- Diagnostic devices: The high frequency and high fields in THz dielectric structures make them an ideal candidate for transverse deflecting structures (TDS) to measure the longitudinal bunch length by applying a time-dependent transverse streaking to the beam. These applications are currently being studied theoretically [702] and experimental setups are under development. In principle, also DLAs can be used for this purpose, but there, the experimental progress is less advanced.

- DLA-type structures can be modified to act as beam position monitors [703] with a very good spacial resolution. Their small transverse aperture is a challenge for the integration into conventional accelerators, though.

## 26.6 Additional Application Beamlines

It could be envisaged in the future to extend the application beamlines foreseen in the EuPRAXIA baseline to broaden the scientific impact of the facility. Two options under particular consideration are (1) a high-field physics beamline at the construction site for laser-driven plasma acceleration and (2) a betatron source at the construction site focused on beam-driven plasma acceleration. The high-energy physics case is described briefly in the following and, as will be shown, could be integrated into the current EuPRAXIA design quite easily using only limited additional resources.

### High-Field Physics Beamline

High-field physics is the study of electrodynamics at fields close to the Schwinger field, $E_{cr} = m_e^2 c^3 / (e\hbar) \approx 10^{18} \text{ V m}^{-1}$ [704]. The electric fields in the focus of a high-power laser are still far below this, but by colliding a high-intensity laser with a high-energy electron beam, the electric fields in the rest frame of the electron beam can approach a significant fraction of $E_{cr}$. In a head-on collision between the electron beam with energy $\gamma m_e c^2$ and laser with peak electric field $E_L$, the field reaches $4\gamma E_L$ in the electron rest frame. In such a collision, the electrons are made to oscillate in the laser field with such vigour that they lose a significant fraction of their energy through the emission of high-energy photons (gamma-rays). At high fields, the quantum nature of this emission must be taken into account and a definitive model of the radiation reaction process has not yet been established.

The electron beams produced by laser wakefield accelerators are ideally suited to these type of experiments as they can be naturally synchronised to the required femtosecond precision with a high-intensity laser pulse and their femtosecond duration and micrometre transverse size allow a large fraction of the electrons to overlap with a tightly focused laser pulse. Recent success in this area has been achieved with the first evidence for radiation reaction in a laser-electron beam collision [705] and first signatures of the quantum nature of that radiation [706].

The LWFA facility producing high-quality electron beams with GeV energies for the betatron beamline would be readily adapted to study high-field physics with the addition of a second high-power laser. This laser would be focussed near the exit of the wakefield accelerator (where the electron beam is small) and the key signature of radiation reaction would be the energy loss and change in spectral shape of the electron beam. The stability and reproducibility of the electron beam that will be produced at the dedicated user facility will allow the detailed discrimination of different models of quantum radiation reaction and so provide key insights into strong-field physics. [707]. This energy loss would be measured using the electron spectrometer on the betatron beamline. Additionally, on-axis measurements of the gamma-rays produced in the collision can be used to gain insight into the interaction. The gamma-ray
<table><caption>**Table 27.1.** Performance level and their respective average probability of dangerous failure per hour [709].</caption><thead><tr><th>Performance level (PL)</th><th>Average probability of a dangerous failure per hour (PFH) in h<sup>-1</sup></th></tr></thead><tbody><tr><td>a</td><td>≥ 1 × 10<sup>-5</sup> to < 1 × 10<sup>-4</sup></td></tr><tr><td>b</td><td>≥ 3 × 10<sup>-6</sup> to < 1 × 10<sup>-5</sup></td></tr><tr><td>c</td><td>≥ 1 × 10<sup>-6</sup> to < 3 × 10<sup>-6</sup></td></tr><tr><td>d</td><td>≥ 1 × 10<sup>-7</sup> to < 1 × 10<sup>-6</sup></td></tr><tr><td>e</td><td>≥ 1 × 10<sup>-8</sup> to < 1 × 10<sup>-7</sup></td></tr></tbody></table>

profile can be used to infer the on-shot laser intensity at the collision, and the spectrum can aid discrimination between models [705]. On-axis diagnostics to measure these can be placed outside the vacuum chamber behind a suitable vacuum window (e.g. Be or Kapton). Profile measurements of the gamma-rays can be made using pixelated scintillators and the spectra can be determined using pixelated scintillator stacks [708]. These on-axis diagnostics would go in place of the on-axis diagnostics of the betatron radiation, but they do not have demanding alignment requirements so this can be done rapidly. High-field experiments on the dedicated LWFA betatron beamline could be undertaken in relatively short access periods without major disruption to the main activities of the beamline, but could make significant impact in the rapidly growing field of experimental strong-field QED physics.

# 27 Safety and Environmental Impact

## 27.1 Safety Aspects

The EuPRAXIA facility will be built within an existing laboratory infrastructure, and therefore, will be governed by the local safety regulations. This includes entrance and access control systems to the laboratory perimeter and experimental areas, fire alarm systems, and evacuation systems.

Both the radiation safety system and the laser safety system are developed, analysed, and built according to the standards set to evaluate and monitor high-level safety systems. These standards ensure that a facility should be constructed in a manner that it is not able to present a hazard to the users or the general public. After this first goal has been achieved reducing further any risks of hazards which still exist is a secondary task any facility has to perform. These standards can be found in the functional safety of machine controls report [709] and are summarised below.

1. **Identification of safety functions:** In the first instance, the risk and dangers are assessed and necessary safety measures are identified. During the risk assessment, the assumption that no other protective measure has been put in place is assumed, so that the severity of each individual risk can be assessed correctly. Figure 27.1 shows an overview of the risk assessment and reduction procedure. Safety measures can be implemented via a control software system or via mechanical safety devices.

2. **Specification of characteristics of each safety function:** The second step lays out the individual specification each of the safety function needs to ensure the experimental environment is safe to operate for the users as well as for the public.
<figure><img src="image_252.png" /><figcaption>Fig. 27.1. Risk estimation and risk reduction (image credits: [709]).</figcaption></figure>

3. Determination of required performance levels: Once the specifications are characterised, the necessary performance level or quality of the safety function needs to be assessed. The performance level can be placed in one of five categories, defined according to the “probability of a dangerous failure per hour (PFH)”. These levels are summarised in Table 27.1. As pointed out in [709], additional measures, such as software robustness or action-to-counter systematic failures, are required, in addition to PFH.

4. Realisation of safety function and identification of safety related parts of control system: After identifying the risks and hazards of the machine and defining what safety measures need to be implemented, the design of the proper safety-related parts of the protection system can be started.

5. Evaluation of performance level for safety related part of control system: The evaluation considers points such as the mean time to dangerous failure, average diagnostics coverage, and common cause of failure. This point also includes a software and systematic failure analysis.

6. Verification: The process checks if the performance level developed and built is higher than the required performance level for a subsystem. If the performance level is inferior to the required performance level, the safety function for this part of the machine has to be changed, until the required safety level has been attained.

7. Validation: The total safety system is checked for requirements met.

8. All safety functions analysed: The final point ensures that all systems have been analysed and implemented.

Points 1. to 7. are performed for each safety function separately. Point 8. ensures all functions laid out in the beginning of the safety assessment were implemented.

The safety of the accelerator parts of the machine will be implemented, based on local rules, by the research institutes hosting the different EuPRAXIA sites. We note in this context that the machine parameters of EuPRAXIA are well within the range of what has been safely handled at many of the partner institutes for
decades. No new records in beam energy, intensity, or brightness will be reached with the EuPRAXIA accelerators. For the laser system, however, the situation is different, as a high-repetition-rate, high-power regime is pursued. We thus describe in the following some key aspects of safety measures related to the EuPRAXIA laser specifically.

## Laser

The purpose of this section is to describe the risk of the laser beam on the EuPRAXIA facility and the means of protection put in place to reduce it to the minimum possible. It is not a full laser risk analysis that can not be led with the current definition of the laser.

The nine general principles of prevention are taken into account in the following manner:

1. **Avoid risks:** Each zone is filtered by an access control by name badge: only authorised persons will be able to enter the zones with presence of the laser. These areas are isolated from the outside (the beam cannot get out). Signage at the entrance of each zone indicates the level of risk with the instructions to be applied.

2. **Assess risks that can not be avoided:** A laser risk analysis has to be written and will have to be updated regularly. This makes it possible to highlight the critical points on which it is necessary to make modifications. In no case should workers be exposed without adequate protection.

3. **Fight risks at the source:** All beam sources are equipped with beam blockers. To limit exposure, collective protection is preferred. In addition, when the collective protections are insufficient or inadequate, we will use the individual protections.

4. **Adapt the work to the Man:** No worker should be exposed to a risk that is not covered by collective or individual protection. The beam height has been defined in such a way that the risk is as low as possible. In addition, all equipment must be at a height very different from that of the beam.

5. **Take into account the evolution of the technique:** Security systems will be monitored on a regular basis and at each major change. Anomalies will be recorded in a hygiene, safety, and working conditions committee register. Room access is only given after receiving adequate security training. The review of the laser risk analysis will take into account technological developments.

6. **Replace what is dangerous with something that is not dangerous or less dangerous:** In the majority of cases, especially during alignment phases, laser sources are used at low energy.

7. **Planning prevention:** If an outside company should work in an area with laser presence, a prevention plan will be systematically written. In addition, the level of risk will be minimised with the presence of an authorised person. Unauthorised persons should not be exposed to risk.

8. **Take collective protection measures:** Many collective protection measures will be installed throughout the path of the beam. To complete these measures, the wearing of glasses adapted to the beam of the area is mandatory. In addition, the wearing of clean room equipment (ISO7 or 8) can hide any reflective objects (watch, bracelet, etc.) which will be prohibited anyway for the operators involved with the laser beams.

9. **Give the appropriate instructions to the workers:** Each person who can work in the presence of a laser must have received training on laser safety. Regulatory signage is present at each zone entrance and inside.
All laser sources used will be Class 4. At the highest level of risk, these lasers are also capable of producing dangerous diffuse reflections. They can cause damage to the skin and can also be a fire hazard. Their use requires extreme caution.

Depending on the area, the beam characteristics will be different (power, energy, repetition rate, wavelength, beam diameter, and pulse duration). The protection will have to be suitable for those characteristics.

There will be two different levels of protection: (1) collective protection, and (2) individual protection.

## Collective Protection

The collective protection consists of three types:

- Zonal protection at each zone: At the entrance of each zone, signalling of the current risk level of the zone by jack and scrolling panels and displays of safety instructions (e.g. to wear safety glasses) will be present. Each zone is accessible through a door with access control. Depending on the level of risk, the persons authorised to enter are different. The list of personnel with their access is validated by the facility management. At the entrance of the zone, an airlock is present to prevent the propagation (direct or by diffusion) of the laser beam out of the zone. Some areas may have windows for visitor tours. These are obscured by components with the same purpose. These protections will be installed before the commissioning of the first laser sources in each zone.

- Global protection at the optical tables: The goal is to add additional protection to local protections that will be linked to the personal security system. This protection is of the hood type encompassing one or more optical tables. These covers will be installed once all equipment on the optical table is installed. In any case, they will be installed before the first tests with the final laser beam.

- Local protection: The objective is to isolate the beam locally using the most appropriate means, such as a single tube to isolate the beam, hoods to isolate a complete block of the optical path, or beam blockers, some of which will be connected to the PSS. These protections will be installed as the optical path progresses. The search for leaks is systematically carried out to guarantee their opacity. In the case where the beam is under vacuum, it is the entire empty system that ensures the protection of personnel. The beam is isolated by tubes or enclosures. The empty system connected to the PSS automatically manages the safety of personnel in the case of a return to atmospheric pressure.

The protection type “hood” will be different and especially adapted to each situation, for example, through the use of:

- a tube for a simple insulation of the beam,

- a hood to isolate a complete block of the optical path,

- a cover enclosing one or more optical tables,

- etc.

In all cases, the material used will allow the absorption and non-diffusion of the beam. The covers enclosing the optical tables are connected to the PSS. Their opening is allowed only for certain levels of risk. An unauthorised opening automatically triggers the zone to a safe level.

Two types of blockers will be used:

- Interzone, which protects staff from the upstream zone,

- Local, which allows to isolate a part of the optical path.
All interzone blockers will be controlled by the PSS. They make it possible to secure the zone in the event of a detected risk. Their functioning is controlled by the PSS. In the case of failure, the interlocks of the sources are opened automatically, which stops the emission of the laser beams.

## Individual Protection

Personal protection is used in addition to collective protection. Goggles are mandatory in areas where laser risk is present. The goggles will be placed in the access locks, on a suitable display. Filters will be selected to protect staff from sources used. Several types of frames will be available to best adapt to the morphology of each. The strongest attenuation will be covered by signals. Permanent staff will have named glasses. Other pairs will be available for casual users.

## Training

All personnel to work in the presence of lasers will have received training in laser safety. A training certificate will be requested from any external person exposed to the laser risk. A visit of the installations will be realised to visualise the locations of the individual protection measures, the various equipment of collective protections, emergency exits, etc.

## Security System

The main purpose of the “PSS” security system is to

- manage collective security loops in danger zones;

- allow the turn on and force the shut down of the laser beams by means of interlocks of the sources;

- report the danger through signaling equipment (verrine, scrolling panels, etc.);

- manage the opening and closing of laser beam blockers;

- control the access and in a general way all the openings of the laser zones; and

- check the closing of the blackout blinds.

Some blockers can be controlled by the supervision system with a link to the PSS.

Only authorised persons can pilot the PSS. Before any change in the level of risk, this person must ensure that those present are authorised and have the necessary protection. The signalling and access to the area concerned is automatically modified accordingly. An audible warning signal is emitted.

## Emergency Situations

Despite all the means of prevention put in place, zero risk does not exist. In the event of an accident, the following measures will be implemented:

- a first aid worker must be present per room;

- all personnel who can work with a laser presence will be trained to the risks as well as for aid measures;

- emergency calls can be accessed in all areas;

- first aid equipment is implemented in each room;

- equipment for fire fighting is present in each zone.
## 27.2 Environmental Impact

Although based on novel acceleration technologies, the proposed EuPRAXIA facility will be very similar to existing conventional accelerator infrastructures in the same beam energy range with regard to its radiological effects, materials and water consumption, environmental emissions, and most other environmental impact factors. As previous sections in this report, such as Chapter 27.1 (on safety), Chapter 11 (on the control-command system) and Chapter 22 (on the electron beam dump design), demonstrate first studies have been completed and strategies have been defined on how to design and implement safety and control systems in a comprehensive and thorough way to limit the facility's environmental effects. This will be carried out in close collaboration with dedicated technical groups at the various partner institutions of EuPRAXIA and will thus built on extensive experience from other operational machines.

The energy consumption will be a particular factor to be investigated in detail as part of the technical machine design. In a short-term view, the operation of laser systems at average powers beyond the current state of the art certainly presents challenges in this respect; on the other hand, EuPRAXIA's mission to strive for a considerable miniaturisation of the accelerator footprint is expected to have positive effects on energy usage, especially in the long run. EuPRAXIA will use RF systems and laser systems at the highest available efficiency; RF power schemes, for example, can achieve 70% efficiency and the EuPRAXIA laser technology is foreseen to reach an efficiency at the few percent level (wall-plug to RF / laser power). The total power consumption of the proposed facility will stay well within the available power at existing research institutes and is therefore not a fundamental issue for the implementation of EuPRAXIA. However, measures to improve the overall system efficiency are highly important and will be pursued in the technical design phase.
# Part 5
## EuPRAXIA Pre-Construction R&D and Technical Design Phase

### 28 Necessary Experiments and Prototypes for the EuPRAXIA Design

With the EuPRAXIA design featuring a wide range of cutting-edge technologies, a thorough experimental campaign of conceptual tests and prototyping activities will be an essential and unavoidable step in the technical design phase of the project.

In the following section we will provide a list summarising the most important R&D activities identified so far in this context. For reader convenience, we have separated them by main topics with R&D on laser systems, plasma components, RF and accelerator technology, and diagnostics. The following list must be considered as a list of ideas to be tested (and possibly improved) before and during the project's technical design and preparatory phases.

#### 28.1 Laser System

EuPRAXIA requires a petawatt laser working at a minimum of 20 Hz and ideally at 100 Hz as a baseline. Such a laser does not exist at the moment and hence several proof-of-principle tests need to be carried out, along with the prototyping of critical components in order to de-risk the project.

##### Pointing stability of drive laser and feedback control

Beams from plasma accelerators are known to have pointing fluctuations. This is a major issue that will limit the applicability of plasma accelerators. Further, this also has safety implications as it is possible for the pointing of the particle and radiation beams from the plasma to exceed the acceptable range beyond which there could be safety implications for the facility as well as the personnel working in the area. For laser-driven plasma accelerators, it is known that the pointing stability of the driver laser affects that of the electron beam. However, the effect of the driver and the inherent fluctuations coming from the plasma medium have not yet been delineated. It is therefore essential to make sure that the effect of laser-beam pointing on the pointing of particle and radiation beams from the plasma accelerator is fully understood and controlled. It is also necessary to test feedback control loops that control the laser pointing to maintain the electron beam pointing within a safe limit. Experiments that test such genetic-algorithm-based loops are underway and are encouraging.

##### Generation of controlled pulse trains

A single pulse of a typical photo-cathode laser has about 200 mJ in energy in the infra-red (800 nm) region. Afterwards, the laser beam has to be compressed, sent to a third harmonic generator (to go from 800 nm to 266 nm), and then it goes through a UV stretcher to be able to switch easily from short pulse to long pulse depending on the linac operation requirements. The final maximum UV energy will be about 2 mJ but it must be possible to reduce it down to a few µJ using filters to have
the possibility to explore a big range of energies. Such systems are nowadays quite standard and do not require additional R&D. Other tasks and schemes, however, may require producing 3D-shaped laser pulses (formation of triangular, cylindrical, ellipsoidal, etc. pulses), R&D on which may be carried out, e.g. by staff at the Institute of Applied Physics of the Russian Academy of Sciences (IAP-RAS).

The EuPRAXIA beam-driven plasma acceleration schemes rely on the possibilities of generating ps-spaced pulse trains, each pulse having the characteristics mentioned before. The driver pulses in the train shall be equally spaced to resonantly drive the plasma wave, while the witness pulse delay should be easily tuned to maximise the acceleration performance. Moreover some schemes foresee also an increasing charge in the driving electron beam, and with this a non-constant intensity in the corresponding optical pulses. Solutions and optical schemes have already been tested for some time, but additional experiments are still needed to find the optimal and most versatile solution.

## Damage testing of optical components

Optical components in the beam transport line, including the last grating in the compressor, highly reflective mirrors and parabolas, are exposed to the highest unfocussed intensities in the laser system. Typically, the laser beam diameter is chosen so as to have a fluence on these optics just below the damage threshold of the components. Although high-damage threshold coatings exist, their behaviour at these fluence levels at high repetition rate is unknown. Joint R&D efforts with optical manufacturing companies are thus required for developing and testing high-damage threshold optics in the system.

## Prototype of a 100 Hz laser system

The repetition rates of a high-power laser system such as the one envisaged in EuPRAXIA are currently limited by the availability of pump laser technologies that can drive these petawatt lasers at high repetition rate. The repetition rate of petawatt and petawatt-class lasers is currently limited to 10 Hz, in both flash-lamp-pumped as well as diode-pumped solid-state laser (DPSSL) technologies. R&D works are thus ongoing to extend this further. Although EuPRAXIA could begin with a 20 Hz petawatt laser system, it aspires to have a 100 Hz petawatt laser for driving plasma accelerators in its next phase. Significant advancements in high-average-power laser technology are required to achieve this. Some of these technologies include, for example, the use of multiple optical fibres, phase-locked to deliver the required brightness. Such systems are not currently available at sufficiently high energy and power, but may offer advantages from a systems engineering aspect in the future if the anticipated performance and cost improvements are realised. It is envisaged that multiple pump laser technologies (DPSSL thin-disk, Big-Aperture Thulium, etc.) will need to be tested in this regard in order to build a prototype for such a system.

## Thermal load and cooling of critical laser components

Even with the right pump laser technology, the thermal management of key components in the laser system becomes a bottleneck for driving high-power lasers at high repetition rates as at such high repetition rates the thermal load induced in the system invariably induces a thermal lens effect that will detrimentally affect the laser
beam quality. For example, the final amplifier, where the maximum pump energy is dumped, needs an active cooling system that can take away the excess heat generated in the gain medium, while maintaining the wavefront quality of the laser beam. This means that turbulent flows of liquid and cryogenics, which are usually used to cool optical systems, need to be employed carefully so that they do not affect the transmitted wavefront quality of the amplifier. Amplifier technologies such as OPCPA, which do not rely on energy storage, will need to be explored in this regard.

The pulse compressor is the final link in the laser chain, one of the most critical and often acts as a fuse in terms of damage threshold for the entire laser chain. The gratings used in high-power laser compressors are typically metallic (gold) although, with the expansion in the numbers of CPA laser systems around the world, grating technology is developing quite rapidly with the goal of increasing the damage threshold of gratings for use in pulse compressors. Recent reports on hybrid / dielectric gratings for petawatt-class laser systems are very encouraging.

While the damage threshold is one key issue with the compressor gratings, their very diffracting nature causes issues with heat absorption. With gold gratings, typically around 94-95% of the energy is diffracted into the first order, and 3% into the zeroth order. The remaining 3% is absorbed by the grating, which can lead to issues with substrate heating and deformation. For example, a compressor grating in a petawatt laser running at 20 Hz can be exposed to as much as 900 W of average power, and there is a significant risk that it will absorb enough energy to deform as a consequence of thermal gradients set up in the substrates. A solution needs to be developed to address this problem in EuPRAXIA.

## 28.2 Plasma Components

### High-throughput plasma targets and plasma mirrors

For LWFA applications at high repetition rates, gas targets that can provide the acceleration medium are a prerequisite. Depending on the necessary acceleration gradient, it is often required to fill gas targets ranging from gas-filled capillaries, which operate at few millibars, and gas-cells with few bar backing pressures to pulsed gas jets, which operate at several tens of bar backing pressure. This creates a significant load on the pumping system as the gas release into the vacuum chamber with pulsed nozzles, running at high repetition rates, and gas cells, leaking continuously through the apertures for laser inlet and exit, must be handled. At high repetition rates, this might require differential pumping systems or techniques that isolate the high-pressure region from the rest of the vacuum beamline. Such systems will be tested and prototyped.

Similarly, it is essential to remove the drive laser pulse after the interaction with the gas target. Current technology (such as plasma mirrors) needs to be able to operate at high repetition rate. While it is possible to use tape-drives as plasma mirrors, their reliability at high repetition rate, subjected to high-pressure and high-radiation environments, needs to be checked. Recent experiments suggest that liquid crystals could provide an alternative but this again needs to be tested at appropriate repetition rates.

Due to dephasing issues in a single stage of a laser-plasma accelerator, adding multiple stages of acceleration will be required to produce electron beams of energies around and beyond 5 GeV. The requirement of high-repetition-rate plasma mirrors is important not just the driver removal but also for enabling staged acceleration at high repetition rate. The current technology for staged acceleration involves the drive laser for the second or additional stage to be reflected into the plasma target by
a plasma mirror. This requires highly reflective and thin optics in order to minimise energy loss from the laser as well as reducing the disturbance of the electron bunch. The development and testing of such plasma mirrors will be an essential aspect of the technical design phase.

## Stability and reliability of active plasma lenses

Active plasma lenses represent compact and affordable tools with radially symmetric focusing and magnetic field gradients up to several kT/m. Such devices represent a reliable and affordable solution because of their compactness, strong focussing, and high tunability.

To be used as focussing devices, however, their effects on the particle beam distribution must be well characterised. Some studies are already reported in literature (e.g. in [305]) and first experimental results focussing a high-brightness electron beam by means of a discharge-capillary of a few centimetres length (pre-filled with hydrogen gas) are available. The magnetic focussing field, when operating at low discharge currents, can be highly non-linear at increasing distance from the lens centre, leading to an emittance increase due to spherical aberrations.

The necessary additional experimental and prototyping studies will focus on the reduction of beam emittance increases due to non-linearities in the focussing field during lensing and / or the possible partial ionisation of the gas in the capillary. To achieve a full optimisation of such a device and a high quality of the focussed beam, a viable solution could be the experimental study of different capillary geometries and discharge circuits. Experiments are also needed to refine the numerical model of the phenomenon to account for the effects, for instance, of misalignment on the properties of the out-coming beam or to design optimised capillaries.

## 28.3 RF and Accelerator Technology

Additional issues that need to be tested concern practical aspects of the implementation of EuPRAXIA as a test facility. We underlined three classes of problems that have emerged during the work towards the present CDR.

### Laser-electron beam synchronisation for external injection schemes

The most stringent requirement for the timing and synchronisation systems concerns the injection and acceleration of a single bunch in a plasma wave excited by a laser pulse. In this case, the relative jitter between laser pulse and electron bunch must be a fraction of the plasma wavelength (i.e. smaller than 20 fs RMS). Once such requirement is met, all other subsystems could benefit of such a high-quality synchronisation performance.

The synchronisation system usually generates and distributes a reference signal to provide a fine temporal alignment among all the relevant sub-system oscillators that guarantees a temporal coherence of their outputs with a precision of 10 ps–10 fs (coherence between RF accelerating fields, laser oscillator frequencies, ADC / DAC clocks, etc.). A typical system is based on industrial standard devices, common to many accelerator infrastructures based on room-temperature RF (e.g. European XFEL, FLASH, LCLS, SwissFEL, ELI_NP GBS, etc.). Testing is still needed to assess that the required <20 fs jitter can be routinely achieved in an complex accelerator environment.
Moreover, the proposed sub-femtosecond synchronisation technique, proposed in Chapter 15 and expecting to achieve even better timing synchronisation, will also need to be tested experimentally and optimised.

## Performance and reliability of a plasma-based beam dump

A plasma beam dump uses the collective oscillations of plasma electrons to absorb the kinetic energy of a particle beam. Recent studies [581] proposed a modified passive plasma beam dump scheme using either a gradient or stepped plasma profile to maintain a higher decelerating gradient compared with a uniform plasma. The improvement is a result of the plasma wavelength change preventing the re-acceleration of low energy particles. Particle-in-cell simulation results show that both stepped and gradient plasma profiles can achieve improved energy loss compared with a uniform plasma for an electron bunch of parameters compatible with those expected for EuPRAXIA.

Plasma beam dumps show great promise both in providing compact deceleration to complement high-gradient novel accelerators and in reducing the complexity of beam dumps in conventional accelerators. Although passive plasma beam dumps are not capable of decelerating the head of the bunch, the rapid reduction in total beam energy would allow for a conventional beam dump to absorb the remaining energy with greatly reduced radio-activation and cooling requirements. Experiments are now needed to assess the reliability of the scheme, which has to satisfy also the radio-protection standards to be included in the final technical design of EuPRAXIA.

## Automatic feedback systems for optimising electron beam properties

The achievement of a high quality of laser-wakefield-accelerated beams comparable with conventional accelerators is an open experimental issue and many innovative ideas have been proposed and tested.

For instance, Dann et al. [710] recently proposed a genetic algorithm to apply active feedback to a laser wakefield accelerator at a higher power (10 TW) and a lower repetition rate (5 Hz) than previous work. The temporal shape of the drive laser pulse has been adjusted automatically to optimise the properties of the electron beam. By changing the software configuration, different properties could be improved. This included the total accelerated charge per bunch, which was doubled, and the average electron energy, which was increased from 22 to 27 MeV.

Moreover, using experimental measurements directly to provide feedback allows the system to work even when the underlying acceleration mechanisms are not fully understood, and, in fact, studying the optimised pulse shape might reveal new insights into the physical processes responsible.

Reference [710] already identifies other promising algorithms to be used in the same way as the genetic one to improve beam parameters. Similar ideas can be used also to design the generation and transport of high-charge, higher-energy laser-driven electron beams. Such an approach needs to be further tested since it may be a practical way to run EuPRAXIA as a user facility.

## 28.4 Diagnostics

The diagnostics for both the beam-driven and laser-driven design options of EuPRAXIA will face similar problems. First of all the (laser or particle) driver will
strongly affect any measurement if the driver is not properly removed. Typically the driver is “intense” enough to trigger efficiently the acceleration mechanism; thus its removal must be quite complete in order not to blind or even damage the diagnostics detectors. Another non-negligible requirement is the compactness of the diagnostic station, which may be not trivial at high energies.

Due to the powerful focussing strength of the plasma channel, which the electron beam exits after acceleration, the beam will have a quite high divergence. Such a characteristic, joined with the high energy spread possible during the commissioning phase, may result in complex capture optics, possibly affecting the accuracy of beam parameter measurements. Additionally, to have an energy spread competitive with conventional accelerators, plasma-accelerated beams must be extremely short (on the fs scale); therefore, fs resolution is required in any time-related measurements (e.g. for the bunch length as well as phase jitters).

Especially in the commissioning phase, the accelerated beam may experience some shot-to-shot instabilities connected to the high accelerating fields acting on the beam itself. Therefore, the measurement techniques should be as much as possible independent on pointing, energy, and time jitters.

Most of these issues as well as possible solutions are extensively discussed in Chapter 21 and [711], where the authors report on the design study of diagnostics for a high-brightness accelerator, based on an X-band linac and a plasma accelerator stage, to be delivered in the framework of the INFN-LNF initiative towards beam-driven plasma accelerators.

The development and implementation of most of the ideas reported in [711] should be experimentally studied to be a baseline also for the technical design phase of EuPRAXIA. Some activities have already started during the EuPRAXIA CDR phase. Although they are of paramount importance to assess EuPRAXIA concepts, some of these experiments are focused on demonstrating reliability or on investigating implementation issues. Therefore, some of them may not have the potential for world-class scientific publications, which is a prerequisite for a successful application to many of Europe's top test laboratories. It is thus likely that some of these proof-of-principle tests will not get experimental time in the open slots in some of the major user facilities through direct application. A proposed strategy is to establish collaborations between EuPRAXIA partners and associate labs in order to facilitate such experiments.

As a general statement, single-shot measurements are preferable for plasma-accelerated beams, including for emittance diagnostics, while a measurement resolution at the µm-level and fs-scale (for beam size and bunch length respectively) are requested. In the following, we will report on the necessary beam measurements trying to give a fast overview of the main issues to be included in the systematic experimental studies needed to complete the technical design of EuPRAXIA.

## Longitudinal phase space

The conventional way to measure longitudinal phase space in high-brightness linacs involves transverse (RF) deflectors for length measurements and dipoles as spectrometers for energy measurement; they are often used together for full longitudinal phase-space measurements and / or as diagnostics for slice energy spread. X-band frequency (i.e. more compact) devices should be tested for EuPRAXIA-like beams to verify that they can be considered as an option for the final design.

Such techniques are intercepting and typically require multiple shots. Single-shot, non-intercepting bunch length measurements may be useful, for instance, when the beam is sent into a plasma module to correlate input and output properties of the
bunch. Such a feature is believed to be very useful in the commissioning phase. In this context, extensive testing and / or prototyping of novel ideas can help significantly.

One idea to be tested could be the use of diffraction radiation, which is emitted when a charged particle passes through a hole with transverse dimension smaller than the radial extension of the electromagnetic field travelling with the charge. There are some studies reported in [312,551,673], but optimisation and testing with a EuPRAXIA-like beam is still to be performed. Similar comments hold for devices for non-destructive bunch length measurements based on Smith-Purcell radiation [712]. A systematic prototyping of devices using both approaches can help significantly for the next EuPRAXIA phases.

Another quite interesting option for single-shot, bunch length measurements is electro-optical sampling. The bunch electric field can rotate the polarisation of a laser impinging on a crystal, and thus it is possible to retrieve the longitudinal beam profile in one shot [713]. Experiments are needed to reduce the temporal resolution (now on the order of 40–50 fs), limited by the crystal bandwidth or by the length of the laser probe.

Since plasma-accelerated beams are in the femtosecond range, the synchronisation with an external RF pulse (e.g. in a transverse RF deflector) is not at all trivial. A class of novel devices, namely passive streakers, are now starting to be discussed. The idea is to deflect the tail of the beam by means of self-induced wake-fields when the beam travels close to properly designed structures, such as dielectric or corrugated pipes. Such devices were conceived to compensate correlated energy spread in free-electron lasers; wakefields are naturally synchronous with the beam and thus researchers consider to use them for deflecting the bunch as in a RF deflector. Interesting and non-trivial R&D is still needed but such an idea could also have an impact for EuPRAXIA.

## Transverse phase space

There are two main measurements for transverse diagnostics: emittance and envelope (i.e. beam size along the machine).

The envelope measurement is needed to properly match the beam along the machine; comparing the measured dimensions with the simulated ones typically helps considerably in the commissioning phase. Beam size measurements in high-brightness linear accelerators is typically done with optical transition radiation. Such an approach is still valid also for EuPRAXIA, even if some testing / prototyping is needed to verify the technique's reliability for µm-size beams, as the ones expected at the entrance or exit from the plasma channel.

Emittance measurement is a more difficult issue; the resolution must be better than 1 mm mrad and, ideally, one needs single-shot, non-destructive measurement means to be used in the tuning of the machine to control the emittance increase possible during the plasma acceleration. A viable solution could be to use betatron radiation for the emittance measurement just at the end of the plasma channel, while other single-shot methods must be proven before a final design and implementation.

Conventional betatron radiation systems were able to measure just the beam profile and divergence, neglecting the correlation term. Only recently a new algorithm has been developed to retrieve the correlation term [711]. By using the simultaneous measurement of the electron and radiation energy spectra, it is possible to have a better reconstruction of the phase space.

A kind of optical pepper pot, based on optical transition radiation produced when a charge passes through a metallic foil, has also been proposed for single-shot emittance measurement [711]. The angular distribution of the emerging radiation contains information about the angular divergence of the beam. By using an optical
system to reproduce outside the vacuum chamber the source radiation field and sample it by means of a microlens array, it is possible to retrieve the value of the beam divergence in different transverse positions.

Such ideas need careful testing, with conventional beams as well as with high-divergence and high-energy-spread beams, which do not preserve emittance in a drift [379].

## Beam trajectory and beam charge monitors

Plasma accelerators require control of the charge and the trajectory at resolutions of a few pC and a few micrometres. Such accuracy is needed at the entrance of plasma channel, since misalignment can induce instabilities in the beam, but also at the entrance of the undulator sections.

Even if commercial systems (e.g. integrated current transformers) allow the measurement of a charge as low as 50 fC, we still need testing devices able to measure both charge and beam position, seeking the most compact solution.

Cavity beam position monitors (BPM) can have µm-level resolution, even at very low charge (few pC), while taking up little space longitudinally. There exist many kinds of cavity BPMs working in different frequency ranges; one of the difficulties is the monitor calibration in an operating machine environment and thus a systematic experimental study of the possibilities is believed to be mandatory.

# 29 EuPRAXIA Consortium Facilities

## 29.1 APOLLON (France)

The APOLLON facility [714] will deliver a set of laser beams, synchronised and possibly overlapped at one single focal spot, for a maximum total energy on target of 265 J. This laser setup includes:

- a main laser beam ("F1"), delivering pulses of 150 J at maximum in 15 fs, i.e. with a peak power of 10 PW (1 shot per minute),

- an intense auxiliary laser beam ("F2"), delivering pulses of 15 J at maximum in 15 fs, i.e. with a peak power of 1 PW,

- an uncompressed "creation" laser beam ("F3"), delivering pulses of duration 1 ns with a maximum energy of 250 J,

- and a fs probe laser beam ("F4"), delivering pulses of 250 mJ at maximum in 20 fs (10 TW).

These beams will be directed into two experimental areas:

- HE1, which – using short focal length focusing optics (f/2.5) – will be more focussed on the study of laser interaction with solid targets at intensities close to $1 \times 10^{22} \text{ W/cm}^2$ to generate proton, ion and X-ray radiation secondary sources for pump-probe experiments,

- HE0, which will be more specialised for studying particle acceleration using long-focal-length focusing optics (f/75).

This facility is located on the Orme des Merisiers site, reusing the ALS building (dismantled in 2006).

The facility will be open to users in 2020 after first experiments devoted to equipment validation and reliability tests. The laser chain and the associated experimental areas will thus be at the heart of a unique centre for experiments at the forefront of research on various topics related to high-power ultra-high intensity lasers and to the sources they allow creating.
<figure><img src="image_253.png" /><figcaption>**Fig. 29.1.** Map of European EuPRAXIA consortium facilities. Divided into laser, accelerator and computing laboratories, these could be used for prototyping and testing concepts and components during the planned technical design phase of the project.</figcaption></figure>

## 29.2 CLARA (United Kingdom)

CLARA (Compact Linear Accelerator for Research and Applications) is a purpose-built dedicated accelerator test facility at STFC Daresbury Laboratory in the UK [715]. Currently CLARA operates at up to 50 MeV, providing electron beams into two independent radiation bunkers for exploitation by accelerator researchers, including LWFA and PWFA experts. One bunker also has the capability to combine the electron beam with a 10 TW laser which is particularly attractive for plasma accelerator experiments. In the future, it is planned to upgrade the beam energy to 250 MeV (the main parameters are summarised in Tab. 29.1), again with a dedicated bunker and high peak power laser, for a range of electron beam experiments including plasma acceleration studies. The electron beams are generated by a high-gradient photo-injector, with a repetition rate up to 400 Hz, and so the electron beam brightness will be very high, with peak currents beyond 5 kA, ideally matched to PWFA experiments. In addition, CLARA has space reserved for an FEL to be installed in the future, enabling advanced FEL concepts to be developed and tested prior to implementation in an X-ray facility. The layout of CLARA, showing the 250 MeV electron exploitation beamline and radiation bunker, and the space reserved for an FEL in the straight-ahead geometry, is shown in Figure 29.3. Access to beam time at CLARA is granted competitively through a call for proposals, open to any researcher (subject to eligibility). Proposals are assessed by an allocation panel, who advise the facility based upon certain criteria, such as scientific excellence and impact.
<figure><img src="image_254.png" /><figcaption>Fig. 29.2. View of the laser facilities at APOLLON (image courtesy of APOLLON).</figcaption></figure>

<figure><img src="image_255.png" /><figcaption>Fig. 29.3. Layout of the CLARA facility, including the 250 MeV electron exploitation beam-line, radiation bunker, and the space reserved for an FEL (image courtesy of CLARA).</figcaption></figure>

<table><caption>Table 29.1. Main parameters for the CLARA operating modes.</caption><thead><tr><th></th><th>Units</th><th></th></tr></thead><tbody><tr><td>Bunch charge</td><td>pC</td><td>25–250</td></tr><tr><td>Energy</td><td>MeV</td><td>250</td></tr><tr><td>Bunch length</td><td>fs RMS</td><td>&lt;30–850</td></tr><tr><td>Energy Spread</td><td>keV</td><td>25–100</td></tr><tr><td>Repetition rate</td><td>Hz</td><td>100–400</td></tr><tr><td>Normalised emittance</td><td>mm–mrad</td><td>&lt;1</td></tr></tbody></table>

## 29.3 COXINEL (France)

COXINEL [65,716] is a test experiment set up by a collaboration of Synchrotron SOLEIL, Laboratoire d'Optique Appliquée (LOA), PhLAM of the University of Lille (all France), and the Weizmann Institute of Science (Israel). It is based at the Salle Jaune hall of LOA, where a 10 m electron transport beamline was designed and installed by SOLEIL. The laser-plasma accelerator uses the 60 TW, 800 nm, 30 fs Ti:Sapphire laser of LOA, and an additional laser beam of several mJ is provided to seed the FEL. The electron beam is handled by a series of permanent-magnet variable-gradient quadrupoles designed for this experiment, followed by a decompressing magnetic chicane, electro-quadrupoles and the 18 mm-period undulator U18 of SOLEIL. The chicane-based beam transport follows the strategy of the longitudinal sorting of electron energies to enable FEL amplification for high beam energy spreads.
<figure><img src="image_256.png" /><figcaption>Fig. 29.4. Schematic view of the COXINEL beamline. The following abbreviations are used to describe the beamline components: LPA = laser-plasma accelerator, PMQ = permanent magnet quadrupole, EMQ = electromagnetic quadrupole, cBPM = cavity beam position monitor (image credits: [716]).</figcaption></figure>

## 29.4 ELBE Centre for High Power Radiation Sources (Germany)

The ELBE Centre for High Power Radiation Sources of the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) [717] combines advanced laser-plasma accelerator research with the user operation of accelerator-driven radiation sources serving a range from intense THz pulses via IR FEL beams and X-rays to pulsed positrons. Basic research as well as interdisciplinary applications of societal relevance, like image-guided cancer radiotherapy, benefit from the leading in-house expertise of the centre. Highest fields are offered at the dual-beam petawatt laser DRACO with key applications in ion and electron acceleration and are complemented by the development of the fully diode-laser-pumped petawatt laser Penelope. Unique synergies of ultra-fast probing and plasma preparation are exploited by the installation and operation of the Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL. Basic research as well as applied experimental projects are complemented by innovative and open-source computing activities focussing on GPU-accelerated simulation tools (PIConGPU), aiming for predictive capabilities and big data management. HZDR operates the DRACO petawatt laser facility providing ~30 fs laser pulses in two independent pulse-cleaned beams of 4 J and 25 J laser energy on target. The main beams can be used individually or combined and are routinely complemented by an independent suite of synchronised probe beams at different non-harmonic wavelengths and pulse durations as well as by ELBE-accelerator electron bunches of ps duration. Two fully equipped target areas are served with a focus on the laser interaction with solid and gaseous targets at short and long focal lengths. With the topical focus of the facility on the development of advanced plasma accelerators and related applications, a key advantage is the provision of single-shot reference diagnostics and probes for the routine on-shot characterisation of the laser-matter interaction and particle beams as well as a variety of targets and target support. A dedicated pulsed magnet infrastructure enables the investigation of magnetised plasmas as well as ion beam transport for the dose-controlled external irradiation of samples like radiobiological probes. For the latter, an integrated biology lab supports handling and evaluation of, for example, cell samples. The development of next-generation high-power lasers is performed with the diode-pumped Yb:CaF2 petawatt laser project Penelope. Pulses of 150 J in 150 fs will be available first for ion acceleration applications within the joint Helmholtz ATHENA project at final repetition rates of up to 1 Hz. One aspect of ATHENA is the implementation of a series of different front-end technologies for advanced temporal pulse cleaning.
<figure><img src="image_257.png" /></figure>

**Fig. 29.5.** Footprint of the ELBE Centre for High Power Radiation Sources, showing from the left the cw superconducting 40 MeV electron accelerator with the SRF photo-gun and downstream experimental areas for secondary radiation (total scale about 100 m). Experimental areas for the Draco petawatt laser system are coloured in green (including areas labelled as “Draco”, “Draco PW”, “Electron lab”, “Ion lab”), providing bunkers for multi-source experiments. The Penelope laser area and lab space hosting ATHENA\_h are coloured in orange (including areas labelled as “Athena-h”, “Penelope”) (image courtesy of Helmholtz-Zentrum Dresden-Rossendorf).

<figure><img src="image_258.png" /></figure>

**Fig. 29.6.** The L1 “Allegra” laser developed in-house by the ELI Beamlines laser team (100 mJ, 1 kHz) (image courtesy of ELI Beamlines).

## 29.5 ELI – Extreme Light Infrastructure

### ELI Beamlines

The main goal at ELI Beamlines [718] is to develop the most advanced laser equipment in the world for basic research as well as for areas such as medical imaging and diagnostics, radiotherapy, new materials, and X-ray optics. The development of a compact laser-driven free-electron laser is one of the main topics of the ELI Beamlines team. All these research activities at ELI Beamlines are based on the laser systems, which are under operation or preparation.

The L1 “Allegra” laser has been developed in-house by the ELI Beamlines laser team (see Fig. 29.6). The concept of the laser is based on the amplification of frequency-chirped picosecond pulses in an optical parametric chirped-pulse amplification (OPCPA) chain consisting of a total of seven amplifiers. The laser system is designed to generate <20 fs pulses with energy exceeding 100 mJ per pulse at a high repetition rate of 1 kHz. The central wavelength of the “Allegra” laser is 830 nm<λ<860 nm with the linear horizontal polarisation of the output beam. The output laser pulse energy stability (RMS) is better than 5%. The output laser beam
<figure><img src="image_259.png" /><figcaption>**Fig. 29.7.** The L2 “Amos” laser system is under development now at ELI-Beamlines (20 J, 10 Hz) (image courtesy of ELI Beamlines).</figcaption></figure>

<figure><img src="image_260.png" /><figcaption>**Fig. 29.8.** The L3 “HAPLS” laser system at ELI-Beamlines (30 J, 10 Hz) (image courtesy of ELI Beamlines).</figcaption></figure>

<figure><img src="image_261.png" /><figcaption>**Fig. 29.9.** The L4 “Aton” laser system is under development now at ELI-Beamlines (2 kJ, 1 shot/min) (image courtesy of ELI Beamlines).</figcaption></figure>

pointing stability (RMS) is less than 10 µrad. The L3 “HAPLS” laser system of ELI Beamlines (see Fig. 29.8) is designed to deliver petawatt pulses with energy of at least 30 J and a pulse duration of 30 fs at a repetition rate of 10 Hz. This system was developed at the Lawrence Livermore National Laboratory (LLNL, USA) with ELI Beamlines cooperating on the development of the petawatt pulse compressor, the short-pulse diagnostics, and the short-pulse controls and timing. The current parameters, achieved now (August 2019) are a peak power of 0.4 PW, a pulse energy of 11.5 J for a pulse length of 28 fs at a repetition rate of 3.3 Hz.

The L2 “Amos” (see Fig. 29.7) and L4 “Aton” (see Fig. 29.9) laser systems are under development now at ELI Beamlines. The L2 “Amos” laser system is designed to generate ultra-short laser pulses with peak power up to 0.5 PW. The laser will be able to operate at a high repetition rate of 10 Hz due to the full utilisation of new technologies, such as laser diode pumping and cryogenic cooling of the laser material. In the nearest future, this laser system will be upgraded to provide an output pulse energy of 10 J with a repetition rate up to 25 Hz and with a pulse compression down
<table><caption>**Table 29.2.** Typical beam parameters at the FLASHForward facility.</caption><thead><tr><th></th><th>Units</th><th></th></tr></thead><tbody><tr><td>Bunch Charge</td><td>pC</td><td>50–800</td></tr><tr><td>Energy</td><td>MeV</td><td>400–1250</td></tr><tr><td>Bunch Length</td><td>fs RMS</td><td>50–6000</td></tr><tr><td>Chirp</td><td>% RMS</td><td>±0.5</td></tr><tr><td>Transverse Emittance</td><td>mm mrad<br>RMS proj</td><td>1–3</td></tr><tr><td>Focal Spot size</td><td>μm × μm</td><td>5×5 (spec.),<br>30×30 (meas.)</td></tr><tr><td>Energy resolution</td><td>%</td><td>0.02</td></tr><tr><td>Macro repetition rate</td><td>Hz</td><td>1–10</td></tr><tr><td>Micro repetition rate</td><td>MHz</td><td>0.040–3</td></tr></tbody></table>

to 30 fs. The L4 “Aton” laser system is designed to generate an extremely high and unprecedented peak power of 10 PW during pulse durations of about 130 fs with a repetition rate of 1 shot per minute. The expected stability of the output laser pulse energy (RMS) is better than 10% with the output laser beam pointing stability (RMS) less than 10 μrad. The delivery of the L4 “Aton” laser system was contracted with the United States-Lithuanian consortium of National Energetics and EKSPLA in September 2014. The main subcontractors of this laser system are Schott and the Lawrence Livermore National Laboratory. ELI Beamlines is in charge of the full diagnostics of the compressed 10 PW beam, the laser timing platform, as well as the design and delivery of opto-mechanics for the 10 PW compressor.

In parallel with the development of the different laser systems of ELI Beamlines, the preparation of the experimental halls for different research activities is on the way. The user operation of the L1 “Allegra” laser for material and bio-molecular applications started at ELI Beamlines in summer 2019. The usage of the L3 “HAPLS” laser for plasma physics and for ion acceleration should start in the second half of 2019. The electron acceleration and development of the undulator X-ray source will start from the middle of 2020.

## ELI-ALPS

The research infrastructure at ELI-ALPS [719] is based on four main laser sources: three operating in the 100 W average power regime in the near-infrared (NIR) and one 10 W mid-IR (MIR) source. These systems are designed to deliver pulses with unique combinations of pulse duration, repetition rate, and pulse energy. The hallmarks of this next-generation laser architecture are the use of sub-ps fibre oscillators: pulse amplification in fibres and white-light-generated seeding pulses which exhibit passive carrier-envelope phase (CEP) stability. Each laser will run synchronised to the central facility clock and is guaranteed to run continuously for at least 8 hours per day. All lasers have been optimised for different regions in the parameter space.

## 29.6 FLASHForward (Germany)

FLASHForward (Future-Oriented Wakefield Accelerator Research and Development at FLASH) [720] is a beam-driven plasma wakefield experiment at DESY that aims to
produce, in a few centimetres of ionised hydrogen, electron beams of energies exceeding 1.5 GeV, which are of sufficient quality to demonstrate gain in a free-electron laser. Situated at the free-electron laser FLASH, the experimental beamline allows for milestone studies assessing several types of plasma internal particle injection regimes, external injection, and controlled beam capturing and release for subsequent applications. The facility provides a combination of low-emittance GeV-class electrons from a superconducting MHz repetition rate accelerator synchronised to a 25 TW laser interacting in a windowless, optically accessible, versatile plasma target. Experiments commenced in 2018, aiming to open up new avenues in the highly dynamic research field of plasma wakefield acceleration.

Through parallel operation with FLASH FEL users and dedicated accelerator R&D beam time, FLASHForward plans to operate for >1000 hours per year, opening up new avenues in the highly dynamic research field of beam-driven plasma wakefield acceleration (PWFA).

To this end, FLASHForward research is composed of an ever-expanding scientific programme, comprised of a number of core experiments starting with both internal and external injection studies, and culminating in the exploration of FEL gain from a PWFA. In addition to these experiments, a number of novel diagnostics and prototypes are in development to diagnose these novel beams, both at FLASHForward and beyond. Table 29.2 summarises some meaningful beam parameters.

## 29.7 HI Jena (Germany)

The Helmholtz Institute Jena and the Institute of Optics & Quantum Electronics at Friedrich-Schiller-University Jena are conducting research on the development of high-power laser systems as well as laser-plasma interactions. Their foci in laser development lie, on the one hand, in petawatt laser systems and their improvement of beam quality, repetition rate, and energy efficiency. On the other hand, the labs investigate the development of novel fibre laser systems with MHz-scale repetition rates and high average power, among others, as FEL seeding sources. In laser-plasma interactions, Jena has a strong track-record in particle acceleration using laser-plasma interactions, both using electrons and protons / ions. A topic of particular focus is the development and application of novel plasma diagnostics, such as shadowgraphy to better understand the dynamics inside plasma accelerators [721].

HI Jena hosts three different high-power laser systems (see Tab. 29.3) that are used on a day-to-day basis for laser particle acceleration experiments as well as the generation of high-order surface harmonics and secondary XUV and X-ray radiation.

The POLARIS (Petawatt Optical Laser Amplifier for Radiation Intensive Experiments) laser [723] is the world's only fully diode-pumped laser system to generate pulses of peak power up to 200 TW. It currently boasts a temporal intensity contrast on the order of $1 \times 10^{-13}$ for amplified spontaneous emission, which is, however, subject to future improvement together with a planned energy upgrade.

The JETI40 and JETI200 lasers, on the other hand, are both Ti:Sapphire-based systems. Each beamline has two experimental chambers available and includes a few-cycle probe beam that can be used, for example, for pump-probe experiments or as a diagnostic tool. Based on a double chirped-pulse-amplification system in combination with a plasma mirror, JETI200 also features improved temporal contrast on the order of $1 \times 10^{-13}$ for amplified spontaneous emission and $1 \times 10^{-10}$ for pre-pulses.
<figure><img src="image_262.png" /><figcaption>**Fig. 29.10.** Control room of the POLARIS laser at the Helmholtz Institute Jena (image credits: FSU Jena and HI-Jena [722]).</figcaption></figure>

<table><caption>**Table 29.3.** Overview parameters of the three high-power laser systems at Helmholtz Institute Jena. Both the POLARIS and JETI200 systems produce pulses with around 200 TW peak power, while JETI40 can reach around 40 TW peak powers.</caption><thead><tr><th></th><th>POLARIS [722]</th><th>JETI40 [724]</th><th>JETI200 [725]</th></tr></thead><tbody><tr><td>Wavelength</td><td>1030 nm</td><td>800 nm</td><td>800 nm</td></tr><tr><td>Bandwidth (FWHM)</td><td>19 nm</td><td>40 nm</td><td></td></tr><tr><td>Pulse duration</td><td>≤100 fs</td><td>≥25 fs</td><td>17 fs</td></tr><tr><td>Energy on target</td><td>≥17 J</td><td>1.0 J</td><td>4 J</td></tr><tr><td>Max. intensity</td><td>1 × 10<sup>21</sup> W cm<sup>-2</sup></td><td>1 × 10<sup>20</sup> W cm<sup>-2</sup></td><td>≥1 × 10<sup>21</sup> W cm<sup>-2</sup></td></tr><tr><td>Repetition rate</td><td>1/50 Hz</td><td>10 Hz</td><td>5 Hz</td></tr></tbody></table>

## 29.8 ILIL (Italy)

The research activities of the Intense Laser Irradiation Laboratory (ILIL) [726] are focused on fundamental studies of high-intensity laser interactions with matter and their applications. The laboratory not only participates in the European infrastructure projects EuPRAXIA and ELI, but it is also part of the European consortium engaged in laser-driven fusion research.

Since 2015, the lab is engaged in the upgrade of the laser and target area facility, in the framework of the Italian Network of the Extreme Light Infrastructure (ELI-Italy), to enable laser-matter interaction studies at extreme laser intensities. Fundamental studies include plasma formation and heating by laser beams, laser-induced instabilities and other non-linear processes, atomic physics of highly-ionised plasmas, ultra-short X-ray emission and the acceleration of charged particles. The laboratory has well-established collaborations with many leading international high-power laser laboratories and facilities, as well as academic groups. The Intense Laser Irradiation Laboratory has long-term experience in the training of young scientists through several schemes including European Union RT Networks.

The ILIL-PW interaction area is equipped with a 140 cm diameter octagonal vacuum chamber connected to the compressor chamber by a two-mirror chicane. Energies on target up to 4 J in <30 fs pulse duration are focused with an f/10
<figure><img src="image_263.png" /><figcaption>Fig. 29.11. ILIL experimental area (image courtesy of CNR-INO).</figcaption></figure>

off-axis parabolic mirror, with a spot radius down to 10 µm and an intensity exceeding 3×10¹⁹ W/cm². Alternatively, the beam can be focused with an f/3 off-axis parabolic mirror, delivering a spot radius of 3 µm and an intensity exceeding 2 × 10²⁰ W/cm².

The ILIL-TW interaction area is equipped with two 80 cm diameter interaction vacuum chambers. One of the interaction chambers is configured with an f/10 off-axis parabolic mirror, with an energy on target of 400 mJ in a 35 fs pulse duration and a focal spot radius of 10 µm, for an intensity of 3 × 10¹⁸ W/cm². The set-up is optimised for repetitive operation (1 Hz) of LWFA with multi-tens of MeV electron energy for applications, gamma-ray generation and detector tests and development. The other chamber is configured with an f/3 off-axis parabolic mirror, with an energy on target of 400 mJ in a 35 fs pulse duration and a focal spot radius of 3 µm, for an intensity of 2 × 10¹⁹ W/cm².

## 29.9 Imperial College London (United Kingdom)

The John Adams Institute at Imperial College hosts a laboratory that is dedicated only to the development of targetry and diagnostics for plasma acceleration experiments. The laboratory hosts an in-house-developed laser system for testing these devices at the repetition rates required for next-generation wakefield facilities, such as EuPRAXIA. The laser is a CPA system based on Titanium:Sapphire as a gain medium and currently delivers:

- a 10 mJ, 30 fs arm that will produce a low-energy (<10 MeV) source of electrons,

- a 50 mJ, 30 fs arm that will produce up to 50 MeV electrons on a table top,

- a 500 mJ, 30 fs arm that can produce up to 200 MeV electron beams in a separate wakefield interaction chamber.

The system currently operates at 10 Hz, which is just below the minimum operation level of the EuPRAXIA facilities and upgrades will allow the first two stages to be operated at 100 Hz. This will thus allow the development of targets and diagnostics that can operate within the full scale of operating rates expected for EuPRAXIA.
<figure><img src="image_264.png" /><figcaption>**Fig. 29.12.** The Zhi lab set up at the John Adams Institute at Imperial College (image courtesy of Imperial College).</figcaption></figure>

<figure><img src="image_265.png" /><figcaption>**Fig. 29.13.** Left: Layout of FLUTE facility. Right: Layout of support rooms as part of the FLUTE facility in front of the bunker: laser room, beamline room for experiments with low energy, soft photons in fs pulses, and control room. The area is to approximate scale with the cleanroom of 30 m² housing the fs laser system for photo-injection of the FLUTE accelerator (image courtesy of KIT).</figcaption></figure>
<figure><img src="image_266.png" /><figcaption>**Fig. 29.14.** Layout of FLUTE accelerator to be placed on 21 m diagonal of the bunker ground level (image courtesy of KIT).</figcaption></figure>

<figure><img src="image_267.png" /><figcaption>**Fig. 29.15.** Left: ATLAS-3000 main amplifier and compressor (60 J, 25 fs, 1Hz). Right: PFS-pro (200 mJ/800fs/5kHz) and PFS (8J, 800 fs, 10 Hz) lasers (image courtesy of Ludwig-Maximilians-Universität München).</figcaption></figure>

## 29.10 KIT (Germany)

The FLUTE facility at KIT [727] is comprised of a two-level bunker, which is fully radiation protected at the ground and at the lower level with near square dimensions, and several support rooms in front of the bunker. The ground level houses the FLUTE accelerator on a 21 m diagonal in a 210 m² area bunker with a free height of 5 m. The VLA compact Storage Ring design fits perfectly within the ground level bunker. The lower level of the bunker, with the same overall area of 210 m², is sectioned and a 140 m² area with a height of 2.5 m is exclusively reserved for the dedicated laser system of the Plasma Injector, while the remaining area with a height of 2.2 m can be used e.g. for support electronics and other installations. FLUTE develops in several phases to benefit from novel technologies including those from Helmholtz partners. In the final phase besides an additional life sciences laboratory, the PICCO-LO mode operation will enhance the capabilities of FLUTE to provide pulse lengths towards 1 fs by implementing a tenfold improved high performance optical synchronization system. Thus, covering the spectral band up to 300 THz and beyond with pulse energies well into the GW range.
## 29.11 LMU-CALA (Germany)

The CALA laboratory at the Ludwig-Maximilians-Universität München (LMU) is dedicated to fundamental and applied research into particle and photon sources for medical applications [728]. The building will host two laser systems:

- ATLAS-3000 is a 2.5 PW Ti:Sa laser currently under commissioning. Its target parameters are 60 J, 25 fs at 1Hz repetition rate delivered to four target bunkers (LION, LUX, HF, ETTF). LION and HF are dedicated to solid-target interactions such as ion acceleration, using short-focal-length geometry to achieve intensities beyond the $1 \times 10^{22}$ W/cm$^2$-range. ETTF is a general-purpose electron acceleration and betatron/Compton scattering beamline with a 14 m long vacuum chamber for long-focal-length and colliding-pulse interactions, while LUX is a dedicated undulator radiation beamline. ATLAS-3000 will have a synchronised 200 TW output that will be coupled into the experiment bunkers on demand.

- PFS/PFS-pro is a Yb-YAG-based laser system under development. In one output, it will provide 200 mJ, 1 ps pulses at a 5 kHz repetition rate, the other one will deliver 8 J, 800 fs pulses at 10 Hz. Ways of converting both outputs to a few-cycle pulse duration are currently being investigated, either by direct compression of by pumping of an OPCPA arm. The short pulses and an unconverted part of the ps-pulses will drive a fifth experimental area called SPECTRE, dedicated to the development of an all-optical Thomson source for imaging purposes.

## 29.12 LPA-UHI100 (France)

The LIDYL laboratory operates the Saclay Laser-Matter Interaction Center (SLIC) infrastructure, including the UHI100 laser facility and experimental area opened for access to ARIES and LASERLAB-Europe users. UHI100 is a Ti/Sa laser system and delivers a laser power of 100 TW at 10 Hz with a 25 fs pulse duration. Intensities on target in the $1 \times 10^{18}-1 \times 10^{19}$ W/cm$^{-2}$ range have been obtained using a deformable mirror. UHI100 also features a very high temporal contrast obtained thanks to a double plasma mirror inserted between the compressor and the experimental chamber. The short pulse duration, ultra-high contrast, and intensity together with the radiation-protected experimental area – fully equipped for ultra-high intensity experiments under vacuum – make this facility unique. The whole facility (laser and experimental area) will be moved to a new location at Orme des Merisiers (CEA) in a completely renovated area, at the beginning of 2020. In this new configuration, there will be the possibility to send the laser at full power into one experimental chamber or to split the energy into two beams with a chosen ratio making it possible to work with two laser beams in one experimental chamber. The two laser beams will benefit from the same performance-improving equipment, such as a double plasma mirror to increase the temporal contrast, if required, and a deformable mirror to optimise the spatial profile of the laser at the interaction point. A probe beam with few mJ energy will also be available.

Services currently offered by the infrastructure include: the UHI100 laser and experimental area fully equipped with diagnostics for the laser (duration, energy, and position after compression); two double plasma mirror chambers, two deformable mirrors, and associated wave front sensors; two experimental chambers of which one will be more dedicated to solid-target interaction and the other dedicated to laser-plasma acceleration. A set of parabolas with variable focal length is also available to explore different interaction regimes. Diagnostics and tools are present to study electron generation (e.g. electron spectrometers and a magnetic transport line for
70 MeV electron beams). The radioprotection has been specifically dimensioned for electron acceleration and the survey is insured by radioprotection services from CEA.

The facility is operated by a team of two technicians, one engineer and one local co-investigator in charge of the access to the experimental room. Users receive complete technical and scientific assistance, from the conceptual design of the experiment to its realisation. A workshop will be accessible during campaigns as well as administrative assistance, if needed.

## 29.13 Lund Laser Centre (Sweden)

The Lund Laser Centre (LLC) is the largest unit in the Nordic countries within the field of lasers, optics, and spectroscopy [729].

Research is performed in basic atomic, molecular and chemical physics as well as in applications to the fields of energy, environmental, medical and information technology. The LLC is characterised by its interdisciplinary nature, fostering a strong exchange of ideas, techniques, and resources. The Centre has extraordinary resources in terms of scientific expertise, advanced laser systems (more than 30 major systems, including a 10 Hz, 40 TW laser), detection, and auxiliary equipment. Experimental techniques range from high-resolution (CW) to ultra-fast (attosecond) spectroscopy with an accessible spectral region from THz radiation to X-rays.

LLC provides access to laboratories which cover a broad range of research activities. High-intensity laser-matter interactions and attosecond science are investigated using three different systems:

- a 40 TW, 10 Hz, 40 fs Ti:Sapphire system with active beam-pointing stabilisation,

- a CEP-stable 1 kHz, 20 fs, 5 mJ tunable Ti:Sapphire system equipped with pulse compression,

- and an OPA to reach mid-IR wavelength with a CEP-stable 200 kHz, 7 fs 10 µJ OPCPA.

The laboratories include pump/probe setups, X-ray and electron spectrometers for advanced time-resolved and particle acceleration studies. Time-resolved atomic and molecular laser spectroscopy experiments can be carried out thanks to a unique laser spectroscopic set-up. Quantum optics/information topics are studied using coherent transient techniques and spectroscopy of low-temperature rare-earth-ion doped crystals. Femtochemistry laser experiments are used for studies of, e.g. natural and artificial photosynthesis, natural pigments, novel types of solar cells and their constituent materials, reaction dynamics and coherent control. Time-resolved diffraction studies are carried out for solids, and advanced single molecule spectroscopy of polymers and biomolecules. Biomedical applications with fluorescence diagnostics, tissue optics and photodynamic tumour therapy can also be accommodated within LLC as well as time-resolved scattering media spectroscopy and gas-in-scattering-media studies. Environmental monitoring can be carried out using a mobile laser radar system, which can be used for atmospheric mapping, marine and vegetation monitoring. Combustion diagnostics of reactive flows using fluorescence and scattering techniques are possible using high-repetition rate and short pulse laser systems.

## 29.14 LUX (Germany)

LUX [66] is a laser-plasma accelerator developed and operated in a collaboration of Hamburg University and DESY. Driven by the 200 TW peak power ANGUS laser system, it provides a continuous-flow plasma-cell target to generate few-100 MeV electron beams at 1 Hz repetition rate. The generated plasma electron beam is captured,
transported, and diagnosed using modern accelerator technology. A miniature undulator provides spontaneous (synchrotron-type) emission down to a few nanometres. The whole facility is fully integrated into a controls system, which provides unique capabilities to correlate drive laser and electron beam parameters.

## 29.15 Queen's University of Belfast (United Kingdom)

The Centre for Plasma Physics at Queen's University Belfast hosts the high-power laser TARANIS, together with the fs-scale system TARANIS-X [730]. The TARANIS laser provides two twin beams originating from the same oscillator and sharing most of the amplification chain. The oscillator delivers a train of 44 fs-long pulses, each with an energy of approximately 5 nJ, at 76 MHz (average power of 400 mW), and a broadband spectrum from 1020 to 1120 nm. The beam is stretched to 1.2 ns and first amplified by a regenerative amplifier up to 0.6 mJ at a repetition rate of 500 Hz (average power of 300 mW). Two Nd:phosphate rod amplifiers take the energy of the beam up to the Joule level, before it is split into two beamlets, each going onto their own third phosphate-glass rod amplifier that takes the energy up to 25 J per beam. A dazzler is used to correct high-order phase distortions, allowing to reach pulse durations as short as 600 fs. An energy efficiency of the compressors of the order of 60 % brings the energy of each beam after compression to approximately 15 J (25 TW peak power). Due to the glass-based technology of the laser, the repetition rate of the system is relatively low, of the order of one full-power shot every 12 minutes.

The TARANIS-X system instead relies on a different architecture, heavily based on an OPCPA system pumped by one of the arms of TARANIS. In a nutshell, TARANIS-X provides two main outputs: one at low-power and high-repetition rate, and one at high-power and low-repetition rate. The first mode of operation provides a train of mJ-scale pulses at 1 kHz, with each pulse having a sub-10 fs duration (2-3 optical cycles). The second mode provides a beam with maximum energy of the order of 1 J and approximately 10 fs duration. Since the final amplification stage of this mode is pumped by one arm of TARANIS, the repetition rate in this case is relatively low, of the order of one full-power shot every 5 minutes.

All these beams can then be directed into two separate target areas, featuring large vacuum vessels (inner diameter of the chambers of the order of 1.5 m) and a whole suite of diagnostics for on-shot monitoring of the main characteristics of the beams. F/3 off-axis parabolas are available together with an adaptive optics system that allows for focusing as tight as 5 µm FWHM. Extension pipes can be attached to the chambers, enabling long-focal length focusing.

Different diagnostics can be implemented for laser-plasma experiments including particle spectroscopy (either based on magnetic dipoles or Thomson parabolas) using different detectors, such as: LANEX scintillation screens, imaging plates, radiochromic films, and CR-39.

The system allows for different beams to be directed, already synchronised, in the target areas. This provides a high-degree of flexibility in the beam configurations available for experiments (i.e., two sub-ps beams, two ns beams, one sub-ps beam and one ns beam, one fs and one ns beam, or one fs and one sub-ps beam). A highly synchronised (<0.1 ps jitter) probe beam capability with variable pulse duration from 400 fs to 1.2 ns, 100 mJ energy, and 2.5 cm beam size is also available.

In the following, a summary of the main parameters for the different modes of operation is given:
<table><caption>**Table 29.4.** Beam parameters of the TARANIS laser system at the Queen's University of Belfast.</caption><thead><tr><th></th><th>TARANIS<br>(compressed)</th><th>TARANIS<br>(stretched)</th><th>TARANIS-X<br>(low-energy mode)</th><th>TARANIS-X<br>(high-energy mode)</th></tr></thead><tbody><tr><td>Wavelength</td><td>1053 nm</td><td>1053 nm</td><td>820 nm</td><td>820 nm</td></tr><tr><td>Pulse duration</td><td>600 fs</td><td>1.2 ns</td><td>10 fs</td><td>10 fs</td></tr><tr><td>Energy on target</td><td>15 J</td><td>25 J</td><td>0.3 mJ</td><td>1 J</td></tr><tr><td>Max. intensity</td><td>2 × 10<sup>19</sup> W cm<sup>-2</sup></td><td>2 × 10<sup>16</sup> W cm<sup>-2</sup></td><td>3 × 10<sup>16</sup> W cm<sup>-2</sup></td><td>1 × 10<sup>20</sup> W cm<sup>-2</sup></td></tr><tr><td>Repetition rate</td><td>1 shot / 12 min.</td><td>1 shot / 12 min.</td><td>1 kHz</td><td>1 shot / 5 min.</td></tr></tbody></table>

## 29.16 Rutherford Appleton Laboratory (United Kingdom)

### Facility Description

The Central Laser Facility (CLF) at STFC-RAL [731] hosts the 350 TW Gemini Ti:Sapphire laser that is used extensively for laser wakefield acceleration experiments by visiting user groups. Gemini has two beams with energy of 15 J in a 40 fs pulse with a maximum repetition rate of 1 shot per 20 seconds. These beams are fed into a dedicated target area (TA3) containing a large vacuum chamber which can be configured to suit individual experimental needs. For gas target experiments, the standard laser focusing uses a long focal length off-axis parabola (f/20) for a spot radius ($1/e^2$) of 16.7 µm with intensity ~ $2.8 \times 10^{19}$ Wcm$^{-2}$ (normalised vector potential $a_0=3.6$). A beam layout is also available using an f/40 off-axis parabola reducing the intensity to ~ $6 \times 10^{18}$ Wcm$^{-2}$. The second Gemini target area (TA2) receives the laser beam that is split off before the final amplifier with an energy of 1 J and compressed to 40 fs. This is focused with an f/17 off-axis parabola to a 20 µm spot with intensity $3 \times 10^{18}$ Wcm$^{-2}$ (normalised vector potential $a_0=1.1$). The maximum repetition rate in TA2 is 5 Hz provided that experiments do not exceed radiological safety limits.

Both target areas are equipped with adaptive optics and have independent control of the spectral phase of the pulse allowing user-defined control over the spatial and temporal properties of the laser pulse. CLF experiments are supported throughout the planning stages and implementation by a team of laser staff, plasma physicists, engineering design and support staff. Specialist target requirements are provided by a dedicated Target Fabrication department.

### Mode of Access

A call for proposals, open to any researcher (subject to eligibility), is issued twice per year for access to Gemini. Proposals are assessed by an independent panel who advise the facility based on certain defined criteria. Experiments in TA3 are allocated a number of weeks (typically 4–6) of access fully supported by a team of specialist scientific and engineering staff. TA2 is operated with longer access slots (8–12 weeks) with a lower level of facility support.

## 29.17 SCAPA (United Kingdom)

### Facility Description

The Scottish Centre for the Application of Plasma-based Accelerators (SCAPA) [732] at the University of Strathclyde houses two high-power Ti:Sapphire laser systems for
laser wakefield acceleration experiments. Visiting user groups can conduct experi-
ments in collaboration with the Strathclyde group. The laser systems are:

(a) 40 TW at a 10 Hz pulse repetition rate (1.4 J per pulse, 35 fs pulse duration). This laser drives two laser wakefield accelerator beamlines in Bunker C (including the ALPHA-X beamline). For ALPHA-X, the laser is focused by an f/16 spherical mirror to a spot radius (1/e2) of 20 µm with an intensity of ~4 × 10¹⁸ Wcm⁻² (normalised vector potential a0 = 1.4).

(b) 350 TW at a 5 Hz pulse repetition rate (8.75 J per pulse, 25 fs pulse duration). This laser drives two laser wakefield accelerator beamlines in Bunker A and, in each case, the laser is focussed by an f/17 off-axis parabola to a spot radius (1/e²) of 22 µm with an intensity of ~ 3.5 × 10¹⁹ Wcm⁻² (normalised vector potential a0 = 4.0). One beamline is able to support longer focal lengths (up to f/34) for larger focal spot size.

Both lasers feature adaptive optics and online full power attenuation of the pulse energy in the 10–100% range. Synchronised probe laser pulses (up to 30 mJ uncompressed) are also available for both systems. Experiments are supported by SCAPA core staff (management, laser and technical) and by the collaborating Strathclyde research team. SCAPA houses a number of auxiliary labs that are at the disposal of users for experimental preparation and post-analysis studies.

Mode of Access

Proposals for laser beam time are submitted to SCAPA management and assessed by an access management panel. For each laser system, there are six nominal experimental slots per year (each for a nominal duration of 6 weeks). SCAPA supports a flexible approach to scheduling in order to respond rapidly to users' needs. SCAPA operations are sustained with access fee income that must come from the user group and / or collaborating Strathclyde team (those parties determine the relative contributions). Travel and subsistence costs are not covered by SCAPA but may be so by the collaborating Strathclyde team. As a first step regarding access, users are encouraged to contact SCAPA management and the relevant collaborating Strathclyde teams.

29.18 SINBAD (Germany)

The Helmholtz Association has set up an accelerator R&D program across six accel-
erator laboratories in Germany, providing sustained funding for project-independent
accelerator research. According to this mission, DESY is currently in the process
of setting up the central, long-term dedicated accelerator research facility SIN-
BAD (Short INnovative Bunches and Accelerators) [733] in the very centre of the
DESY-Hamburg campus (see Fig. 29.16). The main beam parameters are reported
in Table 29.5. This area will provide the necessary space for multiple independent
experiments accessing a common infrastructure. SINBAD will provide a future-proof
home to the accelerator R&D efforts at DESY while providing sufficient room for
developing the setup into one of the two flagship projects of ATHENA, the Helmholtz
collaboration for laser-plasma acceleration for large infrastructure investments. For
this purpose, for example, the high-repetition-rate, high-average-power KALDERA
laser will be installed in the central hall until the end of 2020.

SINBAD will initially host two main, independent experiments: ARES & AXSIS.
At the core of the ARES (Accelerator Research Experiment at SINBAD) experi-
mental area, a conventional S-band electron linac will accelerate ultra-short electron
<figure><img src="image_268.png" /><figcaption>**Fig. 29.16.** 3D visualisation of the SINBAD facility. The ARES and AXSIS experiments as well as the KALDERA laser system will be hosted in this site (image courtesy of DESY).</figcaption></figure>

<table><caption>**Table 29.5.** Design parameters of the SINBAD facility.</caption><thead><tr><th></th><th>Units</th><th></th></tr></thead><tbody><tr><td>Bunch Charge</td><td>pC</td><td>0.5–20</td></tr><tr><td>Energy</td><td>MeV</td><td>100</td></tr><tr><td>Bunch Length</td><td></td><td>sub-fs to few fs</td></tr><tr><td>Rep. rate</td><td>Hz</td><td>10–50</td></tr><tr><td>Electron Time arrival Jitter</td><td>fs (RMS)</td><td>&lt;10</td></tr></tbody></table>

bunches to 100 MeV with an RMS arrival time jitter of less than 10 fs. While the design is optimised for low-charge (pC), ultra-short (sub/single fs) beams, bunch charges with several tens of pC can also be accelerated at the cost of longer bunch duration. Once this goal is achieved, the accelerated electron bunches will be injected into advanced acceleration structures like dielectric structures or plasma cells. The commissioning of the ARES-linac has started and first beams at the linac exit are expected at the end of 2019.

As a second initial experiment, SINBAD will also host the AXSIS experiment which is a collaborative effort of DESY, CFEL, and Arizona State University funded by an ERC synergy grant. It aims to set up an ultra-compact light source based on electron acceleration by a THz-laser in a dielectric loaded waveguide and subsequent inverse Compton scattering.

Finally, SINBAD will host a 400 m² laser laboratory which will be used for the KALDERA laser project. KALDERA is developing kHz laser technology with 3 J single pulse energy for plasma wakefield accelerators, thus enabling high average power.

## 29.19 SPARC_LAB (Italy)

SPARC_LAB (Sources for Plasma Accelerators and Radiation Compton with Lasers and Beams) [734] is an interdisciplinary laboratory and its layout is shown in
<figure><img src="image_269.png" /><figcaption>Fig. 29.17. Layout of the SPARC_LAB facility (image courtesy of SPARC_LAB).</figcaption></figure>

<table><caption>**Table 29.6.** Typical parameters of the SPARC linear accelerator.</caption><thead><tr><th></th><th>Units</th><th></th></tr></thead><tbody><tr><td>Bunch charge</td><td>pC</td><td>10–1000</td></tr><tr><td>Energy</td><td>MeV</td><td>30–180</td></tr><tr><td>Bunch length</td><td>fs RMS</td><td>10–10000</td></tr><tr><td>Energy spread</td><td>% RMS</td><td>±0.1</td></tr><tr><td>Repetition rate</td><td>Hz</td><td>1–10</td></tr></tbody></table>

Figure 29.17. It was born from the integration of a high-brightness photo-injector (SPARC) able to produce high-quality electron beams up to 170 MeV energy with high peak current (>1 kA) and low emittance (<2 mm mrad), and of a high-power laser (>200 TW) (FLAME) able to deliver ultra-short laser pulses (<30 fs).

The SPARC photo-injector is characterised by a copper photo-cathode, illuminated by a UV laser (266 nm) and embedded in a 1.6-cell standing wave RF gun (BNL/UCLA/SLAC type), operating at 2.856 GHz (S-band, normal conducting technology). The high peak field on the photo-cathode (≥120 MV/m) allows beam acceleration up to ≥5.6 MeV. The beam is then properly focussed and matched into three constant gradient $2\pi/3$ travelling wave (TW) structures of the SLAC type, which boost the beam energy up to 180 MeV. The first accelerating section is also used as an RF compressor (in the velocity bunching regime) by varying the beam arrival time. Solenoid coils embedding the first two sections can be powered to provide additional magnetic focussing to better control the beam envelope and the emittance oscillations under RF compression. Typical beam parameters of the SPARC linear accelerator are reported in Table 29.6.

In autumn 2015 the last 3 m long low-gradient (≈15 MV/m) S-band TW accelerating section has been replaced by a 1.4 m long structure operating in the C-band at 5.712 GHz, with an average accelerating field of ≈35 MV/m, and a plasma chamber
<figure><img src="image_270.png" /><figcaption>Fig. 29.18. SPARC PWFA test station (image courtesy of SPARC_LAB).</figcaption></figure>

<table><caption>Table 29.7. Typical parameters of the FLAME laser at SPARC_LAB.</caption><thead><tr><th></th><th>Units</th><th></th></tr></thead><tbody><tr><td>Energy</td><td>J</td><td>7 (after compression)</td></tr><tr><td>Energy stability</td><td>% RMS</td><td>±0.1</td></tr><tr><td>Wavelength</td><td>nm</td><td>800</td></tr><tr><td>Repetition rate</td><td>Hz</td><td>10</td></tr><tr><td>Pulse duration</td><td>fs RMS</td><td>25</td></tr><tr><td>Synchronisation with linac</td><td>fs RMS</td><td>50</td></tr><tr><td>Beam quality</td><td>M2</td><td>&lt;1.5</td></tr></tbody></table>

for PWFA experiments, hosting diagnostics, permanent magnet quadrupoles, and the capillary, i.e. the plasma accelerating structure (see Fig. 29.18).

The integration of the SPARC high-brightness photo-injector and the high-intensity FLAME laser has driven the development and characterisation of a γ-ray source from Thomson backscattering. Electron and photon beams have been synchronised at the scale of <50 fs, an essential requirement for the recent successful operation of the X-ray (≈50 keV) Thomson backscattering source and for the future investigation of new ultra-compact acceleration techniques (>1 GV/m) based on the external injection of high-quality electron beams in a plasma cell.

The operation of the FLAME laser alone has led to successful electron acceleration up to 400 MeV in 2–4 mm long plasma cells with less than 20 % energy spread. Innovative electron beam transverse diagnostics based on betatron radiation have been conceived and tested, and experiments on ion acceleration by target normal sheath acceleration (TNSA) have been carried out. Typical beam parameters are reported in Table 29.7.

## 29.20 University of Oxford (United Kingdom)

The University of Oxford currently houses a TW laser laboratory used as a test bed for laser wakefield experiments, diagnostic and target development, and high-harmonic generation. A new laboratory is currently under construction which will
<figure><img src="image_271.png" /><figcaption>**Fig. 29.19.** The new laser laboratory at the University of Oxford under construction (image courtesy of the University of Oxford).</figcaption></figure>

host an upgraded Ti:Sa laser system and will allow the generation of 10 Hz, 200 MeV electron beams. This facility will also house a separate long-pulse laser which will be used in lab astrophysics experiments.

The laser consists of a Ti:Sa oscillator which delivers a mode-locked train of pulses at a repetition rate of 84 MHz with a spectrum from 780 to 820 nm. This output is currently divided between two regenerative amplifiers outputting multi-mJ level pulses at a rate of 1 kHz. One arm is used for the generation of XUV high harmonics, whilst the other is stepped down to 10 Hz and sent to a multi-pass amplifier. The multi-pass is due to be upgraded in December 2019 during the commissioning of the new laboratory, housed in the basement of the Denys Wilkinson Building, to supply a compressed output of 600 mJ, <50 fs pulses at a repetition rate of 10 Hz.

The new laser line will also include an adaptive optic and wavefront measurement device, a 10 mJ, 50 fs probe beam with the option to be frequency doubled, and a laser machining rig for the manufacturing of targets which will use the 1 kHz pulses that are rejected from the multi-pass. A dedicated target area will house a vacuum chamber and beam dump to perform experiments in controlled injection and plasma channel waveguides with diagnostics including visible/IR spectrometers, interferometry, a magnetic dipole electron spectrometer and LANEX scintillation screens, as well as an X-ray camera for betatron measurements.

## 29.21 Wigner Institute (Hungary)

The Wigner Datacenter (WDC) is a large-scale investment project of the Wigner Research Centre (WRC) for Physics [735]. Our data centre aims to conform to the dynamically changing needs of research and innovation by providing a cutting-edge infrastructure with exceptional energy efficiency, in an environmentally friendly way. For the next decade, the pillars of the European research-related IT infrastructure will be high-security data centres that follow a sustainable operating model. The physical and IT security at the Csillebérc campus – which is outstanding even in international comparison – ensures extremely high availability and service quality to the research projects supported by the data centre. The WDC has the capability to store a huge amount of data in the Wigner Cloud system up to the terabyte scale.

Beyond the WDC, the WRC institute also hosts a GPU grid [736] which is available to develop fast diagnostic tools and perform beam analysis methods in various GPU/Xeon/Phi/FPGA platforms. The experts of Wigner RCP are also capable to run, e.g. PIC simulations on the cloud, thus being able to contribute either to start-to-end simulations or computational studies of smaller, specific parts of the EuPRAXIA project. For CPU computations, we have a total of 4.8384 TFlops computational capacity. For GPU computations, we have 603.444 TFlops and 57.932 TFlops for
<figure><img src="image_272.png" /><figcaption>**Fig. 29.20.** The building of the Wigner Datacenter (image courtesy of Wigner Research Centre for Physics).</figcaption></figure>

single (32 bit) and double (64 bit) precision calculations, respectively. Finally, our MIC system can provide a total of 12.184 Tflops computational capacity.

# 30 International Consortium Facilities

## 30.1 Berkeley Lab Laser Accelerator Center (United States)

The Berkeley Lab Laser Accelerator (BELLA) Center at Lawrence Berkeley National Laboratory is focused on research in applications of femtosecond, high-power lasers, including in electron acceleration, ion acceleration, and the production of secondary photon and particle sources. Currently, there are four laser systems in operation or planned at BELLA: 1) the 1 PW BELLA laser with parameters listed in Table 30.1; 2) a 10–50 TW, 40 fs Ti:Sapphire CPA laser system at 5 Hz operation with two amplifier arms designed for Thomson scattering and other photon generation experiments; 3) a 100 TW laser system in operation since fall 2018 and designed for investigating a laser-plasma-driven FEL; 4) k-BELLA, a 1kHz, 1kW-average-power laser system currently proposed and under design.

Both the BELLA PW-laser and the 10–50 TW-system are equipped with target chambers as well as various electron, photon, neutron and laser diagnostics. While the former features a long focal length beamline to deliver the laser to the target chamber, the lower power system uses paraboloid mirrors with focal length between 1.1 and 1.5 m for beam focusing. User access to both systems is available through the LaserNetUS program.

Besides its experimental capabilities, LBNL also has strong expertise in theoretical and simulation work. Worth mentioning in this context is the BLAST (Berkeley Lab Accelerator Simulation Toolkit) package, an open-access suite of codes developed as part of the LBNL Accelerator and Modeling Program for plasma acceleration simulation optimised to HPC and next generation computing systems.
<figure><img src="image_273.png" /><figcaption>**Fig. 30.1.** Map of international EuPRAXIA consortium facilities. Divided into laser and accelerator laboratories, these could be used for prototyping and testing experiments during the planned technical design phase of the project.</figcaption></figure>

<table><caption>**Table 30.1.** Parameters of the BELLA PW-laser system [737,738].</caption><tr><td>Wavelength [µm]</td><td>800</td></tr><tr><td>Pulse energy [J]</td><td>>42</td></tr><tr><td>Pulse duration [fs]</td><td><40</td></tr><tr><td>Repetition rate [Hz]</td><td>1</td></tr><tr><td>Energy stability [%]</td><td>≈ 1</td></tr><tr><td>Pointing stability [µrad]</td><td><2</td></tr><tr><td>Strehl ratio</td><td>≈ 0.8</td></tr></table>

## 30.2 Institute of Applied Physics at the Russian Academy of Sciences (Russia)

Laser-plasma acceleration of charged particles is studied in the Institute of Applied Physics at the Russian Academy of Sciences (IAP-RAS) with two laser facilities. The key element of the first one is a sub-PW laser PEARL [739]. It is an optical parametric chirped pulse amplification (OPCPA) laser system with pulse durations of 50–60 fs, wavelength of 910 nm and power up to 0.56 PW. The temporal contrast in intensity, and in the nanosecond range, of the laser system after compression is $1/(2 \times 10^8)$ between the main short pulse and the amplified spontaneous emission generated in the OPCPA stages. The facility includes optical lines with adaptive optics providing focal lengths in a wide range from 0.8 m to 8 m ($f/4 - f/40$), as well as a target chamber with a target positioning system and diagnostic systems (Thomson parabola spectrometer, two-screen single-shot electron spectrometer, etc.). The PEARL facility has been used to study electron acceleration [740] and ion acceleration [741] in laser-driven plasmas. There are several projects focused on plasma-based methods of charged particle acceleration supported by Russian funds, such as RSCF and RSBF.

A second IAP-RAS laser facility is capable of generating 1 TW, 60 fs laser pulses with 10 Hz repetition rate. Electron acceleration in plasma wakefields generated in gas-filled capillary tubes by laser pulses [742] and in laser-solid interaction [743] is explored with this facility.

Finally, at IAP-RAS, active work is underway to create lasers with a pulse shape in the form of a 3D ellipse for photo-cathodes [744]. In addition, it is planned to create a laser-plasma accelerator system with external injection based on a radiofrequency
<figure><img src="image_274.png" /><figcaption>**Fig. 30.2.** Layout of the platform for LWFA of electrons at the RIKEN SPring-8 Centre (image credits: Y. Sano).</figcaption></figure>

accelerator. For this purpose, a unique synchronisation system of the petawatt laser source PEARL with an external radiofrequency accelerator is being developed, providing a jitter of tens of femtoseconds. Since the EuPRAXIA project also implies a system with external injection, interaction in this direction can be very fruitful.

### 30.3 Osaka University / KPSI-QST / RIKEN (Japan)

Large R&D efforts in laser-plasma wakefield acceleration of electrons were carried out as a part of the national program ImPACT (2014–2018) under the Cabinet Office of the Japanese government. In ImPACT, major Japanese players in this field, namely Osaka University, KPSI-QST, RIKEN, KEK, and Tohoku University jointly worked to demonstrate stable electron acceleration, including a staging scheme and synchrotron radiation generation with undulators. An electron acceleration platform spanning 60 m was built in RIKEN SPring-8 Centre (see Fig. 30.2), which contains three different laser systems: a 1 J system (50 TW, 20 fs, 10 Hz), a 2 J system (40 TW, 50 fs, 5 Hz), and a 10 J system (100 TW, 100 fs, 0.1 Hz). The laser pulses from these three laser systems are precisely synchronised by means of a common front end. All three offer an energy stability of around 1% (RMS) and a pointing stability of 8 µrad (RMS). The facility also already features an undulator beamline.

The platform is now being used effectively for R&D of electron acceleration as part of the MIRAI program (2017–2026) under NEXT/JST among Osaka University, RIKEN, and KPSI-QST together with several other Japanese institutions. Aiming to develop basic technologies for compact X-ray FEL and ion cancer therapy systems, research foci of the program lie in laser-based small electron and ion accelerator development. Although many of the program member institutes have their own dedicated facilities (RIKEN, Osaka University, KPSI-QST, and KEK), an experimental platform for laser-based ion acceleration is under planning. Electron acceleration up to 1 GeV, two-stage acceleration with a separation of 2 m between stages, and
<figure><img src="image_275.png" /><figcaption>**Fig. 30.3.** Structure and key topics of the MIRAI program (image credits: Y. Sano).</figcaption></figure>

synchrotron radiation generation from compact undulators were confirmed. High-power laser systems for downsizing the facilities are also developed in IMS (Institute for Molecular Science), RIKEN, and Osaka University.

## 30.4 Shanghai Jiaotong University (China)

Research in the Key Laboratory for Laser Plasmas (LLP) at Shanghai Jiaotong University is mainly focussed on laser-plasma-based particle acceleration and radiation. LLP provides cutting-edge research facilities, including two 800 nm high-power femtosecond laser systems (200 TW, 5 J, 25 fs, 10 Hz and 20 mJ, 40 fs, 1 kHz), one mid-infrared (2.2 µm) intense laser system (100 TW, 8 J/100 fs), three multifunctional target chambers, and a high-performance scientific computing system (30 Tflops). Ion acceleration from laser-solid interaction, electron acceleration and betatron radiation generation from laser-driven wakefields in under-dense plasma are carried out on the 200 TW laser and target system. Terahertz radiation generation and its applications from laser filaments in air are carried out on the kHz laser system. Wakefield acceleration will also be investigated on the mid-infrared laser and target system in the coming years.

## 30.5 Tsinghua University Beijing (China)

Tsinghua University Beijing has its own facilities suitable for plasma wakefield acceleration research with a high-power pulsed laser at 30 TW/1 J/30 fs and an electron linac reaching up to 45 MeV. Additionally, it has set up strong collaborations for experimental studies with other institutes in East Asia, including the National Central University (NCU) in Taiwan (multi-pulse laser facility at 100 TW, and 10 Hz)
and the SXFEL facility in Shanghai, China (electron beams with 840 MeV, ≤0.1% energy spread, ≤1 ps duration, 0.5 nC charge, and 10 Hz repetition rate). Research activities at these facilities are focussed on laser- and beam-driven plasma acceleration techniques and applications, ranging from external injection and staging studies to beam manipulation and diagnostics as well as radiation generation. In a joint effort with Qifeng New Light Source Co. and NCU Taiwan, Tsinghua University is also developing compact and robust turn-key laser systems suitable as commercial systems for laser-plasma experiments. The expected performance includes 20–40 TW power, less than 30 fs pulse duration, and better-than 0.7% energy stability.

## 31 Computing Facilities

During the conceptual design study of EuPRAXIA, a significant number of simulations was carried out, some of which, especially particle-in-cell (PIC) simulations of plasma injectors and accelerator stages, are computationally so demanding that they required the use of high-performance computing (HPC) systems. These computational studies were carried out in some cases at smaller, local supercomputing systems, which several of EuPRAXIA’s partner institutes host (e.g. the MAXWELL cluster at DESY (https://maxwell.desy.de/)). In other cases, they were integrated as activities into dedicated computing time grants at larger facilities.

An example of the latter case are the activities of some of the EuPRAXIA Consortium partners at the Juelich Supercomputing Centre (JSC). The JSC provides high-performance computer capacity for scientists at the Research Centre Jülich, at universities and research laboratories in Germany and in Europe – as well as for industrial partners [745]. Since 2012, DESY, the University of Hamburg and IST have led dedicated computing grants for high-performance simulations on plasma wakefield acceleration. Between the years 2016 and 2018, for example, the computing project entitled “Electron-injection techniques in plasma-wakefield accelerators for driving FELs” involved the participation of 20 scientists from four different international institutions (DESY, IST, University of Hamburg and University of Strathclyde) and involved the consumption of more than 30 million CPU-hours in the supercomputer JUQUEEN, using the particle-in-cell (PIC) code OSIRIS. The project included many activities and computational studies relevant or directly related to EuPRAXIA. In 2016, it received an Award for Excellence by the John von Neumann Institute for Computing. Today, the JSC has expanded its capabilities through the implementation of the new state-of-the-art supercomputer JUWELS, which provides more than 2500 computing nodes with 48 Intel Xeon Platinum 8168 CPUs each, enabling parallel computing capabilities beyond 1 Petaflops per second. In addition, 56 accelerated compute nodes counting on 4x Nvidia V100 GPUs each are available in JUWELS, enabling outstanding computing capabilities for highly parallelised PIC codes based on GPUs, such as PIConGPU and, eventually, FBPIC.

For the future of the EuPRAXIA project, especially the technical design phase, such resource-intensive computational studies will become even more important. While a variety of test experiments and prototyping activities at different European and international facilities are foreseen, as described in the previous chapters, simulation-based work will be as essential, for example, for the detailed optimisation of component and machine performances as well as for error & tolerance studies and new code development activities. A short overview of the supercomputing facility landscape on national and European levels is thus presented in the following outlining possible future opportunities.

The national landscapes for high-performance computing in Europe are diverse. In Germany, for example, the main organisational structure is the Gauss Alliance
<table><caption>**Table 31.1.** Some of the largest supercomputing facilities in Europe based on the Top500 list of supercomputers worldwide (June 2019) [746]. R<sub>max</sub> describes the maximal LINPACK performance achieved, where LINPACK is a type of benchmark measuring a system's floating point computing power.</caption><thead><tr><td>Facility</td><td>No. of cores</td><td>R<sub>max</sub> [TFlop/s]</td><td>Application</td></tr></thead><tbody><tr><td>Piz Daint (Swiss National Supercomputing Centre, Switzerland)</td><td>3.9 × 10<sup>5</sup></td><td>2.1 × 10<sup>4</sup></td><td>Research</td></tr><tr><td>SuperMUC-NG (Leibniz Rechenzentrum, Germany)</td><td>3.1 × 10<sup>5</sup></td><td>1.9 × 10<sup>4</sup></td><td>Research</td></tr><tr><td>PANGEA III (Total Exploration Production, France)</td><td>2.9 × 10<sup>5</sup></td><td>1.8 × 10<sup>4</sup></td><td>Industry</td></tr><tr><td>HPC4 (Eni S.p.A., Italy)</td><td>2.5 × 10<sup>5</sup></td><td>1.2 × 10<sup>4</sup></td><td>Industry</td></tr><tr><td>Tera-1000-2 (CEA, France)</td><td>5.6 × 10<sup>5</sup></td><td>1.2 × 10<sup>4</sup></td><td>Research</td></tr></tbody></table>

<figure><img src="image_276.png" /><figcaption>**Fig. 31.1.** Map of European supercomputing facilities ranked in the Top 100 worldwide (based on [746], list of Nov 2018; image adapted from [747]).</figcaption></figure>

with its three-level system of HPC infrastructures [748], the first level being the national supercomputing centres. Many of these systems have user access driven by the evaluation of user proposals. Some of these systems belong to universities or research organisations, such as the Max-Planck and Helmholtz societies. For the field of novel plasma accelerators, local installations at the participating partners, in particular, play a key role in developing and optimising simulation codes, while providing a smaller amount for production runs. Examples include the systems at DESY (as mentioned above), GSI and HZDR for the Helmholtz EuPRAXIA
partners. Large-scale simulations are largely run on the level one Gauss Alliance sys-
tems, with the main installations the Jülich Supercomputing Centre (JSC) in Jülich,
the Leibniz Supercomputing Centre (LRZ) in Garching/Munich and the High Per-
formance Computing Centre (HLRS) in Stuttgart. All of these allow for large-scale
user access. Strategically, EuPRAXIA aims to maintain and foster access to both
the systems for code development as well as those for large-scale production runs.
National access could be coordinated with the access to European resources via the
European PRACE initiative [749] that also provides access to some of the Gauss
Alliance systems. Using EuPRAXIA as an applicant for computing time rather than
individual users within the EuPRAXIA consortium could potentially even allow for
a more stable and strategic allocation of computing resources at scales not accessible
to individual groups.

There are, however, also investments on a national level in supercomputing facil-
ities to be foreseen. In the United Kingdom, the government has recently decided
to spend £79 million to purchase and operate the ARCHER2 supercomputer which
will replace the currently operating ARCHER supercomputer at the University of
Edinburgh. With a peak performance between 20 and 28 petaflops, it will offer about
a five-fold increase in capability related to various numerical simulations, but for the
same power consumption. It will have a homogeneous architecture powered by CPUs.
Once the system is installed and the service is opened early 2020, ARCHER2 will
represent a significant step forward on the road to Exascale computing which should
be available by the mid-2020s [750].

Finally, looking at the European scale, several large-scale high-performance com-
puting systems with several hundred thousand computing cores exist across Europe
(compared to 2.4 Mio. computing cores at the worldwide largest supercomputer Sum-
mit at the Oak Ridge National Laboratory in the US), as has been mentioned above.
Table 31.1 and Figure 31.1 give a good overview of the capabilities of the most highly
ranked of these systems. On the other hand, the United States and Asia remain dom-
inant as leaders in large HPC facilities as well as in the manufacturing of HPC com-
ponents and systems. To coordinate the European landscape and resources better,
the European Union has thus initiated a number of programmes in recent years, such
as HPC-Europa [751]. Another new initiative aiming to boost the supercomputing
ecosystem in Europe has been launched in 2018 with the EuroHPC Joint Undertak-
ing [752]. With a 1 billion euro investment from the EU and European countries, this
project focuses on two topics: firstly, to develop a world-class European supercomput-
ing infrastructure through the construction of new supercomputers; and secondly, to
enable a long-term R&D program to continue the development of the European HPC
landscape towards higher performance, but also to foster a more independent Euro-
pean supercomputing supply industry. The first aspect follows, more specifically, the
goal to buy and implement, by 2020, three new pre-exascale machines (which would
rank within the top 5 globally) as well as five new peta-scale computers in Europe
(to be located in Bulgaria, Czech Republic, Finland, Italy, Luxembourg, Portugal
and Slovenia). This initiative would double the supercomputing resources available
for European users from academia, industry and the public sector [753]. In the long-
term, further supercomputing systems on the exascale and beyond are foreseen to
be installed with a strong focus on using European technology at this point. For
EuPRAXIA, such a development is of great interest and could be pursued further in
parallel to activities and opportunities at national scales.
# Part 6
# Appendix

## 32 Further Working Package Results

### 32.1 Assumptions and Numerical PIC Codes Used

The theoretical framework of most of the studies presented in this report is based on plasma and accelerator theory which has been developed in the last decades and copiously documented in the literature. In the context of plasma acceleration theory in particular, some key features that the EuPRAXIA design makes use of include:

- linear and non-linear plasma waves,

- propagation, self-focusing, and guiding of laser pulses in plasmas,

- methods of injection and trapping plasma electrons in plasma waves, by means of plasma density gradients, ionization, etc.

- limits to electron energy gain, including electron dephasing and laser pulse depletion.

The plasma acceleration scaling laws, in particular the expected energy gain in specific conditions are reported and discussed in Chapters 7, 13 and 16. However, as the wakefield formation and electron acceleration in an underdense plasma cannot be fully predicted by analytic theory owing to non-linear effects of laser pulse propagation, plasma wakes and motion of the accelerated electrons, only numerical simulations taking into account all combined effects can provide the real properties of the excited wave and of the electron bunch exiting the plasma structure.

Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration: a large number of macro-particles are distributed with positions within a grid and momenta. Each time step, the currents are “deposited” onto the appropriate corners or segments of the grid. Maxwell’s equations are then advanced forward to calculate new electric and magnetic fields by using commonly the finite difference time domain (FDTD) method. The force on each particle is then calculated so that their momentum and position can be advanced forward to the next time step after which the current can be determined and the whole sequence can be repeated the desired number of time steps. Some well-known PIC codes are quoted below:

- OSIRIS: R.A. Fonseca et al., “OSIRIS: A Three-Dimensional, Fully Relativistic Particle in Cell Code for Modeling Plasma Based Accelerators”, ICCS 2002, LNCS, vol. 2331, 2002, pp. 342–351

- CALDER: E. Lefebvre et al., “Electron and photon production from relativistic laser-plasma interactions”, Nucl. Fusion 43 (2003) 629–633

- WARP: J.-L. Vay et al., “Novel methods in the Particle-In-Cell accelerator Code-Framework Warp”, Comp. Sci. & Discovery 014019 (2012)

- HiPACE: T. Mehrling et al., “HiPACE: a quasi-static particle-in-cell code”, Plasma Phys. Control. Fusion 56 084012 (2014)

- AlaDyn C. Benedetti et al, “ALaDyn: A High Accuracy Code for the Laser-Plasma Interaction”, Proceedings of EPAC08, Genoa, Italy (2008).

- SMILEI J. Derouillat et al., “SMILEI: a collaborative, open-source, multi-purpose particle-in-cell code for plasma simulation”, 2017, arXiv:1702.05128v1 [hep-ph] www.maisondelasimulation.fr/smilei
<table><caption>**Table 32.1.** PIC codes used by different partners for EuPRAXIA simulation studies.</caption><thead><tr><td>PIC code used</td><td>Users</td></tr></thead><tbody><tr><td>OSIRIS</td><td>IST, DESY</td></tr><tr><td>WARP</td><td>CNRS-LPGP, CEA</td></tr><tr><td>CALDER-Circ</td><td>LOA</td></tr><tr><td>SMILEI</td><td>CNRS-LLR</td></tr><tr><td>ALaDyn, Architect</td><td>INFN, CNR</td></tr><tr><td>HiPACE</td><td>DESY</td></tr><tr><td>PIConGPU</td><td>DESY</td></tr><tr><td>FBPIC</td><td>DESY</td></tr><tr><td>LAPLAC</td><td>JIHT</td></tr></tbody></table>

In order to reduce the amount of computational resources (number of cores and computation time) required for full PIC simulations, various methods have been developed. To quote only a few of them:

- Fourier decomposition along the poloidal direction with respect to the laser propagation axis, first implementation in CALDER-CIRC; A.F. Lifschitz et al, Journal of Computational Physics 228 (2009) 1803-1814

- Boosted Lorentz Frame: In this method the simulation is done in a Lorentz frame moving at a speed near the speed of light; as a result, the plasma is Lorentz contracted and the laser wavelength is Lorentz expanded; J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007)

- Hybrid kinetic-fluid approach, where the relativistic beams are treated kinetically and the background plasma electrons as a fluid (example: Architect, ALaDyn)

- Ponderomotive guiding center (PGC) approximation, where the optical cycles of the laser are averaged out (examples: WAKE, HiPACE, ALaDyn, and optional in OSIRIS); P. Mora, T.M. Antonsen, Phys. Plasmas 4, 217 (1997)

- Quasi-static approximation when the characteristic timescales of the beam evolution are significantly greater than the characteristic timescales of the plasma evolution (examples: WAKE, HiPACE)

The simulation codes that will be used in WP2 making use of laser-driven plasma acceleration, as well in WP9 and WP14 using an electron beam as driver are listed in Table 32.1.

A short description of the codes used as part of the EuPRAXIA project is reported in the following. Detailed simulation results are presented in Part 4.

## Description of the code OSIRIS

OSIRIS [336] is a state-of-the-art massively parallel particle-in-cell code (or particle-mesh) highly optimised for a wide range of architectures and that has been successfully used for the past fifteen years to support high impact scientific results. It is an object-oriented PIC code, written in Fortran 90. Parallelisation is achieved using domain decomposition with MPI, and HDF5 is used for diagnostics. The code contains algorithms for 1D, 2D, and 3D simulations in Cartesian coordinates and for 2D simulations in azimuthally symmetric cylindrical coordinates. The algorithm can be divided into four key steps: (i) particle push using the self-consistent electro-magnetic fields and the relativistic Lorentz force (ii) current deposit into the numerical grid, (iii) electric and magnetic field advance using the full discrete set of Maxwell's equations and (iv) interpolation of up-dated fields at particles positions. OSIRIS makes no
physical approximations up to the extent where quantum mechanical effects can be
neglected. It captures the full laser pulse/particle beam and plasma particle dynam-
ics and it is thus ideally suited for the work associated with this research proposal.
OSIRIS is a proprietary code, being developed by the OSIRIS Consortium (IST and
UCLA), and being available for development and scientific work to collaborators
and partners of the OSIRIS consortium, all team members in this proposal. OSIRIS
incorporates advanced physical algorithms including the boosted frames technique to
relax computational requirements of plasma-based accelerators, a hybrid algorithm
for efficient modeling of fast ignition related scenarios, a new additional laser solver
algorithm using the ponderomotive guiding center (PGC), a quasi-3D algorithm that
uses a finite number of cylindrical field harmonics to speed up calculations, a hybrid
field solver employing finite-differences in the transverse directions and Fourier trans-
forms in the longitudinal direction to ensure perfect dispersion properties in scenarios
in order to mitigate the numerical Cerenkov instability and a radiation back reac-
tion algorithm. The new PGC laser solver can lead to computational speedups larger
than two orders of magnitude in comparison to the standard OSIRIS algorithm in
the conditions relevant for EuPRAXIA.

Description of the code CALDER CIRC

The code CALDER-CIRC [589,754] is a PIC (Particle in Cell) code. It numerically solves Maxwell's equations coupled to Vlasov equation to describe laser-plasma interaction. A kinetic description of the plasma is necessary for LWFA simulations in nonlinear regimes, hence the use of Vlasov equation, which describes, for each species in the plasma, the evolution of the distribution function in the phase space (6 dimensions, 3 dimensions for position, 3 for momenta). To avoid a too heavy computational load, a method of characteristics is used (specifically, a particle method), which avoids to directly discretise the distribution function in a six-dimensional space. The phase space is approximated by an ensemble of N "macroparticles", each one with given position, momentum and charge weight. Maxwell's equations are discretised on a uniform grid in (r,z), separating the multiple azimuthal modes. The code is explicit in time. At each time iteration, the processors perform in a loop the following steps:

- Computation of the electromagnetic fields on the grid nodes by integration of Maxwell's equations

- Interpolation of the fields at the position of each of the N macroparticles

- Advance of the macroparticles in phase space by integration of the equations of motion

- Projection of the charge and current density on the grid nodes from the updated particle positions and momenta

The code has the possibility to save and restart a simulation. CALDER-CIRC code
has not been developed to be used on vectorial machines. Instead, the code is par-
allelised for distributed memory architectures. In a parallel simulation, the spatial
domain is divided into sub-domains, each assigned to one processor. The initial inputs
are read end then processed by a master processor, which distributes the data needed
for the simulation to all the others processors. Each processor then solves Maxwell's
equations in the subdomain to which it has been assigned and performs the position
and momentum evolution of the macroparticles located in its subdomain. Communi-
cations between processors are performed when macroparticles exit the spatial sub-
domain managed by the processor, when the processors exchange the values of the
fields at the boundary cells, or when the global diagnostics are saved on files. The
communications thus only occur at the boundaries between the subdomains, or in
<figure><img src="image_277.png" /><figcaption>Fig. 32.1. Performance scalings for SMILEI code [587].</figcaption></figure>

the (not frequent) iterations when global diagnostics act. The code is also well suited for a highly parallel machine. The code has already been used on supercomputers, among which the supercomputers Curie of TGCC and JADE of CINES.

## Description of the code SMILEI

SMILEI [587] is an explicit Particle-In-Cell (PIC) code written in C++. It uses finite difference schemes to solve Maxwell equations on a grid. Particles, sampling the plasma phase space and able to move freely in the whole domain, are then moved according to the fields evaluated on their local surrounding cells. Once particles have moved, they can deposit their current on the grid. These currents are used as source terms to solve the Maxwell equations again and so goes the PIC cycle. This code uses at most 2 Gb of memory per core and in average less than 1 Gb per core. Two layers of parallelisation are implemented. The first one is a classical MPI domain decomposition. Fields and particles are exchanged only between neighbors and global communications are only needed when reductions are done for outputs. Each MPI process has a copy of its local grid part and a copy of the particles living in this local grid part. As seen in Figure 32.1, the MPI parallelisation has already proven a very good strong scalability on the OCCIGEN system over 50 thousand cores. OCCIGEN is a Bull system. Each node holds 2 Haswell processors of 12 cores 2.6 Gbytes of memory per core. The network is a fat tree Infinyband (IB 4x FDR). The second layer of parallelisation deals with the load division within an MPI process between the several openMP threads it owns. In order to spread the computational load as homogeneously as possible between openMP threads, MPI domains are further divided into many patches which can be seen as sub-domains. They also own their own copy of local grid and particles array. There are many more patches than openMP threads so that the openMP dynamic schedule can keep all threads busy at all times, dispatching the load efficiently between all threads. It is important to note that the number of openMP threads is limited by the number of cores per CPU and that, the efficiency of the load balancing increases with the number of threads. This method therefore benefits a lot from recent CPU with high core counts. But in order to have a real dynamic load balancing, the load must also be balanced between MPI processes. In order to do so, patches exchanges between MPI processes are implemented. An overloaded process is able to offload some of its work to neighbor processes. Patches are ordered along an Hilbert Space-Filing curve, and each MPI process owns a continuous sequences of patches of similar total load. Patches are dynamically exchanged along this curve as their load evolves in order to keep the total load of every single MPI process to a similar level.
## Description of the code WARP

WARP [755] is both a code and a general purpose framework for parallel three-dimensional Particle-In-Cell simulations of beams in accelerators, plasmas, laser-plasma systems, non-neutral plasma traps, sources, and other applications. It contains multiple field solvers (electrostatic FFT, multigrid, electromagnetic), internal conductors (cut-cell method with electrostatic solver), surface physics (space-charge limited emission, secondary emission of electrons or gas from impact of electrons or ions), volumetric ionization. It employs advanced methods such as cutcell boundaries, Adaptive Mesh Refinement, a “warped” coordinate system with no paraxial assumption nor reference orbit required, and boosted-frame support, to name a few. Warp has already been used and experimentally tested on various laser facilities as the Lund Laser Center in Sweden or the UHI100 laser at CEA-Saclay. It is worth noting that the research with Warp is done in close collaboration with the development Team of Lawrence Berkeley National Laboratory (LBNL), especially with J.L. Vay et R. Lehe who are specialists in the laser plasma acceleration modeling and PIC-like numerical methods. The main computationally expensive loops are parallelised using MPI. Warp is written in a combination of i) Fortran for efficient implementation of computationally intensive tasks, ii) Python for high-level specification and control of simulations, and iii) C for interfaces between Fortran and Python. As all computationally relevant tasks are implemented in Fortran, OpenMP will be used on the Fortran level (i.e., there will only be one python interpreter per MPI task, each of which utilises many threads to further parallelise node-level computations). Strong scaling has been demonstrated on various computers. A demonstration example performed by the LBNL Team is shown on Figure 32.2. Warp spectral solver is currently parallelised at subdomain level using MPI (coarse grain parallelism). In turn, every subdomain calls the sequential FFTW 3 library. Additional threadlevel concurrency needs to be added inside the subdomain computations (fine grain parallelism). The spectral solver can use other FFT libraries and we may have to replace the FFTW library calls by calls to a FFT library, like the MKL one, which is better tuned for Knights Landing. One of the special feature of WARP is the possibility to use the boosted-frame technique, reducing the computation time by a large factor, especially for the long accelerator stage. The code can be also used in various geometries, in particular the cylindric one by including a limited number of azimuthal modes has been implemented. As a result, a quasi-3D computation can be performed with a computing time of two orders of magnitude lower than a full 3D computation. This method was initially implemented in the code Calder-CIRC and is operational in Warp since 2014.

## Description of HiPACE – A 3D quasi-static PIC code

HiPACE (Highly efficient Plasma Accelerator Emulation) [756] is a relativistic, fully electromagnetic, three-dimensional (3D) and fully MPI-parallelised particle-in-cell (PIC) code. It uses the quasistatic approximation to efficiently model particle-beam driven plasma-wakefield accelerators. HiPACE exploits the disparity of time scales in the interaction of highly relativistic particle beams with plasma to decouple beam and plasma evolution. This enables time steps which are many times greater than those used in FDTD PIC codes and therefore renders possible a reduction of the required number of core hours by orders of magnitude. While the axial magnetic field was neglected in the original version of HiPACE, it is now computed along with all other field quantities, so as to allow for the fully consistent simulation of non-cylindrically-symmetric phenomena, such as the hose instability.
<figure><img src="image_278.png" /><figcaption>Fig. 32.2. Strong parallel scaling of Warp EM solver on 3D periodic 1024x1024x1024 grid with 8 particles/cell, on up to 131,072 cores (image credits: Jean-Luc Vay).</figcaption></figure>

## Description of the code Architect

The Architect code [600,621] belongs to the family of hybrid approach for plasma and laser wakefield acceleration, where to reduce the computational cost the electron background plasma is treated as a cold fluid. The use of a fluid background significantly reduces the computational cost. Architect uses the particle-in-cell (PIC) approach to evolve the electron bunches to preserve the kinetic nature of bunches, particles are evolved in a 3D3V phase-space. Electromagnetic fields are evolved accordingly to Maxwell's equations. To further reduce calculation time without loss of accuracy the fluid and electromagnetic equations are solved assuming cylindrical symmetry. The integrated equations can be written, in a compact way, as follows:

$$ \partial_t n_e + \nabla(\beta n_e) = 0 $$

$$ \partial_t \mathbf{p}_e + c\beta_e \nabla \mathbf{p}_e = qn_e(\mathbf{E} + c\beta + e \times \mathbf{B}) \qquad (32.1) $$

$$ \nabla \times \mathbf{E} + \partial_t \mathbf{B} = 0 \qquad (32.2) $$

$$ \nabla \times \mathbf{B} - c^2 \partial_t \mathbf{E} = q\mu_0 c(n_e \beta_e + n_b \beta_b) \qquad (32.3) $$

$$ d_t \mathbf{p}_{\text{particle}} = q(\mathbf{E} + c\beta_{\text{particle}} \times \mathbf{B}) \qquad (32.4) $$

$$ d_t \mathbf{x}_{\text{particle}} = \mathbf{v}_{\text{particle}} \qquad (32.5) $$

where $E$ is the electric field, $B$ the magnetic field, $c$ the speed of light, $\beta_e=u_e/c$ the relativistic $\beta$ for the background electrons, $\beta_b$ the relativistic $\beta$ for the electron bunch, $p_e$ the fluid relativistic momentum for electrons, $n_e$ is the electron density and $n_b$ the bunch density. For each single particle of the kinetic bunch(es) we identify a relativistic momentum, pparticle, a relativistic $\beta$, $\beta_{particle}$, a velocity, $v_{particle}$, and a position, $x_{particle}$. The first and second equations are the fluid mass conservation and the fluid momentum conservation respectively. The third and the fourth are Faraday's law and Ampere's law respectively. The last two equations are the kinetic compound to the model, the relativistic Newton's law for each
single particle composing the bunch(es): the momentum equation and the position-velocity equation. The fluid velocity classically written as $u_e$ has been written as a function of $\beta$. Ions are assumed as a static background. The code algorithms are presented in Reference [600], and a full comparison with a PIC code is presented in Reference [621]. Dynamic in plasma-based accelerators spans over a large range of timescales, while beams evolve on a timescale on the order of the inverse beta-tron oscillations, the background plasma evolves on a timescale on the order of the inverse of the plasma frequency. The shortest dominating timescale is the background plasma frequency. The hybrid approach permits to overcome the computational cost imposed by the shortest timescale without renouncing to the full time-explicit formulation. A time-explicit formulation permits to take into account for background density modulation: plasma density ramps and radial plasma channel modulation. We observe background electrons have locally similar behaviour. The evolution of a single particle around the ion bubble resemble the behaviour of the local ensemble averaged behaviour, a fluid description holds. The hybrid approach algorithmic strength consists on the combination of mature state-of-the-art numerical techniques both for the kinetic description as well as for the fluid part. The novelty that a hybrid approach consists is the wise combination of the different algorithms using different timescales. The interaction between the kinetic and fluid scale is made possible via the bunch current, calculated and weighted on the fluid mesh. The novelty introduced by architect is the resolution of evolution equation in a time explicit domain, there is no quasi-static approximation. Moreover, electron bunches are initialised in vacuum with their self-consistent field, we treat the transition from vacuum to plasma.

## Description of the code ALaDyn

The code AlaDyn [362,592,757,758] is a Particle in Cell (PIC) code designed to investigate three main physical regimes:

- Laser-plasma interaction in under-dense gas targets for electron acceleration (LWFA);

- Beam-plasma interaction in under-dense gas targets for electron acceleration (PWFA);

- Laser-plasma interaction in over-dense solid targets for proton(ions) acceleration and related phenomenologies.

A PIC method is based on a hybrid formal setting, whereby plasma particles are represented on a Lagrangian framework whereas self-consistent fields are represented on the Eulerian framework given by Maxwell equations. As most other PIC codes, ALaDyn discretise particle and field dynamical equations by centered finite differences on a staggered space and time grid (Yee's module) using one step second order leap-frog integrator. To connect Lagrangian particles to Eulerian fields collocated on the spatial grid, finite order B-splines are used. B-splines are local polynomials with compact support, allowing to represent delta-like point particles on a grid for charge deposition and, by converse, to assign field grid data to a point particle. Energy preserving PIC schemes do not satisfy local charge conservation and the related Poisson equation. By converse, using one of the many numerical recipes to enforce the continuity equations, energy conservation is heavily damaged. ALaDyn code implements both charge or energy preserving schemes, letting the user to choose, depending on the problem at hand. Besides the standard leap-frog integrator, ALaDyn also implements a fourth order in space and time Runge-Kutta integrator. This scheme requires larger computational resources, of course, but can be of help to improve on accuracy and reduce dispersive effects of wave propagation. The code implements also reduced models based on:
- the envelope (two-scale) approximation of the laser fields and of the particle dynamics;

- a cold fluid approximation of the background plasma dynamics;

- hybrid fluid-kinetic simulations (kinetic particles on top of a fluid background).

Reduced models have been intensively tested from a linear up to a strongly non-linear regime, showing that they are reliable and robust. In particular it has been shown that the breakdown of the implemented numerical models usually is closely related to the breakdown of the physical assumption underlining the theoretical model. In all of the above configurations, field induced ionization (tunneling) is also implemented and can be activated, if requested by the user. All ionization models are based on the ADK scheme plus barrier suppression (BSI) for higher Z ions. For solid targets, impact (collisional) ionization is under development.

## Implementation

ALaDyn is almost completely written in Fortran 90, but a couple of utility modules are written in C++. C can also be easily used to extend code functionalities. Fortran 90 is the most popular computational language in PIC codes, probably because of the higher efficiency in handling multidimensional arrays on a grid. Finite difference integration allows to exploit efficient parallelism by domain decomposition using MPI technique to distribute the computational work among CPU units. ALaDyn has been successfully ported to many HPC architectures, both in Italy at CINECA and in Europe through PRACE Partnerships. From the CINECA IBM-SP6 system in 2011, to the test system at CINECA based on IBM/BGP in 2012, then CINECA FERMI in 2014 and MARCONI in 2016, ALaDyn run on a multitude of HPC architectures, always extracting top range performances. A new version has been recently released open source on the web, with a GPLv3 license. In part it has been rewritten from scratch and it is the basis for future development. Sources can be found, together with other codes, in our organization GitHub page at github.com/AlaDyn

## Description of the code PIConGPU

PIConGPU [759] is a fully relativistic Particle-in-Cell (PIC) code developed and maintained by the Computational Radiation Physics group at the Institute for Radiation Physics at HZDR, Dresden, Germany. The code is written in C++ and it is designed to run on Graphical Processing Units (GPUs) based on the NVIDIA CUDA library, which are in general better suited for heavy parallelisation due to a much higher number of individual cores, as compared to CPUs, allowing a significant speed up of the simulations. The code supports a hybrid architecture consisting of single computation nodes interconnected in a standard cluster topology, with each node carrying one or more GPUs. The internode communication is realised using the message-passing interface (MPI). PIConGPU implements various numerical schemes to solve the PIC cycle. Its features for the electro-magnetic PIC algorithm include:

- A central or Yee-lattice for fields.

- Particle pushers that solve the equation of motion for charged and neutral particles, e.g., the Boris- and the Vay-Pusher.

- Maxwell field solvers, e.g. Yee's and Lehe's scheme.

- Rigorously charge conserving current deposition schemes, such as Villasenor-Buneman, Esirkepov and ZigZag.
- Macro-particle form factors ranging from NGP (0th order), CIC (1st), TSC (2nd), PSQ (3rd) to P4S (4th).

and the electro-magnetic PIC algorithm is further self-consistently coupled to:

- Classical radiation reaction.

- QED synchrotron radiation (photon emission).

- Advanced field ionization methods.

The code is open source and licensed under the GPLv3+.

## Description of the code FBPIC

FBPIC [489,760] is an open-source Particle-In-Cell (PIC) code for relativistic plasma physics. By design, the code is especially well-suited for simulations of plasma-based particle acceleration. It implements a unique algorithm that uses an azimuthal mode decomposition of the electromagnetic fields in a cylindrical geometry, to reduce the computational costs of simulations with close-to-cylindrical symmetry. For typical cases of plasma acceleration, this method results in orders-of-magnitude speed-up when compared to conventional, fully three-dimensional algorithms. By advancing the fields in spectral space, it furthermore avoids numerical errors common to traditional field solvers that are based on finite-difference methods. The implemented Galilean-PSATD (Pseudo-Spectral Analytical Time Domain) solver mitigates artificial beam quality degradation by numerical Cherenkov radiation (NCR) [761] and is free of the numerical Cherenkov instability (NCI) for relativistically drifting plasmas [762,763]. The latter characteristic allows to model the process of plasma acceleration in an optimal, relativistic frame of reference. For many simulation cases, the so-called Lorentz-boosted frame technique leads to orders-of-magnitude reductions in runtime, thereby increasing the overall efficiency of a simulation even more. In order to make all of these algorithmic features available to the user, FBPIC exposes an easy-to-use API to setup a simulation, providing many helper functions to initialise pre-defined physical objects, such as particle beams or laser profiles. The code is written in Python and uses on-the-fly compilation to machine code for high performance. On a first level, the algorithm is optimised to run efficiently on highly parallel hardware, such as GPUs and multi-core CPUs. On a second level, the computation is scaled to distributed compute nodes using MPI (Message Parsing Interface). FBPIC supports the OpenPMD standard [764], which defines a common format for structured output files. This open-source standard allows to use the same post-processing tools for output generated by different codes, facilitating compatibility and comparability of results.

## Description of the code LAPLAC

In the hybrid code LAPLAC [765,766] the electron background plasma, like in the code Architect, is treated as a cold fluid. To describe self-consistently the wakefield generation by a short intense laser pulse propagating in an ionising gas the laser pulse non-linear dynamics and plasma formation due to tunneling ionisation of the gas are taken into account. The Maxwell equation for the total electric field (which includes high-frequency laser fields and also slowly varying plasma wakefields)

$$ \nabla \times \nabla \mathbf{E} + \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} = -\frac{4\pi}{c^2} \frac{\partial}{\partial t} (\mathbf{J} + \mathbf{J}_{\text{ion}}) \quad (32.6) $$
contains the electric current density of free electrons $\mathbf{J} = en_e \mathbf{V}_e$, determined by the momentum of free electrons $\mathbf{P}_e : \mathbf{V}_e = \mathbf{P}_e/(m_e^2 + \mathbf{P}_e^2/c^2)^{1/2}$, and also the ionisation current, which provides the momentum and energy changes of the laser pulse due to direct ionisation losses in the process of tunnel gas ionisation [767]. The hydrodynamic equations for the electron plasma density and the electron momentum can be written in the form of equation (32.1) with additional terms describing the impact of optical field ionisation [768]. The laser pulse propagation and the wakefield generation are described in terms of the slowly varying amplitude approximation which implies that the laser pulse duration is in excess of a few optical cycles.

The PIC method is used to study the motion of the electron beam particles, which is described by the extended equations (32.4–32.5), where the radiation strength in the Landau-Lifshitz form is taken into account. The code also allows to investigate the dynamics of the electron spin precession, which is calculated based on the T-BMT equations [769].

## 32.2 Further Considerations for High-Gradient Plasma-Accelerator Structures

### 32.2.1 Introduction

Several options are envisaged in the frame of EuPRAXIA for a plasma based multi-GeV accelerator. Four concepts in particular are currently under study:

1. Beam generation and acceleration in a single-stage laser-driven plasma injector / accelerator.

2. External injection of an electron bunch into a laser-driven plasma accelerator.

3. External injection of an electron bunch into a beam-driven plasma accelerator.

4. Hybrid schemes including both laser-driven and beam-driven plasma acceleration.

In this frame, the role of WP3 has been to define laser-driven plasma accelerating structures (i) to achieve an injector, by generating a source of electrons of energy 150 MeV or 1 GeV, producing bunches of short duration with reliable parameters, suitable for injection into a laser-plasma accelerating structure; (ii) to achieve a high gradient accelerating structure providing energy gain from 1 to 5 GeV, with controllable plasma parameters, compatible with laser propagation over the acceleration length, and scalable to high electron energy requirements. This section provides additional background information for the plasma target design presented in Chapters 13 and 16.

### 32.2.2 Plasma Stage Parameters

#### Regime of Operation and Parameter Range

Laser and plasma parameters need to be identified to achieve the different types of plasma stages considered in the EuPRAXIA design. They can be classified as:

- Laser wakefield injectors to generate electron bunches at an energy of

* 150 MeV, so that the energy gain in the plasma structure is $\Delta W = 150$ MeV

* 1 GeV, i.e. $\Delta W = 1$ GeV

- Laser-plasma accelerator stages to increase the energy of the electrons

* from 150 MeV to 1 GeV : $\Delta W = 0.85$ GeV

* from 150 MeV to 5 GeV : $\Delta W = 4.85$ GeV

* from 1 GeV to 5 GeV : $\Delta W = 4$ GeV
Laser wakefield injectors, by definition, generate relativistic electrons bunches as a result of laser-plasma interaction, without external injection from an external electron source. Therefore, they operate in a non-linear regime, such that the laser normalised vector potential $a_0 > 1$, corresponding to a peak laser intensity on target $I_L$ larger than $2.1 \times 10^{18}$ W/cm$^2$, for a laser of wavelength $\lambda = 800$ nm.

Laser-plasma accelerator stages by definition provide an accelerating structure where externally injected electron bunches gain energy. Injection or trapping of plasma electrons in this structure should be avoided so that they operate in the quasi-linear regime with $a_0$ of the order of 1.

The maximum energy gain an electron can experience can be estimated by $\Delta W = eE_{acc}L_{acc}$ with $e$ the electron charge, $E_{acc}$ the average electric field and $L_{acc}$ the acceleration length. The optimum acceleration length is the dephasing length $L_\phi$, defined as the distance after which electrons slip out of the accelerating and focussing phase. The acceleration process is the most efficient when it is equal to the laser energy depletion length, $L_{dpl}$, defined as the length over which half of the laser energy is used to excite the plasma wave.

The energy gain over the dephasing length, can be estimated from scaling laws established by Lu et al. [185]. In the non-linear regime relevant for LPI, $a_0$ is larger than 2, and the energy gain evaluated over the dephasing length, is given by :

$$ \Delta W(/m_e c^2) \approx \frac{2 n_c}{3 n_e} a_0. \qquad (32.7) $$

This is an upper limit, as for $a_0 > 2$ the depletion length is always smaller than the dephasing length. If we consider a laser intensity high enough to inject electrons in the wakefield ($a_0 \gtrsim 2$), we obtain estimates in agreement with experimental achievements:

$$ \Delta W = 150 \text{ MeV} : n_e \approx 7.9 \times 10^{18} \text{ cm}^{-3} \text{ and } L_{acc} \approx 1 \text{ mm for } a_0 = 2 $$

$$ \Delta W = 1 \text{ GeV} : n_e \approx 1.8 \times 10^{18} \text{ cm}^{-3} \text{ and } L_{acc} \approx 9 \text{ mm for } a_0 = 3 $$

In the linear regime relevant for LPAS, $a_0 \approx 1$, $L_\phi$ and $L_{dpl}$ scale as follow [185]:

$$ L_{\phi} \approx \frac{n_c}{n_e} \frac{1}{k_p} \qquad (32.8) $$

and

$$ L_{dpl} \approx \frac{n_c}{n_e} \frac{1}{k_p} \frac{\omega_p \tau_L}{a_0^2} \qquad (32.9) $$

The use of laser energy on the dephasing length is optimum for $\omega_p \tau_L \approx 1$ and $a_0 \approx 1$.

For LPAS, the energy gain is estimated over the dephasing length for externally injected electrons trapped in the structure, and $a_0 = 1$, using $\Delta W(/m_e c^2) = n_c/n_e$:

$$ \Delta W = 0.85 \text{ GeV} : n_e \approx 1 \times 10^{18} \text{ cm}^{-3} \text{ and } L_\phi \approx 9 \text{ mm} $$

$$ \Delta W = 4 \text{ GeV} : n_e \approx 2.2 \times 10^{17} \text{ cm}^{-3} \text{ and } L_\phi \approx 88 \text{ mm} $$

$$ \Delta W = 4.85 \text{ GeV} : n_e \approx 1.8 \times 10^{17} \text{ cm}^{-3} \text{ and } L_\phi \approx 118 \text{ mm} $$

These scalings are approximate, and for example they do not take completely into account the evolution of the wakefield amplitude due to laser self-focussing which is significant in most experiments. However they provide estimates of the density and acceleration length corresponding to a given energy gain close to experimental achievements as discussed by S. Mangles [770].

## Overview of Relevant Experimental Efforts

Most of the experimental work to date in the field of LWFA is related to the injector class, and studies the acceleration of small populations of relativistic electrons issued
from the bulk of plasma electrons, with which the intense laser interacts. These accelerated electron bunches are relatively easy to achieve experimentally with existing laser systems, but the properties of the electron bunches are difficult to control and may not be suitable for demanding applications.

Over the past fifteen years, successive improvements have been proposed theoretically and demonstrated experimentally. The use of various physical mechanisms provides different levels of control of the electron beam properties at the expense of simplicity.

A selected number of processes or mechanisms are discussed in this report, based on their strong potential for improving the electron beam quality. Published experimental results were examined and compared not only in terms of achieved electrons properties, but also regarding their reliability, stability, or scalability to larger electron energy, or repetition rate.

External injection and acceleration of electrons in a LWFA have been attempted by only a few groups, and its achievement is complex as it involves femtosecond range timing and micron precision on alignment and stability of beams. The early work of Amiranoff et al. [771] has demonstrated the need of short electron bunches for injection into a plasma structure, and the extension of the plasma length to the dephasing length in order to fully exploit this scheme. Recent work [181] has further demonstrated the potential and challenges of external injection, emphasising the need for compact electron beam transport and shaping.

Following the first tentative experiments for external injection, laser guiding techniques have been developed and demonstrated experimentally in order to provide plasma media able to sustain accelerating structures over dephasing lengths much longer than the Rayleigh length.

Accurate comparison of experimental and simulation results is also extremely challenging as it requires a precision not currently available for two main reasons: on one hand, experimental parameters are not completely known from usual measurements as diagnostics are not necessary available on the scales required; on the other hand, simulations need sizeable computing capacity to correctly describe 3D situations taking into account realistic and non perfect inputs. Undergoing efforts aim at a better knowledge of experimental parameters and the development of numerical tools to provide a more realistic description.

### 32.2.3 Plasma Creation

Targets for laser-driven plasma accelerators can be broadly classified as waveguide or non-waveguide targets; each can be further divided into targets which are pre-ionised or are ionised by the driving laser. It should be emphasised that guiding of the driving laser pulse can, and in general will, still occur in “non-guiding” targets through relativistic self-focussing.

The plasma target can incorporate important additional features such as: structures for controlling injection of electrons into the wakefield; longitudinal variation of the plasma density for extending acceleration beyond the dephasing length [196], or for controlling the properties of the electron bunch as it leaves the acceleration stage. The criteria to be considered when choosing a plasma target are described in the following.

#### Criteria for Choosing Plasma Targets

The choice of the plasma target depends on the constraints on the plasma stage considered:
**Required plasma length:** To achieve a given energy gain, the target must be at least as long as the expected gain divided by the mean accelerating gradient. For optimised operation, the accelerating length is limited by electron dephasing and the accelerating gradient is controlled by plasma density and laser intensity values. As the plasma electron density, the laser intensity and the laser power are the main parameters that determine the dynamics of the interaction, a valid strategy would be to fix those parameters according to the desired energy gain. The length of the target must then be set to match the dephasing length. A variable length target provides a degree of freedom to adjust the plasma length independently from the density, for example to tune finely the electron energy without changing the other parameters.

**Appropriate density profile:** For a laser wakefield electron injector, a tailored density profile can be useful. For example when the density gradient injection scheme is used, the plasma target should exhibit a steep density gradient to limit the volume of injection to a controlled area. When the laser amplitude $a_0$ in vacuum is lower than the injection threshold, self-focusing and self-compression play a significant role to achieve injection. As these mechanisms depend on the local plasma density, the shape of the density profile along the propagation direction provides a way to control the injection length. Moreover gradients can be used in the injector to compensate the energy chirp of the injected electron bunch and therefore reduce the energy spread [32].

In an accelerator stage, an upward gradient can be used to keep the externally injected electrons in phase with the plasma wave driven by laser, and a downward gradient to control the beam properties at the transition between plasma and vacuum.

**Stability of the plasma density:** In order to use the electron beam for applications, the stability of its properties is crucial. All sources of fluctuations of experimental parameters should be characterised and minimised to reduce the electron bunch property fluctuations. However, determining contributions of each parameter fluctuations on the electron bunch fluctuations is difficult to achieve experimentally. A study by Desforges et al. [197,198] shows that the plasma electron density is a key parameter for the stability of the injector. The acceptable level of fluctuations on the value of the density could be investigated numerically in conjunction with WP2.

**The lifetime of the target and the repetition rate it can sustain:** The target should be able to sustain a 10 Hz repetition rate and to be used for at least a day. From these considerations, two strategies can be adopted: a robust target that can sustain a large number of shots (typically hundreds of thousands of shots assuming a 10 Hz repetition rate during a day of operation) or a remotely interchangeable target that can sustain a smaller number of shots but can be replaced without interrupting operation.

**Possibility to probe the target:** It can be useful to have the possibility to probe the target, either to trigger the injection in the case of colliding pulse injection for the injector(s), to monitor the density of the plasma, or to discriminate sources of trouble in the case of abnormal operation.

**Compactness and compatibility with diagnostics:** Finally, the target design must be compatible with other diagnostics that may be implemented in the experimental chamber such as laser or electron diagnostics.
# Gas Cells and Gas Jets

## Gas jets

Gas jets have seen a very wide use as targets for laser-plasma interactions. Much early work in laser wakefield acceleration was performed with gas jets, for example the three seminal experiments presenting electron beams with narrow peaked energy spectrum (PES) employed gas jets as the target [11,12,273]. Kneip et al. [772] used gas jets as targets to obtain narrow PES electron beams with energies to the GeV level. More recently a novel dual gas jet design has been used to obtain stable, narrow PES electron beams with central energy tunable in 50 – 300 MeV range [773].

Supersonic gas jet nozzles can be optimised to provide nearly flat-top density profiles required for laser wakefield acceleration, where a plateau in plasma density can be many millimetres long. Semushin and Malka [289] showed this can be done by optimising the opening angle of the conical nozzle $θ$, the throat diameter $d_C$ and the diameter of the exit $d_E$. Simulations agree with experimental measurements and show a 5 mm long flat density plateau is obtained. However, as the density profile is generated by a supersonic expansion, density is typically only flat to ≈ 10%. Schmid and Veisz [276] further show that the scale length of density gradients on either side of the density plateau follow a linear dependence on the product $Ld_E$, where L is the length of the divergent section.

The peak plasma density is controlled by changing the backing pressure of the jet; the plasma density varies linearly with backing pressure. Typically pressures up to 100 bar are used to obtain plasma densities up to $n_e \simeq 1 \times 10^{20} \text{cm}^{-3}$. For a fixed throat diameter, increasing the nozzle diameter results in lower density plateau values. As an example, for an optimised nozzle with $d = 2 \ (15) \text{ mm}$, a backing pressure of 100 bar results in peak electron density of $n_e = 2 \times 10^{20} (4 \times 10^{18}) \text{cm}^{-3}$. The high pressure solenoid valves usually used to control the gas flow out of the jet are typically open for a few tens of milliseconds which presents heavy vacuum system loads. This can be reduced through the use of faster solenoids and careful design of the valve/nozzle system to minimise the volume of gas released per shot.

Gas jets rely on expansion into vacuum and as such provide an entirely open geometry for diagnostic access. This allows for the plasma density profile to be measured for every high power shot. In addition, by using ultra-short, nearly single-cycle probe pulses, Buck et al. [532] directly measured the phase of the self-injected electrons within the accelerator cavity.

For very high repetition rate ($f > 100$ kHz) operation of laser wakefield accelerators, it will be desirable to remove plasma from the beam path prior to the arrival of the next laser pulse. In gas jet targets, the supersonic flow perpendicular to the accelerator axis means that plasma removal occurs naturally.

## Gas cells

Osterhoff et al. [774] have investigated laser-wakefield acceleration in steady-state flow gas cells. In this work the gas “cell” is a gas-filled capillary, but it is important to note that, unlike the waveguides described in this section, reflections from the capillary wall play no role in guiding the laser since the capillary diameter is much larger than the laser spot size.

The capillaries are constructed by laser-machining channels of semi-circular cross-section in sapphire plates; additional channels are machined into the plates to provide a route for gas to flow into the main capillary. Contacting two such plates together forms the capillary.

Fluid simulations show that within a few hundred milliseconds of the gas valve opening, the gas within the central 80% of the capillary is highly homogeneous and stationary. Further, turbulence in the gas plumes formed immediately outside the
capillary is low, and supersonic shock fronts of the type found in some high-Mach number gas jets, are avoided.

As an example, Osterhoff et al. [774] constructed steady-state 15 mm long gas cells from capillaries of 250µm diameter. Using 850 mJ, 42 fs full width at half maximum (FWHM) laser pulses from a Ti:sapphire laser they generated electron beams of up to 200 MeV. These beams were emitted within a low-divergence cone of (2.1 ± 0.5) mrad FWHM, and had shot-to-shot stabilities of 2.5% RMS in energy, 1.4 mrad RMS pointing, and 16% RMS in charge. The high stability of gas cell targets was used by Weingartner et al. [569] to perform a quadrupole focussing scan to measure the emittance of laser wakefield accelerated electron beams.

A different approach was introduced by Vargas et al. [775], presenting the use of three-dimensional printing of gas cells. Single-stage or two-stage gas cells can be printed with ease. Due to the cell being a rectangular enclosure windows can be used to allow for diagnostic access. Improved stability as compared to gas jets is observed, along with higher electron beam energies.

## Waveguide Targets

In general terms waveguides utilise a transverse variation of the refractive index to guide the driving laser pulse, and these may usefully be divided into step-index and gradient refractive index waveguides. In the context of plasma accelerators, gradient refractive index guiding can be achieved by creating a transverse variation of the plasma density to form a “plasma channel”. Step-index waveguides can be achieved via grazing-incidence reflections from the inner wall of a gas-filled capillary tube [350]. A key difference between the operation of plasma channels and hollow-core capillary waveguides is that the guiding properties of the former usually depend on the on-axis density, whereas in hollow-core capillaries the guiding is much less strongly dependent on the plasma density. Confinement of the driving laser pulse in waveguides, and by relativistic self-guiding, is considered in detail in this section.

## Complex or Novel Structures

### Variable-length gas cells

It can be useful to be able to adjust the length of the target, either: (i) to match the target length to the dephasing or pump depletion lengths, without also changing the gas density; or (ii) to study the evolution of the particle with longitudinal position in the plasma accelerator.

One example has been provided by Heigoldt et al. [776]. In their design, the rear gas cell pinhole was mounted on a cylinder which could be driven longitudinally within the gas cell, thereby varying the length of the gas cell between 2 mm and 4 mm. This cell was used to study the evolution of the longitudinal bunch profile with longitudinal position within the plasma accelerator.

Hydrodynamic simulations of a variable-length gas cell with two separate chambers have been reported by Kononenko et al. [286]: an “injector section”, and an “accelerator section”. In such a target the plasma density in the accelerator region is always below the self-trapping threshold. A single laser pulse is self-guided throughout the interaction, with the density and length of the first injection section determining the phase space volume of the accelerated beam. Such cells of varying density, driven by a single pulse, can have a number of applications. In the case of an increasing plasma density between the steps, the shortening of the plasma wave wavelength can rephase electrons into the accelerating phase of the wakefield, thus increasing the
maximum dephased energy (as described in the paragraph below). By contrast, density decreases can help make injection easier, thus potentially reducing the trapping threshold even for relatively low intensity laser drivers.

### Tapered density targets

Targets in which the plasma density varies with longitudinal position could be used to extend acceleration beyond the dephasing length $L_φ$. In this approach, the plasma density increases longitudinally, so that the plasma wavelength decreases as the particle bunch slips forward with respect to the laser driver. For the correct longitudinal variation of the plasma density, the particles maintain their location (i.e. phase) relative to the plasma wave.

This idea was first described for particle-driven plasma accelerators by Katsouleas [188]. Sprangle et al. have derived an expression for the longitudinal density profile for the case of a laser-wakefield accelerator driven in a plasma channel [777]. Rittershofer et al. [196] extended this work to account for the transverse variation of the plasma density in the plasma response, and derived conditions for phase locking the location of the bunch to the transverse or longitudinal accelerating fields, or both. We note that Pukhov and Kostyukov [778] have also considered the use of layered plasmas to optimise simultaneously the energy gain and quality of laser-accelerated electron bunches, and Yoon et al. have studied quasi-phase-matched laser wakefield acceleration [779].

Varying density, steady-state flow gas cells were investigated by Rittershofer [780]. Gas cells were formed from 15 mm long, laser-machined capillaries with an inner diameter of 200-300 µm. Gas was introduced into the capillaries via 500 µm diameter inlets located 750 µm from the capillary ends. The gas pressure at each end could be set independently, allowing the formation of a close-to-linear variation with a ratio as high as approximately two in gas density between the gas inlets. For example, using hydrogen, a change in the atomic density from $3 \times 10^{18}$ to $1.5 \times 10^{18} \text{ cm}^{-3}$ over a distance of 10.8 mm was demonstrated. The density ramps formed in this way were found to agree with fluid flow simulations.

Tapered plasma channels have also been investigated. For example, Kaganovich et al. [781] have described a segmented discharge-ablated capillary discharge. In this device, three plastic capillaries of inner diameter 500 µm were joined coaxially to form a capillary with a total length of a 60 mm. By driving different current pules in each section it was possible to generate three, coaxial plasma channels of different axial density. The mean plasma density was approximately $2 \times 10^{19} \text{ cm}^{-3}$.

Abuazoum et al. [782] have described a tapered gas-filled capillary discharge waveguide which utilises an alumina capillary with a linearly-varying inner diameter. Measurements of the variation of the transmitted laser spot size as a function of the input spot size indicated the formation of a plasma channel with an axial plasma density which changed from $1.8 \times 10^{18}$ to $2.9 \times 10^{18} \text{ cm}^{-3}$ over the 40 mm length of the waveguide.

### Targets incorporating structures for localised injection

Different approaches to controlling injection by density transitions have been proposed. Gonsalves et al. [658] use an integrated gas jet within a capillary discharge waveguide to produce localised injection via density gradient injection. Narrow PES beams with 5% energy spread and charge of $\simeq 10 \text{ pC}$ were observed with peak energies up to 400 MeV.

Schaper et al. [783] have incorporated multiple gas inlets or outlets to steady-state gas cells, with the objective of tailoring the longitudinal profile of the gas density. Similarly to above a nozzle has been included for controlling electron injection. Additionally, the density profile for exiting electron beam can be tailored to ensure optimum electron beam quality.
The density tailoring approaches above rely on the phase velocity of the wakefield changing and thus electrons becoming injected. Alternatively one can introduce a localised section of an impurity gas to employ ionisation injection. This approach was first explored by Pollock et al. [282] to demonstrate the generation of PES beams of 5% energy spread at 0.5 GeV using a 200 TW laser. The concept was also tested by de la Ossa et al. [652] in the context of beam-driven wakefield acceleration. Through simulations, a 2.6 GeV, 6% RMS energy spread beam is predicted as a result of localised ionisation injection.

### 32.2.4 Laser Confinement

At the intensity required for high gradient plasma acceleration, the laser beam has to be focussed to a spot size in the range $10^{-100} \mu m$ corresponding in vacuum to a diffraction length of the order of $3 \times 10^{-4}$ to 0.03 m. Assuming an average accelerating gradient in the range 1 - 10 GV/m, the distance required to achieve 1 (5) GeV is in the range 1 - 0.1 (5 - 0.5) m. As the laser diffraction in free space limits the volume over which a high intensity can be achieved, the laser beam has to be confined transversely to prevent diffraction. This can be achieved by employing the non-linear self-guiding effect or by imposing external guiding structures, such as waveguides. Two main types of waveguides are of interest at the intensity and plasma parameters required: plasma channels and capillary tubes or a combination of both.

#### Self-Guiding

##### Guiding mechanism

The self-guiding of short laser pulses in an underdense plasma is based on refractive guiding. This is achieved by laser-driven modifications to the refractive index of plasma yielding a maximum on axis, i.e. $\partial\eta/\partial r < 0$. This causes self-focussing of the pulse as laser wavefronts will curve towards the axis, where the phase velocity is the lowest. When the self-focussing effect induced by the laser balances the natural diffraction of the pulse, self-guiding can be achieved.

The refractive index response in the standard self-guiding theory is due to relativistic electron quiver motion [784,785] or self-channelling [786]. In the weakly relativistic regime ($a_0 < 1$) the refractive index of the plasma is given by,

$$ \eta \approx 1 - \frac{\omega_p^2}{2\omega_0^2} \left( 1 - \frac{a^2}{4} + \frac{\Delta n_p}{n_e} + \frac{\delta n}{n_e} \right) \quad (32.10) $$

for a linearly polarised laser. Laser pulses with an intensity maximum on-axis can undergo self-focussing; this is described by the $-a^2/4$ term in equation (32.10). The mass of the electrons in the laser field is increased by a factor of $\gamma_{\perp} = \sqrt{1 + a_0^2/2}$, meaning the axial electrons will have higher mass and thus respond slower to the laser field. This results in a spatially varying $\eta$, with the highest refractive index being in the regions with highest intensity. For laser pulses with durations much longer than a plasma wavelength, the laser can expel a fraction of electrons from the axis and set up a density channel. For very high intensities ($a_0 > 1$), self-channelling can also occur for short pulses, where the laser is guided in its own self-generated density cavity, which is sometimes known as a plasma “bubble” [787]. These effects are accounted for in the laser pulse guiding by the $\delta n/n_e$ term above; a reduced density on-axis results in a higher axial value for $\eta$. A pre-generated density channel, characterised by the $\Delta n_p/n_e$ term in equation (32.10), will also guide the pulse.
### Main properties of guided pulses

Self-guiding relies on non-linear self-focussing, which occurs for pulses with an intensity maximum on-axis. The guided spot size depends weakly on the laser power, with $k_p w_m = 2 (2P/P_c)^{1/6}$ in the weakly relativistic regime [344] and $k_p w_m = 2 (P/P_c)^{1/6}$ in the 3D non-linear regime [363]. Here, $w_m$ is the matched or guided mode size. As the laser power is usually chosen to be close to or a few times higher than $P_c$, the transverse extent of guided spots is of the order of a plasma wavelength $\lambda_p$. For ultra-short very intense pulses, the guided spot size can be recast to read $k_p w_m = 2\sqrt{a_0}$, showing that the matched mode size depends also on laser intensity.

### Parameters range

Self-focussing is possible for laser pulses with power that is larger than the critical power for self-focussing, $P_c = (n_c/n_e)17.4$ GW. The critical power is a function of plasma electron density; requiring higher laser powers for self-focussing to occur at lower background densities. For an example, a 30 TW laser can self-focus at $n_e = 1 \times 10^{18}$ cm$^{-3}$ whereas the critical power for self-focussing at $n_e = 1 \times 10^{17}$ cm$^{-3}$ is 300 TW.

The matched mode size will depend on the laser power and the plasma density. Thomas et al. [788] show that in order to achieve optimum coupling, the laser vacuum waist size $w_0$ should be close to the matched value in plasma. Given a fixed power laser for $w_0 < \lambda_p$, the laser diffraction is too fast for the plasma to provide a sufficient guiding response leading to pulse filamentation and breakup. Only when $w_0 \simeq \lambda_p$ is stable self-guiding achieved, which in turn results in high quality electron beams. In general, there exists no upper limit for the laser intensity for self-guiding as long as $w_0$ is suitably matched to the guided mode size.

Self-focussing is effective for the body of long pulses ($c\tau_L \gg \lambda_p$), but the tail of such pulses may undergo other laser-plasma instabilities. Early theoretical work [343,344] raised doubt on the effectiveness of relativistic self-guiding for short pulses ($c\tau_L \lesssim \lambda_p$). However, simulations [185] and experimental [789] work have shown guiding of the body of short pulses can be achieved via self-channelling and non-linear blowout.

It has been shown theoretically [790] and experimentally [791] that only the energy contained within the central spot is self-guided. For poor quality focal spots, where a lot of energy is displaced from the central FWHM of the pulse, the energy contained in the wings is lost. Hence maximising the energy in the focal spot enhances the guiding efficiency.

The guiding length is mainly limited by energy depletion of the main pulse. As the intense pulse propagates in the plasma, the front edge of the laser loses energy to the plasma and continuously etches away. This happens in a length characterised by the pulse depletion length $L_{dpl} = c\tau_L \omega_0^2 / \omega_p^2$. Once the pulse power falls below $P_c$, self-focussing will no longer occur and thus the pulse will undergo slow diffraction.

### State-of the art

Many experimental results have been obtained by employing self-guiding in laser wakefield accelerators. Two of the initial demonstrations of PES electron acceleration in 2004 used self-guiding [12,273]; details regarding these experiments are presented in Table 32.2. Kneip et al. [772] measured 0.8 GeV electron beams generated by 200 TW laser self-guided over $1 \text{ cm} \gtrsim 10z_R$ with plasma electron density $n_e = 5 \times 10^{18}$ cm$^{-3}$. Clayton et al. [19] report electron ionisation assisted injection and acceleration beyond GeV energies driven by a 250 TW self-guided over $1.3 \text{ cm} \simeq 15z_R$ at $n_e = 1.5 \times 10^{18}$ cm$^{-3}$. Wang et al. [792] reported the acceleration to 2 GeV of PES beams using a PW laser. However, they also noted that with that available laser power, theoretically they should be able to reach the 10 GeV level,
thus highlighting the importance of good focal beam quality for good self-guiding and acceleration.

A detailed study of self-guiding was performed by Ralph et al. [789]. It was shown that guiding over tens of Rayleigh lengths can be achieved by choosing a suitable plasma density. Self-guided laser modes over a distance of 8.5 mm were measured with $n_e = 4.5 \times 10^{18}$ cm.

### Expected extension of performance

The scalability of self-guiding has been experimentally verified in the density range of $1 \times 10^{18} - 2 \times 10^{19}$ cm$^{-3}$. Experimental characterisations of self-guiding at lower plasma densities have not been performed to date. However, simulations [793] predict self-guiding of petawatt pulses at plasma densities as low as $n_e = 1 \times 10^{17}$ cm$^{-3}$. Lowering the plasma density will require higher laser powers to facilitate self-guiding as $P_c \propto n_e^{-1}$.

The reliability of self-guiding is determined by the driving laser itself. As self-focussing is an inherently non-linear process high input laser stability is essential. However, as the guiding is driven by the laser pulse itself and relies on no external equipment, since the gas medium is typically ionised by the leading edge of the pulse, it is reliable so long as there is gas present in the target with a controlled value and distribution.

The stability of self-guiding is determined by the stability of the laser pulse intensity profile and the reproducibility of gas distribution.

The repetition rate of self-guided experiments has to date been limited by the laser repetition rate. The highest repetition rate, determined by the plasma relaxation time, has been discussed by authors presenting beam-driven collider designs and is typically of the order of 10s kHz [794]. Repetition rates nearer 1 MHz could be possible provided fast removal of the gas (100 m/s) is performed.

Additional repetition rate limitations will be imposed by the thermal load in the target. If 10% of a 10 J laser pulse firing at 10 kHz is left behind in the wakefields, this represents a thermal load of 10 kW in the target. Such a high heat load will require efficient cooling, or removal of unused wakefield energy by one or more trailing laser pulses.

## Guiding in Plasma Channels

Here we give a brief overview of the optical properties of plasma channels before describing several methods for creating them.

### Guiding mechanism

A plasma channel is a cylindrical plasma in which the electron density $n_e(r_\perp)$ varies with the transverse coordinate $r_\perp$; of course, the electron density may also vary with the longitudinal position, $z$, but this is usually of secondary importance.

For non-relativistic intensities, the refractive index of a plasma varies as,

$$ \eta = \sqrt{1 - n_e(\mathbf{r})/n_{cr}} \approx 1 - n_e(\mathbf{r})/2n_{cr}. \qquad (32.11) $$

Hence a column of plasma in which $n_e(r_\perp)$ increases smoothly with radial distance from the axis will have a refractive index which decreases away from the axis. As such, each transverse slice of the plasma column acts as a positive lens, which focuses light as it propagates along the axis. A plasma channel, therefore, is an example of a gradient refractive index (GRIN) waveguide.

An alternative configuration, known as a “hollow plasma channel”, is one in which the plasma column comprises a uniform density core surrounded by a coaxial cylinder
of higher density. Light propagating at sufficiently small angles to the axis of this structure will suffer total internal reflection at the core-cladding boundary, and hence be guided. This is an example of a step-index waveguide, and is analogous to a standard silica optical fibre.

Unless otherwise specified, we will use the term “plasma channel” when the electron density varies continuously with the transverse coordinate, and “hollow plasma channel” when the density varies discontinuously.

## Main Properties of Guided Modes

The mode structure of plasma channels has been described in detail by Milchberg et al. [795–797]. If we write the electric field of a mode as $E(\mathbf{r}_{\perp}, z) = u(\mathbf{r}_{\perp}) \exp(i\beta z)$, then the modes are given by solutions of,

$$ \nabla_{\perp}^2 u(\mathbf{r}_{\perp}) + k_{\perp}^2 u(\mathbf{r}_{\perp}) = 0, \qquad (32.12) $$

where $\nabla_{\perp}^2$ is the transverse Laplacian, and $k_{\perp}$ is given by,

$$ k_{\perp}^2(\mathbf{r}_{\perp}, \omega) = k_0^2 - \beta^2 - 4\pi r_e n_e(r_{\perp}) + 4\pi k_0^2 \chi(\mathbf{r}_{\perp}, \omega), \qquad (32.13) $$

in which $k_0 = \omega/c$ is the angular wavenumber in vacuum, $r_e$ is the classical electron radius, and $\chi(\mathbf{r}_{\perp}, \omega)$ is the total electric susceptibility of ions and neutrals in the plasma. Three categories of modes can be identified:

- **Radiation modes:** $k_{\perp}^2 > 0$ for all $\mathbf{r}_{\perp}$. In this case the solutions to (32.12) are freely propagating waves.

- **Bound modes:** $k_{\perp}^2 > 0$ within some region, say $|\mathbf{r}_{\perp}| < r_m$, and $k_{\perp}^2 < 0$ outside this. In this case, radiation in the inner region is trapped and propagates without loss. This is an idealisation, however, since in most real plasma channels the electron density falls to zero at large distances from the axis or there is a material boundary.

- **Leaky modes:** $k_{\perp}^2 < 0$ for $r_m < |\mathbf{r}_{\perp}| < r_{\text{out}}$ but $k_{\perp}^2 > 0$ elsewhere. In other words, the modes are partially confined for some inner region ($|\mathbf{r}_{\perp}| < r_m$), but some of this radiation can tunnel through the intermediate region to the outer region ($|\mathbf{r}_{\perp}| > r_{\text{out}}$) where it radiates away from the axis.

It is worth noting that, provided the contribution of the ions and neutrals to the refractive index can be ignored, the transverse profiles of the modes of the plasma channel are independent of wavelength. To see this we note that in this case (32.12) can be written as,

$$ [\nabla_{\perp}^2 - 4\pi r_e n_e(r_{\perp})] u(\mathbf{r}_{\perp}) = [\beta^2 - k_0^2] u(\mathbf{r}_{\perp}). \qquad (32.14) $$

The left-hand side of this equation is independent of wavelength, and hence so must be the eigenvalues ($\zeta^2 = \beta^2 - k_0^2$) and the eigenmodes $u(\mathbf{r}_{\perp})$. Of course, the propagation constant $\beta$ will depend on wavelength since $\zeta$ depends on $k_0$.

## Infinite Parabolic Channels

The infinite parabolic channel is an idealisation in which the electron density increases quadratically with radial distance to infinity. The electron density can be written in the form,

$$ n_e(\rho) = n_{e0} + \frac{1}{\pi r_e w_m^2} \left(\frac{\rho}{w_m}\right)^2, \qquad (32.15) $$
where $\rho$ is the radial distance from the axis, $n_{e0}$ is the electron density on axis, and $w_m$ describes the curvature of the channel.

In this idealised case the modes are bound, and described by Laguerre-Gaussian functions:

$$u(\rho, \phi) = \exp(im\phi) \left(2 \frac{\rho^2}{w_m^2}\right)^{\frac{m}{2}} L_l^m \left[2 \left(\frac{\rho}{w_m}\right)^2\right] \exp\left[-\left(\frac{\rho}{w_m}\right)^2\right], \quad (32.16)$$

where $l = 0, 1, 2, 3, \dots$ and $m = 0, 1, 2, 3, \dots$ are the radial and azimuthal mode numbers, and $L_l^m(x)$ is a Laguerre-Gaussian function. The propagation constant is given by,

$$\beta_{l,m}^2 = k_0^2 - 4\pi r_e n_{e0} - (2l + m + 1) \frac{4}{w_m^2}. \quad (32.17)$$

We see that the channel parameter $w_m$ is related to the transverse size of the modes. In particular, the lowest-order mode ($l = 0, m = 0$) is a gaussian beam of spot size (radius at which the amplitude of the field falls to $1/e$ of the value on axis) $w_m$. Hence the parameter $w_m$ is also known as the “matched spot size” of the channel.

## Infinite Power Law Channels

The parabolic channel described above can be generalised to the case of an infinite power-law channel in which the electron density is described by,

$$n_e(\rho) = n_{e0} + \frac{1}{\pi r_e w_m^2} \left(\frac{\rho}{w_m}\right)^s, \quad (32.18)$$

where $s \ge 2$. Calculating of the modes of such channels requires numerical solution of (32.12). However, it can be shown [795] that the lowest order modes of channels of this type are very close to Gaussian beam with a matched spot size of $w_m$. This is an important result since it shows that the transverse profile of the lowest-order mode does not depend strongly on the shape of the channel.

## Truncated Parabolic Channels

Real plasma channels are not infinite in extent. To gain an understanding of a more realistic scenario, Durfee et al. have also considered [795,796,798] the case of a plasma channel in which the electron density increases quadratically for $\rho \le r_m$, but has a constant value of $n_e(r_m)$ outside this region. Their analysis shows that low-loss propagation requires that the mode numbers satisfy:

$$2l + m + 1 < \frac{r_m}{w_m}. \quad (32.19)$$

## Capillary Discharge Waveguides

In a capillary discharge waveguide, a pulsed electrical discharge is used to create, and heat, a plasma contained within the capillary. In early work the plasma was formed by discharge ablation of a polypropylene capillary [799,800]. This approach has the disadvantages that: (i) the plasma contains partially ionised carbon ions which can
become further ionised by the guided laser pulse, leading to distortion or destruction of the plasma channel [801]; (ii) the capillary wall is ablated on each shot, limiting the electrical lifetime of the device.

These short-comings were overcome by forming the capillary in a refractory material, to reduce ablation, and filling it with gas: the gas-filled capillary discharge waveguide (CDW). Of particular interest is the case of a hydrogen-filled CDW [802] since the plasma formed by the discharge is nearly fully ionised, and hence the plasma channel is not distorted by further ionisation by the guided laser pulse [801].

In discharge-ablated and gas-filled CDWs, the plasma channel is formed by conduction of heat to the capillary wall. Since pressure across the capillary is equilibrated rapidly, the temperature gradient formed by heat conduction creates a density gradient: the plasma is hot, and of lower density, near the axis; and cooler and denser near the capillary wall [803–805].

### Parameter ranges

The guiding properties of hydrogen-filled CDWs have been measured interferometrically by Gonsalves et al. [806], yielding the following approximate scaling laws for the on-axis density and the matched spot size in square cross-section capillaries of side X:

$$n_{e0}[\text{m}^{-3}] = 0.87 n_{H_2}^i m^{-3} = 0.11 \times 10^{24} \qquad (32.20)$$

$$w_m[\mu\text{m}] = 6.6 \times 10^4 \left( \frac{X[\mu\text{m}]}{2} \right)^{0.651} (n_{H_2}^i m^{-3})^{-0.1875}, \qquad (32.21)$$

where $n_{H_2}^i$ is the initial density of hydrogen molecules. Although these scaling laws were determined for square cross-section capillaries, they are expected to be approximately correct for circular cross-section capillaries of diameter X [805]. The scalings were determined from measurements in the range $2 \times 10^{17} \text{ cm}^{-3} \le n_{e0} \le 3 \times 10^{18} \text{ cm}^{-3}$, and for capillaries of side 210 µm $\le X \le 465 \text{ µm}$; they should therefore be used with caution outside this domain.

The Berkeley group [518,807] have also deduced the axial electron density and the matched spot size of hydrogen-filled CDWs from measurements of the transverse oscillations of the centroid of low-intensity laser pulses and by spectral interferometry. These measurements were found to be in approximate agreement with eqns (32.20) and (32.21); however, there are differences, which illustrate that the properties of the channel depend in detail on the design of the capillary and of the discharge circuit.

### State-of the art

Hydrogen-filled CDWs have been operated with axial plasma densities in the range $n_{e0} = 7 \times 10^{17}–10^{19} \text{ cm}^{-3}$ [27,808,809]. The matched spot is typically in the range $w_m = 40–60 \mu\text{m}$. Plasma channels with lengths up to 90 mm have been demonstrated and used in electron acceleration experiments [27].

Hydrogen-filled CDWs have successfully guided relativistically intense laser pulses [351]. They have also been used extensively in electron acceleration experiments [27, 277,290,808,809], generating electron beams with energies up to 4.2 GeV.

Plasma density evolution of hydrogen-filled capillaries has been investigated using spectroscopic analysis of Balmer lines showing a good shot to shot reproducibility (shot to shot variations of the order of $\sim 10\%$) and reliability [810].

### Expected extension of performance

The Berkeley group have increased the pulse repetition rate of hydrogen-filled CDWs up to 1 kHz [811]. This was achieved by: (i) reducing the peak discharge current from the few hundred ampères used in early work to around 100 A; and (ii) water
cooling the capillary. No erosion of the capillary wall was observed within the 0.6 µm
measurement error after 10 million shots. Given that the wall could be eroded by a few
microns without affecting the guiding performance, operation at a 1 kHz repetition
rate should be possible for at least 20 hours [812].

Although the parameters have not yet been achieved simultaneously, the summary
of the state of the art is that plasma channels with lengths of order 100 mm, an axial
density as low as $n_{e0} \approx 5 \times 10^{17} \text{ cm}^{-3}$, a matched spot size of 50–60 µm, and a pulse
repetition rate up to 1 kHz would seem to be possible with this approach.

It is worth noting that one disadvantage of the CDW is that optical access to the plasma channel is difficult owing to surface roughening of the inner wall by the electrical discharge, although it may be that this can be alleviated by using lower discharge currents [812]. A second issue to be aware of is that jitter in the pointing of the driving laser can lead to laser-induced damage at the entrance to the capillary. Finally, it is not known whether it will be possible to decrease the axial electron density below $n_{e0} \approx 5 \times 10^{17} \text{ cm}^{-3}$.

## Plasma Channels Formed by Hydrodynamic Expansion

### Channel formation

As first described by Durfee and Milchberg [345], plasma channels can also be formed by hydrodynamic expansion of a hot plasma column into a cold gas. If a well defined boundary is formed between the heated plasma and the surrounding gas, the large pressure gradient drives a shock wave as the hot electrons move out, pulling the ions at the ion sound speed $c_s = (Zk_B T_e / M_{\text{ion}})^{1/2}$. Behind the shock front the electron density increases with radial distance, and hence a plasma channel is formed.

### Parameter ranges

In early work the initial plasma column was formed and heated using ≈ 100 ps pulses from a Nd:YAG laser; an extended focus was produced using an axicon lens [345, 795, 796, 812, 813, 814]. In this approach the initial plasma is formed by a seeded avalanche breakdown, the seed electrons being formed by multiphoton ionisation of the target gas. These seed electrons are rapidly heated by inverse bremsstrahlung, leading to additional collisional ionisation and heating of the plasma.

Efficient plasma heating requires that the intensity of the heating laser is less
than approximately $10^{13} \text{ W cm}^{-2}$, and in order to reach temperatures of 10–100 eV
it is necessary that the laser pulse duration is of order 100 ps. These parameters
limit the target to reasonably high-Z gases (e.g. Ar), for which the weakest bound
valance electrons can be ionised by multi-photon or barrier suppression ionisation.
As a consequence the plasma channel will not be fully ionised, although the ions in
the plasma channel will typically have a closed shell (e.g. Ar$^{8+}$). The plasma channel
would, ideally, be fully ionised so that it cannot be distorted by further ionisation by
a guided laser pulse with an intensity of order $10^{18} \text{ W cm}^{-2}$. To address this issue,
Volbeyn et al. developed the “ignitor-heater” technique, in which the target gas is
ionised by a short, intense laser pulse (e.g. 100 fs, $10^{14} \text{ W cm}^{-2}$), and subsequently
heated by a long, energetic laser pulse (10–100 fs, 100 mJ) [815]. This approach has
been used to generate plasma channels in nitrogen and fully-ionised hydrogen [11,815].

Efficient plasma heating by collisions also requires that the initial target density
is relatively high, which restricts the axial electron density of the plasma channel
to $n_{e0} \gtrsim 10^{19} \text{ cm}^{-3}$. To overcome this limit, the Milchberg group have studied the
formation of plasma channels by hydrodynamic expansion of laser-heated clusters
[816,817]. Within each cluster, the local density is near that of a solid, and hence it
can be ionised, then rapidly collisionally heated by a picosecond-duration laser pulse;