertheless it is unlike to expect gradient in the range of GV/m with high-frequency metallic structures because of the additional limitations related to fabrication tolerances and beam instability due to enhanced wake fields effects in corrugated structures, as discussed above.

## 3 Dielectric structures

As discussed in the previous section both the increase in operational frequency and reduction in pulse length play a role in increasing the breakdown limit. To overcome the limitations imposed by the small corrugated structures, necessary to keep the phase velocity synchronous with the particle velocity but producing enhanced wake field effects, one can consider a simpler circular metallic waveguide filled by a dielectric liner that allows matching the phase velocity of the wave to the speed of particles.

Using optical generation techniques, one can have very short THz pulses (<100 ps) generated by picosecond lasers readily available at high average power. This approach has been adopted by the AXSIS collaboration that has recently reported experimental demonstration of electron acceleration using the axial component of an optically generated 10 $\mu$J THz pulse centred at 0.45 THz propagating in a fused silica capillary waveguide. A maximum energy gain of 7 keV has been observed in a 3 mm long structure of 400 mm inner diameter. Using more intense THz sources ($\sim$ 10 mJ) the AXSIS collaboration expects to achieve $\sim$ GV/m accelerating gradients in the near future.

Breakdown limits in similar dielectric structures have been investigated at FACET where a Dielectric Wakefield Acceleration scheme (DWA) is under investigation. In the DWA scheme two bunches are injected in a dielectric-filled waveguide so that the first high-charge bunch excites a wake field that can be used to accelerate a collinear trailing lower charge bunch, see fig. 3. First measurements of the breakdown threshold in a dielectric structure, subjected to GV/m wake fields produced by short (30–330 fs) 28.5 GeV electron bunches, have been made at FACET.

Fused silica capillaries of 100 mm inner diameter were exposed to a range of bunch lengths, allowing surface dielectric fields up to 27 GV/m to be generated. The onset of breakdown was observed to occur when the peak electric field at the dielectric surface would reach ~13.8 GV/m. In a more recent experiment, accelerating gradients of about 1.3 GV/m have also been measured in a 15 cm long dielectric structure.

The use of infrared lasers to power optical-scale lithographically fabricated dielectric structures, which is referred to as dielectric laser acceleration (DLA), is another developing area in advanced acceleration techniques. This accelerating structure consists of two opposing binary gratings, separated by a vacuum gap where the electron beam travels perpendicular to the grating rulings, see fig. 4.

To generate the required accelerating fields, being the dielectric material transparent to the optical radiation, a linearly polarized laser pulse is incident on the structure perpendicular to both the electron beam direction of propagation and the plane of the gratings. The structure essentially acts as a longitudinally periodic phase mask, where each grating pillar imparts a $\pi$-phase shift on the electric field. As a result, electrons launched at the correct optical phase remain phase-synchronous and experience a net energy gain. In this configuration gradients beyond 250 MV/m in acceleration tests of electrons in a DLA have been measured.

More advanced designs based on photonic band gap structures are currently under investigation and are extensively discussed.

Dielectric structures are a very promising option to achieve gradients above GV/m but more experimental data on operational breakdown rates and with accelerated beams are needed before deriving realistic conclusions on the possibility of achieving high-energy and high-quality beams with this technology.

## 4 Plasma structures

Plasma-based accelerators replace the metallic or dielectric walls of the accelerating structures with an ionized gas, or plasma, see fig. 5.

Plasma accelerator relies on a wake field excited by a driving pulse to provide the accelerating force. The drive pulse, which can be a short pulse of either a laser (LWFA) or an electron beam (PWFA), blows the electrons in an ionized gas, or plasma, outward, leaving behind a region of positive charge. Along the axis where the beam propagates, the electric field causes a trailing pulse of electrons injected near the rear of the bubble to undergo a very strong forward acceleration. This use of plasma to generate accelerating field allows avoiding metallic or dielectric structure damage problems due to breakdown encountered in high-gradient operation since the outer “walls” of the plasma are already “melted”.

Plasma accelerators have been tested with active lengths ranging from the mm to the meter scale. Accelerating gradients up to 160 GV/m have been demonstrated in experiments. A number of advanced accelerator facilities are in operation or under construction in Europe (AWAKE, FLASH_Forward, SPARC_LAB, SINBAD) and in Asia, complementing the two large R&D facilities that are currently spearheading advanced accelerator research in the U.S.: FACET at SLAC, which is dedicated to PWFA studies and BELLA at LBNL, which leads the field of LWFA.

Three fundamental milestones have been recently achieved:

• At BELLA, multi-GeV electron beams with energy up to 7.8 GeV, 6% rms energy spread, 5 pC charge, and 0.2 mrad rms divergence have been produced from a 20 cm long laser-heated capillary discharge waveguide with a plasma density near to $3\times 10^{17}$ cm-3, powered by 850 TW laser pulses.
• At FACET (PWFA), acceleration of about 74 pC of charge contained in the core of the trailing bunch in an accelerating gradient of about 4.4 GV/m has been demonstrated. The core electrons gained about 1.6 GeV of energy per particle, with a final energy spread as low as 0.7%, and an energy transfer efficiency from the wake to the bunch that can exceed 50%.
• More recently at FACET, using a nonlinear plasma wake driven by a single positron bunch, a substantial number of positrons has been accelerated and guided over a meter-scale plasma, in a unique and unexpected new collective regime.

To proceed towards high-energy physics (HEP) applications, however, one must demonstrate progress in beam quality and control. Indeed, for any variant of plasma wake field accelerator to be practical as a linear collider, a range feasibility and practicality issues must be resolved in the context of an integrated system test. Plasma accelerators, like standard accelerator modules, must be capable of being staged in a series of segments. Both PWFA and LWFA approaches must demonstrate simultaneous electron and positron acceleration with stable focusing in plasma and transport lines with performance consistent with preserving electron and positron beam quality. Both must demonstrate timing, pointing, and focusing control that fulfil the demands of high-luminosity operation required by a lepton collider. Finally, both must demonstrate that single-and multi-bunch plasma instabilities can be overcome with operation at the tens of kHz repetition rate required for high luminosity. Beyond the feasibility issues are practical questions related to overall cost, efficiency, and reliability.

To this end, new initiatives are now arising, such as the EuPRAXIA program, which seeks, through intermediate application goals, to push plasma accelerators from an exciting concept to a mature approach. It is in fact widely accepted by the international scientific community that a fundamental milestone towards the realization of a plasma-driven future linear collider will be the integration of a high-gradient accelerating plasma modules in a short-wavelength Free Electron Laser (FEL) user facility. The capability of producing the required high-quality beams and the operational reliability of the plasma accelerator modules will be certainly certified when such an advanced radiation source is able to drive external user experiments. The realization of such a new generation light source thus serves as a required stepping stone for HEP energy applications and it is a promising new tool for photon science in its own right. The Italian accelerator community, in the framework of the European initiative EuPRAXIA, is now giving an important contribution in this direction with the recently established project named EuPRAXIA@SPARC_LAB under design at the INFN Laboratori Nazionali di Frascati (LNF). The main characteristics of the project are described in the next section.

## 5 The EuPRAXIA@SPARC_LAB design study

The EuPRAXIA@SPARC_LAB facility is a unique combination of a high brightness GeV-range electron beam generated in an X-band RF linac, and a 0.5 PW-class laser system. The infrastructure will be of top-class quality, user-oriented and at the forefront of new acceleration technologies. EuPRAXIA@SPARC_LAB is in fact conceived as an innovative and evolutionary tool for multi-disciplinary investigations in a wide field of scientific, technological and industrial applications. It could be progressively extended to be a high-brightness “particles and photons beams factory”: it will be eventually able to produce electrons, photons (from THz to gamma rays), neutrons, protons and positrons, that will be available for a wide national and international scientific community interested in taking profit from advanced particle and radiation sources. The layout of the EuPRAXIA@SPARC_LAB infrastructure is schematically shown in fig. 6.

From left to right one can see a 55 m long tunnel hosting a high-brightness 150 MeV S-band RF photoinjector equipped with a hybrid compressor scheme based on both velocity bunching and magnetic chicane. The energy boost from 150 MeV up to a maximum of 1 GeV will be provided by a chain of high-gradient X-band RF cavities. At the linac exit a 5 m long plasma accelerator section will be installed, which includes the plasma module ($\sim$ 0.5 m long) and the required matching and diagnostics sections. In the downstream tunnel a 40 m long undulator hall is shown, where the undulator chain will be installed. Further downstream after a 31 m long photon diagnostic section the users hall is shown. Additional radiation sources as THz and gamma-ray Compton sources are foreseen in the other shown beam lines. The upper room is dedicated to klystrons and modulators to drive the X-band linac. In the lower light-blue room the 300 TW FLAME laser will be installed eventually upgraded up to 500 TW. The plasma accelerator module can be driven in this layout either by an electron bunch driver (PWFA scheme) or by the FLAME laser itself (LWFA scheme). A staged configuration of both PWFA and LWFA schemes will also be possible in order to boost the final beam energy in excess of 5 GeV. In addition FLAME is supposed to drive plasma targets in the green room in order to drive electron and secondary-particle sources that will be available to users in the downstream 30 m long user area.

One of the most innovative devices of the project is the plasma accelerating module, in one of its possible configurations, see fig. 7.

It consists of a 10 cm long, 0.5 mm diameter capillary tube in which the plasma is produced by a high voltage discharge in hydrogen. Another fundamental component included in the design is the X-band accelerating technology adopted for the 1 GeV RF drive linac. It is a very interesting option because it allows reducing the overall drive linac length, taking profit of the high-gradient operation of the X-band accelerating structures. In addition it will allow implementing at LNF in the next 2 years the frontiers of high-gradient RF technology. This technology has already shown its usefulness for medical and industrial applications but it is also another possible technological option for compact radiation sources and for the future Linear Collider, as discussed in the previous sections.

In the PWFA scenario driven by a single electron bunch, the maximum possible energy gain for a trailing bunch is less than twice the incoming driver energy (transformer ratio $R=2$). In this regime a driver bunch energy of 600 MeV is enough to accelerate the witness bunch up to 1 GeV. A method to increase the energy gain is the so-called ramped bunch train and consists of using a train of 4 or more equidistant bunches, wherein the charge increases along the train producing an accelerating field resulting in a higher transformer ratio. For this application, it is essential to create trains of high-brightness tens of femtosecond-long microbunches with stable and adjustable length, charge and spacing. Considerable efforts are now ongoing worldwide to produce the required bunch train configurations. The method we will use to achieve the required bunch train quality is based on the Laser Comb Technique that has been tested with the SPARC_LAB photoinjector. Higher witness bunch energy will thus be accessible when the comb technique is implemented. With a transformer ratio > 4 the 5 GeV threshold will be achievable with a 1 GeV driver bunch energy, thus exploiting the full energy provided by the X-band linac.

In the LWFA scenario the 0.5 PW upgrade of the FLAME laser is a necessary step to keep the FLAME laser in the group of leading installations and further establish expertise on advanced laser sciences. High-energy staging in combination with high-brightness beam external injection will be the main applications of the upgraded FLAME system, leading to multi-GeV high-brightness electron beam production as required by the final EuPRAXIA goals.

To support our design in both plasma acceleration options (PWFA and LWFA), we have performed Start To End Simulations with promising results. The reported performances show that our FEL design, driven by a plasma accelerator in SASE configuration, is expected to meet the challenging requests for the new generation synchrotron radiation sources by a 30 pC electron bunch. We have investigated also the possibility to drive the FEL with higher charge/bunch i.e. up to 200 pC, in order to produce a larger number of photons as required by some application. This is possible in a conventional configuration driven by the X-band linac alone without using the plasma module.

The experimental activity will be initially focused on the realization of plasma-driven short-wavelength FEL with one user beam line. This goal is already quite challenging but it is affordable by the EuPRAXIA@SPARC_LAB collaboration and will provide an interesting FEL radiation spectrum in the so-called “water window”. The first foreseen FEL operational mode is based on the Self Amplification of Spontaneous Radiation (SASE) mechanism with tapered undulators. More advanced schemes like Seeded and Higher Harmonic Generation configurations will be also investigated. The users end station, called EX-TRIM (Eupraxia X-ray Time Resolved coherent IMaging), will be designed and built to allow performing a wide class of experiments using a schematic apparatus. As specific example of EuPRAXIA@SPARC_LAB applications, it is worth remarking that the FEL radiation in the soft X-ray spectrum opens possibilities for novel imaging methodologies and time-resolved studies in material science, biology and medicine, along with non-linear optics applications.

In addition, the upgrade of the FLAME laser system to 0.5 PW power will enable new regimes of plasma-based particle accelerators and will enable to access the region of high electromagnetic fields of non-linear and quantum electrodynamics (QED) where new fundamental physics processes and promising new radiation emission mechanisms can be explored.

Together with the driving motivation to candidate LNF to host the EuPRAXIA facility, the realization of the EuPRAXIA@SPARC_LAB infrastructure at the LNF will allow INFN to consolidate a strong scientific, technological and industrial role in a competing international context. A national multi-purpose facility, along the scientific applications discussed, not only paves the road for a strong role for the Italian contribution to the European EuPRAXIA, but also to possible future large HEP international projects. We are confident that this project will represent a further step forward in the mainstream of a long lasting history of success in particle accelerators development in Frascati.

## 6 Conclusions

Accelerator-based high-energy physics will at some point become practically limited by the size and cost of the proposed $e^{+}e^{–}$ colliders for the energy frontier. Novel acceleration techniques and plasma-based, high-gradient accelerators open the realistic vision of very compact accelerators for scientific, commercial and medical applications. The R&D now concentrates on beam quality, stability, staging and continuous operation. These are necessary steps towards various technological applications. To this end, pilot users facilities are planned in the near future. A major milestone is an operational, 1 GeV compact accelerator. This unit could become a stage in a high-energy accelerator.

The progress in advanced accelerators will benefit also from strong synergy with general advances in technology, for example in the laser and/or high-gradient RF structures industry.

To accomplish the final dream of a compact and cost-effective accelerator, a parallel effort should be addressed also in the development of compact devices such as beam focusing and manipulations elements, diagnostics components and eventually short-period undulators.

Advanced accelerator science and technology is certainly an exciting and fast growing field of research that stimulates the interest of an increasing number of young scientists and research institutes. We are confident that in the near future a large number of our dreams will come true.

## Acknowledgements

Suggestions and discussions with: E. Gschwendtner, W. Leemans, D. Alesini, B. Spataro, A. Mostacci, A. Cianchi, E. Chiadroni, C. Vaccarezza and the EuPRAXIA, XLS, BELLA, FLASH_Foward, SINBAD, AWAKE, AXSIS and EuPRAXIA@SPARC_LAB collaborations have been greatly appreciated. This work was partially supported by the European Union’s Horizon 2020 Research and Innovation programme under grant agreement No. 653782 (EuPRAXIA) and under grant agreement No 777431 (XLS).