<figure><img src="image_61.png" /><figcaption>**Fig. 6.2.** Map of areas of impact expected through the implementation and operation of the EuPRAXIA research infrastructure.</figcaption></figure>

regard to the operation and practical challenges of this technology. Both research
groups new to particle acceleration as well as more experienced parties established in
RF acceleration could therefore benefit from such knowledge. On a more international
scale, training and education programs with developing countries are envisaged as
an additional, very interesting opportunity; ideas in this context will be developed in
further detail as part of the project future stages.

Finally, EuPRAXIA can offer societal opportunities through public engagement and cultural effects. Thanks to its distributed organisation in various countries and regions, outreach campaigns can be designed with broad, geographical impact to inform the general public about plasma accelerators and particle acceleration in general. As Chapters 5.6 and 32.4 demonstrate, the EuPRAXIA Consortium has been very active in this direction already with events at schools, conference centres, and universities and will aim to expand its public engagement program further in the future.

**6.3 Consistency with the Scientific Strategy of Research Areas**

Large accelerator research facilities are at an increasing level encountering practical limitations in size and cost. Proving performance reach and cost benefits of compact accelerator technologies, such as plasma acceleration, has started to play a more and
more visible role in the strategy for future particle accelerators and accelerator appli-
cations. The report of the Particle Physics Project Prioritisation Panel on “Building
for Discovery – Strategic Plan for U.S. Particle Physics in the Global Context”, from
May 2014, for example, states clearly the need for cost-effective particle accelerators:
“There is a critical need for technical breakthroughs that will yield more cost-effective
accelerators” [174].

The Physics Briefing Book (CERN-ESU-004 [175]) summarises the input for the
European Strategy for Particle Physics Update 2020. It lists EuPRAXIA explicitly
as a study “of high interest also for possible future HEP applications” (Chap. 10,
page 176). EuPRAXIA addresses several of the challenges and near-term goals listed
in the briefing book.

LEAPS – the League of European Accelerator-based Photon Sources – is a strategic consortium initiated by the directors of the synchrotron radiation and free-electron laser (FEL) user facilities in Europe (see https://www.leaps-initiative.eu). Its primary goal is to actively and constructively ensure and promote the quality and impact of the fundamental, applied and industrial research carried out at their respective facilities to the greater benefit of European science and society. The LEAPS Strategy 2030 [176] lists as one of its future challenges: “A longer-term goal is the development of compact sources based on plasma wakefield acceleration to make some of the capabilities of the current RIs available for industrial applications, hospitals and smaller laboratory environments”.

Plasma acceleration also moved into the focus of national strategies in various European countries, among others with the ATHENA project in Germany, the Extreme Photonics Applications Centre in the United Kingdom, and the EuPRAXIA@SPARCLab project in Italy.

Listed as part of its key goals (see Chap. 2.1), EuPRAXIA aims to assess and advance beam quality, the compactness, and cost benefits of plasma-accelerator technology compared to RF-based machines. The proposed long-term strategy towards high beam quality and miniaturisation is well in line with the strategic demand for a new cost-effective accelerator technology that offers photon science discovery reach, medical applications, industrial potential, and a clear perspective for high-energy physics.

We conclude that the concept and approach of the EuPRAXIA research infras-
tructure are fully consistent with the strategies in accelerator-based photon sci-
ence and high-energy physics. It is noted that plasma acceleration and specifically
EuPRAXIA are also explicitly mentioned in the landscape analysis of the ESFRI
Roadmap 2018.

6.4 Competition and Worldwide Context

Important new projects have started in recent years in Europe and worldwide at a
total approved investment level of well above 150 M€:

1. The international Advanced Wakefield Experiment (AWAKE) at CERN, a collaboration of 18 institutes, pursues electron plasma accelerators that are driven by high-energy proton beams from the CERN-based SPS accelerator. It aims at very-high-energy electron beams for high-energy physics experiments. AWAKE is fully complimentary with the goals of EuPRAXIA, which aims at applications in the several-GeV energy range (AWAKE: A. Caldwell (MPP), M. Wing (UCL), E. Gschwendtner (CERN), P. Muggli (MMP), K. Lotov (BINP) et al., see https://awake.web.cern.ch and [50]).

2. The international ALEGRO study aims at the design of a plasma-based linear collider, the step beyond EuPRAXIA. The ALEGRO roadmap lists EuPRAXIA
as an intermediate facility on the route to a plasma linear collider (Advanced LinEar collider study GROup ALEGRO: An international study group to promote advanced and novel accelerators for high-energy physics applications; sponsored by ICFA; B. Cros et al, http://www.lpgp.u-psud.fr/icfaana/alegro, see also [142]).

3. In the UK, the Plasma Wakefield Accelerator Steering Committee (PWASC) has defined a national roadmap and has proposed the successful EPAC (Extreme Photonics Applications Centre) project. PWASC and EPAC are connected to EuPRAXIA and form part of its consortium (Plasma Wakefield Accelerator Steering Committee (PWASC) in the UK, coordinated by S. Hooker, B. Hidding et al, see [145,177]).

4. The multi-institutional laser-plasma acceleration project ATHENA in the Helmholtz Association brings together all accelerator-related Helmholtz centres in Germany for the construction of two common flagship plasma accelerators in Hamburg and Dresden. ATHENA is connected to EuPRAXIA, and most of the ATHENA partners are a part of the EuPRAXIA Consortium (Accelerator Technology Helmholtz Institute for StructureATHENA, project on laser-driven plasma acceleration by DESY, FZJ, and GSI with HI Jena, HZB, HZDR, and KIT, see https://www.athena-helmholtz.de).

5. The IMPACT program in Japan aims at constructing a laser-driven, multi-stage plasma accelerator that drives a free-electron laser (see Chap. 30 for a more detailed description). The Japanese research labs have joined EuPRAXIA as associated partners.

6. In China, in the key laboratory for laser plasmas at Shanghai Jiao Tong University, the “Synergetic Extreme Condition User Facility” (SECUF) will install a two-laser-beam system (200 TW + 300 TW) aiming at studies on staged laser wakefield acceleration, non-linear Thomson scattering, and QED-plasma physics. In the next ten years, a 30 PW (15 PW x 2) laser and target system will be built in the TD Lee Institute in Shanghai. Studies on extreme laboratory astrophysics, such as radiation reaction, positron, $\gamma$, and axion generation, will be carried out. Several Chinese institutes have joined EuPRAXIA as associated partners.

7. In Russia, the “Exawatt Center for Extreme Light Studies” (XCELS) is under study, aiming to use sources of laser radiation with unprecedented giant (exawatt) peak power. The XCELS complex will house laboratories for experiments on the physics of strong fields, high-energy physics, laboratory astrophysics and cosmology, nuclear optics, and neutron physics as well as laboratories for studying the properties of vacuum, attosecond and zeptosecond physics, and fundamental metrology. XCELS includes the investigation of laser-plasma acceleration in the kJ regime of laser energy, including multi-stage acceleration, external injection, and multi-pulse acceleration. Several Russian institutes have joined EuPRAXIA as associated partners.

8. In the United States, the BELLA facility at LBNL is the world-leading laboratory for laser-driven plasma acceleration in what concerns the maximum beam energy reached. A strong program towards higher beam quality, radiation generation, and applications is under way. LBNL has joined EuPRAXIA as an associated partner.

9. In the United States, the FACET facility at SLAC is the world-leading facility on beam-driven plasma acceleration, in as far as maximum beam energy for electrons and acceleration of positrons are concerned. Presently, an upgrade of the facility (FACET-II) is being implemented, which will allow improved beam quality and extended positron studies.

It is noted that there are other national projects with significant investments not mentioned above. Some of them are described in Chapters 29 and 30.
The list of competing projects and investments shows that the international landscape for plasma accelerators is rapidly expanding and attracting significant funding support from national governments. This reflects the clear promise in this novel accelerator approach and the worldwide race in bringing the new technology to the market and into the scientific area. It is seen that EuPRAXIA has attracted a large fraction of the relevant international R&D community into its consortium, both at a European and at an international level. This illustrates the strong potential for a European leadership role, for international scientific collaboration, and for a lively yet constructive worldwide competition.

## 6.5 Long-Term Future Accelerator Roadmap and the Role of EuPRAXIA

Several exercises for defining long-term accelerator roadmaps in the domain of plasma accelerators have been undertaken in recent years. In 2017, for example, the European Network for Novel Accelerators, EuroNNAc, published a “European roadmap”, which includes an R&D vision on developing plasma accelerators for the next 35 years [178]. The EuroNNAc roadmap from 2017 lists the EuPRAXIA facility as a required stepping stone for demonstrating high-quality electron beams from plasma accelerators at multi-GeV energies and with a reduced footprint. High beam quality is a necessary prerequisite for applications, which demand high beam brightness such as free-electron lasers, or high luminosity like particle colliders.

The plasma accelerator roadmap has been further detailed and developed in the recent exercise of the ALEGRO study group, as summarised in [179]. ALEGRO is a fully international effort with input from laboratories and experts worldwide, aiming at a broad international consensus. ALEGRO defines a 30 year roadmap towards a high-energy plasma-based linear collider. It defines various critical R&D challenges for arriving at this goal. These include the external injection of a high-quality electron bunch in an accelerator section. Emittances at the mm-mrad level should be produced and maintained, while the final energy spread should be at the percent level or lower. Levels of bunch quality, efficiency, stability, and reproducibility equivalent to those produced by conventional accelerators shall be achieved. Plasma sources with sufficient density uniformity, control, and reproducibility of the density, as well as tapering of the entrance and exit density ramps to assist in beam manipulation between stages should be developed. Operation at high repetition rate is identified as an important step towards a plasma-based linear collider. Challenges in producing high-quality electron (e⁻) and positron (e⁺) bunches in the 10 to 20 GeV energy range shall be addressed. Positron capabilities shall be expanded to other facilities beyond FACET-II with its world-leading positron program. The ALEGRO roadmap reviews the existing and planned facilities on plasma accelerator R&D. It lists their capabilities with respect to the challenges that need to be addressed. The EuPRAXIA facility is included, and its role in addressing various critical challenges is described and acknowledged.

We conclude that the EuPRAXIA research infrastructure is part of a long-term future accelerator roadmap. It fulfils an important role in the present R&D roadmaps. The positioning of the project is illustrated in the schematic diagram in Figure 6.3. The EuPRAXIA project will bridge the gap between successful proof-of-principle experiments (today) and a reliable technology with many applications. It should be considered as a ground-breaking, full-scale demonstration facility with first pilot users and unique ultra-fast science features. EuPRAXIA would address several technical shortcomings with novel solutions and prove the potential of plasma accelerators for first users in the multi-GeV energy range. The EuPRAXIA technology could then later be scaled up to higher beam energies, as required for high-energy physics discovery science.
<figure><img src="image_62.png" /><figcaption>**Fig. 6.3.** Positioning of EuPRAXIA in the technological accelerator landscape of the next decades.</figcaption></figure>
# Part 4
## Systems Design and Performance

## 7 Technology Background

### 7.1 Plasma-Accelerator Physics

While RF accelerators are limited in maximum sustainable field gradient by vacuum breakdown, plasma accelerators do not exhibit this issue as they remove the need for metallic or even dielectric cavities and instead use an underdense plasma as the

<figure><img src="image_63.png" /><figcaption>**Fig. 7.1.** Wakefield generation and electron beam acceleration in a plasma accelerator. The top plot shows the behaviour in a laser-driven plasma accelerator (LWFA), while the bottom plot depicts the case of a beam-driven plasma accelerator (PWFA) (image credits: A. Martinez de la Ossa).</figcaption></figure>
acceleration medium. Thus, these devices can exhibit accelerating field gradients on the order of tens to hundreds of GeV/m compared to up to 100 MeV/m with RF-based machines [177].

In plasma acceleration, a drive beam – either a laser pulse (LWFA) or a relativistic electron beam (PWFA) – is propagated through a plasma target, i.e. a jet or confined channel of ionised gas, and in the process induces electron density oscillations, as shown in Figure 7.1. The associated wakefields exhibit field strengths in excess of

$$E_0[V/m] \approx 96\sqrt{n_0[\text{cm}^{-3}]} \qquad (7.1)$$

and with a characteristic plasma wavelength

$$\lambda_p = \frac{2\pi c}{\omega_p} = \frac{2\pi c}{e} \sqrt{\frac{m\varepsilon_0}{n_0}} \approx 3.3 \times 10^4 / \sqrt{n_0[\text{cm}^{-3}]}, \qquad (7.2)$$

where $n_0$ is the background plasma density, $\varepsilon_0$ the vacuum permittivity, c the speed of light in vacuum, and e, m the electron charge and mass, respectively. Placed into the correct phase of this plasma wakefield, a short electron beam, termed the witness beam, can be accelerated and focussed simultaneously to reach GeV energies over centimetre to metre distances [180].

As mentioned in Chapter 1, two different mechanisms can be employed to place the witness beam into this plasma wakefield. It can be either generated directly inside the plasma target through a self-injection process or propagated into the plasma from an external source. In the former case of self-injection, a fraction of electrons from the background plasma becomes, through one of several possible injection techniques (further details in Chaps. 13 and 32.2), trapped inside the accelerating wakefield and forms an electron beam that continues to co-propagate with the wakefield and gains energy. The plasma target in this case acts primarily as an injector (laser-plasma injector LPI or particle-plasma injector PPI) creating the electron beam, but can also significantly accelerate it already within the same device. For the case of external injection, the plasma target simply boosts the energy of the pre-generated witness beam as an accelerator stage (laser-plasma accelerator stage LPAS or particle-plasma accelerator stage PPAS). The electron beam itself is created and pre-accelerated in an RF injector or a plasma injector in this scenario. Using such a staged setup, multiple plasma accelerators can be coupled to one another to reach particularly high energies [181,182].

### 7.1.1 Laser-Driven Wakefield Acceleration (LWFA)

In laser-driven plasma acceleration, the plasma wakefield is driven by a TW-scale, fs-duration laser pulse. The properties of the wakefield in this case are largely determined not only by the plasma density but also by the laser parameters,
including, in particular, the laser normalised vector potential $a_0$, which can, for a bi-Gaussian pulse, be expressed in practical units as

$$a_0^2 \approx 7.3 \times 10^{-19} (\lambda_l[\mu\text{m}]^2) I_L[\text{W/cm}^2] \quad (7.3)$$

with $\lambda_l$ as the laser wavelength and $I_L$ as the laser intensity. Depending on the value of $a_0$ in combination with the laser spot size and plasma density, three different operation regimes can be distinguished: a linear regime with $a_0^2 \ll 1$, a quasi-linear regime for $a_0^2 \sim 1$, and a non-linear regime in the case of $a_0^2 \gg 1$ [83,180]. The accelerating field gradient increases with higher non-linearity, and in the non-linear regime the self-trapping of background electrons in the plasma can be observed. While the latter may be used in a controlled way for a plasma-based injector, in an accelerator stage with an externally injected electron beam any dark current due to self-injection should be avoided, thus making the linear and quasi-linear regimes typically more suitable [183,184].

Besides the field gradient, another limit to the maximum electron beam energy gain in a plasma accelerator is the acceleration length. This can, depending on the operating regime, be affected by three different phenomena: laser diffraction, electron beam dephasing, and pump depletion. If the natural diffraction of the laser pulse is the dominant process, as is often the case in linear plasma accelerators, the useful acceleration length is limited to a few Rayleigh ranges

$$z_R \approx \pi \frac{w_0^2}{\lambda_l} \quad (7.4)$$

before the laser intensity decreases significantly. Note that $w_0$ is the laser focal spot size and $\lambda_l$ the laser wavelength here.

Electron dephasing, on the other hand, often also plays a factor in this regime. It occurs as the accelerated electron beam travels at close to the speed of light $c$ and outruns the plasma wave, which moves at close to the group velocity of the driving laser pulse within the plasma. Because of this velocity mismatch, the beam eventually slips into the decelerating phase of the wakefield and starts to lose energy, thus limiting the useful accelerating distance to the dephasing length $L_{dp}$. In the linear regime, this length can be expressed as [185]

$$L_{dp} \approx \frac{n_{cr}}{n_0} k_p^{-1}, \quad (7.5)$$

with $\gamma_{ph}$ as the electron beam Lorentz factor, $n_{cr} = (2\pi c)^2 \epsilon_0 m / (e\lambda_l)^2$ the critical plasma density, and $k_p = 2\pi/\lambda_p$ the plasma skin depth.

Finally, pump depletion becomes mostly relevant in the non-linear acceleration regime as the laser energy is lost through driving the plasma wave. The depletion length is defined as the distance over which half of the laser energy is depleted and, in the linear regime, scales as [185]

$$L_{dpl} \approx \frac{n_{cr}}{n_0} k_p^{-1} \frac{\omega_p \tau_L}{a_0^2}, \quad (7.6)$$

with $\tau_L$ as the laser pulse duration.
### 7.1.2 Beam-Driven Wakefield Acceleration (PWFA)

In beam-driven plasma wakefield acceleration (PWFA), a relativistic charged particle beam is used as a driver generating the plasma wakefield; in the case of EuPRAXIA, it is more specifically an electron beam. Similarly to LWFA, different wakefield regimes can be distinguished depending on the properties of the drive beam. For a bi-Gaussian electron beam, a single value $\alpha$ as the ratio of peak beam density and background density, $\alpha = \frac{n_{bunch}}{n_0}$, is relevant with a value larger than one, designating the blowout regime. For non-ideal drive bunches of a different shape, an additional measure is the reduced charge factor $Q_{rc}$, which defines how much charge the drive bunch carries compared to the maximum charge that can be contained in a plasma skin depth volume:

$$Q_{rc} = Q_{bunch} \frac{k_p^3}{n_0 e}, \qquad (7.7)$$

where $k_p$ is the skin depth and $Q_{bunch}$ the bunch charge. Again, values strongly above one indicate a non-linear response and the formation of a full plasma blowout. Values below or around unity, on the other hand, point to a linear or weakly non-linear wakefield, respectively.

To maximise the accelerating field strength reached in a PWFA stage, the drive beam dimensions can be optimised with an ideal RMS length of $\sigma_z = \sqrt{2}/k_p$ and an ideal transverse beam size of $\sigma_{x,y} = \sqrt[4]{2/\gamma\sqrt{\epsilon_{n,xy}/k_p}}$. $\epsilon_{n,xy}$ is the transverse normalised emittance in this context, as defined below. If these conditions are fulfilled, the radius of the bubble structure in the plasma wakefield can be approximated as

$$R_{bubble} = 2.5\sigma_r\sqrt{\alpha}, \qquad (7.8)$$

with $\sigma_r$ as the radial transverse beam size [186].

Finally, another important variable for efficient acceleration in a beam-driven plasma accelerator is the transformer ratio $R_T$. It is defined as the ratio between maximum accelerating field in the witness bunch and maximum decelerating field in the driver bunch [49,187]. In practical terms, it determines the ratio between energy gain by the witness beam and energy loss by the driver, thus defining the maximum energy gain of the witness bunch inside the beam-driven wakefield as $\Delta E_{wit,max} = R_T \times \Delta E_{driv,max}$, with $\Delta E_{driv,max}$ as the average particle energy loss in the driver bunch. With the acceleration length being another practical limitation to the energy gain, the goal for efficient PWFA is to achieve a high transformer ratio and to continue the acceleration process until the drive beam reaches depletion. As symmetrical drive beams have a limit in $R_T$ of at maximum 2, PWFA setups, including also EuPRAXIA, typically work with asymmetric beams. Specific ways to reach higher transformer ratio values include, for example, bunch shaping [188–191] as well as the use of shaped bunch trains [192], which is explored further in this design report.

### 7.1.3 Challenges in Plasma Acceleration

Besides the usual challenges of particle acceleration, plasma accelerators exhibit several issues specific to their technology. These have been tackled with particular focus during the conceptual design study, with solutions presented throughout the remainder of this part.
## Bunch length and energy spread

Because of the high accelerator frequency – on the order of THz instead of GHz as for most RF accelerators – the accelerating section of the wakefield in plasma-based devices is only a few tens of micrometres in size, hence limiting the acceptable witness bunch durations to fs and tens of fs. In plasma injectors, such bunch lengths are produced naturally; however, with RF injectors bunch compressors need to be implemented, and space-charge forces can become an issue at lower energies. At the same time, given the short accelerating field period, the variation of the accelerating field along the electron beam is typically large enough to generate a significant correlated energy spread of at least a few percent in the beam. This common feature constitutes a major issue for many applications, such as free-electron lasers, but also proves, for example, challenging for electron beam transport due to chromatic dependences in most beamline components.

Several concepts to remove this correlated energy spread (energy chirp) either inside the plasma [33] or through beam manipulation outside the target [34] have been proposed. One relatively old strategy involves beam loading, i.e. using the witness beam’s own electric field, which has an opposite curvature to the plasma wakefield, to level the overall accelerating field shape that the beam experiences [28,193]. Through tuning the electron beam shape and charge, this effect can, in principle, be optimised to create a flat field along the beam; however, over longer acceleration distances, additional factors such as the evolution of the driver, plasma wave, and witness beam shape also need to be taken into account.

## Transverse matching

Another particular challenge for staged acceleration is presented by transverse beam matching into plasma targets. In accelerator physics, the transverse dynamics of an accelerated electron beam are typically described by two specialised quantities: the transverse beam emittance and Courant-Snyder (Twiss) parameters [194,195]. The normalised transverse RMS emittance $\epsilon_n$ is defined in this context (exemplary in the horizontal direction x) as

$$ \epsilon_{n,x} = \frac{1}{mc} \sqrt{\langle x^2 \rangle \langle p_x^2 \rangle - \langle xp_x \rangle^2} \qquad (7.9) $$

with $\langle x^2 \rangle = \sum x_i^2/N$, $\langle p_x^2 \rangle = \sum p_{x,i}^2/N$, and $\langle xp_x \rangle = [\sum x_i p_{x,i}/N] - [(\sum x_i \sum p_{x,i})/N^2]$, where $x_i$ and $p_{x,i}$ are the x-positions and x-momenta of the N electrons within the beam. A second measure for the transverse beam distribution is the normalised trace-space emittance (again exemplary for the horizontal x-direction):

$$ \epsilon_{tr,n,x} = \frac{\bar{p}_z}{mc} \sqrt{\langle x^2 \rangle \langle x'^2 \rangle - \langle xx' \rangle^2}, \qquad (7.10) $$

where $\bar{p}_z$ is the mean longitudinal momentum in the z-direction, whereas $x' = p_x/p_z$ is the horizontal divergence. The Courant-Snyder (or Twiss) parameters are then expressed as

$$ \alpha_x = -\frac{\langle xx' \rangle}{\epsilon_{tr,x}}, \quad \beta_x = \frac{\langle x^2 \rangle}{\epsilon_{tr,x}}, \quad \gamma_x = \frac{\langle x'^2 \rangle}{\epsilon_{tr,x}}, \qquad (7.11) $$

with $\epsilon_{tr,x} = \epsilon_{tr,n,x}(mc/\bar{p}_z)$. In all cases, equivalent values can be calculated for the vertical direction y.

As the inward-focussing forces on the electron beam need to match its outward space-charge forces for stable beam propagation, the transition from one beamline
element to the next with differing focussing fields requires the transverse beam size and divergence to be adapted and matched to the element. The following matching conditions in particular need to be fulfilled for the witness beam in a plasma – in the blowout regime, assuming negligible beam loading – to avoid oscillations of the beam envelope:

$$ \beta_{matching} = \frac{\sqrt{2\gamma_{ph}}}{k_p} \qquad (7.12) $$

$$ \sigma_{matching} = \sqrt{\frac{\beta_{matching}\epsilon_n}{\gamma_{ph}}} \qquad (7.13) $$

where $\sigma$ is the transverse electron beam RMS size. As discussed further in Chapters 14 and 19, these matching values are extremely small for plasma-accelerator stages, thus requiring strong and well-controlled focussing before the plasma entrance. Similarly, the electron beam is also strongly focussed when it leaves the plasma stage, thus putting considerable challenges on the capturing and transport line behind the plasma accelerator / injector where the matched beam size increases again.

### 7.1.4 Plasma Sources

Targets for plasma accelerators can be broadly classified as waveguide or non-waveguide targets, specifically for LWFA, depending on whether they are designed with a guiding mechanism for the drive laser. For the non-waveguide target, typically used for plasma injectors or low-energy accelerators, most often, a gas jet or a simple gas cell is used. Waveguide targets, on the other hand, mostly in use for high-energy acceleration, include a variety of different technologies, such as capillary discharge waveguides, plasma channels formed by hydrodynamic expansion, and gas-filled capillaries (more details in Chaps. 16 and 32.2). Each type of target can be further divided into being pre-ionised, almost always the case in PWFA, or being ionised by the driving laser. Further additional features can be important to implement in plasma targets to improve their performance, such as structures for controlling the injection of electrons into the wakefield, longitudinal variations of the plasma density for extending acceleration beyond the dephasing length for LWFA, or for controlling the properties of the electron bunch as it leaves the acceleration stage [196].

The specific properties of the plasma target depend on the following constraints:

- Plasma length: For LWFA stages, the acceleration length is usually optimally set to the dephasing length $L_{dp}$, thus determining the density and length of the stage. However, in some circumstances, it may be preferable to accelerate at lower intensities (e.g. to prevent target damage, to minimise emittance growth, etc.). This necessitates increasing the target length. For PWFA, both the length and the density are determined almost entirely by the desired final beam energy. The depletion length is an important parameter to name in this context as the distance over which the beam driver has lost all of its energy through driving the wake, thus representing the scenario of most efficient energy transfer between driver and witness.

- Density profile: For a laser wakefield electron injector, a tailored density profile can be useful; for example, injection can be assisted by a density downramp [15]. Similarly, density upramps can provide an energy boost at the end of a stage, and density profile shaping can be used to control the self-focussing and self-compression of the drive laser. Moreover, gradients can be used in the LWFA injector to compensate the energy chirp of the injected electron bunch and therefore reduce the energy spread [32]. Controlling the density profiles at both the
<figure><img src="image_64.png" /><figcaption>**Fig. 7.2.** Examples of different types of plasma sources used in plasma injectors and accelerators. The image on the left-hand side shows a setup used to produce a gas jet, while the image on the right-hand side depicts a capillary gas cell (image credits: Gwangju Institute of Science and Technology, Korea).</figcaption></figure>

entrance and the exit of plasma-accelerator stages is also vital to properly couple accelerated beams between stages [35,36].

- Density stability: It has been shown that the plasma electron density is a key parameter for the stability of the injector [197,198]. For EuPRAXIA, the acceptable level of fluctuations on the value of the density has been examined in a preliminary numerical tolerance study [171]. Further, more detailed investigations will be carried out in the future.

- Target repetition rate and lifetime: Most plasma accelerators currently operate at only a few Hz repetition rate, but for EuPRAXIA, this should be increased to a baseline of 20–100 Hz. For the plasma stages, this means that either targets should directly sustain hundreds of thousands of shots, or a remotely interchangeable target must be designed that can be replaced after a smaller number of shots without interrupting the operation.

## 7.2 Laser Science

As it has been pointed out in the previous chapters, the EuPRAXIA infrastructure will require several laser beamlines with peak power up to some petawatts (PW), pulse energy in the range of tens to hundreds of Joules, pulse duration in the range of some tens of femtoseconds up to 100 femtoseconds, and pulse repetition rates of 20 or 100 Hz. The implementation of the foreseen plasma acceleration schemes will require the simultaneous operation of up to three laser beamlines, with tight synchronisation requirements. The purpose of this chapter is to provide a general overview of the available laser technologies that can be employed to achieve the performance level exposed above. It must be pointed out that no system in the world is currently capable to achieve these requirements, in particular at a high repetition rate. Existing PW laser systems can achieve even higher energies or even shorter pulse duration but at a very low repetition rate (from a single shot to a few Hz at maximum).

All the existing high-peak-power (> few TW) laser technologies are based on the so-called chirped pulse amplification (CPA) technique. A short (e.g. tens of fs), broadband, low-energy seed laser pulse is first temporally stretched in a suitable delay line (stretcher), up to several hundreds of thousands of fs; then it is amplified in a
<figure><img src="image_65.png" /><figcaption>**Fig. 7.3.** Operating principle of chirped pulse amplification (CPA) and optical parametric chirped pulse amplification (OPCPA) (image credits: [200]).</figcaption></figure>

laser amplification chain up to the desired energy level. Finally, it is compressed to (about) the original pulse duration in a second delay line (compressor) conjugated with the stretcher. CPA (invented by G. Mourou, recently awarded the Nobel Prize for this achievement [199]) allows one to reach very high peak-power levels, avoiding severe non-linear optical effects in the amplifiers that would spoil the pulse duration and the laser beam quality and eventually could destroy the amplifier itself.

Following this approach, the architectures for the laser systems envisaged in EuPRAXIA will comprise at least a master oscillator, a pulse stretcher, one or more pre-amplification stages, one or more high-energy amplification stages, a pulse compressor, a beam transport system, and a final focussing system. As it will appear in the following parts, one of the most critical elements for the achievement of the required laser parameters is the pulse amplification system (in its broader meaning, i.e. including the gain elements, the pump system, and the cooling system), which must sustain the high-average-power regime imposed by the desired performance and keep non-linear optical effects below a given threshold. Another critical element is the pulse compression system, mainly because of the high-peak-power density handled by its last stage. Conversely, the master oscillator and the pre-amplifier stages appear less critical, given the lower average power involved, the relatively long pulse duration required, and the relatively low coherent contrast ratio. It must be underlined that the required repetition rate of 20 Hz is at the border between two alternative technologies for the pumping system. A repetition rate of 20 Hz on the desired energy range can still be obtained with flashlamp pumped systems. Under this limit, flashlamps still have advantages in terms of initial cost and operation costs with respect to solid state pumping (laser diode arrays), and are then a viable option. Above 20 Hz, pumping with laser diode arrays is probably the only option.

The available solid-state high-energy laser pulse amplification technologies that can be reasonably adopted for the development of the laser source foreseen by the project can be classified in the following main streamlines:

**Ti:Sapphire-based systems:** In this case, the gain medium is titanium-doped Al2O3 (Sapphire). Given the broad gain bandwidth, this gain medium allows the generation of laser pulses with a duration down to a few fs and the amplification in the timescale of a few tens of fs at a wavelength of about 800 nm.
On the other hand, Ti:Sapphire must be pumped in the visible (typically in the range of 500–550 nm), which is commonly obtained by using frequency-doubled Q-switched lasers operating in the near infrared (e.g. Nd:YAG, Yb:YAG). As a consequence, the wall plug efficiency of the pumping system is usually quite low, in particular when flashlamp pumped lasers are used. Moreover, the quantum defect between the pump photon energy and the fluorescence photon energy is quite high (about 34%). This imposes a relatively high level of thermal load on the gain medium, the effects of which are nonetheless mitigated by the high thermal conductivity of the host. For these reasons, the operation at high average power of these systems can be quite challenging. Finally, the development of a high-energy laser system will require large aperture gain elements. Ti:Sapphire can only be produced as a single crystal, and this can be a limitation for the size of the gain elements. Anyhow, Ti:Sapphire crystals with a size exceeding 7 inches were already delivered by Crystal System for ELI-NP and Apollon (see below) to reach up to 200 J of energy (corresponding to 100 J on target). Currently operating PW laser systems based on Ti:Sapphire amplification are, for instance, APOLLON [201] and LASERIX in France [202], BELLA in the United States [203], PULSER in South Korea [204], and Xtreme Light III in China [205].

**Yb-based systems:** Compared to Ti:Sapphire, Yb-based gain media have many advantages in terms of pumping efficiency. First of all, they allow direct pumping by semiconductor lasers in the wavelength region of 930–970 nm without further wavelength conversion stages. Moreover, the quantum defect between the pump photon energy and the laser photon energy is rather low (around 10%) because the emission wavelength (usually 1030–1050 nm, depending on the host) is close to the pumping wavelength. This reduces the thermal load on the gain medium, and thus, the power dissipation requirements. Both of these elements are advantageous in view of a high-average-power operation regime. The main drawback of Yb-based gain media is the reduced gain bandwidth, which makes it difficult to achieve the desired pulse duration of 100 fs for high energy pulses, whereas operation in the range of 100–200 fs is more easily achieved. Moreover, in Yb-doped media, the saturation fluence of the laser transition often largely exceeds the damage threshold of the host; in these cases, the amplification stage cannot operate in saturation, which limits the energy extraction and jeopardises the overall system efficiency [206]. Two high-energy sub-PW laser systems, both based on amplification in Yb:CaF2, have been realised in Germany, namely, PEnELOPE [207] and POLARIS [208].

**Nd:glass-based systems:** Some high-energy laser systems adopt Nd:glass as a gain medium for the final power amplification stages. Nd-doped glasses provide a gain bandwidth suitable for the generation and amplification of pulses in the 100 fs time range. Large gain elements can be produced with glasses more easily than with crystal growth technologies. Moreover, Nd:glasses can be directly pumped with semiconductor lasers, which is advantageous for the overall efficiency and power dissipation requirements of the pump system. On the other hand, even though the thermally dissipated pump power fraction is moderate (around 20%), the operation at high-average-power levels of Nd:glass bulk amplifiers is hampered by the poor thermal conductivity of the glass host, which makes the cooling of the gain elements difficult, unless special provisions are adopted. An example of a PW laser system based on this technology is the Texas Petawatt Laser in the United States [209].

**OPCPA systems:** An alternative method for the amplification of high-peak-power pulses is based on parametric light amplification in non-linear optical crystals (optical parametric chirped pulse amplification, OPCPA) [210,211]. Instead of using ordinary laser media (based on the excitation/de-excitation of an atomic
<table><caption>**Table 7.1.** Main parameters of some PW laser systems worldwide. Operational systems are shown in bold. The energy value is reported after compression.</caption><thead><tr><th>System</th><th>Country</th><th>Ampl. medium (last stage)</th><th>Wavelength (nm)</th><th>Energy (J)</th><th>Pulse length (fs) (FWHM)</th><th>Peak power (PW)</th><th>Rep. rate (Hz)</th><th>Contrast</th></tr></thead><tbody><tr><td>APOLLON</td><td>FRA</td><td>Ti:Sa</td><td>800</td><td>150</td><td>15</td><td>10</td><td>0.017</td><td>10<sup>10</sup></td></tr><tr><td>ALPS HF*</td><td>HUN (EU)</td><td>Ti:Sa</td><td>800</td><td>34</td><td>&lt;17</td><td>2</td><td>10</td><td>10<sup>11</sup></td></tr><tr><td>BELLA</td><td>USA</td><td>Ti:Sa</td><td>800</td><td>40</td><td>30</td><td>1</td><td>1</td><td>10<sup>10</sup></td></tr><tr><td>HAPLS L2*</td><td>CZE (EU)</td><td>OCPA</td><td>800-850</td><td>18</td><td>15</td><td>1</td><td>10</td><td>N/A</td></tr><tr><td>HAPLS L3*</td><td>CZE (EU)</td><td>Ti:Sa</td><td>800</td><td>30</td><td>30</td><td>1</td><td>10</td><td>N/A</td></tr><tr><td>HPLS*</td><td>ROM (EU)</td><td>Ti:Sa</td><td>800</td><td>200</td><td>20</td><td>10</td><td>0.017</td><td>10<sup>12</sup></td></tr><tr><td>LASERIX</td><td>FRA</td><td>Ti:Sa</td><td>800</td><td>40**</td><td>50</td><td>0.8</td><td>0.1</td><td>N/A</td></tr><tr><td>PEnELOPE</td><td>GER</td><td>Yb:CaF2</td><td>1035</td><td>150*</td><td>140</td><td>1*</td><td>1</td><td>N/A</td></tr><tr><td>POLARIS</td><td>GER</td><td>Yb:CaF2</td><td>1030</td><td>17</td><td>&lt;100</td><td>0.17</td><td>0.02</td><td>10<sup>9</sup></td></tr><tr><td>PULSER</td><td>KOR</td><td>Ti:Sa</td><td>820</td><td>83</td><td>20</td><td>4</td><td>0.1</td><td>10<sup>9</sup></td></tr><tr><td>QUIANG- GUANG 5 PW</td><td>CHN</td><td>Ti:Sa</td><td>800</td><td>138***</td><td>27***</td><td>5.1***</td><td>0.0083</td><td>N/A</td></tr><tr><td>RAL 10 Hz PW*</td><td>UK</td><td>Ti:Sa</td><td>800</td><td>30</td><td>30</td><td>1</td><td>10</td><td>10<sup>10</sup></td></tr><tr><td>SHENGUANG II</td><td>CHN</td><td>OCPA</td><td>808</td><td>37</td><td>21</td><td>1.76</td><td>S.S.</td><td>N/A</td></tr><tr><td>TEXAS PW LASER</td><td>USA</td><td>Nd Glass</td><td>1060</td><td>186</td><td>&lt;170</td><td>1.1</td><td>0.0017</td><td>10<sup>5</sup></td></tr><tr><td>VULCAN 20 PW*</td><td>UK</td><td>OCPA</td><td>1053</td><td>300</td><td>30</td><td>10</td><td>0.0011</td><td>N/A</td></tr><tr><td>XTREME LIGHT III</td><td>CHN</td><td>Ti:Sa</td><td>800</td><td>32.3</td><td>29</td><td>1.16</td><td>0.0083</td><td>10<sup>6</sup></td></tr></tbody></table>

transition), the amplification is based on optical difference frequency generation in non-linear crystals. Compared to standard amplification, OPCPA has several specific features that can be potentially advantageous, including a very high amplification factor of chirped pulses (up to 3–4 orders of magnitude per pass in terms of energy) and a high contrast because the parametric gain exists only when the pump pulse is present. Finally, the process is non-dissipative because the energy difference between the pump (highest energy) photon and the amplified signal (lower energy photon) is emitted as a third photon (the so-called idler), and it is not dissipated into the crystal, as it happens in the stimulated emission process. Therefore, the parametric amplification process imposes a much lower thermal load on the amplified medium with respect to amplification based on the emission from atomic transitions. The amplification of high-energy pulses requires large aperture crystals; this limits the choice of possible non-linear materials, mainly to KDP, DKDP, and LBO. OPCPA is used in the last amplification stage of the Shenguang II laser system in China [212].

Table 7.1 shows a synopsis of the emission parameters of several PW laser systems worldwide, currently operating or in advanced construction phase, in alphabetical order. Data are derived from published papers [213] and documentation available on the websites of the various facilities.

Many of the above approaches to high-average-power amplification are developing fast and hold the promise to deliver revolutionary performances to drive plasma acceleration and other major applications of such high-intensity lasers. However, in the perspective of a short-term approach, a driver for a plasma accelerator capable of outstanding parameters, like those required by the EuPRAXIA laser, should be based on components with a high technology readiness level (TRL), ideally sourcing from a lab environment where specific technologies have been explored in depth. Ti:Sa technology is currently used in the HAPLS system (ELI Beamlines) to deliver today’s highest available average power (design value: 300 W) and is certainly the preferred platform that can lead to the required specifications by scaling existing systems.

<footnote>*Design specifications. **Before compression. ***Small-scale test.</footnote>
However, as anticipated, scaling to kW average power still requires innovative solutions for high repetition rate, including a transition from a flashlamp to fully DPSSL-based pumping and efficient thermal management in both the amplifier and the whole transport chain from the compressor to the target plasma. kW-scale lasers suitable for pumping Ti:Sa in the 10–20 Hz repetition rate range are just emerging with industrial systems, like the P60 by Amplitude Technologies (FR), or prototypes, like the DiPOLE system developed at the Central Laser Facility (UK), and can be integrated into advanced Ti:Sa amplifier designs, provided a geometry with efficient cooling ensures heat removal from the amplifier head. This is a crucial issue that is taking much of the design effort. In fact, existing amplifier architectures, including those successfully used in systems, like HAPLS, feature cooling schemes (e.g. multi-slab with gas cooling) that cannot be easily scaled to the required heat removal capacity for a kW-scale system. Possible solutions include the use of liquid cooling, requiring a major effort in counteracting the depletion of beam quality stemming from propagation through a non-uniform, highly refractive material, or implementing alternative cooling concepts to avoid propagation through the cooling liquid, like the “active mirror” concept used in the P60 system.

Both pumping schemes and cooling architectures are key conceptual aspects of the laser design that have an impact on both the complexity and the compactness of the final system.

## 7.3 Free-Electron Lasers

Relativistic charged particles moving subject to a magnetic field lose energy, while emitting synchrotron radiation, an intrinsic limiting factor to accelerate electrons at high energy with circular machines that turn out to have an increasingly important role in many areas of basic and applied sciences. In particular, the kinetic energy of a relativistic electron beam is transformed into an intense laser beam of electromagnetic radiation by wiggling the electrons transversely in a long undulator: the free-electron laser (FEL) [215–218]. An FEL consists of a laser where the basic emission process does not occur in a bound atomic or molecular system with population inversion. Such machines are becoming the main source of tunable, intense, and coherent photons of either ultra-short time resolution or ultra-fine energy resolution on a broad band of frequencies that cannot be covered with most of other conventional light sources. In existing facilities, they can cover a range from the terahertz to the hard X-ray regime.

An electron beam is associated with a power equal to the product of beam energy $E$ and current $I$:

$$P_E[\text{MW}] = I[\text{A}] E[\text{MeV}]. \qquad (7.14)$$

Such power is delivered to the beam by the particle accelerator. The magnetic field associated with an undulator with period $\lambda_u$ and on-axis peak field $B_0$, on the other hand, is

$$\mathbf{B} = \left( 0, B_0 \sin \frac{2\pi z}{\lambda_u}, 0 \right). \qquad (7.15)$$

The Lorentz force due to the undulator field introduces a transverse component in the electron motion, described by the deflection strength parameter $K$,

$$K = \frac{eB_0\lambda_u}{2\pi m_e c} \approx 0.943 B_0[\text{T}] \lambda_u[\text{cm}], \qquad (7.16)$$

where $e$, $m_e$, and $c$ are, respectively, the electron charge, the electron mass, and the speed of light in vacuum. For a single electron of given energy $E = \gamma m_e c^2$ and Lorentz
<figure><img src="image_66.png" /><figcaption>Fig. 7.4. Operating principle of a free-electron laser (FEL) (image credits: [214], reprinted with permission of Springer Nature).</figcaption></figure>

factor $\gamma$, the resonance condition on the wavelength $\lambda_0$ of the emitted radiation is

$$ \lambda_0 = \frac{\lambda_u}{2\gamma^2} \left( 1 + \frac{K^2}{2} \right) \qquad (7.17) $$

The efficiency of the energy transfer from electrons to the radiation field, and the gain of the process are described by the FEL Pierce parameter $\rho$:

$$ \rho = \frac{1}{4\pi\gamma} \sqrt[3]{2\pi \frac{J}{I_0} (\lambda_u K f_b(K))^2} \approx \frac{8.36 \times 10^{-3}}{\gamma} \sqrt[3]{(\lambda_u [\text{m}] K f_b(K))^2 J \left[ \frac{A}{\text{m}^2} \right]}, \quad (7.18) $$

where $f_b(K) = J_0(\xi) - J_1(\xi)$ is the planar undulator Bessel correction factor with the argument $\xi = \frac{K^2}{2+K^2}$ and $I_0 = 17$ kA as the Alfvén current. The beam current is expressed in terms of the bunch root mean squared (RMS) time duration $\sigma_\tau$ and the bunch charge $Q_b$ as

$$ I[A] = \frac{Q_b[C]}{\sigma_\tau[s]\sqrt{2\pi}} \qquad (7.19) $$
The current density $J$ is given by

$$J \left[ \frac{A}{m^2} \right] = \frac{Q_b[C]}{\sigma_{\tau}[s] \sigma_x[m] \sigma_y[m] (2\pi)^{3/2}} \quad (7.20)$$

where $\sigma_{x,y}[m]$ is the RMS transverse size of the electron beam.

Equation (7.18) plays a crucial role in the theory and design of high-gain self-amplified spontaneous emission (SASE) FEL devices as it specifies efficiency, laser growth rate, bandwidth, and the role of inhomogeneous broadening. In fact, estimates of the SASE FEL bandwidth $\Delta\omega/\omega$ and saturation power $P_S$ are, respectively, provided by

$$\frac{\Delta\omega}{\omega} \approx \rho \quad \text{and} \quad P_S \approx \sqrt{2\rho} P_E. \quad (7.21)$$

The gain length determining the FEL growth rate can be expressed in terms of $\rho$ as follows:

$$L_g = \frac{\lambda_u}{4\pi\sqrt{3}\rho}. \quad (7.22)$$

The power growth can be expressed [219] in terms of the following logistic equation:

$$P(z) = P_0 \frac{A(z)}{1 + \frac{P_0}{P_S} [A(z) - 1]}, \quad (7.23)$$

$$A(z) = \frac{1}{9} \left[ 3 + 2 \cosh \left( \frac{z}{L_g} \right) + 4 \cos \left( \frac{\sqrt{3} z}{2L_g} \right) \cosh \left( \frac{z}{2L_g} \right) \right],$$

with $P_0$ being the input seed and $z$ the longitudinal propagation coordinate. Accordingly, the length of the undulator section needed to reach the saturated power, the so-called saturation length, is

$$L_S \approx 1.066 L_g \ln \left( \frac{9 P_S}{P_0} \right). \quad (7.24)$$

The effects of inhomogeneous broadening – namely, the gain deterioration because of non-ideal electron beam qualities, in particular significant energy spread and emit-tance values – are embedded in the previous formulae by means of the $\mu$ parameters. These quantify the main contributions to the effective $\rho$ reduction, and so to the gain length increase, leading to $L_{g,\epsilon}$ as an effective quantity.

Regarding the energy spread, we have the following:

$$L_{g,\epsilon}(\chi) = \chi L_g, \quad \chi \approx 1 + \frac{0.185\sqrt{3}}{2} \mu_{\epsilon}^2, \quad (7.25)$$

$$\mu_{\epsilon} = 2 \frac{\sigma_{\epsilon}}{\rho}, \quad \sigma_{\epsilon} = \frac{\Delta E}{E}, \quad \Delta E = \sqrt{\langle E^2 \rangle - \langle E \rangle^2}.$$

A reliable estimate of $L_S$ requires also to consider inhomogeneous broadening effects due to three-dimensional diffraction contributions, which modify the Pierce parameter by introducing the $\mu_D$ diffraction parameter, as described below:

$$\mu_D = \frac{\lambda\lambda_u}{(4\pi\sigma_T)^2\rho}, \quad \rho_D = \mathcal{F}(\mu_D)\rho, \quad \mathcal{F}(\mu_D) = \frac{1}{\sqrt[3]{1 + \mu_D}}, \quad (7.26)$$

where we considered a transversely symmetric electron beam with $\sigma_x = \sigma_y = \sigma_T$ and $\epsilon_x = \epsilon_y$.
Together with these formulae describing the fundamental harmonic, similar expressions are found regarding the non-linear higher harmonics generation FEL mechanism, characterised by the $n^{th}$ harmonic radiation wavelength as follows:

$$ \lambda_n = \frac{\lambda_u}{2n\gamma^2} \left(1 + \frac{K^2}{2}\right) \qquad (7.27) $$

The theory described above has been used for guiding the FEL design of EuPRAXIA. Specific performance estimations and simulations with numerical codes are described in Section 24.1.

# 8 Description of the Overall Facility Layout and Its Building Blocks

The conceptual design presented in this part is focussed on the two machine sites of EuPRAXIA and based on complementary plasma-accelerator technologies, as introduced in Section 3.3.2.

In the following chapters, the main components foreseen for the two construction sites are presented, and an overview over the technical solutions found in each case is given. Figures 8.1 and 8.2 highlight the main technical sub-systems envisaged for each site and provide a reference to the respective chapters and sections where further information on these components can be found. Six types of sub-systems are considered, in this context, in the facility design:

* laser systems

* RF injectors and accelerators

* plasma injectors and accelerators

* transport lines for different types of beams (electrons, positrons, photons)

* beamline sections for generating secondary sources or conditioning the beams

* user areas

Some of these, such as the electron beam transport lines, have very similar characteristics in both sites and are thus described in a general way. Others, such as the plasma injectors and accelerators, are targeted to a specific site only. For certain components, as described in the following, multiple design options are considered, with some foreseen as baseline solutions, while others are backup options or paths for future developments. A further down-selection of the proposed techniques and components is planned only during the technical design phase, once further test experiments and prototyping have validated the performance of the different technical options. This strategy takes into account the potential and excellent computational results for the solutions considered while, at the same time, mitigating the risk of building a machine based on technologies not tested in a user-operation setting before.

## 8.1 EuPRAXIA Site for Beam-Driven Plasma Acceleration

Before going into the technical details and tables of parameters, here, we first summarise the main building blocks from an overview perspective. As Figure 8.1 highlights, the following sub-systems and design solutions are proposed for the EuPRAXIA site for beam-driven plasma acceleration:

**RF injector and accelerator:** The baseline design for the RF-based accelerator consists of an S-band injector with velocity bunching combined with an X-band
<figure><img src="image_67.png" /><figcaption>**Fig. 8.1.** Overview layout of the EuPRAXIA site for beam-driven plasma acceleration.</figcaption></figure>

linac producing electron beams with energy of around 500 MeV. An extension of the accelerator to 1 GeV is further considered as an *upgrade / backup option* as the plasma accelerator stages could be omitted or used to reach higher energies than with the baseline design. More details on the RF injector and accelerator for generating the driver and witness electron beams at the PWFA site can be found in Chapters 14 and 12, respectively.

**Plasma accelerators:** Two types of plasma accelerators are foreseen at the PWFA site of EuPRAXIA: one focussed on high beam quality for radiation generation and the other aiming to produce high-charge, high-average-power electron beams suitable for positron generation and as test beams. The *baseline* in both cases considers the external injection of the electron drive and witness beams from the RF accelerator into a weakly non-linear plasma stage to achieve beam-driven wakefield acceleration up to 1 GeV. The generated electron bunches based on current results comply with the requirements for both types of accelerator stages but could be optimised further towards high charge or high quality in the future. A detailed design is described in Section 17. Additionally, potential *future development paths* are foreseen through (1) increasing the energy reach to 5 GeV (see Sect. 17.2) as well as (2) improving the beam quality further, for example through using the RF-accelerated electron beam as a driver in a beam-driven plasma wakefield injector based on the Trojan horse injection mechanism (more details in Sect. 26).

**Free-electron laser:** The EuPRAXIA facility *baseline* foresees the use of conventional undulators in all of its FEL beamlines as a risk-mitigating measure, as described in Chapters 18 and 24.1. The adoption of more compact, novel
<figure><img src="image_68.png" /><figcaption>Fig. 8.2. Overview layout of the EuPRAXIA site for laser-driven plasma acceleration.</figcaption></figure>

undulator concepts, at least for parts of the undulator line, will be examined
as a potential *future development path*.

**ICS γ-ray source:** The inverse Compton scattering (ICS) interaction section and considerations for the user area are described in Section 24.3.

**HEP detector testing and GeV-class positron source:** The high-energy physics (HEP) detector testing application and the generation of high-energy positron beams are foreseen with a common beamline as complementary user applications. The section comprises two parts the first of which is a target and transport line for the conversion of the high-energy electron beam to a positron beam, its energy filtering, and collimation. Second, the remaining electron beam is conditioned for use in detector testing and transported to the respective user area. Detailed designs for both aspects are presented in Sections 25.1 and 25.2.2.
## 8.2 EuPRAXIA Site for Laser-Driven Plasma Acceleration

Similarly to the PWFA site, here, we first summarise the main building blocks of the design of the laser-driven construction site from an overview perspective, before going into the technical details and tables of parameters. The main sub-systems proposed for the EuPRAXIA site for laser-driven plasma acceleration are shown in Figure 8.2. The following design solutions are considered for each component:

**Laser system:** The high-power laser system design of EuPRAXIA consists of three sub-systems optimised for the different types of plasma stages on site: (1) a 5–7 J laser suitable to drive a plasma injector; (2) a 15–30 J targeted for plasma acceleration to 1 GeV; and (3) a 50–100 J laser for plasma acceleration to 5 GeV. Two performance levels are foreseen as part of the *baseline*, including, among others, operation at 20 Hz and 100 Hz. A main *future development path* for the laser system will be towards higher average power and repetition rate at the kHz level. Further details are presented in Chapter 10.

**RF injector:** The *baseline* design for the RF injector line consists of an S-band injector combined with a hybrid bunch compression scheme (combining velocity bunching and magnetic compression) producing electron beams with energy of around 250 MeV. A second presented option is the same setup as foreseen for the PWFA construction site; here, an S-band injector with velocity bunching is combined with an X-band linac to reach an electron beam energy of ~500 MeV. Both designs are described in Chapter 14.

**Plasma injector:** Three *baseline* designs are under consideration for the plasma injector with electron beam energy variable between 140 and 250 MeV:

1. Resonant multi-pulse ionisation (ReMPI) injection

2. Density downramp injection

3. Ionisation injection with a density gradient

As detailed in Chapter 13 and, partly, Chapter 23 (start-to-end simulations), for all three schemes, state-of-the-art performance is predicted, while space and cost requirements are similar and very small compared to the overall beamline. It is thus foreseen to validate and optimise all three designs during the coming technical design phase before making a decision on the injection technique implemented for the final design.

**High-quality plasma accelerator:** Similarly to the plasma injector, three *baselines* with excellent performance have been identified for the high-quality plasma accelerator and will be optimised during the technical design, as Chapters 23 (start-to-end simulations) and 16 demonstrate:

1. External injection of the RF-accelerated electron beam into two consecutive plasma-accelerator stages separated by a chicane-based dechirping mechanism

2. External injection of the RF-accelerated electron beam into a single plasma-accelerator stage

3. External injection of an electron beam generated from a plasma injector into a single plasma-accelerator stage

In all three cases, the final electron beam energy is 1 GeV during the first preliminary operation phase before increasing to 5 GeV during full operation. Note that given the small size of the plasma stages, all three concepts are compatible with a single beamline layout, as the first plasma-accelerator stage in the first proposed scheme can easily be removed for setup number two or replaced by a plasma-injector stage to achieve the third setup, thus not affecting the size and cost estimation of the machine significantly. Furthermore, several *upgrade / backup options* are investigated for this challenging beamline design, including
the use of different plasma-injector techniques. Finally, a hybrid plasma acceler-
ator with a laser-driven plasma injector producing the driver beam for a second
beam-driven, high-energy plasma-injector stage is further studied as a poten-
tial *development path* (see Chap. 26). Three types of injection mechanisms for
the second beam-driven injector stage are, in this case, considered as promising
solutions.

**High-charge plasma accelerator:** For this type of setup, focussed less on beam quality and more on large beam charge but benefiting strongly from a compact design, an all-optical *baseline* is proposed with a plasma injector followed by external injection into a single plasma-accelerator stage, accelerating the beam to 5 GeV. As with the high-quality accelerator, different techniques for the plasma injector – such as ReMPI injection, downramp injection, and ionisation injection – are examined as different options. A *future development path* is a high-energy plasma injector based on the ReMPI injection mechanism where electrons could be internally injected and accelerated up to 1 to 5 GeV, achieving an extremely compact setup.

**Free-electron laser:** Equivalently to the PWFA site design, the *baseline* for the LWFA-driven FEL will also use conventional undulators, as described in Chapters 18 and 24.1. The implementation of more compact, novel undulator concepts will be a common *future development path*.

**Life-science and materials X-ray imaging:** A compact X-ray source based on betatron radiation inside a plasma target is foreseen for this application. As a *baseline*, the radiation can be directly created inside the plasma injector used for electron beam generation leading to a relatively simple and flexible beamline setup. *Future development paths* will focus on the optimisation of the source, for example, through separating the electron beam injection process from the radiation generation, with an additional dedicated plasma target as a betatron source. The design for this part of the beamline is described in Section 21.7.

**Ultracompact positron source and tabletop test beams:** Similarly to the PWFA site, both of these applications, the generation of an ultra-compact positron source, and the creation of tabletop test beams are foreseen with a common beamline. The section comprises two parts the first of which is a target and transport line for the conversion of the high-energy electron beam to a positron beam, its energy filtering (keeping the low-energy part of the positron beam), and collimation. Second, the remaining electrons are conditioned for use as test beams. They could be used in a similar way to the high-energy physics detector test stand at the PWFA site but will also be suitable for other applications yet to be determined. Detailed designs for both aspects are presented in Sections 25.1 and 25.2.1.

**8.3 Beam Distribution Concept**

Throughout many of the following chapters, describing the detailed design of machine
components, six possible accelerator and beam distribution configurations are con-
sidered. They are shown schematically in Figure 8.3 and listed with their abbreviated
names in Table 8.1. Further details are also included in Chapter 23 in the context of
start-to-end simulations of the accelerator.

The following schemes are foreseen as possible beamline configurations for one or
several of the proposed beamlines at EuPRAXIA:

**Scheme 1** is a laser-driven plasma injector (LPI) where the electron beam is gener-
ated and also accelerated up to 5 GeV in a single plasma stage.
**Table 8.1.** Naming convention of the different accelerator schemes investigated as part of the EuPRAXIA conceptual design study. In each case, the energy value after a stage's name indicates the electron beam energy at the end of this stage. Different stages are connected by transport lines, which are detailed in Chapter 19. The following abbreviations are used: LPI = laser-plasma injector, RFI = radiofrequency injector, LPAS = laser-driven plasma-accelerator stage, PPAS = beam-driven plasma-accelerator stage.

<table><thead><tr><td>Scheme no.</td><td>Short descriptive name</td></tr></thead><tbody><tr><td>1</td><td>LPI-5 GeV</td></tr><tr><td>2</td><td>LPI-150 MeV + LPAS-5 GeV</td></tr><tr><td>3</td><td>RFI-500 MeV + LPAS-5 GeV</td></tr><tr><td>4</td><td>RFI-240 MeV + LPAS-2.5 GeV + chicane + LPAS-5 GeV</td></tr><tr><td>5</td><td>RFI-500 MeV + PPAS-1 GeV</td></tr><tr><td>6</td><td>LPAS-3 GeV + PPAS-5 GeV</td></tr></tbody></table>

<figure><img src="image_69.png" /><figcaption>**Fig. 8.3.** Beam distribution and acceleration configurations under consideration for the various EuPRAXIA beamlines. The following abbreviations are used besides those listed in the main text: LETL = low-energy transport line, HETL = high-energy transport line. A detailed description and assessment of the performance of each of these schemes as a whole is presented in Chapter 23 (image credits: [171]).</figcaption></figure>

**Scheme 2** is a staged setup where the electron beam is generated in a laser-driven plasma injector (LPI), then transported and injected into a laser-driven plasma-accelerator stage (LPAS), where its energy is boosted up to 5 GeV.

**Scheme 3** is a staged setup where the electron beam is generated in an RF photo-injector and pre-accelerated in an RF linac (RFI), then transported and injected into a laser-driven plasma accelerator stage (LPAS) where its energy is boosted up to 5 GeV.

**Scheme 4** is a staged setup where the electron beam is generated in an RF photo-injector and pre-accelerated in an RF linac (RFI), then transported and injected into two consecutive laser-driven plasma-accelerator stages (LPAS); in each stage the beam experiences an energy gain of approximately 2.5 GeV, while propagation through a magnetic chicane in the transport between the LPAS induces an energy dechirping process.

**Scheme 5** is a staged setup where two electron beams – a driver and a witness – are generated in an RF photo-injector and pre-accelerated in an RF linac (RFI), then
transported and injected into a beam-driven plasma-accelerator stage (PPAS), where the energy of the witness beam is boosted up to 5 GeV.

**Scheme 6** is a staged hybrid accelerator setup where a laser-driven plasma injector (LPAS) generates an electron beam that is in turn used as the beam driver in a second beam-driven plasma injector (PPAS); in the latter a higher quality electron beam is generated and accelerated up to 5 GeV.

Schemes 1 to 4 are all based on laser-driven plasma acceleration and are thus relevant for implementation at the laser-driven construction site of EuPRAXIA. For a versatile and optimised layout, it is foreseen that different beamlines will be designed based on different schemes; the central laser system of EuPRAXIA will allow to feed several of these lines in parallel. Scheme 5, on the other hand, is a beam-driven plasma accelerator configuration and forms the baseline for the accelerator at the beam-driven construction site. Multiple user areas can be served by splitting the central line either before or after the plasma-accelerator stage (PPAS). In the former case, the plasma sections could be customised to each application, while, in the latter scenario, the transport of the beam may be less challenging. Finally, Scheme 6 provides a potential future development option for both sites with a configuration that combines laser-driven and beam-driven plasma acceleration, with the promise of exceptional electron beam quality.

## 9 Summary Tables of Parameters and Technical Data

The design of the technical components for EuPRAXIA has been guided by a set of goal parameters defining successful performance through the realisation of key applications. A particularly challenging target in this context has been identified with the capability to run an FEL and this has consequently been chosen as a baseline goal for the electron accelerator performance. Considering that most of the other applications foreseen for EuPRAXIA have comparably relaxed conditions for the more challenging beam parameters in plasma acceleration, such as energy spread and emittance, they should thus also be attainable through fine-tuning such an FEL-capable machine. Table 9.1 summarises the key goal parameters for the electron accelerator following this derivation (see [220] for the original complete parameter list, some updates to which have been made since its publication).

<table><caption>**Table 9.1.** Estimated goal parameters of the electron beam at the entrance of an undulator for FEL lasing. These values have been determined by the EuPRAXIA collaboration and form an updated version of the original design concept in [220]. Most of the design work on technical components has been informed by these aimed performance ranges.</caption><thead><tr><td>Quantity</td><td>Baseline Goal</td><td>Range of Exploration</td></tr></thead><tbody><tr><td>Energy</td><td>5 GeV</td><td>≥1 GeV</td></tr><tr><td>Charge</td><td>30 pC</td><td>5–100 pC</td></tr><tr><td>Bunch length (FWHM)</td><td>10 fs</td><td>≤30 fs</td></tr><tr><td>Peak current</td><td>3 kA</td><td>2–5 kA</td></tr><tr><td>Energy spread</td><td>1 %</td><td>&lt;1 %</td></tr><tr><td>Normalised emittance in x,y</td><td>1 mm mrad</td><td>&lt;1 mm mrad</td></tr><tr><td>Slice energy spread</td><td>0.1 %</td><td>&lt;0.1 %</td></tr><tr><td>Normalised slice emittance in x,y</td><td>&lt;1 mm mrad</td><td>≤1 mm mrad</td></tr></tbody></table>
Based on the goals of Table 9.1, in-depth conceptual solutions have been developed and the expected performance of different working points has been simulated in detail. The resulting performance predictions are summarised in the parameter tables following in this chapter. Experimental results are also taken into account in this context, as far as possible (e.g. for the plasma injector). More detailed explanations of the origins of the listed values can be found in the relevant component chapters, as defined in the respective table captions.

## 9.1 Laser System

**Table 9.2.** Summary table of parameters and technical data of the laser system. More detailed parameters and further context are found in Chapter 10.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td>Laser 1 – Energy on target</td><td>≤ 5–7 J</td></tr><tr><td>Laser 1 – Pulse duration</td><td>≥ 20–30 fs</td></tr><tr><td>Laser 2 – Energy on target</td><td>≤ 15–30 J</td></tr><tr><td>Laser 2 – Pulse duration</td><td>≥ 20–30 fs</td></tr><tr><td>Laser 3 – Energy on target</td><td>≤ 50–100 J</td></tr><tr><td>Laser 3 – Pulse duration</td><td>≥ 50–60 fs</td></tr><tr><td>Wavelength</td><td>800 nm</td></tr><tr><td>Repetition rate</td><td>20–100 Hz</td></tr><tr><td>Energy stability (RMS)</td><td>0.6–1 %</td></tr><tr><td>Pointing stability (RMS)</td><td>~1 µrad</td></tr></tbody></table>

## 9.2 RF Injector and Accelerator

**Table 9.3.** Summary table of parameters and technical data of the RF injector and accelerator. More detailed parameters and further context are found in Chapters 12 and 14.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td colspan="2">RF Injector / Accelerator – Full RF Compression Scheme (for LWFA / PWFA)</td></tr><tr><td>Photoinjector – Operating frequency</td><td>2.856 GHz</td></tr><tr><td>Photoinjector – Gun field amplitude</td><td>120 MV m<sup>-1</sup></td></tr><tr><td>Photoinjector – Gun output beam energy</td><td>5.6 MeV</td></tr><tr><td>Photoinjector – TW sections field amplitude</td><td>20–28 MV m<sup>-1</sup></td></tr><tr><td>Photoinjector – solenoid magnetic field (gun, linac)</td><td>3.0–3.05 kG, 0.32–0.52 kG</td></tr><tr><td>Photoinjector – Length</td><td>12 m</td></tr><tr><td>Linac – Operating frequency</td><td>~12 GHz</td></tr><tr><td>Linac – Field amplitude</td><td>≥60 MV m<sup>-1</sup></td></tr><tr><td>Linac – Length</td><td>10 m</td></tr><tr><td colspan="2">Witness Electron Beam Parameters after the RF Injector / Accelerator</td></tr><tr><td>Charge</td><td>30 pC</td></tr><tr><td>Energy</td><td>535–570 MeV</td></tr><tr><td>Energy spread (RMS)</td><td>0.07 %</td></tr><tr><td>Bunch length (RMS)</td><td>17–20 fs</td></tr><tr><td>Peak current (FWHM)</td><td>3.0 kA</td></tr><tr><td>Normalised emittance in x,y (RMS)</td><td>0.5–0.7 mm mrad (x),0.44–0.9 mm mrad (y)</td></tr><tr><td colspan="2">Driver Electron Beam Parameters after the RF Injector / Accelerator</td></tr><tr><td>Charge</td><td>200 pC</td></tr><tr><td>Energy</td><td>580 MeV</td></tr><tr><td>Bunch length (RMS)</td><td>20 fs</td></tr><tr><td>Normalised emittance in x,y (RMS)</td><td>4.0 mm mrad (x), 6.4 mm mrad (y)</td></tr><tr><td colspan="2">RF Injector – Hybrid Compression Scheme (for LWFA)</td></tr><tr><td>Photoinjector – Operating frequency</td><td>2.856 GHz</td></tr><tr><td>Photoinjector – Gun field amplitude</td><td>110 MV m<sup>-1</sup></td></tr><tr><td>Photoinjector – Gun output beam energy</td><td>5 MeV</td></tr><tr><td>Photoinjector – TW sections field amplitude</td><td>25.5 MV m<sup>-1</sup></td></tr><tr><td>Photoinjector – Length</td><td>12 m</td></tr><tr><td colspan="2">Witness Electron Beam Parameters after the RF Injector</td></tr><tr><td>Charge</td><td>29.8 pC</td></tr><tr><td>Energy</td><td>240.8 MeV</td></tr><tr><td>Energy spread (RMS)</td><td>0.27 %</td></tr><tr><td>Bunch length (RMS)</td><td>7.5 fs</td></tr><tr><td>Peak current (FWHM)</td><td>4.0 kA</td></tr><tr><td>Normalised emittance in x,y (RMS)</td><td>0.81 mm mrad (x), 0.46 mm mrad (y)</td></tr></tbody></table>
## 9.3 Plasma Injector

**Table 9.4.** Summary table of parameters and technical data of the plasma injector. More detailed parameters and further context are found in Chapter 13.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td colspan="2"><strong>Low-energy LPI</strong></td></tr><tr><td>Plasma electron density</td><td>3 × 10<sup>18</sup>–8 × 10<sup>18</sup> cm<sup>-3</sup></td></tr><tr><td>Plasma length</td><td>0.6–1.6 mm</td></tr><tr><td>Plasma entrance / exit ramp length</td><td>0.3–0.8 mm</td></tr><tr><td>Normalised laser vector potential on target</td><td>1.4–4.5</td></tr><tr><td>Beam energy at injector exit</td><td>140–250 MeV</td></tr><tr><td>Beam charge at injector exit</td><td>27–32 pC</td></tr><tr><td>Beam energy spread at injector exit</td><td>0.9–4%</td></tr><tr><td>Bunch length at injector exit</td><td>3–8 fs</td></tr><tr><td>Beam norm. emittance in x,y at injector exit</td><td>0.1–0.8 mm mrad (x), 0.15–1.8 mm mrad (y)</td></tr><tr><td colspan="2"><strong>High-energy LPI</strong></td></tr><tr><td>Plasma electron density</td><td>10<sup>18</sup>–6 × 10<sup>18</sup> cm<sup>-3</sup></td></tr><tr><td>Plasma length</td><td>9–30 mm</td></tr><tr><td>Plasma entrance / exit ramp length</td><td>0.9–2.1 mm</td></tr><tr><td>Normalised laser vector potential on target</td><td>1.2–3.9</td></tr></tbody></table>

## 9.4 Plasma Accelerator

**Table 9.5.** Summary table of parameters and technical data of the plasma accelerator stages. More detailed parameters and further context are found in Chapters 16 and 17.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td colspan="2"><strong>Laser-Driven Plasma Accelerator (LPAS)</strong></td></tr><tr><td>Plasma electron density</td><td>~10<sup>17</sup> cm<sup>-3</sup></td></tr><tr><td>Plasma length</td><td>0.25–1 m</td></tr><tr><td>Plasma entrance / exit ramp length</td><td>3.5–7 mm</td></tr><tr><td>Normalised laser vector potential on target</td><td>1.0–2.0</td></tr><tr><td>Accelerating field gradient</td><td>~10 GV m<sup>-1</sup></td></tr><tr><td>Beam energy at accelerator exit</td><td>5.0–6.0 GeV</td></tr><tr><td>Beam charge at accelerator exit</td><td>23–30 pC</td></tr><tr><td>Beam energy spread at accelerator exit</td><td>0.1–0.9%</td></tr><tr><td>Bunch length at accelerator exit</td><td>2.9–11 fs</td></tr><tr><td>Beam norm. emittance at accelerator exit</td><td>0.09–1.38 mm mrad</td></tr><tr><td colspan="2"><strong>Beam-Driven Plasma Accelerator (PPAS)</strong></td></tr><tr><td colspan="2"><strong>PPAS to 1 GeV</strong></td></tr><tr><td>Plasma electron density</td><td>10<sup>16</sup> cm<sup>-3</sup></td></tr><tr><td>Plasma length</td><td>40 cm</td></tr><tr><td>Plasma entrance / exit ramp length</td><td>~0.5 cm</td></tr><tr><td>Accelerating field gradient</td><td>1.1–3.0 GV m<sup>-1</sup></td></tr><tr><td>Beam energy at accelerator exit</td><td>1.03 GeV</td></tr><tr><td>Beam charge at accelerator exit</td><td>30–34 pC</td></tr><tr><td>Beam energy spread at accelerator exit</td><td>1.1%</td></tr><tr><td>Bunch length at accelerator exit</td><td>13 fs</td></tr><tr><td>Beam norm. emittance in x,y at accelerator exit</td><td>0.96 mm mrad (x), 1.2 mm mrad (y)</td></tr><tr><td colspan="2"><strong>PPAS to 5 GeV</strong></td></tr><tr><td>Plasma electron density</td><td>2.5 × 10<sup>16</sup> cm<sup>-3</sup></td></tr><tr><td>Plasma length</td><td>2.4 m</td></tr><tr><td>Plasma entrance / exit ramp length</td><td>~1 cm</td></tr><tr><td>Accelerating field gradient</td><td>1.6–2.7 GV m<sup>-1</sup></td></tr><tr><td>Beam energy at accelerator exit</td><td>5.0 GeV</td></tr><tr><td>Beam energy spread at accelerator exit</td><td>0.4%</td></tr><tr><td>Beam norm. emittance at accelerator exit</td><td>~ 0.7 mm mrad</td></tr></tbody></table>
## 9.5 Beam Transport Line

<table><caption>**Table 9.6.** Summary table of parameters and technical data of the beam transport. More detailed parameters and further context are found in Chapter 19.</caption><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td colspan="2">Low-Energy Transport Line (LETL)</td></tr><tr><td>Six-quadrupole setup: magnetic field gradients</td><td>(211/-189/86/-101/190/-161) T m<sup>-1</sup></td></tr><tr><td>Six-quadrupole setup: length</td><td>0.7 m</td></tr><tr><td>Eight-quadrupole setup: magnetic field gradients</td><td>(97/-182/162/-62/-67/-161/-171/94) T m<sup>-1</sup></td></tr><tr><td>Eight-quadrupole setup: length</td><td>2.04 m</td></tr><tr><td>Active-plasma-lens setup: magnetic field gradients</td><td>(316/301) T m<sup>-1</sup></td></tr><tr><td>Active-plasma-lens setup: length</td><td>2.02 m</td></tr><tr><td>Solenoid setup: magnetic field</td><td>(7.6/-7.3) T</td></tr><tr><td>Solenoid setup: length</td><td>2.2 m</td></tr><tr><td>Beam energy spread after LETL</td><td>2.2-3.1%</td></tr><tr><td>Bunch length after LETL</td><td>3.7-4.7 fs</td></tr><tr><td>Beam norm. emittance in x,y after LETL</td><td>0.45-0.66 mm mrad (x),<br>0.38-0.67 mm mrad (y)</td></tr><tr><td colspan="2">High-Energy Transport Line (HETL)</td></tr><tr><td>Length</td><td>8 m</td></tr><tr><td>Number of quadrupoles</td><td>7</td></tr><tr><td>Transport line length</td><td>6-8 m</td></tr><tr><td>Beam energy after HETL (beam core)</td><td>4.96-5.9 GeV</td></tr><tr><td>Energy spread after HETL (beam core)</td><td>0.10-0.32%</td></tr><tr><td>Bunch length after HETL (beam core)</td><td>0.3-3.5 fs</td></tr><tr><td>Norm. emittance in x,y after HETL (beam core)</td><td>0.087-1.64 mm mrad (x),<br>0.085-0.88 mm mrad (y)</td></tr></tbody></table>
## 9.6 Free-Electron Laser

<table><caption>**Table 9.7.** Summary table of parameters and technical data of the free-electron laser. More detailed parameters and further context are found in Chapter 24.1.</caption><thead><tr><th>Quantity</th><th>Baseline Value<br>Free-Electron Laser – 1 GeV</th></tr></thead><tbody><tr><td colspan="2"><strong>Long-Wavelength Setup</strong></td></tr><tr><td>Undulator period</td><td>30 mm</td></tr><tr><td>K parameter</td><td>4.36</td></tr><tr><td>Peak undulator field</td><td>1.56 T</td></tr><tr><td>Radiation wavelength</td><td>34.5–35.9 nm</td></tr><tr><td>Pierce parameter</td><td>0.45–0.57%</td></tr><tr><td>Saturation power</td><td>2.5–4.9 GW</td></tr><tr><td>Saturation length</td><td>~16–23 m</td></tr><tr><td>Linewidth</td><td>0.5–3.6%</td></tr><tr><td>Pulse duration</td><td>~7.8–15 fs</td></tr><tr><td>Photons per pulse</td><td>1.6 × 10<sup>11</sup>–3.1 × 10<sup>11</sup></td></tr><tr><td>Brightness</td><td>2 × 10<sup>28</sup>–8.6 × 10<sup>29</sup> photons/[mm<sup>2</sup>mrad<sup>2</sup>s(0.1%BW)]</td></tr><tr><td colspan="2"><strong>Short-Wavelength Setup</strong></td></tr><tr><td>Undulator period</td><td>20 mm</td></tr><tr><td>K parameter</td><td>1.5</td></tr><tr><td>Peak undulator field</td><td>0.81 T</td></tr><tr><td>Radiation wavelength</td><td>4.67–4.86 nm</td></tr><tr><td>Pierce parameter</td><td>0.19–0.24%</td></tr><tr><td>Saturation power</td><td>1.29–1.94 GW</td></tr><tr><td>Saturation length</td><td>16–28 m</td></tr><tr><td>Linewidth</td><td>0.25–0.59%</td></tr><tr><td>Pulse duration</td><td>2.0–2.4 fs</td></tr><tr><td>Photons per pulse</td><td>1.3 × 10<sup>10</sup>–2.3 × 10<sup>10</sup></td></tr><tr><td>Brightness</td><td>8 × 10<sup>28</sup>–5 × 10<sup>29</sup> photons/[mm<sup>2</sup>mrad<sup>2</sup>s(0.1%BW)]</td></tr><tr><td colspan="2"><strong>Long-Wavelength Setup</strong></td></tr><tr><td>Undulator period</td><td>30 mm</td></tr><tr><td>K parameter</td><td>4.36</td></tr><tr><td>Peak undulator field</td><td>1.56 T</td></tr><tr><td>Radiation wavelength</td><td>1.40–1.67 nm</td></tr><tr><td>Pierce parameter</td><td>0.2–0.23%</td></tr><tr><td>Saturation power</td><td>14–17.8 GW</td></tr><tr><td>Saturation length</td><td>20–26 m</td></tr><tr><td>Linewidth</td><td>0.3%</td></tr><tr><td>Pulse duration</td><td>0.7–2.2 fs</td></tr><tr><td>Photons per pulse</td><td>4.2 × 10<sup>10</sup>–7.2 × 10<sup>11</sup></td></tr><tr><td>Brightness</td><td>2.8 × 10<sup>31</sup>–4.8 × 10<sup>32</sup> photons/[mm<sup>2</sup>mrad<sup>2</sup>s(0.1%BW)]</td></tr><tr><td colspan="2"><strong>Short-Wavelength Setup</strong></td></tr><tr><td>Undulator period</td><td>20 mm</td></tr><tr><td>K parameter</td><td>1.5</td></tr><tr><td>Peak undulator field</td><td>0.81 T</td></tr><tr><td>Radiation wavelength</td><td>0.19–0.30 nm</td></tr><tr><td>Pierce parameter</td><td>0.084–0.099%</td></tr><tr><td>Saturation power</td><td>1.75–4.39 GW</td></tr><tr><td>Saturation length</td><td>38–126 m</td></tr><tr><td>Linewidth</td><td>0.18–0.23%</td></tr><tr><td>Pulse duration</td><td>0.4–2.0 fs</td></tr><tr><td>Photons per pulse</td><td>1.9 × 10<sup>9</sup>–3.2 × 10<sup>10</sup></td></tr><tr><td>Brightness</td><td>3.7 × 10<sup>30</sup>–4.0 × 10<sup>31</sup> photons/[mm<sup>2</sup>mrad<sup>2</sup>s(0.1%BW)]</td></tr></tbody></table>
## 9.7 Other Radiation Sources

**Table 9.8.** Summary table of parameters and technical data of the betatron and inverse Compton scattering sources. More detailed parameters and further context are found in Sections 24.2 and 24.3.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td><strong>Betatron Source</strong></td><td></td></tr><tr><td>Photon energy</td><td>0.6–110 keV</td></tr><tr><td>Source size</td><td>1.4–2.4 µm</td></tr><tr><td>Divergence</td><td>0.7–70 mrad</td></tr><tr><td>Peak X-ray brightness</td><td>2 × 10<sup>21</sup>–1 × 10<sup>26</sup> photons/(mm<sup>2</sup>mrad<sup>2</sup>s[0 1%BW])</td></tr><tr><td>Photons per pulse</td><td>2 × 10<sup>8</sup>–4 × 10<sup>10</sup></td></tr><tr><td><strong>Inverse Compton Source</strong></td><td></td></tr><tr><td>Photon energy</td><td>>100 MeV</td></tr><tr><td>Pulse duration</td><td>~30 fs</td></tr><tr><td>Source size</td><td>single µm</td></tr><tr><td>Divergence</td><td>&lt;1 mrad</td></tr></tbody></table>

## 9.8 Secondary Particle Sources

**Table 9.9.** Summary table of parameters and technical data of the secondary particle sources. More detailed parameters and further context are found in Section 25.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td><strong>Low-Energy Positron Source</strong></td><td></td></tr><tr><td>Positron energy</td><td>0.5–10 MeV (tunable)</td></tr><tr><td>Energy bandwidth</td><td>±50 keV</td></tr><tr><td>Beam duration</td><td>20–90 ps</td></tr><tr><td>Beam size at user area</td><td>2–5 mm</td></tr><tr><td>Positrons per shot</td><td>≥ 10<sup>6</sup></td></tr><tr><td><strong>High-Energy Positron Source</strong></td><td></td></tr><tr><td>Positron energy</td><td>≥ 1.0 GeV (tunable)</td></tr><tr><td>Energy bandwidth</td><td>±5%</td></tr><tr><td>Beam duration</td><td>&lt; 10 fs</td></tr><tr><td>Beam size at user area</td><td>20 µm</td></tr><tr><td>Positrons per shot</td><td>~ 10<sup>7</sup></td></tr></tbody></table>
## 9.9 Accelerator Start-to-End Simulations

**Table 9.10.** Summary table of parameters from the start-to-end simulations of different acceleration schemes. All parameters are given for the beam core at the end of the final transport line matched exemplarily to the undulator entrance. The following abbreviations are employed: RFI = RF injector, LPI = laser-plasma injector, LPAS = laser-driven plasma accelerator, PPAS = beam-driven plasma accelerator. Slice parameters and peak current are calculated based on 0.1 µm long slices. More detailed parameters and further context are found in Chapter 23.

<table><thead><tr><th>Quantity</th><th>Baseline Value</th></tr></thead><tbody><tr><td colspan="2"><strong>Scheme 1: LPI-5 GeV</strong></td></tr><tr><td>Beam energy</td><td>5.0 GeV</td></tr><tr><td>Charge</td><td>30 pC</td></tr><tr><td>Peak current</td><td>3.8 kA</td></tr><tr><td>Bunch duration</td><td>2.9 fs</td></tr><tr><td>Energy spread</td><td>0.9 %</td></tr><tr><td>Normalised emittance in x,y</td><td>0.10 mm mrad (x), 0.06 mm mrad (y)</td></tr><tr><td>Energy spread (best slice)</td><td>0.08 %</td></tr><tr><td>Normalised emittance (best slice)</td><td>0.07 mm mrad (x), 0.04 mm mrad (y)</td></tr><tr><td colspan="2"><strong>Scheme 2: LPI-150 MeV + LPAS-5 GeV</strong></td></tr><tr><td>Beam energy</td><td>5.0 GeV</td></tr><tr><td>Charge</td><td>5 pC</td></tr><tr><td>Peak current</td><td>3.3 kA</td></tr><tr><td>Bunch duration</td><td>0.4 fs</td></tr><tr><td>Energy spread</td><td>0.1 %</td></tr><tr><td>Normalised emittance in x,y</td><td>0.76 mm mrad (x), 0.88 mm mrad (y)</td></tr><tr><td>Energy spread (best slice)</td><td>0.08 %</td></tr><tr><td>Normalised emittance (best slice)</td><td>0.85 mm mrad (x), 1.00 mm mrad (y)</td></tr><tr><td colspan="2"><strong>Scheme 3: RFI-500 MeV + LPAS-5 GeV</strong></td></tr><tr><td>Beam energy</td><td>5.3 GeV</td></tr><tr><td>Charge</td><td>22 pC</td></tr><tr><td>Peak current</td><td>3.3 kA</td></tr><tr><td>Bunch duration</td><td>2.9 fs</td></tr><tr><td>Energy spread</td><td>0.11 %</td></tr><tr><td>Normalised emittance in x,y</td><td>0.32 mm mrad (x), 0.29 mm mrad (y)</td></tr><tr><td>Energy spread (best slice)</td><td>0.03 %</td></tr><tr><td>Normalised emittance (best slice)</td><td>0.32 mm mrad (x), 0.32 mm mrad (y)</td></tr><tr><td colspan="2"><strong>Scheme 4: RFI-240 MeV + LPAS-2.5 GeV + chicane + LPAS-5 GeV</strong></td></tr><tr><td>Beam energy</td><td>6.0 GeV</td></tr><tr><td>Charge</td><td>23.8 pC</td></tr><tr><td>Peak current</td><td>5.1 kA</td></tr><tr><td>Bunch duration</td><td>3.1 fs</td></tr><tr><td>Energy spread</td><td>0.39 %</td></tr><tr><td>Normalised emittance in x,y</td><td>1.50 mm mrad (x), 0.69 mm mrad (y)</td></tr><tr><td>Energy spread (best slice)</td><td>0.06 %</td></tr><tr><td>Normalised emittance (best slice)</td><td>0.85 mm mrad (x), 0.40 mm mrad (y)</td></tr><tr><td colspan="2"><strong>Scheme 5: RFI-500 MeV + PPAS-1 GeV</strong></td></tr><tr><td>Beam energy</td><td>1.1 GeV</td></tr><tr><td>Charge</td><td>10.5 pC</td></tr><tr><td>Peak current</td><td>2.0 kA</td></tr><tr><td>Bunch duration</td><td>0.6 fs</td></tr><tr><td>Energy spread</td><td>0.26 %</td></tr><tr><td>Normalised emittance in x,y</td><td>0.91 mm mrad (x), 0.68 mm mrad (y)</td></tr><tr><td>Energy spread (best slice)</td><td>0.07 %</td></tr><tr><td>Normalised emittance (best slice)</td><td>0.62 mm mrad (x), 0.48 mm mrad (y)</td></tr></tbody></table>
# 10 Laser Systems as Innovative Power Drivers

## 10.1 Introduction

The use of lasers as power drivers for plasma accelerators has been emerging dramatically in the past decades, not only for the well-known effectiveness in exciting and driving plasma waves, but also for the fast-developing technologies that drive the continuous improvement in performances.

Beyond that, entirely new technologies are also maturing while we write, laying the foundations for the migration of laser drivers from the context of pioneering laser-driven acceleration R&D to the realm of viable drivers for plasma accelerators. In fact, while currently available off-the-shelf technology is limited in average power and repetition rate, new pump power approaches based on robust solid-state technologies are already emerging as powerful alternative solutions to overcome such limitations.

In view of that, the proposed EuPRAXIA infrastructure relies on a range of unique petawatt-power, ultra-short pulse laser systems to drive plasma acceleration in a range of different configurations, including a 150 MeV injector and 1 and 5 GeV accelerators. For the development of the conceptual design, we have investigated a broad range of technologies, concepts, and approaches to petawatt laser technology capable of fulfilling the specifications set by the design of the injector and the accelerators. In doing so, a technology survey has been carried out (see [221]), and the main conclusions are presented in Sections 7.2 and 32.3 of this report. In the study, an accurate examination of relevant laser developments was carried out, identifying applicable technologies and corresponding technology readiness levels (TRL). The requirement of ultra-short pulse duration, down to 30 fs, combined with the significant energy per pulse needed by the three laser-driven schemes, finally made Ti:Sa emerge as the most suitable technology based on the foreseen temporal constraints. The baseline design of the main EuPRAXIA lasers could be delivered using Ti:Sa laser technology and exploiting the fast ongoing developments in pump lasers, i.e. lasers capable of delivering ns pulses with approximately 100 J energy per pulse at a 100 Hz repetition rate. The baseline concept includes the main amplifiers, a description of the key components and sub-components, and the analysis of all the main transport sections, from the compressor down to the interaction point. At the same time, a number of development paths for alternative technologies for longer term solutions were also tackled given the potential further exploitation of laser drivers in terms of efficiency, very high repetition rate, compactness, and overall cost.

This chapter delivers the baseline design of the laser system and identifies the pivotal development paths with step-by-step instructions for the transition to the technical description.

## 10.2 Baseline Design

### 10.2.1 Layout and Amplifiers

The development of the laser driver for EuPRAXIA relies on chirped pulse amplification (CPA) and uses Ti:Sapphire (Ti:Sa) as a gain medium. The required performance and reliability is currently beyond the state of the art of available industrial or prototype systems, especially for what concerns the 100 Hz operation. However, in recent years, a number of advancements have been consolidated or are in progress, making it possible not only to conceive a viable design but also to identify the development
<figure><img src="image_70.png" /><figcaption>Fig. 10.1. Block diagram of the three laser driver chains.</figcaption></figure>

path to take this design to a technical level in a few years, a time compatible with
the envisaged construction of EuPRAXIA.

The implementation of the plasma acceleration schemes considered in EuPRAXIA requires the simultaneous use of up to three different laser beamlines with accurate relative synchronisation to ensure controlled plasma acceleration. Auxiliary laser beams for diagnostics and a photocathode laser, tightly synchronised with the three main laser pulses, are also included. The overall architecture of the EuPRAXIA laser system is shown in Figure 10.1. It consists of three different laser chains, with different output pulse parameters (LASER1, LASER2, and LASER3) to drive three different plasma acceleration configurations. Each laser chain consists of a front-end segment, an amplification section – made of one, two, or three amplification stages depending on the required output energy – a beam shaping segment, a compressor, and the final transport system to the target.

The three laser chains share a common master oscillator to ensure intrinsic synchronisation accuracy; the front-end segments share a similar design but are separated to allow independent control on seed pulse properties.

Our design focussed on the following aspects of the layout:

- the technology for the laser systems for pumping the Ti:Sa amplifiers at a high repetition rate;

- the design of the Ti:Sa amplifiers, especially for the thermal load management and cooling strategies, and the optimisation of the extraction efficiency; and

- the design of the pulse compression system, mainly in relation with the optical damage and thermal management of the gratings.

For each system, two levels of performance have been envisaged, with different energy levels and pulse repetition rates:

(a) Low-performance level (named P0), featuring low pulse energy and a 20 Hz repetition rate

(b) High-performance level (called P1), with higher energy at a repetition rate of 100 Hz
**Table 10.1.** Laser parameters for the three laser driver beamlines envisaged for laser plasma injection and acceleration stages, at the performance levels P0 and P1. The maximum output energy has been calculated from the requirements of energy on target, assuming an overall efficiency of 80% of the compression and the beam transport system.

<table><tbody><tr><th colspan="4">LASER1 – Injector 150 MeV</th></tr><tr><th>Parameter</th><th>Unit</th><th>P0</th><th>P1</th></tr><tr><td>Wavelength</td><td>nm</td><td>800</td><td>800</td></tr><tr><td>Max Energy on Target</td><td>J</td><td>5</td><td>7</td></tr><tr><td>Max Total Output Energy</td><td>J</td><td>8.8</td><td>12.5</td></tr><tr><td>Shortest Pulse Duration</td><td>fs</td><td>30</td><td>20</td></tr><tr><td>Repetition Rate</td><td>Hz</td><td>20</td><td>100</td></tr><tr><td>Energy Stability RMS</td><td>%</td><td>1</td><td>0.6</td></tr><tr><th colspan="4">LASER2 – Injector 1 GeV</th></tr><tr><th>Parameter</th><th>Unit</th><th>P0</th><th>P1</th></tr><tr><td>Wavelength</td><td>nm</td><td>800</td><td>800</td></tr><tr><td>Max Energy on Target</td><td>J</td><td>15</td><td>30</td></tr><tr><td>Max Total Output Energy</td><td>J</td><td>18.8</td><td>37.5</td></tr><tr><td>Shortest Pulse Duration</td><td>fs</td><td>30</td><td>20</td></tr><tr><td>Repetition Rate</td><td>Hz</td><td>20</td><td>100</td></tr><tr><td>Energy Stability RMS</td><td>%</td><td>1</td><td>0.6</td></tr><tr><th colspan="4">LASER3 – Accelerator 5 GeV</th></tr><tr><th>Parameter</th><th>Unit</th><th>P0</th><th>P1</th></tr><tr><td>Wavelength</td><td>nm</td><td>800</td><td>800</td></tr><tr><td>Max Energy on Target</td><td>J</td><td>50</td><td>100</td></tr><tr><td>Max Total Output Energy</td><td>J</td><td>62.5</td><td>125</td></tr><tr><td>Shortest Pulse Duration</td><td>fs</td><td>60</td><td>50</td></tr><tr><td>Repetition Rate</td><td>Hz</td><td>20</td><td>100</td></tr><tr><td>Energy Stability RMS</td><td>%</td><td>1</td><td>0.6</td></tr></tbody></table>

The performance level P0 is less challenging in terms of required technologies. According to our study, it can be implemented with the currently available technologies, requiring mainly integration efforts and optimisation. Level P1 is more challenging and can be considered as lying one step ahead with respect to the current technological capabilities, in particular regarding the repetition rate of the pump sources. The target performances of the three laser chains, at the level of performances P0 and P1, are reported in Table 10.1.

The performance level P0 can be implemented with the currently available technologies, requiring mainly integration efforts and optimisation.

### 10.2.2 Front End

The design of the front-end segment, at the performance levels P0 or P1, is based on commercially available configurations. It includes a common master oscillator shared among the three systems. A first CPA stage is devoted to the amplification of the pulse at the 1 mJ level, which is required to efficiently pump a PW stage immediately downstream. The resulting pulse, with typical energy of the order of 10–100 µJ, is then seeded into the main CPA chain. A regenerative amplifier and two multi-pass amplifiers increase the energy up to about >1 J needed to efficiently seed the first stages of the three amplification chains.
### 10.2.3 Power Amplifiers

The amplification of the pulses generated by the front end is based on chirped pulse amplification (CPA) in Ti:Sapphire pumped by frequency-doubled, solid-state Nd- or Yb-based lasers with an emission in the range of 515–532 nm. The basic amplifier configuration is similar to many of the systems operating worldwide, with the significant difference of the very high repetition rate of 20–100 Hz compared to the typical Hz or sub-Hz repetition rate of current petawatt systems. This results in high average pump power requirements, thus placing a severe thermal load on the amplification stages.

The thermal load management was therefore the main driver in the design of the amplification stages, in particular for the cooling strategy. The baseline design foresees the use of a fluid cooling of the end surfaces of the amplification crystals shaped as disks, with a relatively large diameter-to-thickness ratio, to provide an adequately large surface for heat exchange. Water at near room temperature is used as the cooling fluid, following an approach that was recently proposed in the framework of the ELI-ALPS developments [222].

Effort was also directed towards the optimisation of the extraction efficiency to reduce the pump energy needed for a given level of output energy, thus reducing both the requirements on the pump lasers and the overall thermal load. This optimisation has been pursued by a careful repartition of the amplification level between the different amplification stages and by implementing the extraction during pumping (EDP) method to prevent the build-up of excessive transverse gain and thus the occurrence of energy losses from transverse parasitic lasing [223,224].

Finally, modularity and scalability were included in the design, conceiving the amplifiers as a set of amplification modules arranged in different combinations dimensioned to operate at the highest level of performance (P1, see Tab. 10.1), provided that a sufficient pump pulse energy is available. This approach was deemed as advantageous in view of an industrial development of the system, and of the scaling up of its performance during the facility lifetime. Following this approach, as shown in Figure 10.1, the amplification chain of LASER1 consists of a single amplification stage (named AMP1). The amplification chain of LASER2 consists of two amplification stages, AMP1 and AMP2, the first one having the same design of the single amplification stage of LASER1 and operating at the same seed pulse energy, pump energy, and output pulse energy. Finally, LASER3 consists of three amplification stages (AMP1, AMP2, and AMP3), the first two being identical to LASER2, and the third one featuring a dedicated design.

### 10.2.4 Ti:Sapphire Amplifier Structure and Geometry

A dedicated analysis was carried out to define the geometrical layout of the multi-pass amplifier suitable for the required cooling management. As exposed above, one of the main outcomes of the conceptual design is that the amplifying crystals need to be water-cooled with a high flow speed to remove the heat generated by the pumping process. For this purpose, the amplifying crystals must be shaped as thin disks with a high diameter-to-thickness ratio. Cooling must be applied on the crystal faces to have a sufficient heat-exchange surface. To achieve sufficient pump absorption and energy storage, several disks (2 to 4) must be used in each amplification stage, depending on the pump energy and repetition rate. To achieve efficient amplification and energy extraction, the amplified beam must cross the crystal several times, from 4 to 6 passes, depending on the configuration. As for the cooling strategy, two possible approaches were considered for the disks: a transmission geometry and a reflection geometry.
<table><caption>**Table 10.2.** Amplified beam diameters, Ti:Sapphire crystal diameter and clear aperture (CA), crystal thickness, and number of passes for the various amplification stages.</caption><thead><tr><th>Amplifier</th><th>Beam FWHM (mm)</th><th>CA/diameter (mm)</th><th>Thickness (mm)</th><th>Passes P0 or P1</th></tr></thead><tbody><tr><td>AMP1</td><td>4.5</td><td>50/60</td><td>6</td><td>6/6</td></tr><tr><td>AMP2</td><td>8</td><td>100/120</td><td>10</td><td>6/6</td></tr><tr><td>AMP3</td><td>12.8</td><td>160/180</td><td>16</td><td>6/4</td></tr></tbody></table>

In the transmission geometry, the amplifying crystal is water-cooled on both faces, and both the pump beams and the amplified beam cross the crystal, the water-cooling flow, and the flow containment windows. This solution has been proposed and numerically analysed in [222]. It offers a good performance in terms of heat extraction and allows for the implementation of simpler layouts from the geometrical point of view, but it presents a potential drawback because the amplified beam crosses the cooling flow and is potentially subjected to optical aberrations due to turbulences as the fluid flows at high values of the Reynolds number.

In the reflection geometry, one of the faces of the crystal is highly reflective for the amplification beam. The amplified beam enters in the crystal from the front face, and it is reflected back in the incoming direction on the back surface. The same occurs with the pump beams. The reflective surface is water-cooled, whereas the front face is uncooled, as shown in Figure 10.2. In this way, the beam path does not cross the turbulent cooling flow, so no optical aberrations occur. On the other hand, this arrangement allows for a less favourable surface/volume ratio for cooling and requires a more complex optical geometry.

Details of the amplifiers in the transmission geometry have been described in a previous paper [225] [Gizzi 2018]. Both reflection and transmission geometry designs are still under consideration on the basis of theoretical considerations and simulations, and they will be addressed by suitable pilot studies. The laser modules were dimensioned by means of numerical simulations using the code MIRO, developed by CEA [226], using the built-in amplification model for Ti:Sapphire. The simulations were validated by comparison with real laser systems [224,227]. These case studies were considered relevant because the operating parameters of these systems are similar in terms of pump fluence, single-pass gain, and output energies. As a baseline design, all the amplifying modules feature a multi-pass amplification architecture with four passes, depending on the stage.

## Transmission Geometry

The structure of the amplifier crystals for the transmission geometry is similar for all three amplifying stages, and it is shown schematically in Figure 10.3. The gain length is split into two elements to increase the available cooling surface. For each surface, the flow of cooling water is contained between the surface of the crystal and a transparent window made of glass or fused silica. The crystals are surrounded by a layer of index matching, absorbing fluid to suppress optical feedback from the side surfaces and prevent parasitic lasing. The size of each crystal of the pair is reported in Table 10.2.

The thickness of the cooling flow is dictated by fluid-dynamic considerations, and it is in the range of 5 to 7 mm, regardless of the diameter of the disks. For the geometrical layout of the amplifiers in the transmission geometry, the classical bowtie arrangement was adopted. The paths of the various passes of the amplifier are multiplexed in angle in a plane perpendicular to the crystal faces, as shown in the
<figure><img src="image_71.png" /><figcaption>**Fig. 10.2.** Investigated geometries of the amplifier head with disk gain material and water cooling. Top: Reflection geometry. Bottom: Transmission geometry.</figcaption></figure>

diagram in Figure 10.3, for a six-pass arrangement (the reduction to the four-pass case is straightforward). This scheme is common to all the amplifiers (AMP1, AMP2, AMP3) at both performance levels P0 and P1. For increasing the size of the crystals and cross-section of the beams, the geometry is scaled proportionally, keeping fixed values for the offset angles.

For increasing the number of passes, the angle of the beam path with respect to the crystal axes increases from 1.2° (passes 1,2) to 2.4° (passes 3,4) to 3.6° (passes 5,6). To obtain a sufficient separation of the beams at the steering mirrors (i.e. to avoid mechanical obstructions), the overall length of the system is 4 m for AMP1, 5 m for AMP2, and 8 m for AMP3. Regarding the pump injection path, as said before, the pulse coming from each pump source must be split into two parts, which must arrive at the crystal at different times: the first one just before the injection of
<figure><img src="image_72.png" /><figcaption>**Fig. 10.3.** Schematic structure of the twin amplifying crystals in the transmission geometry, along with the cooling flow arrangement. Some passes of the pump beams and of the amplified beam are also shown.</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>**Fig. 10.4.** Top view of the general layout of the amplifier crystals for the transmission geometry for a six-pass arrangement. The red line is the beam path of the amplified beam, which lies in the x-y plane of the drawing. The numbers exemplify the sequence of passes. The pump beam's path is not shown for clarity. The dashed line indicates the axis of the crystals.</figcaption></figure>

the seed pulse, the second one just before one of the subsequent amplification passes (the third and fourth depending on the amplification stages).

The recombination of the two sub-pulses on the same beam path after the splitting was considered technically too complicated as it would require large-aperture active components, such as Pockel's cells, with fast-switching capabilities. For this reason, the sub-pulses will be sent to the Ti:Sapphire crystals along different beam paths using angular multiplexing, as exemplified in the diagrams below (Fig. 10.5). To avoid obstruction from the steering optics of the amplified beam, the beam paths for the pump beams are slanted with respect to the horizontal plane (i.e., the plane of the amplified beam passes).

Moreover, each sub-pulse is further split into two equal parts before the injection in the amplifier. The two parts enter the crystals from opposite directions to obtain a more uniform pump density distribution needed to mitigate parasitic lasing effects. Two passes of the pump beam across the crystals are needed to roughly obtain complete pump absorption.

It must be noted that the diagram of Figure 10.5 shows the beam path for the pulse generated by a single pump source. The different stages are pumped by at least two and up to eight individual pump sources. This requires four to sixteen separated pump beam paths with different incidence angles at different offsets in the horizontal and vertical planes. The transverse size (i.e. along the y-axis of Figs. 10.4 and 10.5)
<figure><img src="image_74.png" /><figcaption>Fig. 10.5. Beam paths for the injection in the Ti:Sapphire crystals. The upper frame shows the top view, evidencing the beam paths for the first (green line) and for the second (yellow line) delayed pump sub-pulses. The lower frame shows the side view, evidencing the angular offset in the vertical direction of the pump beam paths. The path and the steering mirrors for the amplified beam are also shown (red line).</figcaption></figure>

of the amplifiers is determined by the pump injection beam paths, and it can be
estimated to be about 1 m for AMP1 and AMP2 and 1.5 m for AMP3. Overall, the
footprint of the amplification stages is about 4 m² for AMP1, 5 m² for AMP2, and
12 m² for AMP3.

Reflection Geometry

The most challenging performance is set by AMP3, which is the amplifying module running at the highest energy and power level and therefore requiring a demanding design of the thermal management. In our design, the unit consists of three equal amplification disks. The main parameters are reported in Table 10.3 for the performance levels P0 and P1. A possible geometrical layout of the disk arrangement is shown in Figure 10.6, which depicts separately the amplified beam path (left) and the pump beam path (right). The seed pulse enters the first disk of the chain, and it is routed to the second and third disks by a suitable steering mirror arrangement. After a first pass along the disk sequence, the pulse travels along a delay line, and then it is sent backward along the chain, meeting the three disks in reverse order. Angular multiplexing is used to separate the forward and the backward beam paths.

The three disks are pumped with the same amount of energy, equally distributed
from the same pump pulse by the two beam splitters of Figure 10.6. On each disk, the
pump pulse is partially absorbed on the first two passes and then reflected back on
the disks for two further passes to achieve almost complete energy absorption. The
path of the pump beams is slanted in the vertical (z) with respect to the horizontal
(x-y) plane to avoid obstruction by the steering mirrors for the amplified beam. The
<table><caption>**Table 10.3.** Main design and operational parameter for the amplifier AMP3 in the reflection configuration.</caption><thead><tr><td>Parameter</td><td>P0</td><td>P1</td></tr></thead><tbody><tr><td>Crystal diameter (cm)</td><td>16</td><td>16</td></tr><tr><td>Crystal clear aperture (cm)</td><td>13.2</td><td>13.2</td></tr><tr><td>Crystal thickness (mm)</td><td>10.7</td><td>10.7</td></tr><tr><td>Crystal doping (% Wt)</td><td>0.045</td><td>0.045</td></tr><tr><td>Beam diameter FWHM (cm)</td><td>12</td><td>13</td></tr><tr><td>Pump beam energy (J)</td><td>109</td><td>198</td></tr><tr><td>Seed pulse energy (J)</td><td>18.8</td><td>37.5</td></tr><tr><td>Output pulse energy (J)</td><td>62</td><td>126.7</td></tr><tr><td>Pulse bandwidth (FWHM)</td><td>27</td><td>23</td></tr></tbody></table>

distance between the steering mirrors and the Ti:Sapphire disks is about 4 m, and the angles of the amplified beam path with respect to the normal to the disks' surface are 1.2° and 2.4°.

The pump beam path includes suitable delay lines so that the arrival of the pump pulse on each disk is synchronised with the arrival of the amplified pulse. The extraction during pumping (EDP) strategy can be implemented by temporal multiplexing; through a proper synchronisation between the injection of the seed pulse and that of the pump pulse, the amplification on the first reflection on each disk can be made to occur when only the desired fraction of the pump energy has been absorbed, leaving the remaining part available for the next pass. To obtain this result on all disks, the transit time of the pump pulse from one disk to the next one must match the transit time of the amplified pulse, hence the need for delay lines on the pump beam path. This is shown in the diagram of Figure 10.7, which represents the time of arrival of the amplified pulses, of the pump pulses, and of the stored energy in each disk.

## Fluid-Cooling Simulations

A simulation of the temperature distribution and of the thermomechanical stresses affecting the amplifier disks was carried out by means of a finite element analysis (FEA) software available in a commercial software package, i.e. LAS-CAD (ver. 3.6.1), developed by LAS-CAD GmbH (www.las-cad.com). The FEA thermal modelling was used to calculate the spatial temperature distribution in the gain material resulting from the heat input given the pump absorption and from the cooling at the surfaces. The stress mechanical modelling was then used to calculate the stress distribution and the deformation distribution in the crystal, induced by the thermal expansion. This allowed for the calculation of the thermal aberrations computing the optical path difference (OPD) distribution across the crystal aperture, resulting from the variation in the optical path length due to the variation of the refractive index with temperature integrated along the crystal length and the variation in the crystal thickness due to thermal expansion and thermally induced stresses. Thermally induced birefringence [229] was not considered, and the dependence of the thermal and mechanical parameters of the Ti:Sapphire from the temperature was neglected, as well as the slight anisotropy of some parameters in the orientation with respect to the crystalline axes. Detailed results of this approach are described in [225]. A key point to obtain meaningful results from the FEA simulations outlined above is the modelling of the heat exchange between the solid and the fluid.
<figure><img src="image_75.png" /><figcaption>**Fig. 10.6.** Top view of the seed beam path through the sequence of Ti:Sapphire disks (top). Side view of the pump beam through the sequence of Ti:Sapphire disks (middle). Top view of the combined seed and pump layout (bottom) [228].</figcaption></figure>

In these simulations, the heat exchange between the fluid and the solid was modelled by means of a film coefficient $k=Q/\Delta T$, where $\Delta T$ is the local difference of temperature between the solid surface and the fluid and $Q$ is the power per unit surface transferred from the solid to the fluid. This is an approximated approach yet very effective to reduce the computational effort to acceptable levels, in particular when full 3D problems are modelled. The heat transfer process between the fluid and the solid was studied by means of dedicated fluid-dynamical simulations in 2D geometry, to obtain reliable values for the heat transfer coefficient used in the full 3D simulation. The computational method was a numerical solution of the Navier-Stokes equations for mass and energy transport, using the so-called Low Reynolds $k-\epsilon$ method capable of a quite accurate simulation of the behaviour of the fluid-solid
<figure><img src="image_76.png" /><figcaption>**Fig. 10.7.** Overview of the synchronisation scheme for the implementation of the EDP strategy. The red peaks represent the amplified pulses, the green trapezoids represent the pump pulses, and the dashed line is the stored energy. The time is the pulse transit time from one disk to the other (24 ns for AMP3). The fraction of stored energy f1/f2 available for the amplification on the first/second transit can be adjusted by finely tuning the delay between the arrival of the amplified pulse and the pump pulse on each disk [228].</figcaption></figure>

interface layer with a reasonable computational effort. The fluid-dynamics simula-
tions were carried out using a commercial software package (COMSOL Multiphysics
Version 5.3a). An example of these simulations is shown in Figure 10.8 depicting the
fluid flow in contact with the back (reflective) surface of the disks. The calculated
temperature distribution of the boundary layer of the water flow in contact with the
Ti:Sapphire surface is shown in Figure 10.9. It depicts the temperature profile at
the heated interface calculated for different flow speeds at a constant heat input of
25 W/cm². Under fully developed heat-transfer conditions, the temperature increase
in the surface is about spatially proportional to the heat input. This allows for the
calculation of an effective film coefficient as k=Q/ΔT (where Q is the heat input
in W/cm² and ΔT is the temperature increase with respect to unperturbed fluid),
which expresses the cooling capability of the fluid flow. The effective film coefficient
was found to be independent from the heat input and proportional to the flow speed
(proportionality constant of about 0.04 J cm⁻³). The simulations show that with the
channel configuration presented in Figure 10.8 (i.e. parallel walls), only a very thin
layer of fluid near the surface is actually involved in the heat-exchange process. To
improve the cooling performance, other channel configurations were studied with
ridges meant to enhance the fluid turbulence and increase the heat exchange. An
example is shown in Figure 10.10. The channel profile of Figure 10.8 was modified
by introducing triangular protrusions on the upper wall (height 2 mm, base 4 mm,
spaced by 10 mm). The fluid speed distribution shows strong turbulence caused by
the unevenness of the upper channel wall, which stirs the water, locally increases the
fluid velocity up to about two times the input velocity, and improves the heat transfer
from the lower surface. As a result, the temperature increase in the heated surface is
significantly lower (more than a factor of 2) than in the case of the smooth channel
for the same heat-input conditions. This results in a roughly threefold increase in the
film coefficient k. Such a configuration can be applied for the cooling of the disks in
the reflection configuration as the back face of the cooling channel is not crossed by
the light beams, so it can be shaped to optimise heat-exchange processes.
<figure><img src="image_77.png" /><figcaption>Fig. 10.8. Fluid velocity distribution in the cooling channel under the simulation conditions specified in the text. The position of the Ti:Sapphire crystal is shown for clarity, but in the thermal simulation, it is considered only as a thermal boundary condition for the fluid flow (constant surface heat flux).</figcaption></figure>

<figure><img src="image_78.png" /><figcaption>Fig. 10.9. Left: Temperature profile along the Ti:Sapphire crystal surface for different flow speeds, at a heat input of 25 W/cm², with an input temperature of 288.15 K (15°C). Right: Effective film coefficient calculated for various flow speeds and heat input values.</figcaption></figure>

### 10.2.5 Pump Lasers

Pump laser requirements are a critical aspect of our design. Our approach was to minimise pump laser needs while optimising extraction efficiency and relying on efficient transport and compressor throughput and optimised second harmonic conversion efficiency of pump lasers. The compressor throughput was assumed to be 80%, achievable with a single grating reflectivity better than 95%. Such a value is not far from current commercial grating technology [230] providing dielectric or gold-coated gratings with demonstrated reflectivity between 90% and 94% at 800 nm. We also assumed a conversion efficiency from 1 µm pump energy to 0.5 µm of 70%, a conservative value if compared to the 80% conversion efficiency demonstrated recently [231]. Based on these assumptions, we obtain average IR pump power requirements ranging from 0.5 kW for the first amplifier module AMP1 at 20 Hz to approximately 30 kW for the last amplifier module AMP3 at 100 Hz. The corresponding total pulse energies at 0.5 µm range from 20 J to 200 J, resulting in an IR pump pulse energy ranging from 27 J to 280 J.

The choice of suitable pump lasers capable of delivering these performances was based on an extensive evaluation of currently available technologies. A detailed analysis of potentially suitable pumping technologies was included in the previous technology survey [221]. Moreover, a similar analysis was carried out in the framework of the k-BELLA project [232]. These investigations consistently suggest that diode-pumped Yb-based systems are emerging as candidates to sustain the envisaged average power.
<figure><img src="image_79.png" /><figcaption>**Fig. 10.10.** Top: Fluid velocity distribution in the cooling channel, with triangular ridges on the upper wall. The thickness of the channel between the ridges is 7 mm, with an input flow speed of $6 \text{ m s}^{-1}$. The position of the Ti:Sapphire crystal is shown for clarity, but it is considered in the thermal simulation only as a thermal boundary condition for the fluid flow (constant surface heat flux). Bottom: Temperature profile along the channel position at the interface between the fluid and the Ti:Sapphire for the case of the smooth channel (blue line) and for the case of the ridged channel (red line). The other conditions of the simulation are the same [228].</figcaption></figure>

At the same time, Nd-based systems also proved to be capable of rep-rated operation at average power levels relevant for our aims. At this stage, we can identify three different pumping systems and technologies for the three EuPRAXIA lasers, all based on diode pumping or adaptable to diode pumping and all having been demonstrated at a sufficient average power level to give confidence on their readiness. A detailed description of pump laser technology is given in Section 32.3.

### 10.2.6 Transport to Plasma

This section is dedicated to the beam transport from the last amplifier output towards the plasma cell. The equipment that will be installed for each laser includes the following:

- a deformable mirror (DFM) to ensure a good wavefront phase at the input of the compressors and to be sure to be able to reach the required pulse duration;

- a telescope with a pinhole to act as a spatial filter for high frequencies coming from the Ti:Sa crystals [this will expand the beam to the required beam diameter at the compressors to respect the laser induced damage threshold (LIDT) of the gratings and relay the image plane of the deformable mirror into the compressor];

- a change polarisation system, if needed, depending on the technology of the gratings;
- a compressor to reach the required pulse duration;

- a series of mirrors to transport the beam from the output of the compressor to the final focussing optic; and

- a focussing optic, the focal length of which will be calculated to meet the $a_0$ required on target, taking into account the beam profile, the energy, and the pulse duration.

From each amplifier section, we will arrive with an average power for the P1 level of the following:

- LASER1: 1.2 kW (12 J @ 100 Hz), needed 20 fs after compression (62 nm bandwidth), spectral acceptance required: 140 nm

- LASER2: 4 kW (40 J @ 100 Hz), needed 20 fs after compression (62 nm bandwidth), spectral acceptance required: 140 nm

- LASER3: 13 kW (130 J @ 100 Hz), needed 60 fs after compression (23 nm bandwidth), spectral acceptance required: 60 nm

For the deformable mirror (DFM), we can use a DFM based on the mechanical actuator principle. Mechanical actuators use macroscopic part displacements, which create a change of the force applied on the back of the DFM. This change of the applied force creates a nanometric displacement of the front surface of the mirror. In this way, a macroscopic displacement is converted into a microscopic change of the mirror's surface shape. However, this technology is today limited in repetition rate, and since we will have probably some thermal effects in the membrane of the DFM, it will be needed to cool down. Today there is very limited work carried out on cooling down a membrane linked to actuators. The beam diameter on these DFMs will be, respectively, 4.5 cm for LASER1, 8 cm for LASER2, and 12 cm for LASER3.

The beam diameter in the compressor for each laser is determined by the laser induced damage threshold (LIDT) of the gratings. This LIDT depends on the gratings technology, but it is around 250 mJ cm⁻². As we know that we will have modulations in the beam profile and temporal spatial modulations, we will consider a mean fluence of 100 mJ cm⁻². Once we have determined a range of possible beam diameters, we have to check that the intensity on the gratings remains below $1 \times 10^{14} \text{ W cm}^{-2}$. Then we have to check that the size of the gratings is compatible with existing technology, since we do not want to tail the gratings, as is done on PETAL, because of the difficulty in operating for pulse durations under 100 fs. Following this process, we have determined that the beam size (FWHM) in the compressor will be 12 cm for LASER1, 19.5 cm for LASER2, and 34 cm for LASER3.

With this size, it is easy to design the spatial filter. The spatial filters would be set up with a 45° off-axis parabola in a Z-configuration for LASER1 and LASER2 since the pulse duration is below 30 fs and chromatism will be of importance. For LASER3, refractive optics (doublet) can be used.

For the compressor configuration, we have to take into account the compression ratio, and the size of the vacuum vessel that will keep the gratings under $1 \times 10^{-5}$ to $1 \times 10^{-6}$ mbar. Doing so, we have chosen for the three lasers a two-gratings compressor folded by a vertical retro-reflector with gold gratings with 14801/mm. This design leads to a very compact compressor with a size of around $1 \times 1 \times 1 \text{ m}^3$ for LASER1, $1.5 \times 1.5 \times 2 \text{ m}^3$ for LASER2, and $1.5 \times 1.5 \times 2.5 \text{ m}^3$ for LASER3. However, for LASER2 and LASER3, a design with four gratings will have to be considered if thermal studies show that the heating in the gratings is too dominant, even if we envisage to cool them down. Considering the material for the gratings, we stay with gold gratings for now as a fallback solution. Indeed, MMLD and MD gratings could be a good solution, but we do not have enough experience on their LIDT. MLD could also be an interesting option if a large-enough bandwidth can be demonstrated, especially for LASER3, where the pulse duration is 60 fs and, for some acceleration
schemes, may rise up to 100 fs. Using MLD gratings will avoid having to turn the polarisation between the amplifiers and the compressor. It should also be noted that for LASER1, we could increase the size of the beam to reduce the average intensity under 10 W/cm² and avoid the necessity of cooling down the gratings.

Concerning the beam transport and the focussing system to reach the plasma target, the main requirements are the transmission, pointing stability, and intensity at the target. The transmission has to be 83% for LASER1, 88% for LASER2, and 89% for LASER3. For the transmission, we have to take into account the energy directly in the spot on target. Some recent results require a reassessment of the need of a second deformable mirror on this transport line (publication in preparation). Indeed, the results showed that the impact of wavefront correction with a deformable mirror before the compressor to get a focal spot in the target chamber with a Strehl ratio better than 0.85 is less than 1 fs on the pulse duration after compression. It is to be noticed that in existing facilities currently operated and working on plasma acceleration, there is typically only one deformable mirror placed before compression (BELLA, APOLLON). However, not having a deformable mirror after the compression would make it impossible to shape the focal spot as needed for specific applications. Another point is that a Strehl ratio of 0.85, an already very good value, is not sufficient to reach the required 83–89% transmission. Further studies will thus be necessary on this point to decide whether or not a second deformable mirror is necessary. For the following sections, we will consider a Strehl ratio of 0.9, which has been demonstrated at several existing facilities. In this case, the transmission of the other mirrors and the focussing system has to be 92% for LASER1, 97.8% for LASER2, and 98.9% for LASER3.

Given the laser energy and pulse duration, the focal spot size has to be 15 µm for LASER1, 33 µm for LASER2, and 130 µm for LASER3. To reach such spot sizes, the focussing system has to have an equivalent focal length of 3.5 m for LASER1, 9 m for LASER2, and 75 m for LASER3. For LASER1 and LASER2, our preferred design is to use an off-axis parabola. The axis could go from 10° to 45°, keeping in mind that the larger the angle is, the more expensive the parabola becomes. The off-axis parabola will be defined once the layout of the laser and the target chamber (with all the laser and electrons diagnostics) is established. In this way, it will be possible, with three mirrors and the focussing parabola, to reach the required transmission with a reflectivity of 99.4%. For LASER2, because the parabola is too expensive, we may envisage a telescope with a flat pinhole mirror and an on-axis parabola (or an on-axis spherical mirror for reduced cost). Another reason to envisage another design could be the footprint of the system which will be higher with an off-axis parabola. However, using a flat mirror with a pinhole would decrease the transmission of the system by about 6%, meaning that the desired 97.8% transmission cannot be reached and that less than 30 J pulse energy reaches the target. For LASER3, if we want to keep the design compact and cheap, we may have to change the optical system to focus the beam, except if the beam path is along the beamlines. If not, it is suggested to use a zoom design with spherical concentric mirrors. This design has the advantage of being very compact, but a lot of energy is lost because of the secondary mirror (around 15%). Thus, for this design, we will need to increase the energy at the output of the amplifier, which is not desirable since it will increase the average power. Another way could be to envisage a different design for the gas jet, e.g. to not use a capillary and decrease the spot size to reduce the focal length. More detailed studies for optimising and testing this aspect are planned during the technical design phase.

Finally, regarding stabilisation, an active system will not be easy to implement since it will require either to tip-tilt a big and heavy mirror at a high repetition rate or to tip-tilt a small mirror, the image of which is placed through the optical system of all laser beamlines on the target. Alternatively, we envisage passive stabilisation as
an option. Besides the current techniques to minimise instabilities from mechanical parts, a new technology could allow the gain of one order of magnitude on the stability by dumping the mechanical deformation and transforming it into thermal energy. This technique has been demonstrated by CEA and the company ISP but so far only for operation in air. The development of this technique to work under vacuum is also planned. Additionally, LULI and UNIMI have developed a new apparatus to measure mechanical instabilities over a range of 0.1 Hz to MHz to detect instabilities of the order of 100 nrad [233]. This diagnostic will need to be implemented in the transport section and the nearby focal spot region.

### 10.2.7 Development Paths

With the high average power required by systems like the EuPRAXIA laser, both the optical-to-optical and the overall wall-plug efficiency of the laser system become increasingly important; the laser cooling capacity and complexity of the laser amplifier design scales with the amount of energy directly converted into heat in the laser gain medium. The output energy of a pulsed diode-pumped laser system can be written as follows:

$$E_{out} - E_{in} = E_{elec} \eta_{DC} \eta_{P} \eta_{EO} \eta_{PT} \eta_{abs} \eta_{QE} \eta_{QD} \eta_{decay} \eta_{ext} \eta_{MO} \eta_{trans}, \quad (10.1)$$

where $E_{elec}$ is the electrical input energy, $\eta_{DC}$ is the overall efficiency of the laser diode power supply, $\eta_{P}$ is the efficiency of the pulse forming network for pulsed laser diodes (if applicable), $\eta_{EO}$ is the electrical-to-optical efficiency of the laser diode arrays, $\eta_{PT}$ is the pump light transfer efficiency to the amplifier gain medium, $\eta_{abs}$ is the gain medium absorption efficiency, $\eta_{QE}$ is the quantum efficiency (QE, the number of upper laser-level ions produced for each pump-laser photon absorbed by the active ions), $\eta_{QD}$ is the laser gain medium quantum defect efficiency, $\eta_{decay}$ is the decay efficiency, defined as the fraction of the excited upper-state population that remains when the extraction pulse arrives, $\eta_{ext}$ is the fraction of the excited-state population that is extracted on each pulse, $\eta_{MO}$ is the pump-to-extraction mode-coupling efficiency, and $\eta_{trans}$ is the passive optical system transmission efficiency. For architectures that rely on laser-pumped lasers (e.g., Nd:YAG-pumped Ti:Sa systems), efficiencies for each laser frequency converter and optical transfer must be included and eventually become a limiting factor because of prohibitive electricity requirements. For this reason, our baseline Ti:Sa design is accurately designed, adopting the most effective strategies to minimise power needs to acceptable levels while providing a viable solution compatible with EuPRAXIA's construction timeframe.

On the other hand, in view of an evolutionary infrastructure design, we also consider the possibility of extending laser performances, e.g. increasing the repetition rate to the kHz level, further improving efficiency and enabling a long-term use of the facility. In this perspective, one way to reduce electricity power needs is to replace the two-step DPSSL-laser-pumped laser architecture with a single-step DPSSL-pumped architecture using lasing materials that can be pumped directly with diodes. This direct CPA option would ideally provide high wall-plug efficiency, lower complexity, dramatically lower thermal loading, and improved mean time to failure.

Indeed, in a comparison of system efficiency for a CW-diode-pumped direct CPA laser system vs. a diode-pumped indirect CPA laser system, the energy losses per joule of output energy are shown in Figure 10.11, where estimated losses have been grouped into logical categories to emphasise waste heat pathways. Finally, to calculate the overall wall-plug efficiency of the laser, the power consumption of the laser support systems (e.g. cooling and the laser control system) must be factored in. It is important to note that the cooling system size and cost, power consumption, and
<figure><img src="image_80.png" /><figcaption>Fig. 10.11. Wall-plug efficiency comparison between direct CPA (here: Multi-Pulse-Extraction, Big Aperture Thulium (BAT) laser architecture utilising multi-pulse extraction), a pulsed, diode-pumped, indirect CPA system (here based on Nd:glass-pumped Ti:Sa) and a flashlamp-pumped Ti:Sa (image credits: C. Siders, European Advanced Accelerator Concepts Workshop 2017).</figcaption></figure>

overall contribution to the system wall-plug efficiency scale with the waste heat to output energy ratio.

This possibility was, in fact, examined within Work Package 4 of the EuPRAXIA project and is discussed in further detail in Section 7.2. It is, in particular, emphasised that besides Ti:Sa technology, an alternative/complementary configuration involves direct CPA with mixed glass or other materials, directly pumped with semiconductor lasers. Several issues, mainly concerning the available gain bandwidth, prevented these architectures from developing at a level to compete with Ti:Sa technology. However, since then, significant innovation has been shown in this area of direct CPA, successfully addressing key uncertainties and significantly mitigating the risk of this approach for EuPRAXIA. In addition to the technology platform discussed in the Section 7.2, we outline here an additional possible solution based on Tm:YLF as a paradigmatic approach to the EuPRAXIA development path towards a higher repetition-rate laser driver solution.

A careful analysis of factors introduced above, determining the final output laser energy, identifies Tm:YLF as a laser amplifier medium with specifications compatible with a long-term solution for an efficient laser wakefield driver. As shown in Figure 10.12, Thulium (Tm)-doped gain media offer a significant lifetime advantage over the well-established Yb-doped materials traditionally used for diode-pumped fiber and bulk systems [234].

Interestingly, Tm multi-pulse extraction becomes efficient at repetition rates >1 kHz, making it a well-matched evolutionary solution beyond the 100 Hz limit of Ti:Sa-based architectures.

A key requirement for Tm-based concepts to be relevant for sub-100-fs applications is clearly the gain bandwidth of Tm in the chosen laser host material – that must be >100 nm – which is satisfied by most of the host materials considered. Among the relevant host materials, YLF offers several attractive properties, including a negative $dn/dT$, low linear and non-linear refractive indices, and natural birefringence. These properties support laser architectures that exhibit high-fidelity laser pulses with very low non-linear phase accumulation, low wavefront aberration, and high polarisation purity at very high average power (up to hundreds of kW).

Tm is characterised by a long upper-state lifetime (15 ms), and above all, Tm can easily be pumped with commercially available, technologically mature, high-brightness, continuous-wave laser diodes that operate at 800 nm. CW pumping of the gain material eliminates laser diode pulse-forming networks (pulsers) and associated electrical losses. Furthermore, the overall brightness requirement is reduced given the longer time available for storing the pump energy in the gain media. Because of the well-known cross-relaxation process, pumping in the ~800 nm band yields approximately two excited state ions per pump photon, resulting in an effective quantum
<figure><img src="image_81.png" /><figcaption>Fig. 10.12. Extraction efficiency (stimulated emission rate divided by the sum of stimulated emission rate and spontaneous decay rate). In multi-pulse extraction, higher repetition rates (while maintaining the extraction fluence) are beneficial to the overall wall-plug efficiency [234].</figcaption></figure>

defect of ~84% (depending on doping), so only 16% of the pump energy is converted to heat [235,236]. Therefore, the quantum defect for Tm lasers is comparable to the quantum defect for Nd lasers. Furthermore, Tm:YLF is commercially available in boule sizes consistent with 300 kW average-power operation of 30 J, compressed at 10 kHz, or up to 160 J at lower repetition rates.

A novel aspect of the Tm dopant in YLF is the lasing wavelength of ~1.9 µm. Considering that most of the experimental work carried out so far in the laser-plasma acceleration of electrons was driven by the availability of intense radiation from Ti:Sa systems at 800 nm, the possibility of using 1.9 µm calls for an exploration of the wavelength-scaling properties of candidate acceleration and injection schemes. Preliminary considerations emerged from the EuPRAXIA community, in particular from the theory and modelling work package, and indicate that while the change of wavelength may have a major impact on current models, no obvious drawbacks exist, and some benefits related to the longer wavelength may arise.

### 10.2.8 Risk-Mitigating Solutions

The current laser conceptual design builds mostly on high technical readiness level (TRL) components. A full technical design will, however, need some targeted work to address open issues, currently in the development stage at leading institutions of the EuPRAXIA collaboration. This will ensure that progress in the respective areas is immediately reflected in the design work.
## Prototyping of Ti:Sa Amplifiers

As discussed above, the EuPRAXIA preliminary laser driver design is foreseen to consist of a Ti:Sa main amplifier pumped by frequency-doubled DPSSL-pumped lasers. A preliminary development of all components is needed prior to the definition of the architecture of the Ti:Sa amplifier head. R&D is crucial for the definition of the design of the main amplifier(s), the testing of key components and the prototype demonstration using established expertise at existing facilities and in collaboration with industry (e.g. Amplitude and Thales). A definition of the preliminary architecture of a Ti:Sa amplifier head based on scaled but similar systems will be developed using numerical simulations to address thermal management and reach a stable configuration for the baseline EuPRAXIA parameters.

A risk-mitigating solution here includes building a prototype of this system to validate numerical modelling. This will be done in close collaboration with laser developer groups involved in EuPRAXIA Work Package 4, using existing equipment with the partial integration of EuPRAXIA-specific components. This activity will provide details of the architecture of the baseline laser for EuPRAXIA to be included in the final laser design. At the same time, it will help to make a robust assessment of the possibility of reaching the higher repetition rate (100 Hz) expected for the goal of the laser configuration.

## Addressing 100 Hz Pump Laser Developments

Demonstrated DPSSL laser technology is already capable of providing kW-scale systems at 10 Hz. With moderate additional investment in R&D, the pump light required for LASER3 at P0 can be delivered by a reduced number of units, such as the DiPOLE 100 (from the Central Laser Facility, UK) or the P60 (from Amplitude Technologies, France) systems, possibly scaled to the 20 Hz repetition rate required by the P0 specification level. Delivering pump pulses at 100 Hz for the >100 J energy level design should be feasible, but is likely to be very costly given the large number of laser systems required or would require the timely introduction and qualification of alternative higher performance diode laser technology. In view of these considerations, both new diode laser pump approaches (such as alternative cooling and diode laser technology) and also new amplifier approaches (such as liquid cooling and room-temperature operation) should be considered.

Alternative amplifier concepts, such as BAT, will also require the timely introduction of new diode laser pumps at a potential cost in overall performance and commercial availability. These new approaches will require substantial R&D investment and have the potential to significantly reduce the number of lasers and therefore the cost required for a given amount of average power. This is a high-priority task that will require the EuPRAXIA laser community to promote and support necessary developments at participating laboratories and in cooperation with industry.

## Thermal Management of Compressor Gratings

As discussed above, the laser drivers for the EuPRAXIA accelerator will need to operate at a high repetition rate between 20 Hz and 100 Hz with the goal of industrial beam quality in mind. Higher laser repetition rates will allow for an increase in stability in operation parameters and enable feedback loops for active monitoring and control not only for the laser system itself but also for enabling feedback loops and active control over parameters in the electron-generating plasma stage. In today's
laser-plasma acceleration experiments, the repetition rate is practically limited to a fraction of 1 Hz. One crucial limiting factor is the performance of the laser compressor gratings, which includes the yet not fully understood limitations due to laser-induced single-shot catastrophic damage threshold, limitations in average power, and thermal management of the gratings required for long-term operation. These are all issues that need to be fully understood and controlled to enable the driver laser for EuPRAXIA. A detailed design study for the modelling of the thermal properties of the EuPRAXIA laser compressor under high-average-power operation will help us to define the most crucial technical bottlenecks and assist us in the preparation of an experimental campaign which will reveal the parameters for safe operation at high repetition rates and high average powers.

A preliminary indication of the steps to be followed to mitigate the risk includes the modelling of the thermal effects and their impact on compression using established modelling capabilities at existing partner institutes, tests at existing facilities to compare with models, and the design of a new setup to manage the thermal load, including options for a suitable new gratings design (without gold and metal). Following this path, the goal of reliably determining the configuration for the operation of the EuPRAXIA laser compressor will be safely achieved.

## Stability and Active Control

As specified in the requirement tables, EuPRAXIA will require an outstanding stability of the laser driver beam spatial properties, including in terms of beam pointing, intensity distribution in the focal spot, longitudinal focal spot position, etc. Current standard laboratory LPA systems exhibit moderate to poor stability specifications, and depending on the specific system architecture, special measures are required to enable any sort of repetitive operation. Knowledge concerning current state-of-the-art laser parameter stability is needed to develop novel control and correction schemes to reach EuPRAXIA requirements, including dedicated development activities for the design, implementation, and testing of diagnostic and control systems as well as active stabilisation systems as required. These activities are crucial to the definition of the interface between the laser system and the plasma stage, where laser coupling with the target plasma is being optimised.

## Driver Pulse Temporal Shaping and Synchronisation

The control of temporal issues of the laser pulse – e.g. multi-pulse (pulse train) development, laser pulse contrast, and chirped pulse control for the delivery of 100 fs pulses – are aspects relevant for laser-driven plasma acceleration. Multi-pulse operation is explored as a way to efficiently drive plasma waves, relying on the use of a train of moderate-intensity ultra-short pulses. This is foreseen as an alternative to current schemes based on a single high-intensity laser pulse and would allow advanced schemes based on ionisation injection to be investigated, potentially providing injection stages delivering bunches with very low energy spread and ultra-low emittance. The aim here is to investigate the generation of a train of ultra-short pulses, with 100 fs delays to one another, starting from a single ultra-short pulse and relying on easy-to-implement optical schemes, e.g. wave-front division. The design and prototyping of time-manipulation techniques, including testing at existing facilities at EuPRAXIA-participating institutions, are being planned. Available and novel schemes for multi-pulse operation will be designed and tested, including interaction with plasmas to demonstrate effectiveness. Pulse stretching will be explored
for the delivery on target of longer pulses, and plasma interaction models will be implemented in LWFA experiments under scaled conditions to test numerical models. Finally, temporal contrast at different time-scales will be tested at existing labs, and a comprehensive set of values will be given for the stability of such parameters. Where required, the implementation of established or newly developed temporal contrast control techniques will be taken into account to meet additional EuPRAXIA requirements, especially for what concerns the use of high-contrast lasers for solid target interactions and the control of pre-ionisation in gases. These activities are crucial to the definition of the interface between the laser system and the plasma stage, where laser coupling with the target plasma is being optimised.

## 10.3 Conclusion

The first generation of high-quality laser-plasma accelerator designs is progressing rapidly towards a user infrastructure and needs a new generation of ultra-short pulse laser drivers with high average power and high stability. A range of candidate technology paths are being considered and developed according to the timescales available for implementation and the required driver performance. A step-like evolution of a widely explored Ti:Sa based system is proposed as a viable short-term solution for kW-scale drivers with a repetition rate of up to 100 Hz. The proposed system will enable a robust operation of the EuPRAXIA facility, establishing plasma acceleration technologies at an industrial level. As for higher repetition-rate (kHz and beyond), higher average-power (10 kW and beyond) solutions, these will build on highly efficient direct DPSS CPA laser technologies.

# 11 Laser Control-Command System

## 11.1 Introduction

This chapter gives an overview of the control-command system for the laser system, keeping in mind that it will have to be interfaced with the control-command of the EuPRAXIA facility. The design will evolve in the future with the definition of the control-command system of the EuPRAXIA facility and with the definition of the laser system itself. More general aspects on machine operation, data management, and safety are described in Sections 5.3, 3.5, and 27.1, respectively. Aspects of the control-command system specific to the particle beam are not described here since they will be very similar to existing accelerator facilities, such as SOLEIL and ESRF.

This document gives a list of the requirements that this system will have to fulfill and defines the interface with the control-command system of the EuPRAXIA facility. This document further provides an account of the laser diagnostics and a general outline of the proposed system structure. Such an outline is based upon available information from existing laboratories and/or facilities (or those under construction) where laser systems with an architecture conceptually analogous to that envisioned for EuPRAXIA are employed. In particular, a broad overview of the kind of devices needed to be controlled for most of the EuPRAXIA laser diagnostics will be given, as well as a conceptual description of the timing and synchronisation architecture.

It is to be noted that the laser control-command system (LCC) will have to be interfaced with the general EuPRAXIA facility control-command system (FCC). In this context, since the control-command system of the facility has not been defined yet, we emphasise the following points:
- The implementation details – such as, for instance, the suggested toolkit (TANGO, EPICS, etc.) of the EuPRAXIA laser control-command system – may be better defined at a later stage at a higher (facility) level. For this reason, it is too early to provide details on the software and protocols implementation and related issues such as the following:

* the way to develop, upgrade, and integrate different software or data-analysis methods;

* the way to exchange information; and

* the way to access databases, configuration data, and results data.

- The mission profile of the facility has to be better deepened yet. In particular, the user profiles, types of experiments, and operation modes have to be better identified to identify the possible links between the laser- and beam-related parts of the control-command infrastructure. In this context, different user categories may possibly be identified, having access (through the FCC) to different laser operation modes and / or parameter-tuning modes (laser energy, laser shot sequences, etc.). The envisioned LCC must take into account different levels of external (i.e., by the FCC) actions.

## 11.2 Overview

Figure 11.1 gives an overview of the hardware architecture of the EuPRAXIA laser control system. Vertically, the system can be divided into several layers:

PSS: Personal Safety System

SSS: Synchronisation and Sequencing System (also including pump lasers)

ALS: Alignment Systems

DLS: Laser Diagnostics Systems

VFS: Vacuum and Fluids Systems

TAS: Target Areas Systems (one per experiment hall)

For some of the subsystems, a stand-alone operation mode may be needed; to this purpose, local GUI stations are required. In all operation modes, the PSS and SSS are needed to generate laser beams. The VFS can work independently, only providing interlock signals to the LCC. The blue line in Figure 11.1 gives the perimeter of the control-command system.

Starting from the top, we first find Level 2 with servers and operator workstations. The operator console and servers are localised in control rooms. Local operator stations are also necessary, to be used during initial setup, new components integration phases, laser warming up, and maintenance periods. Through the GUI, operator workstations display data exchanged with front-end computers at Level 1. At Level 1, we find the front-end processors (FEPs) running software modules, such as device drivers and local interfaces. FEPs control process devices, sensors, and actuators through specific electronic drivers and can be operated locally by laser operators. Finally, at Level 0, we find the facility with all devices under control.

Taking into account the number of systems to control and the size of the facility, the control system must be a scalable and distributed control system.

Programming technologies have to use object-oriented programming, and the system must support common object-oriented programming languages (Python and C/C++). In addition, bindings should be available for commonly used commercial software, such as Labview, Matlab, and supervisory software, if necessary. Protocols used for communications must enable separate pieces of software written in different languages and running on different computers to work with one another like a single application or set of services.
<figure><img src="image_82.png" /><figcaption>Fig. 11.1. Possible hardware architecture for the control-command system.</figcaption></figure>
This control system must have a centralised database containing properties of the
devices to control and tools to administer the system through the network.

11.3 Needs and Requirements

11.3.1 Operational Requirements

Operational Modes

Different laser(s) operation modes will be defined according to the different phases of laser operation: warming up, different phases of beam alignment (from the front end to the target), and end user needs (for instance, in terms of pulse energy, pulse train generation, etc.). Operation modes should differ with respect to one another, roughly speaking, for the status of actuators (for instance, those activating beam shutters), electronic trigger timings and triggering, as well as optical attenuators (for instance, those protecting CCDs).

Since the mission profile of the facility is not defined yet, the definition of these
operation modes has to be postponed to a later stage.

Laser Alignment/Setup and Tuning

Laser beam characteristics are defined by parameters which have to be adjusted from
control systems. For particular parameters, it can be expected that they can only be
adjusted using local computers not connected to the central system. In this case, the
drawbacks are (1) the inability to save and have an overview of the global setup to
control the setup integrity, and (2) the inability to verify the conformity between the
shot model and user needs.

So the facility needs to have within the control system a centralised set of setup
data allowing control over the setup before launching a sequence.

Sequencing and Machine Protection System

The repetition rate of the EuPRAXIA laser systems will be between 20 Hz and 100 Hz as a baseline. In some circumstances, pulse sequences may be needed on demand, i.e. depending on final user needs. This demand is described by a sequence which can have all the topologies coming from continuous shot to complex bursts. Sequences should be configurable.

Setting up a shot sequence includes the following:

- parameters of sequence timing: sequencer setup;

- energy variations: action on pump lasers (delay);

- pulse duration variations: action on motors on stretcher/compressors;

- delay variations between beams: action on motors of delay lines;

- number of beams: action on beam shutters;

- targets: action on target holder motors.

Supervision Functions

General supervision functions are necessary to monitor the laser operation. Graphic
user interfaces (GUI) display graphic objects to control and visualise laser operation.
Except for dedicated and stand-alone software and computers, all instrumented systems can be controlled over the control network. CCD cameras are expected to be the most widely used detector for the diagnostics so that graphic objects are supplied with basic image-processing functions.

## Data Acquisition and Devices to Control

### Instrumentation buses

Diagnostics supply data through specific buses which can be serial bus, USB, or GPIB. In most cases, Ethernet is recommended when it is available.

### Pump laser control system

Many pump lasers will be used in the EuPRAXIA laser system. Some of them will be delivered with their stand-alone control software, some with a GUI, but most of them should be interfaced with the distributed control system to ease operation.

### Vacuum systems

A great number of devices (pumps, valves, gauges, etc.) for vacuum systems will be used for laser beam transport, compressors, and interaction chambers.

Vacuum processes need to be subdivided into several subsystems. Each of them covers a perimeter defined by specific operation and maintenance requirements. These subsystems are:

- spatial filter vacuum systems in the amplification section,

- compressors,

- beam transport,

- switchyard,

- 150 MeV beam transport and target chamber,

- 1 GeV beam transport and target chamber, and

- 5 GeV beam transport and target chamber.

There are also other vacuum devices in the front end and the pump laser, but this kind of equipment does not need a control system, or it is controlled by the pump laser control system itself.

Vacuum processes are controlled by industrial programmable logic controllers (PLCs) programmed with languages defined in the CEI 61131-3 norm. The PLCs used will communicate through a local network. Vacuum devices can be controlled from supervision through a distributed control system with communication software modules (OLE for process control and device servers) between PLCs and the fieldbus.

### Cameras

Digital cameras will be widely used in the EuPRAXIA facility. Gigabit standard CCD cameras are the preferred choice. Gigabit cameras will be widely used in the laser beam alignment and diagnostics systems. Cameras included in automatic alignment loops will be directly connected to the hosted FEP, while cameras included into diagnostics systems will be connected to the dedicated gigabit cameras VLAN.

### Motion devices

In the long run, more than 100 motors will be in operation in the EuPRAXIA laser subsystem. Motors are located in motorised mirror mounts, stretchers, compressors, and alignment and diagnostics sensors. The electronic motor controller/driver must be selected to supply a universal solution for most applications by taking into account the capacity to drive bipolar stepper motors, and to read data from absolute or incremental encoders, maintenance, features, and durability. The chosen solution must be interfaced with the distributed control system.
### Automatic closed loops

Alignment functions may consist of manual and automatic controls. Manual alignment by an operator with the control systems consists of centring or pointing the laser beam by observing an image and controlling a motorised mirror. The automatic alignment loop is the same except that software replaces the operator. This software analyses a CCD image, then calculates and sends the corrections to the motorised mirrors. Many iterations could be necessary. The speed of the loop is adjusted according to the requirements of the localisation of the correction. Most of them have to correct slow deviation due to thermal variation. However, some of them require faster loops to correct laser beam pointing fluctuations caused, for example, by the laser itself or by air turbulence.

Another example is wavefront correction. This system is usually a dedicated system. The interconnection and data exchange with the distributed control system of such a system is to be studied.

### Specific diagnostics

To deliver a usable electron beam, it is mandatory to control the laser performances. In this document, we will not present the loop that allows to control the laser parameters based on the electron beam parameters. The relationship between laser and electron beam performance needs to be further studied during a prototyping step.

To do so, it is crucial to implement a complete series of diagnostics and control tools along the three laser beamlines. Diagnostics are needed to characterise the energy, laser pulse duration, spectral and spatial phase, wavefront, and spatial profile.

In this section, we describe the main controls/diagnostics that are considered mandatory along the laser chain. A description of their actual implementation (possibly with the addition of further controls) will be addressed when the final architecture will be defined and validated.

At the current stage, it appears that the alignment will be mainly controlled on (a) the Ti-Sa crystal (assuming the baseline design) to ensure that the pump and the signal beams are well overlapped, and (b) the input of the compressor since the angle of incidence has to be maintained around ±20 µrad in the target plane.

A description of the set of main diagnostics is given in Table 11.1. It does not take into account the alignment process. The repetition rate of operation of each diagnostic is also given in the table and designated by the following numbers and abbreviations:

(1): Near field and far field are intended to be displayed on monitors at 100 Hz. The raw data of the near field will be processed at 100 Hz just to check the peak intensity (hot spots) (see the section on system security below for more details). However, only the raw data will be saved at 100 Hz on text files or other formats, which will allow a post-treatment of data. We will not save images to avoid the excessive use of disk space to handle at 100 Hz since the facility mission profile is 7 days a week, 24 hours a day.

(2): These measurements will be performed by using a relay imaging insertable system.

(3): This is the ns, ps, and fs contrast measurement.

(4): This is the measurement of the ns contrast only to check if some coatings are evolving in time.

(TBD): To be defined. The synchronisation between different lasers at the focal plane (i.e. in the target chamber) will be defined according to the specific experimental configuration when available.
<table><caption>Table 11.1. Set of laser diagnostics, their proposed positioning along the beamline, and data taking rates. Note that “once a week” here means that we will store the data only one time a week; “x”; means no measurement. Some of those diagnostics will have to be performed just after maintenance, requiring the replacement of optics. The footnotes in the table are explained in the main text.</caption><thead><tr><th></th><th></th><th>Energy</th><th>Near Field</th><th>Far Field</th><th>Spectrum</th><th>Temporal Contrast</th><th>Wavefront sensor</th><th>Pulse Duration</th><th>Synchronization</th><th>Pointing Stability</th></tr></thead><tbody><tr><td>Front-End Oscillator</td><td>Fs oscillator</td><td>100 Hz</td><td>100 Hz (1)</td><td>x</td><td>100 Hz</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>1st Before AOPDF</td><td>x</td><td>x</td><td>100 Hz (1)</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>1st Output AOPDF</td><td>x</td><td>100 Hz (1)</td><td>x</td><td>100 Hz</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>1st Before compressor</td><td>100 Hz</td><td>100 Hz (1)</td><td>x</td><td>100 Hz</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End XPW</td><td>1st Before XPW</td><td>x</td><td>x</td><td>100 Hz (1)</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End XPW</td><td>1st Output XPW</td><td>100 Hz</td><td>100 Hz (1)</td><td>x</td><td>100 Hz</td><td>Once a week</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>2nd Output Stretcher</td><td>100 Hz</td><td>x</td><td>100 Hz (1)</td><td>100 Hz</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>2nd Output Regen</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>2nd Output Multipass</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Front-End CPA</td><td>2nd Output Front-End</td><td>100 Hz</td><td>100 Hz (1)</td><td>x</td><td>x</td><td>x</td><td>x</td><td>100 Hz</td><td>x</td><td>x</td></tr><tr><td>Amplification Section</td><td>Before AMP1</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>100 Hz</td><td>Once a week (4)</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Amplification Section</td><td>Before AMP2</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>100 Hz</td><td>Once a week (4)</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Amplification Section</td><td>Before AMP3</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>100 Hz</td><td>Once a week (4)</td><td>x</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Amplification Section</td><td>Before compressor</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>100 Hz</td><td>Once per hour (3)</td><td>Once per hour (3)</td><td>x</td><td>x</td><td>x</td></tr><tr><td>Propagation</td><td>Before focusing</td><td>100 Hz</td><td>100 Hz (1)</td><td>100 Hz (1)</td><td>100 Hz</td><td>Once per hour</td><td>Once per hour (3)</td><td>100 Hz</td><td>x</td><td>100 Hz</td></tr><tr><td>Experimental Chamber</td><td>At focal spot</td><td>x</td><td>x</td><td>Once a week during 1000 shots (2)</td><td>Once a week during 1000 shots (2)</td><td>x</td><td>Once a week during 1000 shots (2)</td><td>x</td><td>(TBD)</td><td>Once a week during 1000 shots (2)</td></tr></tbody></table>
<table><caption>**Table 11.2.** A strategic view of protection measures put into place along the laser chains.</caption><thead><tr><th></th><th>Spectrum</th><th>Beam Profile</th><th>Vacuum Level</th></tr></thead><tbody><tr><td>AMP1</td><td>if outside<br>reference limits:<br>block the beam</td><td>if outside<br>reference limits:<br>block the beam</td><td></td></tr><tr><td>AMP2</td><td>if outside<br>reference limits:<br>block the beam</td><td>if outside<br>reference limits:<br>block the beam</td><td></td></tr><tr><td>AMP3</td><td>if outside<br>reference limits:<br>block the beam</td><td>if outside<br>reference limits:<br>block the beam</td><td></td></tr><tr><td>Compressor</td><td>if outside<br>reference limits:<br>block the beam</td><td></td><td>if &gt; 1 &times; 10<sup>-5</sup> mbar: block the beam</td></tr><tr><td>Beam Transport</td><td></td><td></td><td>if &gt;1 &times; 10<sup>-5</sup> mbar: block the beam</td></tr></tbody></table>

Some of these diagnostics will be used to set up a system security control, as explained in the next paragraph.

We still have to define on which component we will act to close the loop with these diagnostics. For this, we need to perform a detailed model of the performances. We plan to achieve this task before the end of the final design.

Pump lasers are considered as industrial products. So we do not describe here all the internal diagnostics that will be needed to drive their performance. However, we need to check at the output of those pump lasers the near field and the energy. Associated with these measurements, we will need to have a view of the main amplifying crystals to monitor depletion levels.

## Security – Protection from Damage of Laser Components

For security reasons, we will implement a check of the spectrum of the main beam and the vacuum level in the vacuum chambers and vacuum transport lines. If the pressure in the vacuum chamber of the compressors gets higher than $1 \times 10^{-5}$ mbar, there is a risk of damage to the gratings. The system needs to guarantee that the pressure stays below $1 \times 10^{-5}$ mbar. In the relay imaging system stages in the beam propagation and in the presence of real foci (e.g. spatial filters), it needs to ensure that the pressure in these stages is below $1 \times 10^{-3}$ to $1 \times 10^{-2}$ mbar to avoid any plasma creation.

For the same reasons, we need to check the spectrum along the amplification section to be sure that there is no distortion of the spectrum of the chirped pulse, implying modifications in the temporal shape of the pulse (in particular, pulse narrowing) and possibly leading to a high risk of damages on the mirror and/or the crystals.

Additionally, the diagnostics of the beam profiles can be used to implement a safety lock; a deviation from the expected beam profile (both in shape and in pointing) can lead to the formation of hot spots with a risk of damage on the mirrors, on the crystal, and on the gratings. We thus need to check the beam profile in real time and stop the beam if it shows an excessive deviation from a reference profile.

To avoid any damage, we will have to block the beam between the front end and the amplification section (to be confirmed) and block the pump beam before entering the amplifiers (to be confirmed). A schematic view of the conditions and actions put in place in strategic points of the laser chains is given in Table 11.2.
Finally, we will implement closed loop stauts for every piece of equipment that
could be inserted in the beam, such as a cross hair needed for the alignment of the
beam or a mirror to inject a cw laser as a reference.

Data Archiving

A huge amount of data is expected to be produced during the EuPRAXIA operations,
from both the laser side and the experimental areas. Data from the lasers must be
archived for two main purposes. First, we need to follow the laser operation by making
statistics and an analysis to detect a decrease in performances and prevent failures.
For that, we need a historical data-archiving system recording laser shot results. In
this case, data are supplied by instrumented laser diagnostics dispatched over the
four subsystems: front end, amplification section, compression section, and transport
and focussing system.

Second, a part of this data is needed to optimise the laser-driven acceleration.
For this purpose, only data supplied by diagnostics looking at the output beams are
useful. All laser data are stored in databases.

To preserve data integrity and allow data access from office computers, data-
archiving servers may have a duplication system from a control network of the
machine to the laboratory network.

Computerised maintenance management system

The EuPRAXIA laser system is composed of a large quantity of optical, electrical, and
mechanical components and pieces. For maintenance, inventory, and stock manage-
ment purposes, a maintenance team needs a computerised maintenance management
system.

This system will be based on a commercial product or developed by a database
software developer to have a customised system.

11.3.2 Personnel Safety System

The aim of the Personnel Safety System (PSS) is to secure a particular area of the
laser facility when risks are too high for workers; this system has to be designed to
make it the least intrusive possible, to avoid any unnecessary laser halt. A balance
between safety and service must be sought.

We do not know yet how the PSS of the facility will work at EuPRAXIA. However,
it is clear that the laser sub-system will have to send data to this system and will
have to answer to some commands from the PSS of the facility.

Based on risk studies conducted at other laser facilities, a Safety Integrity Level
of 2 [237] seems to be the minimum required. This level is applied to every security
loop: sensors -> cables and fieldbus -> digital input modules -> fail-safe CPU ->
digital output modules -> cables and fieldbus -> actuators.

The facility will have to define levels of risk and define for each level the protection
needed. From this study, it will be possible to determine which data the laser sub-
system will have to display. The following scheme is an example of a risk outside a
zone:

In this case, the entry door of Zone 3 is opened in spite of the fact that it is strictly
forbidden (third level of laser risk, meaning that no one could be in the presence of
the laser). The PSS activates the laser beam shutter No. 1. If we assume this shutter
does not work, then PSS activates laser beam shutter No. 2 to secure both Zones 2
and 3. Finally, if necessary, the laser interlock is opened by the PSS to stop every
laser light emission. With this example, we show that the laser system will have to be
<figure><img src="image_83.png" /><figcaption>**Fig. 11.2.** Schematic of the beamline divided into different zones.</figcaption></figure>

able to “say” which level of risk is triggered and will let the PSS control the interlock to stop the beam.

### 11.3.3 Electrical Timing and Synchronisation

#### Overview

##### *Synchronisation of the laser sub-system*

The EuPRAXIA laser has several pump lasers with different frequencies in the range of 1 kHz to 20 (100) Hz. Each pump laser needs at least two synchronisation signals, one for flashlamps or diodes and one for the Qswitch with, respectively, 1 ns and 100 ps uncertainty. Laser components which need the best temporal precision are chopper Pockels cells with 100 ps peak-peak uncertainty; a better temporal precision should be useful to improve contrast.

Other components needing synchronisation are diagnostics: calorimeters, CCDs, and spectrometers but with no specific temporal requirements.

Another feature of the EuPRAXIA laser is the large distances between systems, more than 50 m in most cases. Thus, synchronisation signals must be distributed over the entire facility with the same uncertainty and reliability.

##### *Synchronisation of interaction area systems*

Interaction areas need also synchronisation signals to trigger diagnostics, such as CCDs, scopes, and more specific diagnostics. These diagnostics need the same temporal precision as the laser diagnostics. Slow timing signals will occur up to a few tens of ms before each laser pulse. The pulse duration is up to 10 µs for fast timing signals and 10 ms for slow timing signals.

Target shots are delivered and controlled by specific opto-mechanics shutter devices with programmable sequences. All sequence topologies must be generated and are characterised by a given number of parameters not yet defined.

Finally, it will be necessary to control the synchronisation of the laser beams with the particle beams. While this topic will need to be investigated further in considerable detail in the future, a possible solution for sub-femtosecond synchronisation is described in Chapter 15. Clearly, the main emphasis here will be on the control and monitoring of the jitter value, which will need to remain on the fs level or below.

#### *Architecture*

The synchronisation system will be designed to operate with large distances between the modules. Typically, the distances between the laser sub-system and the interaction chambers will exceed several hundred metres by taking into account the length of the cable trays layout.
<figure><img src="image_84.png" /><figcaption>**Fig. 11.3.** Scheme of timing and synchronisation. The master and the delay generators are controlled via Ethernet.</figcaption></figure>

Signals between modules are transmitted through optical fibers to obtain a high immunity from electromagnetic interferences generated by interaction, particle creation, and high voltage pulsed systems. The architecture of the synchronization system could be similar to the one described in Figure 11.3.

The system will be designed to be compliant with the possibility to manage three delay generators in each location, and all fiber optic links will be redundant. Wherever it is necessary, we use distribution amplifiers to duplicate triggers which do not need separate adjustments of both the delay and the amplitude, especially for CCD cameras.

*Reference master*

The first solution, as shown in Figure 11.3, is to master the system by a reference clock with a high-stability reference clock based on an oven-controlled crystal oscillator (OCXO). The stability and aging (for one day) required are ±0.1 ppm.

The second solution could be to use an external RF signal from the oscillator. Long-term stability requirements of this RF signal must be defined. To achieve this stability, slow frequency drifts due to the temperature of the oscillator cavity need to be compensated.

The master delivers a serial data stream synchronised to the RF signal. The data stream contains coded information to generate at least frequencies between 20 Hz and 1 kHz. This data stream is used by delay generators to deliver delayed signals.

*Delay generators*

Delay generators receive from the master a serial data stream through a mono-mode optic fibre. The limits of the system are 1 km between the master and delay generators and 2048 simultaneous channels. The type of delay generator is not yet defined.

*Time stamping*

Time stamping is based on a clock signal supplied by the SSS to a counter/timer card mounted in the host. This card receives a signal at at least 100 Hz from a delay generator. The counter value is incremented by one with each pulse of this signal.
This value is used to time-stamp the acquired data. With this time-stamping system, for each sensor, a subsystem should archive data at 100 Hz. A list of data to be archived in such a system has been defined and is described in [238]. The codification for the names of the data is not yet defined.

An acquisition can be made at different frequencies or can follow the sequence. So, to catch the counter value at the right time, the counter cards receive a trigger signal. This signal is delivered by a delay generator and can have a frequency of 100 Hz or less, or it can be synchronous with the sequence.

To reset counters, two signals are used – a gate and a reset signal. These two signals are generated by the SSS. To ensure the synchronisation of all counters, we need to reset them and restart counting at the same time. The gate signal is put on a high level to stop counting; when the counters stop to count, a reset signal is sent to reset the counter values. When the counter values are initialised, the gate signal is put on a low level, and the counters restart counting.

# 12 RF Accelerator to 500 MeV as Beam Driver

## 12.1 Introduction

The RF accelerator of the EuPRAXIA facility is meant to provide a maximum energy of 500 MeV for electron bunches generated at a laser-illuminated photo-cathode. It consists mainly of two parts:

1. an S-band RF photo-injector made up of an RF gun equipped with a photo-cathode and followed by an S-band linac booster for a maximum final energy of 170 MeV and

2. an X-band RF linac to raise the electron beam energy up to a maximum final value of 500 MeV by means of X-band RF sections providing accelerating gradients of the order of $E_{acc} \ge 50$ MV/m. In the following paragraphs, the two systems are described in detail.

## 12.2 S-band RF Photo-Injector

The RF photo-cathode gun and associated systems are meant to reliably produce, at the most critical point in the injector, the extremely high-quality beam demanded by the EuPRAXIA facility. For this reason, it has to be based on technology that is both proven and, at the same time, at the cutting edge. Similar considerations apply to the other critical components associated with the beam generation and emittance compensation process, i.e. the photo-cathode drive laser and the solenoid after the gun itself. The EuPRAXIA electron bunches will be generated by an injector with a maximum energy of 170 MeV, which consists of a 1.6-cell RF gun cavity, followed by three accelerating structures. The system will operate at the frequency of 2.856 GHz, which is the same frequency as the SPARC photo-injector in operation at LNF since 2005. The RF gun has a metallic photo-cathode, located in the high electric field region of the cavity and illuminated by short ps-scale UV laser pulses at a 50 Hz repetition rate.
<table><caption>**Table 12.1.** Main parameters of the RF gun.</caption><thead><tr><th>Gun Parameter</th><th>Unit</th><th>Value</th></tr></thead><tbody><tr><td>Resonant frequency</td><td>GHz</td><td>2.856</td></tr><tr><td><i>E</i><sub>cath</sub>/<i>P</i><sub>diss</sub></td><td>MV/(m·MW<sup>0.5</sup>)</td><td>37.5</td></tr><tr><td>RF input power</td><td>MW</td><td>14</td></tr><tr><td>Cathode peak field</td><td>MV/m</td><td>120</td></tr><tr><td>Repetition rate</td><td>Hz</td><td>50</td></tr><tr><td>Quality factor</td><td></td><td>14600</td></tr><tr><td>Coupling coefficient</td><td></td><td>3</td></tr><tr><td>RF pulse length</td><td>μs</td><td>1.0</td></tr><tr><td>Mode separation</td><td>MHz</td><td>41.3</td></tr><tr><td><i>E</i><sub>surf</sub>/<i>E</i><sub>cath</sub></td><td></td><td>0.9</td></tr><tr><td>Pulsed heating</td><td>°C</td><td>&lt;30</td></tr><tr><td>Average diss. power</td><td>W</td><td>400</td></tr><tr><td>Working temperature</td><td>°C</td><td>30</td></tr></tbody></table>

### 12.2.1 RF Gun

A robust solution for the RF gun of the EuPRAXIA facility can be a 1.6-cell gun of the BNL-SLAC-UCLA type [239,240], with modifications foreseen and implemented during the last years for the gun developed for the ELI-NP GBS project [241] and integrated in the new gun recently developed for the SPARC photo-injector. With respect to the original design [239,240], this gun, whose parameters are given in Table 12.1, will implement several features described in the following.

The iris profile has been designed with an elliptical shape and a large aperture to simultaneously reduce the peak surface electric field, increase the frequency separation between the two resonant modes (i.e. the working π-mode and the so-called 0-mode), and improve the pumping efficiency on the half-cell. Furthermore, a high-frequency separation of the resonant modes strongly reduces the residual field of the 0-mode due to the transient regime, which is particularly important if the structure is fed with short pulses [242]. The coupling window between the rectangular waveguide and the full cell has been strongly rounded to reduce the peak surface magnetic field and, as a consequence, the pulsed heating [243]. Figures 12.1b and 12.1c show, respectively, the magnetic field in the coupler region at a 120 MV/m cathode peak field and the longitudinal accelerating field profile. The input coupling coefficient (β) has been chosen to be equal to 3 to reduce the filling time, allowing an operation with short RF pulses [241]. Finally, to compensate the dipole field component, induced by the presence of the coupling hole, a symmetric port (connected to a circular pipe below cutoff) has been included in the gun [244–246] and is also used as a pumping port. The residual quadrupole field component from the presence of the two holes does not significantly affect the beam quality [247].

The electromagnetic design of the gun has been carried out using 2D and 3D electromagnetic codes (Superfish [248] and HFSS [249]). Figure 12.1a shows the HFSS geometry of the gun with its main dimensions.

A new fabrication technique for this type of structure has been recently developed at LNF [250] and successfully applied to the realisation of two RF guns: the ELI-NP gun and the first prototype gun currently in operation at UCLA at a low repetition rate (i.e. 5 Hz) and a relatively low cathode peak field [251]. The new technology is based on the use of special RF-vacuum gaskets, which allow a brazing-free realisation process, avoiding copper annealing from the brazing process itself, with the advantage of potentially reaching higher accelerating field with a lower breakdown rate [252].
<figure><img src="image_85.png" /><figcaption>Fig. 12.1. (a) HFSS geometry of the gun; (b) H field in the coupler region; (c) longitudinal accelerating field profile.</figcaption></figure>

The photo-cathode is centred on the flange that closes the half-cell. The requirement of a short response time of the cathode to allow electron beam shaping through laser pulse manipulation limits, in the case of the EuPRAXIA photo-injector, the choice of the cathode materials to metals that usually present response times of the order of a few tens of femtoseconds [253]. Based on the results so far obtained worldwide in different laboratories, the most promising candidate metals that can be used as sources for electron generation are copper (Cu) [254], magnesium (Mg) [255], and yttrium (Y) [256]. One of the parameters that is critical for the final choice and operation of the photo-cathode is represented by the quantum efficiency (QE) at the drive laser wavelength. The QE of these metals has been measured in similar conditions under UV laser irradiation at 266 nm, resulting in values of about $4 \times 10^{-5}$ [257], $5 \times 10^{-4}$ [255], and $\sim 2 \times 10^{-4}$ [256] for Cu, Mg, and Y, respectively.

In the first phase of EuPRAXIA, a copper cathode can be adopted. Copper is a robust material with well-proven photo-emissive behaviour that guarantees uniformity of the emission distribution over the laser spot illuminated by the laser. Its drawback is the low emission efficiency (i.e. quantum efficiencies of the order of $5 \times 10^{-5}$), which entails large laser pulse energy. Different cathode materials (e.g. Mg, Y) can be used in future phases once their reliability is demonstrated for operation in user facilities. In any case, all types of cathodes demand very good vacuum conditions, at the level of $10^{-9}$ mbar during high-gradient operation, which typically implies that the vacuum without RF should be even better by one order of magnitude. These demands are to be met by stringent control of the gun manufacturing and cleaning processes and by implementing a pumping system with high pumping
<figure><img src="image_86.png" /><figcaption>Fig. 12.2. Left: Photo of the SPARC gun solenoid. Right: The solenoid field distribution in the SPARC configuration ++−, as computed by the Poisson-Superfish code.</figcaption></figure>

<table><caption>Table 12.2. Parameters of the gun solenoid.</caption><thead><tr><th>Parameter</th><th>Unit</th><th>Value</th><th>Conditions</th></tr></thead><tbody><tr><td>Typical operation axial field peak (+−)</td><td>Gauss</td><td>2700 (−2700)</td><td>@ 14.3 cm (25.0 cm)</td></tr><tr><td>Residual axial field @ cathode</td><td>Gauss</td><td>&lt;10</td><td>@ 2700 Gauss field peak</td></tr><tr><td>Maximum coils current (typical)</td><td>A</td><td>~280 (180)</td><td></td></tr><tr><td>Distance cathode to solenoid edge</td><td>cm</td><td>9.6</td><td></td></tr><tr><td>Solenoid bore</td><td>cm</td><td>7.6</td><td></td></tr></tbody></table>

speed through direct pumping ports on the accelerating cells waveguide and cathode flange.

### 12.2.2 RF Gun Solenoid

The design of the solenoid, immediately after the gun, together with the gun design itself, is crucial for the emittance compensation process [258] and final beam performances at the linac exit. The proposed design consists of four coils, embedded and separated by iron armatures, that can be powered independently. In this way, it is possible to shape the magnetic field profile and move the field peak around the central position. This solenoid design, as tested at SPARC_LAB, allows one to power the coils with alternate signs (e.g. +−− or +++), giving a better compensation for alignment errors and multi-polar components. The magnetic field lines of the solenoid, as computed using the Poisson-Superfish FEM code [259], are shown in Figure 12.2, while the main design parameters are reported in Table 12.2.

The solenoid will also be mounted on a movable support to allow a beam-based fine alignment of the magnetic centre with a precision below ~10 µm in the transverse planes.

### 12.2.3 Photo-Cathode Drive Laser System

The EuPRAXIA photo-injector is required to produce both single and comb-like electron bunches, with a charge ranging from tens to a few hundreds of pC, with a
high peak current and normalised transverse emittance <1 mm mrad. Therefore, the laser pulses have to be tailored to minimise the beam emittance and, at the same time, have enough power to produce relative high-current bunches.

Photo-cathode drive lasers for high-brightness electron beam applications must have very specific capabilities driven by two major considerations: (1) the low photo-emission efficiency for robust photo-cathodes requires high UV pulse energy to generate the needed charge; and (2) the emittance compensation process is most successful with a uniform temporal and spatial laser energy distribution. Additionally, low amplitude and time jitters from pulse to pulse, as well as pointing stability are needed to ensure repeatable SASE FEL performance. The laser pulses have to be synchronised with the master oscillator to extract electrons at the specified phase of the RF wave. Other laser systems will be used at EuPRAXIA for laser-driven plasma acceleration, electron and photon diagnostics, and a variety of possible pump and probe experiments. All these lasers are required to be synchronous within very tight tolerances. The timing and synchronisation of the laser system are discussed in more detail in Chapters 11 and 15. The allowed variations in parameters concerning the laser system and its relationship to the RF system have been specified with the aid of simulation codes.

The laser system for EuPRAXIA is required to deliver energies per pulse in excess of ~150 µJ at a wavelength of 266 nm to the photo-cathode at a repetition rate of up to 50 Hz. This energy requirement comes from the typical quantum efficiency of a copper photo-cathode. Indeed, the drive laser supplies photons that are absorbed by electrons within the RF gun cathode, producing via the photo-electric effect emitted electrons only if their kinetic energy exceeds the material's work function. The energy per laser pulse $U$ (J) needed to produce a bunch of charge $q$ (C) using photons of energy $E_γ$ (eV) incident on a cathode surface with quantum efficiency $QE$ is given by $U = q E_γ / QE$. A cathode's quantum efficiency depends on many conditions, such as material, preparation, excess of photon energy over the work function, RF field, and vacuum levels. Nevertheless, we may extrapolate the needed performance of the photo-cathode drive laser based on our experience at SPARC_LAB. Assuming a typical quantum efficiency value of $5 \times 10^{-5}$ for copper, $20\mu J$ are required to produce a $400pC$ electron beam; allowing for an energy overhead of one order of magnitude, this implies that $200\mu J$ of laser energy are necessary. This required value at the photo-cathode must be considerably larger at the harmonic-generation crystal exit as light will be absorbed by various optical elements needed for pulse shaping and transport to the photo-cathode. In addition, the emittance compensation scheme requires that the laser pulse must show a uniform transverse and longitudinal profile to compensate the non-linear space-charge field with a proper magnetic focussing. The temporal and spatial flat-top laser energy distribution on the cathode has been demonstrated to reduce the emittance [256,257]. We foresee to change the pulse length on a range between 100 fs to a few ps (RMS) and the number of pulses from one to five to explore different machine working points based on the different foreseen experiments.

#### 12.2.4 S-band Linac

The EuPRAXIA photo-injector is finally completed with three S-band accelerating structures that allow one to accelerate and manipulate the beam through the velocity-bunching compression scheme. RF compression or velocity bunching [260] consists of compressing the beam by injecting it in the first RF structure ahead of the field crest with a phase near the zero of the accelerating field; the beam slips back up to acceleration phases undergoing less than a quarter of synchrotron oscillation and
<figure><img src="image_87.png" /><figcaption>**Fig. 12.3.** Solenoid coils embedding the first accelerating S-band structure; the upper iron shield is removed.</figcaption></figure>

is compressed. The emittance growth occurring during the compression can be con-
trolled by the proper shaping of an additional magnetic field around the accelerating
structures. For this purpose, two solenoids around the first two structures are used
for emittance compensation. Simulations show that compression factors larger than
three require an accurate tuning of the coils composing the solenoids embedding the
structures, as also experimentally demonstrated at SPARC_LAB [261].

The solenoid structure will be covered by de-mountable soft iron magnetic shields to shield the fringing field that, at a distance of 80 mm from the beam axis, is still not negligible (≈150 Gauss). Figure 12.3 shows the solenoid coils around the first linac sections with the shielding opened. The advantages of this configuration are the following:

- a higher magnetic field, about 1900 Gauss, as opposed to 1660 Gauss with the same number of ampere-turns;

- a sharper magnetic fringe field tail;

- an improved transverse alignment of the solenoid as it will depend partially on machined iron, not simply on wound coils with dielectric coatings;

- no fringing field outside the structure, i.e. no constraints for materials, external apparata, and personnel safety;

- the iron shielding, realised by means of semi-annular rings, which can be easily removed for checks, tests, or other necessities; and

- thermal confinement of the accelerating structure, which means less sensibility to ambient temperature variations.

The main parameters of each solenoid are summarised in Table 12.3.

The accelerating structures of the EuPRAXIA S-band linac are travelling wave
(TW), constant gradient (CG), 2π/3, and 3 m long operating at 2.856 GHz. These
types of accelerating sections, known as SLAC-type structures [262], are made of
a series of 86 RF copper cells, joined with a brazing process performed in high-
temperature vacuum furnaces. The cells are coupled by means of on-axis circular irises
with decreasing diameter, from input to output, to achieve the constant-gradient field
profile in case of uniform input power. The RF power is transferred to the accelerating
section through a rectangular slot coupled to the first cell. The power not dissipated