once heated, the gas clusters explode to form a uniform, hot plasma column, which will expand radially to form a plasma channel. The use of a clustered gas therefore allows the use of a target gas with a low initial *average* density. This approach has been used to generate fully ionised plasma channels with $n_{e0} \approx 10^{18} \text{ cm}^{-3}$.

## State-of the art

Durfee et al. have reported [796] the formation of plasma channels of lengths up to 15 mm with $n_{e0} \approx 5 \times 10^{18} \text{ cm}^{-3}$ and $w_m = 25–30 \mu\text{m}$. The $1/e$ intensity attenuation length for waveguides of this type has been measured to be $L_{1/e} \approx 350$ mm. Geddes et al. [11] used the ignitor-heater approach to generate quasi-monoenergetic electron of energy 80 MeV in 2 mm long, $n_{e0} \approx 2 \times 10^{19} \text{ cm}^{-3}$ plasma channels formed in hydrogen gas. The Milchberg group has also demonstrated the formation of longitudinally modulated plasma channels in clustered-gas targets [817] suitable for quasi-phase-matched electron acceleration [818].

## Expected extension of performance

It is worth noting two significant advantages of plasma channels formed by hydrodynamic expansion which both arise from the fact that the channels are formed in free space: (i) it is straightforward to probe the channels transversely; and (ii) fresh channels can, in principle, be created with a high repetition rate, the upper limit being determined by the repetition rate of the channel-forming laser, and the time taken for fresh gas to replace a used channel. It should therefore be possible to produce plasma channels of this type at kilohertz pulse repetition rates. The channels can also be expected to be reliable, with a stability determined by that of the channel-forming laser.

Previous work suggests that hydrodynamic plasma channels could be generated with an axial density as low as $n_{e0} \approx 10^{18}–5 \times 10^{18} \text{ cm}^{-3}$, with lengths of a few tens of mm, and a matched spot size of $w_m = 25–30 \mu\text{m}$.

A significant issue with this approach is the difficulty in reducing the on-axis plasma density below $n_{e0} = 10^{18} \text{ cm}^{-3}$. It may be possible to reduce the axial plasma density by using optical field ionisation (OFI) to form the initial plasma column [348], since with this ionisation mechanism the heating of the electrons depends on the polarisation of the laser field, and not on the initial density. Initial simulations of OFI-heated hydrodynamic plasma channels are promising [348], but more remains to be done. It is worth noting that Lemos et al. have shown that hydrodynamic plasma channels with $n_{e0} \approx 10^{18} \text{ cm}^{-3}$ can be formed in hydrogen and helium following OFI [346,347], but generation of plasma channels at lower density has not been reported.

## Hollow Plasma Channels

An ideal hollow plasma channel comprises a cylindrical, evacuated core surrounded by a uniform “cladding” of plasma with an electron density $n_w$. As first described by Chiou et al. [819,820], an intense laser pulse (or a particle beam) propagating along the axis will excite surface currents on the core-cladding boundary which generate electromagnetic fields which extend into the core. These wakefields are therefore fundamentally different from the electrostatic fields arising from the density modulations generated by a driving beam propagating in a homogeneous plasma. The wakefields generated in a hollow plasma channel are about a factor of two lower [819] in amplitude than would be generated by the same driver propagating in a uniform plasma of density $n_w$, but they offer several distinct advantages:

- The accelerating field is transversely uniform in the core region

- For a relativistic particle the transverse focussing forces are weak and linear, helping to preserve emittance
- Scattering of the accelerating bunch is avoided, preventing emittance growth; this is likely to be particularly important for plasma-based colliders.

Schroeder et al. [821] have considered the case of a partially filled hollow channel, in which the core region has an electron density $n_{core}$. The show that the accelerating fields are governed by $n_w$, but that the focussing is determined by $n_{core}$, and that therefore matched beam propagation is in principle possible.

### Guiding mechanism

In a hollow plasma channel the refractive index of the core ($\eta_1 = 1$) is greater than that of the cladding ($\eta_2 = (1 - n_w/n_{cr})$), and hence light can be guided through the core by total internal reflection, exactly as in a conventional step-index fibre.

### Main properties of guided modes

The modes of a hollow plasma channel are the same as in a step-index fibre; since in this case $\eta_1 - \eta_2 \ll 1$, these can be approximated by the linearly-polarised modes. For radiation polarised in the x-direction the lowest order linearly-polarised mode (LP01) can be written as,

$$E_x = E_0 \begin{cases} J_0(hr) \exp(i\beta z) & r < a \\ \frac{J_0(ha)}{K_0(qa)} K_0(qr) \exp(i\beta z) & r > a \end{cases} \quad (32.22)$$

where $a$ is the core radius, $h^2 = k_0^2 - \beta^2$ and $q^2 = \beta^2 - \eta_2^2 k_0^2$. The propagation constant $\beta$ is determined from the following characteristic equation:

$$h \frac{J_1(ha)}{J_0(ha)} = q \frac{K_1(qa)}{K_0(qa)}, \quad (32.23)$$

where $J_n(x)$ is the Bessel function of the first kind, and $K_n(x)$ is the modified Bessel function of the second kind.

The group velocity of the mode is found to be $v_g = (\beta/k_0)c$, which, for typical parameters, is close to $c$.

### Parameter ranges and state of the art

Although hollow plasma channels have been much discussed there are only a few examples of their generation in practice. Kimura et al. [822] have described a method for generating a partially-filled hollow plasma channel by directing a high-order Bessel beam through a target gas: in a high-order Bessel beam the locus of peak intensity is a narrow ring; this can ionise a target gas to form an annulus of plasma, surrounding an unionised core. Kimura et al. describe the parameters for a partially-filled hollow channel of length 100 mm and 22 µm wall radius. The Ti:sapphire laser parameters required to generate this channel are: an energy of 50 mJ and a pulse duration of 60 fs.

Gessner et al. [51] have demonstrated the use of this method to create a partially-filled hollow plasma channel of length 80 mm and wall radius $\approx 256$ µm. This was used to generate a plasma wakefield with a positron driver beam.

### Expected extension of performance

It is difficult to predict the future performance of hollow plasma channels since they would seem to be at an early stage in their development.

It is worth noting that for the channels described by Kimura et al. the core has the same atomic density as the wall; as such, full ionisation of the core would destroy the channel, and hence these channels can only be used with low intensity drivers.
For example, in the work described by Gessner et al. it was necessary to reduce the density of the positron driver beam to prevent ionisation of the gaseous core. Similar considerations would apply to the application of these channels to laser-driven plasma wakefields; in this context it is worth pointing out that the driving the wakefield by a train of low-intensity laser pulses [607] could be advantageous since it might be possible to prevent additional ionisation of the core, whilst driving a wakefield of useful amplitude.

## Guiding in Capillary Tubes

### Guiding mechanism

When a capillary tube is used the laser beam is guided by reflections at the inner capillary wall [350], and laser guiding can thus be achieved in vacuum or at low plasma density. This guiding scheme does not rely on laser power, or plasma density, and provides the opportunity to explore a large domain of laser-plasma parameters. Laser guiding can, in principle, be achieved inside capillary tubes with total or partial reflection at the inner wall, depending on the material of the tube wall, which may be either a conductor or a dielectric material. Metallic tubes could be used to guide the laser beam without loss at the inner wall. In practice, their surface is usually not optically smooth for the laser wavelength and tube diameters used for laser guiding at high intensities. Dielectric capillaries, such as glass capillaries, are optically smooth and can be manufactured with a good reliability for a large range of inner diameter (10 µm to several mm), wall thickness (50 µm to several mm) and lengths (mm to meter).

### Main properties of guided modes

Quasi transverse electromagnetic waves with wavelength smaller than the tube radius are eigenmodes, described by Bessel functions for cylindrical dielectric capillary tubes. An incident linearly polarised gaussian laser beam can be efficiently coupled to the linearly polarised family of hybrid modes, namely the $EH_{1m}$ modes [350].

The electric field is damped along the direction of propagation, $z$, as each reflection at the dielectric capillary wall is associated with a refracted fraction of the laser beam inside the dielectric wall. This refracted fraction is minimum for the smallest perpendicular wavenumber, corresponding to the grazing incidence. Laser damping is usually described by the *attenuation length* $L_m^l$, defined as

$$L_m^l = \frac{1}{k_m^l} = \frac{2k_{z0}^2 R_{\text{cap}}^3 \sqrt{\epsilon_r - 1}}{u_m^2 (1 + \epsilon_r)}. \qquad (32.24)$$

After a propagation distance of $L_m^l$, the field magnitude decreases by a factor $1/e$ and the beam energy by a factor $1/e^2$, owing to refraction losses. $L_m^l$ drops rapidly with increasing mode order, which means that higher-order modes are damped over shorter distances. Therefore, the use of the fundamental mode is preferable to achieve laser guiding over a long propagation distance.

The *group velocity* is determined from the dispersion relation of an electromagnetic wave in a capillary tube, $k_0^2 = (k_z^2 + k_{\perp m}^2)$, for $k_{\perp m}^2 \ll k_0^2$, as

$$v_{\text{gm}} \approx c \left( 1 - \frac{k_{\perp m}^2}{k_0^2} \right)^{1/2}. \qquad (32.25)$$

The group velocity is close to the velocity of light in free space, and decreases as the mode order increases. This again supports the use a lower-order mode with higher group velocity, corresponding to a higher phase velocity for the wakefield.
Another important aspect associated with the use of a capillary tube is the threshold of material damage at the inner wall where reflection occurs, which determines the ability of capillary tubes to guide intense lasers. It is linked to the *contrast* between the intensity at the capillary axis and at the wall, which is one order of magnitude larger for the fundamental mode compared to the ninth mode. Once again, it emphasises the advantage of using the fundamental mode. For a glass capillary, the ionisation threshold is of the order of $10^{14} \text{ Wcm}^{-2}$ for an 800 µm laser pulse with duration shorter than or of the order of 100 fs. [823]. The maximum intensity on-axis which can be guided by a capillary of 50 µm radius on the fundamental $\text{EH}_{11}$ mode without wall ionisation is thus of the order of $10^{19} \text{ Wcm}^{-2}$.

## Coupling

When a laser beam is focussed at the entrance of a capillary tube, its energy has to be coupled to the capillary eigenmodes before propagation. The *coupling coefficient* of an incident Gaussian beam on the first four eigenmodes depends on the ratio of capillary radius to laser waist, $R_{\text{cap}}/w_0$. Monomode coupling can be achieved when $R_{\text{cap}}/w_0 \simeq 1.55$ (or $w_0/R_{\text{cap}} \simeq 0.65$). In this case, almost 98% of the incident laser energy is coupled to the fundamental $\text{EH}_{11}$ mode, and only 1% of laser energy is coupled to higher-order modes. The remaining 1% of laser energy is the energy contained in the wings of the gaussian function outside the capillary diameter, and it is lost into the material at the front surface of capillary tube.

The *quality of coupling* of laser energy to the capillary tube depends on the contrast in time and space in the entrance plane of the capillary tube, and on the pointing stability. At high intensity, the lifetime of the capillary tube can also be shortened by pointing fluctuations. The effect of pointing fluctuations and symmetry variations on the coupling of a laser beam to a capillary tube radius have been studied theoretically and confirmed experimentally [824]. The angle between the laser axis and the capillary tube axis has to be smaller than 5 mrad and the displacement of the laser spot centre to the centre of the tube should be smaller than 10% of the tube radius for matched condition to the fundamental mode.

## Electron acceleration

Simulations [353] show that electron acceleration to several GeV can be achieved. Some issues occurring at coupling were pointed out: the excitation of higher modes by a gaussian pulse at the % level introduces transverse modulation of the laser envelope, which can in turn defocus electrons. To mitigate this issue, either the pulse structure in the entrance plane should be closer to a Bessel function, selecting only the fundamental mode, or electrons could be injected into the accelerating structure a few cm after the entrance, when the modulation is smoothed out.

Alternatively, a slightly non linear regime favours a compensation by the plasma of this locally transverse modulation. An other potential solution is the presence of a low density plasma channel [825].

To summarise, quasi-monomode guiding can be selected by coupling the input laser energy to the fundamental $\text{EH}_{11}$ mode: 98% of the energy of a gaussian beam can be coupled to the fundamental mode for a waist size $w_0 = 0.645 R_{\text{cap}}$. This mode is preferable for laser wakefield acceleration as its group velocity is close to the velocity of light in free space, its damping factor is a minimum for a given capillary radius and wavelength, and the transverse electric field exhibits a variation similar to a gaussian beam.
### Parameter range

Laser guiding on the fundamental mode exhibits the best properties for laser-plasma acceleration. Conditions on the main parameters are determined as follows:

**Laser intensity:** maximum value determined by material damage at the wall. Higher for larger diameter capillary tube.

**Spot size:** matched value depends on energy distribution, usually a fraction of the capillary radius (from 0.6 to 1 for a Gaussian function or Airy function respectively).

**Plasma density:** can be chosen from zero to the value where self-focussing is significant as determined by laser power becoming of the order of the critical power.

**Plasma can be homogeneous or exhibit a density profile:** the condition for mode coupling in varying density profile needs to be studied.

**Damping length of laser energy along the propagation direction:** is proportional to the cube of the tube radius and can be extended to several metres.

### State-of-the-art

Guiding in capillary tubes at low intensity has been measured and corresponds to theoretical predictions in terms of coupling and transmission. The sensitivity of the coupling and transmission to misalignments has been studied theoretically: predictions are in excellent agreement with experimental results and are discussed in Ref. [824].

**Monomode guiding** has been demonstrated experimentally for laser intensities of the order of $I_0 \simeq 10^{16} \text{ Wcm}^{-2}$ in a vacuum [826] and the transmission has been measured for different values of the capillary tube radius. The measured transmissions correspond to the predicted values for quasi-monomode guiding, which was thus measured in a vacuum over a distance of 100 Rayleigh lengths. Analytical predictions for coupling conditions and damping length have been confirmed experimentally for tubes under vacuum.

The excitation of plasma waves over a length of up to 8 cm was demonstrated by guiding intense laser pulses through hydrogen-filled glass capillary tubes [525]. Laser guiding at input intensities up to $10^{18} \text{ Wcm}^{-2}$ was achieved with more than 90% energy transmission in evacuated or hydrogen-filled gas tubes up to 8 cm long, with a radius of $R_{cap} = 50 \mu\text{m}$. To investigate the linear regime, the input intensity was kept below $3 \times 10^{17} \text{ Wcm}^{-2}$, and the electron density was varied in the range $0.05 - 5 \times 10^{18} \text{ cm}^{-3}$. The plasma wave amplitude was diagnosed by analysing the spectrum of the transmitted laser radiation.

The longitudinal accelerating field, inferred from a detailed analysis of laser wakefield dynamics in capillary tubes and numerical simulations [827], is in the range of 1–10 GV/m for an input laser intensity of the order of $I_0 \simeq 10^{17} \text{ Wcm}^{-2}$. The average product of gradient and length achieved in this experiment was thus of the order of 0.4 GV at a pressure of 50 mbar; it could be increased to several gigavolts by increasing the length and diameter of the capillary tube with higher laser energy.

### Expected extension of performance

Scalability can be achieved easily by the use of longer capillary tube. The damping length due to refraction losses limits the maximum value of propagation to values which can be larger than the dephasing length. As the damping length is strongly dependent on capillary radius, the tube radius should also be increased. Typically, guiding can be extended to the metre range for capillary tube radius of the order of 100 microns. Plasma density has no lower limit for guiding, and it can be matched to resonant conditions for plasma wave excitation independently of guiding condition.

**Reliability, stability, repetition rate:** these three properties mainly depend on laser beam quality at the entrance of the capillary tube and reproducibility of plasma density.
As guiding is passive the reliability of the accelerating structure is related to the reliability of plasma wave characteristics, determined by the stability of laser coupling, and the reproducibility of the gas concentration at the time of interaction with the laser.

Stability of laser parameters in the focal plane is required. The required laser pointing stability at the entrance of the capillary was calculated and measured by Veysman et al. [824], to achieve a transmission of laser energy within 5% of the maximum value, the angle $\theta_{inc}$ between the laser and tube axis should be smaller than 5 mrad, with a displacement between the centre of the laser spot and the centre of the tube smaller than 10% of capillary tube radius. Most of the energy is guided within the fundamental mode for a symmetrical spot at the entrance with angle $\theta_{inc}$ smaller than 1.5 mrad.

The stability of plasma density is mostly determined by the gas injection system. The standard deviation of density fluctuations was measured by Ju et al. [352] to be of the order of 15% in the stationary state following the injection of gas. It should be possible to reduce this value to a few percent by improving the gas feed system.

A repetition rate at 10 Hz should be possible provided the laser quality and pointing is controlled.

### 32.2.5 Injection Techniques for the LPI

#### Self-Injection (SI)

*Physical mechanism*

In the self-injection scheme a large amplitude plasma wave is excited in the wake of the laser pulse. With the laser intensities currently achieved, the self-injection process relies on the laser self-focussing leading to a lengthening of the bubble. As a consequence, some electrons passing through the bubble during its lengthening gain enough energy to be injected in the plasma wave [533]. For sufficiently high laser intensities ($a_0 > 3 - 4$) [185,639] electrons at the back of the bubble near the laser axis can be injected in the cavity, where they experience a longitudinal accelerating field.

Perturbation of the accelerating field due to the field generated by the accelerated electron beam can lead to increased energy spread and unintended trapping of background electrons generating the so-called “dark current”. Beamloading effects can eventually cancel the accelerating field and limit the charge of the accelerated beam.

In experiments, for a given laser system, a density threshold is commonly observed, below which no electron beam is generated. The highest beam quality (energy spread, stability) and electron energy are achieved for a working point just above the density injection threshold [828]. Nevertheless, the plasma density needs to be high enough to accelerate a significant charge and to reach electron self-injection conditions sufficiently early in the interaction for acceleration to occur after injection. Mangles et al. [828] determined a threshold on laser power to achieve self-injection, taking into account the proportion of laser energy contained in the FWHM of the laser pulse $\alpha$, as a function of plasma electronic density. This threshold is illustrated in Figure 32.3.

*State-of-the-art*

Sävert et al. [533] use gas jets as targets to measure non-linear lengthening of the first plasma period behind the laser. These measurements provided experimental
<figure><img src="image_279.png" /><figcaption>Fig. 32.3. Laser power threshold for self-injection as a function of plasma electronic density for a laser wavelength of $\lambda = 0.8$ µm and assuming a gaussian energy distribution ($\alpha = 0.5$).</figcaption></figure>

evidence that in that regime, self-injection was caused by the lengthening of the first plasma period. Electron acceleration to energies of hundreds of MeV are achieved experimentally by SI [11, 12, 273, 533, 829, 830]. The generation of high quality electron beams with a charge of tens of pC is rarely observed, as the highest charge (50-100 pC) is accompanied by large energy spread. However the highest electron energy achieved in LWFA was obtained with SI combined with laser guiding, demonstrating 6 pC of charge at 4.2 GeV in a single stage with an energy spread as low as 6% (RMS) and a divergence below 1 mrad [27].

### *Advantages and disadvantages*

Self-injection is the simplest and most straight-forward injection scheme to be implemented in Laser Wakefield Acceleration (LWFA) [180]. However, in the self-injection scheme, electron injection and trapping in the plasma wave continues until the amplitude of the wakefield is reduced through beam loading, that is the electric field generated by the trapped electrons reduces and finally cancels the wakefield, or laser energy depletion. Typically, self-injection is accompanied by a large energy spread of the accelerated electron bunch. Within the self-injection scheme highest quality electron beams are achieved in the bubble regime [787], where the laser with relativistic laser intensity is focussed to a sphere of radius shorter than the plasma wave wavelength. The laser and plasma parameter range for the generation of high-quality electron beams is generally narrow [533] and shot-to-shot fluctuations are typically large in this acceleration regime.

As the self-injection scheme relies on the non-linear evolution of the plasma wave, the stability of the electron beam can be unacceptable for many applications.

### *Expected extension of performance: scalability, reliability, stability*

With this injection scheme, electron energy can be increased to the 5 GeV level, considering 4.2 GeV have already been achieved [27]. However, since this scheme relies on the non-linear evolution of the plasma wave, it needs precise control of the laser and plasma parameters to ensure stability and reproducibility of the electron bunch properties.
## Colliding-Pulse Injection (CPI)

### Physical mechanism

The colliding-pulse injection scheme is based on the use of two laser pulses: a drive laser pulse creates the plasma wave without injecting electrons and a second laser pulse, called the injection pulse, is used to locally trigger the injection [368]. The interaction of the two laser pulses creates a beat-wave pattern, which can, if the intensity is high enough, give a sufficient velocity to some electrons for them to be trapped.

### State-of-the-art

This technique was used to produce electron bunches of ~100 to ~200 MeV. Relative energy spread as low as $\sigma_E/E \sim 1\%$ have been produced for a beam charge of the order of $Q \sim 10$ pC [657,831,832].

### Advantages and disadvantages

This technique allows control of the location of injection by adjusting the location of the laser pulses interference and consequently provides a mean to control the acceleration length and the electron energy. Though relatively low charge electron bunches are produced with current experimental parameters, this scheme also allows control of the injection volume by controlling the intensities of the laser pulses, and therefore the energy spread. This technique imposes particular challenges on the laser system. It requires the use of two laser pulse with good stability for both laser pulses to achieve low fluctuations of electron bunches properties. Furthermore, in a directly counter propagating geometry, laser systems would require extra protection to prevent propagation of laser energy back down the laser amplifier chain.

### Expected extension of performance: scalability, reliability, stability

Colliding pulse injection can potentially be used to inject and accelerate electrons to energy levels similar to SI given the same length of plasma. However as this scheme relies on two laser pulses, a good stability of the two laser pulses is required for stable operation.

## Density Gradient Injection (DGI)

### Physical mechanism

Control of electron injection can be achieved through tailoring of the plasma density profile [275,833]. The relativistic plasma wave wavelength, $\lambda_p = 2\pi c\sqrt{\varepsilon_0 m_e / n_e e^2}$, being inversely proportional to the electronic density, a decreasing density gradient leads to an increase in this plasma wave wavelength, which reduces the wake phase velocity. In general, injection of electrons in the plasma wave occurs when the velocity of the background electrons approaches the wake phase velocity. The reduction of the phase velocity lowers the injection threshold and some background electrons can then be injected in the wakefield.

Injection through plasma density profile tailoring has been investigated both numerically and experimentally for a number of plasma density profiles and/or laser parameters. In most cases, plasma density profiles consist of two plasma density plateaux of electron density $n_{e1}$ and $n_{e2}$, both below the self-injection threshold, with $n_{e1} > n_{e2}$ and connected by a negative density gradient. Depending on the density gradient length $L_g$ two regimes can be distinguished. For $L_g > \lambda_p$, a slowing down of the plasma wave phase velocity occurs that lowers the threshold for wave-breaking and causes trapping of background electrons at a specific position. For a sharp density transition ($L_g \le \lambda_p$), a sudden increase in the plasma wavelength is
produced leading to rephasing of the plasma electrons into the accelerating phase of the plasma wave.

## State-of-the-art

The density gradient can be the falling edge of a single gas jet [17]: in this case the electron energy is low as electrons are injected at the exit of the density profile.

The density gradient can also be produced by using a secondary laser pulse [16, 834], by a shock generated by introducing a sharp object in the gas flow of a jet [18,381,659], or by using two separate overlapping gas jets [32,835]. In those cases, the location of the density gradient can be changed relative to the density profile and the energy of the electrons can thus be tuned.

DGI has been used to achieve electron beams with energy in the range $E \approx [25 - 600]$ MeV, with energy spreads of the order of $\sigma_E/E \approx [1 - 25] \%$, and with a charge in the range $Q \approx [1 - 1000]$ pC [17,32,381,659,834].

## Advantages and disadvantages

With respect to self-injection in a homogeneous plasma, in the scheme based on injection in a steep density downramp, higher quality, nearly dark-current free electron beams are obtained. Injection probabilities close to 100% and improved (with respect to self-injection) shot-to-shot stability are generally achieved in experiments. Shot-to-shot fluctuations as low as ~2% of the electron energy, ~6% of the charge and pointing stability better than 1 mrad have been reported [658].

Experimental studies indicate that a good control of the plasma density profile is needed, small changes can affect the electron beam quality and the stability. One of the major difficulties of this injection technique is the realisation and the control of the sharp density downramp. More investigation on the realisation of the density transition is needed, with particular attention to the robustness and the life-time of the adopted technique.

## Expected extension of performance: scalability, reliability, stability

This scheme relies on a precise density profile and the stability of this scheme is therefore linked to the reproducibility of the density profile as well as the laser stability. The possibility that it can lead to injection at lower densities than self-injection could lead to higher energy gain.

## Ionisation-Induced Injection (III)

### Physical mechanism

The ionisation-induced injection scheme depends on the addition of a small fraction of high-Z gas to the low-Z gas, Z being the atomic number. Outer shells of the high-Z atoms are ionised at relatively low intensities (typically below $I_L = 10^{16}$ W/cm$^2$) so that electrons appear at the front of the laser pulse and contribute to the plasma wake. Inner-shell electrons are ionised closer to the laser intensity peak and are more likely to be injected in the wake. As illustrated in Figure 32.4, an electron born close to the laser peak intensity (at $k_p\xi_1$ in Fig. 32.4) experiences a larger difference of potential than an electron born at the front of the laser pulse (at $k_p\xi_2$) and is thus more likely injected into the wake. Chen et al. [281] describe how an electron born stationary inside the wake is turned around by the potential of the non-linear wake provided that the wakefield driving laser potential exceeds:

$$a_0 \gtrsim 1.7(1 - n_e/n_c) \qquad (32.26)$$
<figure><img src="image_280.png" /><figcaption>Fig. 32.4. Example of laser envelope and wake potential energy for $a_0 = 2.5$.</figcaption></figure>

## State-of-the-art

This technique was first observed in plasma wakefield experiments to observe the acceleration of very narrow energy spread electron beams directly from a plasma in the blow-out regime [836]. A laser wakefield experiment performed in hydrogen filled capillaries measured 150 MeV electrons with < 10% energy spread at very low laser intensity $a_0 < 1$, which was coupled to rapid ionisation of the target with arrival of the driving laser pulse [277]. Simulations performed later demonstrated that III of impurity atoms from the surface of the capillary walls, coupled with laser pulse intensity amplification such that the trapping threshold was just reached, could explain the appearance of these PES beams [837]. Subsequent experiments were able to utilise this technique with purposely introduced dopant species to produce electron bunches of $Q \simeq 1$ pC to $Q \simeq 100$ pC and relative energy spreads of the order of $\sigma_E/E \sim 5$ to $\sim 10\%$ [278,282,773,838,839].

## Advantages and disadvantages

This technique provides a way to trigger electron injection into the accelerating phase; injection continues as long as the laser intensity is high enough to ionise inner shell electrons, leading to accelerated electrons with broad energy distributions [278,279, 840].

The energy spread can be reduced by tuning the laser intensity to be above the threshold only in a small volume of interaction, at the expense of the accelerated charge. Using carefully controlled low laser intensities, the maximum intensity achieved through pulse compression can be enough to allow trapping for only a small duration [837]. It is also possible to use structured targets composed of a region containing a gas mixture for the injection followed by a region of pure gas to further accelerate injected electrons [282,773], or tailored density profile to combine ionisation-induced injection to a density gradient [838]. A similar effect has been suggested by using a secondary high-intensity laser pulse which acts to ionise atomic electrons which otherwise would not be liberated by the wakefield driving pulse. By using fast focussing, the volume of which this electron liberation occurs can be small leading to PES beams [681,841].

The main benefits of the III technique are that it is very easy to implement experimentally, the charge can be increased compared to self-injection[840], it can
lower the intensity threshold compared to SI [281] (which is beneficial for a potential increase in repetition rate) and can potentially reduce the transverse emittance [281].

*Expected extension of performance: scalability, reliability, stability, repetition rate*

This scheme can potentially be scaled up to higher energies but generally produces broad electron energy distributions. However, combined with either DGI or CPI, it is a way to increase the injected charge. This combination of mechanisms offers tunability of charge, energy, energy spread, and emittance by increasing the number of control parameters, together with increased complexity of implementation and higher constraints on stability.

## Comparison of Injector Performance

In Tables 32.2–32.5 a summary of electron properties achieved by each injection technique is presented, corresponding to experimental results found in the cited references. Selected publications were chosen for electron parameters close enough (less than one order of magnitude in electron energy) to the range expected for EuPRAXIA. The last two columns on the right hand side of each table are the target parameters for plasma, laser and electrons, identified in the EuPRAXIA baseline as injectors at 150 MeV and 1 GeV.

References in these tables were selected for their proximity to EuPRAXIA target parameters, first using the energy, then the energy spread. Some references were included because they highlight an original experimental implementation of the scheme considered such as ref [834] in Table 32.4. However there may be other publications relating results closer to EuPRAXIA target parameters that the authors are unaware of.

*Discussion of Table 32.2 Self-Injection*

Faure *et al.* [273] observed 170 MeV energy beams with 24% energy spread, 10 mrad divergence and a charge of 0.5 nC. Geddes *et al.* [11] obtained electron beams with 86 MeV energy, 300 pC, 2% energy spread and 1–2 mm mrad normalised RMS emittance. In this work the laser is guided over $10 z_R$ in a laser-preformed channel. It should be noted that the total charge in references [11] and [273] was evaluated with an Integrating Current Transformer (ICT). In a later publication [536], it is highlighted that the ICT used in such conditions yield values for charge that are on average an order of magnitude too high. To take this into account the values included in Table 32.2 for these reference are the published results divided by ten.

Banerjee *et al.* [829] reported on electron beams with 100–800 MeV energies, 1–4 mrad divergence and 5–25% energy spread.

Mangles *et al.* [12] obtained 50–80 MeV beams with down to 3% energy spread, 90 mrad divergence and a charge of 22 pC. Froula *et al.* [830] observed electron energies up to 720 MeV with divergence 2.85 mrad, an estimated normalised emittance of 5 mm mrad and a charge of 6.7 pC.

*Discussion of Table 32.4 Density-Gradient Injection*

In Faure *et al.* [834] a relatively sharp (30 µm density gradient) transition is generated using a crossing laser beam to create a channel. Electron beams with 50–200 MeV energy, 40 ± 20 pC charge and 5 ± 2 mrad divergence are produced. The injection probability is 95%, but large shot-to-shot fluctuations of the energy and the energy spread are observed. In particular, the energy spread increases with charge, which is attributed to beamloading effects. A comparison with the colliding pulse injection scheme at the same density is performed. The colliding pulse scheme leads to better stability, whereas better collimation of the electron beam occurs in the density gradient injection scheme.
In Schmid et al. [18] a knife edge is inserted into the gas jet to produce a shock front with estimated density transition width of 5 µm. Electron beams with 23 MeV energy, 9% energy spread, 8.9 mrad divergence and 3.3 pC charge are generated with up to 95% injection probability.

Buck et al. [659] produce a sharp density transition by insertion of a knife edge into the gas-jet target. They obtain up to 133 MeV energy electron beams with 6.5 MeV energy spread and 1.2 pC charge. Higher charge beams are obtained with 50 MeV energy and 5.3 MeV energy spread.

Gonsalves et al. [658] report on experiments with a gas-jet followed by a capillary discharge. Electron beams with energy 300-400 MeV, average divergence (FWHM) 2.2 mrad and energy spread (FWHM) 11% are obtained with 100% injection probability. The highest quality beams obtained have 1.8% energy spread and 1.4 mrad divergence with a charge of 1 pC. Shot-to-shot RMS variations were measured to be 1.9% in energy, 45% in charge and 0.57 mrad pointing stability. By small changes in the plasma density profiles, a charge stability of 6% is achieved.

In Fourmaux et al. [842] a crossing high-intensity laser is used to generate the plasma density gradient with an estimated gradient length of 25 µm. Electron beams with 280 MeV energy, energy spread 11%, divergence 6 mrad and more than 300 pC charge are accelerated. The shot-to-shot standard deviations are measured to be 28% in energy and 40% in charge.

In Thaury et al. [20] a comparison of density transition injection with (gas mixture 99% He + 1% N2) and without (pure He) ionisation injection is performed. Electron beams with 123 MeV energy and 11% energy spread, divergence of 5 mrad and 2.6 mrad (elliptical beam) and 1 pC charge are generated. The shot-to-shot charge stability (12%), energy stability (2.5%), RMS pointing stability (1.5 mrad) and injection probability (100%) are improved in the case of the gas mixture with respect to pure He (24%, 7%, 3.2 mrad, < 100%). Additional lower energy peaks are present in the case of the gas mixture, indicating that regular ionisation injection occurs after the density transition. An increased percentage of N2 in the gas mixture leads to increased charge in the electron beam without affecting the beam quality.

Burza et al. [843] create a more complex density profile by the insertion of a thin (25 µm) wire into the gas-jet. The life-time of the wire is 60–100 shots. The obtained density profile is characterised by three density plateaus (the second plateau having half the density of the first and third plateau) connected by two transition regions consisting of a shock and a downward gradient each. Electron beams with energies up to 100 MeV, energy spread below 4% at 100 MeV, divergence 2–8 mrad, 10–100 pC charge and 95% injection probability are obtained.

Recent results reported by Wang et al. [32] are obtained with a different approach showing very promising results. With the use of two gas-jets and a wall inserted at the end of the first gas-jet, a density profile consisting of a first plateau, a density bump followed by a density downramp and a second plateau is generated. Injection occurs in the first plateau and reversal of the electron beam chirp is achieved in the density downramp. Electron beams with 200–600 MeV energy, 0.4–1.2% RMS energy spread, 0.2 mrad RMS divergence and 10–80 pC charge are observed.
Comments

The properties of electron bunches reported in Tables 32.2–32.5 illustrate the main features of each injection technique. However, other properties can also be relevant, such as the electron bunch pointing fluctuations, its transverse slice emittance or its length (i.e. longitudinal size).

In Tables 32.2–32.5, the “traffic light system” is used to highlight results corresponding to EuPRAXIA parameter requirements (in green), close to requirements but with further improvements needed (in yellow) and far from EuPRAXIA requirements (in red).

Most experimental studies focus on the control of the injection to reduce the energy spread, the transverse emittance or increase the energy. The stability of electron properties has not yet been intensively studied. To develop a reliable electron beam, stability and reproducibility of electron properties are needed. They are currently limited by the stability and reproducibility of the parameters of the laser and plasma target. More work is necessary to quantify clearly the main mechanisms and propose ways to stabilise acceleration processes.
<table><caption>Table 32.2. Comparison of selected published performances to EuPRAXIA baseline for self-injection (SI).</caption><thead><tr><th colspan="2">Injection technique</th><th colspan="10">SI</th><th colspan="2">Baseline 150 MeV</th><th>Baseline 1 GeV</th></tr><tr><th colspan="2">References</th><th>[12]</th><th>[273]</th><th>[11]</th><th>Jet</th><th>[774]</th><th>[829]</th><th>[290]</th><th>Capillary discharge</th><th>H<sub>2</sub></th><th>H<sub>2</sub></th><th>Report D 1.2.</th><th>Report D 1.2.</th></tr></thead><tbody><tr><th rowspan="7">Plasma</th><th>Target</th><td>Jet</td><td>Jet</td><td>Jet</td><td>H<sub>2</sub></td><td>H<sub>2</sub></td><td>He</td><td>Jet</td><td>Capillary discharge</td><td>H<sub>2</sub></td><td>3 &times; 10<sup>18</sup></td><td>Cell / capillary / jet</td><td>Cell / Capillary</td></tr><tr><th>Gas</th><td>He</td><td>He</td><td>Jet</td><td>H<sub>2</sub></td><td>H<sub>2</sub></td><td>He</td><td>Jet</td><td>Capillary discharge</td><td>H<sub>2</sub></td><td>3 &times; 10<sup>18</sup></td><td>Cell / capillary / jet</td><td>H<sub>2</sub></td></tr><tr><th>n<sub>e</sub> (cm<sup>-3</sup>)</th><td>2 &times; 10<sup>19</sup></td><td>6 &times; 10<sup>18</sup></td><td>1.9 &times; 10<sup>19</sup></td><td>7.3 &times; 10<sup>18</sup></td><td>5 &times; 10<sup>18</sup></td><td>4.3 &times; 10<sup>18</sup></td><td>4.3 &times; 10<sup>18</sup></td><td>4.3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>2 &times; 10<sup>17</sup></td><td>2 &times; 10<sup>17</sup></td></tr><tr><th>Length (mm)</th><td>2</td><td>3</td><td>1.7</td><td>15</td><td>4</td><td>33</td><td>5</td><td>5</td><td>5</td><td>5</td><td>5</td><td>5</td></tr><tr><th>E<sub>L</sub> (J)</th><td>0.5</td><td>1</td><td>0.5</td><td>0.850</td><td>3.5</td><td>33</td><td>3.5</td><td>3.5</td><td>3.5</td><td>3.5</td><td>3.5</td><td>3.5</td></tr><tr><th>&tau;<sub>L</sub> (fs)</th><td>40</td><td>33</td><td>55</td><td>42</td><td>30</td><td>38</td><td>30</td><td>30</td><td>30</td><td>30</td><td>30</td><td>30</td></tr><tr><th>P<sub>L</sub> (TW)</th><td>~ 12.5</td><td>30</td><td>9</td><td>20</td><td>80</td><td>40</td><td>40</td><td>40</td><td>40</td><td>40</td><td>40</td><td>40</td></tr><tr><th>I<sub>L</sub> (W/cm<sup>2</sup>)</th><td>N/A</td><td>3.2 &times; 10<sup>18</sup></td><td>1.1 &times; 10<sup>19</sup></td><td>1.7 &times; 10<sup>18</sup></td><td>N/A</td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td><td>3 &times; 10<sup>18</sup></td></tr><tr><th>a<sub>0</sub></th><td>N/A</td><td>1.3</td><td>2.3</td><td>0.89</td><td>N/A</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td><td>13.6 (1/e<sup>2</sup>)</td></tr><tr><th>w<sub>0</sub> (µm)</th><td>~ 25 (FWHM)</td><td>21 (FWHM)</td><td>24 (FWHM)</td><td>23 (FWHM)</td><td>No</td><td>No</td><td>Channel</td><td>Channel</td><td>Channel</td><td>Channel</td><td>Channel</td><td>Channel</td></tr><tr><th>Guiding</th><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td><td>No</td></tr><tr><th>E (MeV)</th><td>70</td><td>170</td><td>86</td><td>198</td><td>550</td><td>1000</td><td>550</td><td>1000</td><td>550</td><td>1000</td><td>550</td><td>1000</td></tr><tr><th>&sigma;<sub>E</sub>/E (%)</th><td>~ 3</td><td>24</td><td>~ 2</td><td>8.2 (FWHM)</td><td>&le; 25</td><td>2.5 (RMS)</td><td>&le; 25</td><td>2.5 (RMS)</td><td>&le; 25</td><td>2.5 (RMS)</td><td>&le; 25</td><td>2.5 (RMS)</td></tr><tr><th>Q (pC)</th><td>22</td><td>500</td><td>300</td><td>10</td><td>&gt; 50</td><td>30</td><td>&gt; 50</td><td>30</td><td>&gt; 50</td><td>30</td><td>&gt; 50</td><td>&gt; 50</td></tr><tr><th>&sigma;<sub>&perp;</sub> (mrad)</th><td>~ 87</td><td>10</td><td>N/A</td><td>1.6 (FWHM)</td><td>&lt; 4</td><td>1.6</td><td>&lt; 4</td><td>1.6</td><td>&lt; 4</td><td>1.6</td><td>&lt; 4</td><td>1.6</td></tr><tr><th>&epsilon;<sub>N,&perp;</sub> (mm.mrad)</th><td>N/A</td><td>N/A</td><td>&le; 2</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><th>&Delta;E/E (%)</th><td>~ 30</td><td>N/A</td><td>N/A</td><td>6 (RMS)</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><th>&Delta;Q/Q (%)</th><td>N/A</td><td>N/A</td><td>N/A</td><td>40 (RMS)</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><th>f (Hz)</th><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><th>P<sub>i</sub> (%)</th><td>N/A</td><td>N/A</td><td>N/A</td><td>80</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr><tr><th>Comments</th><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<table><caption>**Table 32.3.** Comparison of selected published performances to EuPRAXIA baseline for colliding pulse injection (CPI).</caption><thead><tr><th colspan="2">Injection technique</th><th colspan="3">CPI</th><th colspan="2">Baseline 150 MeV</th><th colspan="2">Baseline 1 GeV</th></tr><tr><th colspan="2">References</th><th>[657]</th><th>[831]</th><th>[832]</th><th colspan="2">Report D 1.2.</th><th colspan="2">Report D 1.2.</th></tr></thead><tbody><tr><td rowspan="5">Plasma</td><td>Target</td><td>Jet</td><td>Jet</td><td>Jet</td><td colspan="2">Cell / capillary / jet</td><td colspan="2">Cell / Capillary</td></tr><tr><td>Gas</td><td>He</td><td>He</td><td>He ?</td><td colspan="2">H<sub>2</sub></td><td colspan="2">H<sub>2</sub></td></tr><tr><td>n<sub>e</sub> (cm<sup>-3</sup>)</td><td>7.5 &times; 10<sup>18</sup></td><td>5.7 &times; 10<sup>18</sup></td><td>~ 1 &times; 10<sup>19</sup></td><td colspan="2">3 &times; 10<sup>18</sup></td><td colspan="2">2 &times; 10<sup>17</sup></td></tr><tr><td>Length (mm)</td><td>2</td><td>3</td><td>1.5</td><td colspan="2">&ge; 5</td><td colspan="2">&gt;10</td></tr><tr><td>E<sub>L</sub> (J)</td><td>0.72 and 0.25</td><td>N/A</td><td>0.4</td><td colspan="2">5</td><td colspan="2">100</td></tr><tr><td colspan="2">&tau;<sub>L</sub> (fs)</td><td>30</td><td>30</td><td>42</td><td colspan="2">30</td><td colspan="2">100</td></tr><tr><td colspan="2">P<sub>L</sub> (TW)</td><td>~ 24</td><td>N/A</td><td>10</td><td colspan="2">167</td><td colspan="2">1000</td></tr><tr><td rowspan="5">Laser</td><td>I<sub>L</sub> (W/cm<sup>2</sup>)</td><td>3.4 &times; 10<sup>18</sup> and 4 &times; 10<sup>17</sup></td><td>4.6 &times; 10<sup>18</sup> and 4 &times; 10<sup>17</sup></td><td>~ 3 &times; 10<sup>18</sup></td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>a<sub>0</sub></td><td>1.3 and 0.4</td><td>1.5 and 0.4</td><td>1.2 and 0.6</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>w<sub>0</sub> (&mu;m)</td><td>16 &times; 21 and 31 (FWHM)</td><td>N/A</td><td>N/A</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>Guiding</td><td>No</td><td>No</td><td>No</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>E (MeV)</td><td>117</td><td>206</td><td>~ 150</td><td colspan="2">150</td><td colspan="2">1000</td></tr><tr><td colspan="2">&sigma;<sub>E</sub>/E (%)</td><td>11 (FWHM)</td><td>~ 7 (FWHM)</td><td>~ 1.4 (FWHM)</td><td colspan="2">5 (RMS) ~ 11.8 (gaussian FWHM)</td><td colspan="2">5 (RMS) ~ 11.8 (gaussian FWHM)</td></tr><tr><td rowspan="6">Electrons</td><td>Q (pC)</td><td>19</td><td>13</td><td>7.6</td><td colspan="2">100</td><td colspan="2">100</td></tr><tr><td>&sigma;<sub>&perp;</sub> (mrad)</td><td>5.8 (FWHM)</td><td>4.5</td><td>~ 1</td><td colspan="2">5.8 (RMS) ~ 13.7 (gaussian FWHM)</td><td colspan="2">0.71 (RMS) ~ 1.7 (gaussian FWHM)</td></tr><tr><td>&epsilon;<sub>N,&perp;</sub> (mm.mrad)</td><td>N/A</td><td>N/A</td><td>N/A</td><td colspan="2">1</td><td colspan="2">1</td></tr><tr><td>&Delta;E/E (%)</td><td>6</td><td>5 (RMS)</td><td>N/A</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>&Delta;Q/Q (%)</td><td>36</td><td>30 (RMS)</td><td>25 (RMS)</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td>f (Hz)</td><td>N/A</td><td>N/A</td><td>N/A</td><td colspan="2">10</td><td colspan="2">10</td></tr><tr><td colspan="2">P<sub>i</sub> (%)</td><td>100</td><td>N/A</td><td>N/A</td><td colspan="2">-</td><td colspan="2">-</td></tr><tr><td colspan="2">Comments</td><td colspan="2">Tunable</td><td colspan="2">Tunable</td><td colspan="2">-</td></tr></tbody></table>
<table><caption>Table 32.5. Comparison of selected published performances to EuPRAXIA baseline for ionisation-induced injection (III).</caption><thead><tr><th colspan="2">Injection technique</th><th colspan="6">III</th><th colspan="2">Baseline 150 MeV</th></tr><tr><th colspan="2">References</th><th>[278]</th><th>[282]</th><th colspan="2">[773]</th><th>[839]</th><th colspan="2">Report D 1.2.</th></tr><tr><th colspan="2">Target</th><td>Jet</td><td>Two-stage cell</td><td colspan="2">Two jets</td><td>Jet</td><td colspan="2">Cell / capillary / jet</td></tr></thead><tbody><tr><td rowspan="4">Plasma</td><td>Gas</td><td>99%He + 1%Ar</td><td>99.5%He + 0.5%N<sub>2</sub></td><td colspan="2">99.5He + 0.5%N<sub>2</sub> / He</td><td>99.5%He + 0.5%N<sub>2</sub></td><td colspan="2">H<sub>2</sub></td></tr><tr><td>n<sub>e</sub> (cm<sup>-3</sup>)</td><td>2 × 10<sup>19</sup></td><td>3 × 10<sup>18</sup></td><td colspan="2">3.4 × 10<sup>18</sup> + 1.2 × 10<sup>18</sup></td><td>5 × 10<sup>18</sup></td><td>3 × 10<sup>18</sup></td><td>2 × 10<sup>17</sup></td></tr><tr><td>Plasma Length (mm)</td><td>3</td><td>8</td><td colspan="2">0.5 + 2</td><td>4</td><td>≥ 5</td><td>> 10</td></tr><tr><td colspan="2">E<sub>L</sub> (J)</td><td>N/A</td><td>N/A</td><td colspan="2">1.7</td><td>N/A</td><td>5</td><td>100</td></tr><tr><td colspan="2">τ<sub>L</sub> (fs)</td><td>30</td><td>60</td><td colspan="2">34</td><td>30</td><td>30</td><td>100</td></tr><tr><td colspan="2">P<sub>L</sub> (TW)</td><td>24</td><td>40</td><td colspan="2">47</td><td>30</td><td>167</td><td>1000</td></tr><tr><td rowspan="5">Laser</td><td>I<sub>L</sub> (W/cm<sup>2</sup>)</td><td>~ 2.8 × 10<sup>19</sup></td><td>~ 10<sup>19</sup></td><td colspan="2">N/A</td><td>~ [1.8 - 5.0] × 10<sup>18</sup></td><td>-</td><td>-</td></tr><tr><td>a<sub>0</sub></td><td>~ 3.6</td><td>~ 2 - 2.8</td><td colspan="2">2.5 (sim)</td><td>[0.9 - 1.5]</td><td>-</td><td>-</td></tr><tr><td>w<sub>0</sub> (μm)</td><td>10 (FWHM)</td><td>15 (1/e<sup>2</sup>)</td><td colspan="2">10 (1/e<sup>2</sup>)</td><td>28 (1/e<sup>2</sup>)</td><td>-</td><td>-</td></tr><tr><td>Guiding</td><td>No</td><td>No</td><td colspan="2">No</td><td>No</td><td>-</td><td>-</td></tr><tr><td>E (MeV)</td><td>~ 115</td><td>460</td><td colspan="2">175</td><td>300</td><td>150</td><td>1000</td></tr><tr><td rowspan="6">Electrons</td><td>σ<sub>E</sub>/E (%)</td><td>~ 20 (FWHM)</td><td>~ 5 (FWHM)</td><td colspan="2">~ 17 (FWHM)</td><td>5 (FWHM)</td><td>5 (RMS)</td><td>5 (RMS)</td></tr><tr><td>Q (pC)</td><td>~ 12</td><td>35</td><td colspan="2">~ 20</td><td>N/A</td><td>~ 11.8 (gaussian FWHM)</td><td>~ 11.8 (gaussian FWHM)</td></tr><tr><td>σ<sub>⊥</sub> (mrad)</td><td>2.9 ± 0.8</td><td>2.3</td><td colspan="2">N/A</td><td>N/A</td><td>5.8 (RMS)</td><td>0.71 (RMS)</td></tr><tr><td>ε<sub>N,⊥</sub> (mm.mrad)</td><td>N/A</td><td>N/A</td><td colspan="2">N/A</td><td>N/A</td><td>~ 13.7 (gaussian FWHM)</td><td>~ 1.7 (gaussian FWHM)</td></tr><tr><td>ΔE/E (%)</td><td>N/A</td><td>N/A</td><td colspan="2">N/A</td><td>N/A</td><td>1</td><td>1</td></tr><tr><td>ΔQ/Q (%)</td><td>~ 40</td><td>N/A</td><td colspan="2">N/A</td><td>N/A</td><td>-</td><td>-</td></tr><tr><td>f (Hz)</td><td>N/A</td><td>N/A</td><td colspan="2">N/A</td><td>N/A</td><td>10</td><td>10</td></tr><tr><td>P<sub>t</sub> (%)</td><td>N/A</td><td>N/A</td><td colspan="2">75</td><td>N/A</td><td>-</td><td>-</td></tr><tr><td colspan="2">Comments</td><td>-</td><td>-</td><td colspan="2">Tunable</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
### 32.2.6 Summary: Preliminary Design Elements

Table 32.6 summarises the main properties (state-of-the-art or expected to be achieved soon) of four general type of plasma targets of interest for EuPRAXIA design:

<table><caption>**Table 32.6.** Summary of plasma targets main properties</caption><thead><tr><th>Target type</th><th>Length mm</th><th>n<sub>e</sub> value cm<sup>-3</sup></th><th>n<sub>e</sub> tailoring</th><th>n<sub>e</sub> stability</th><th>rep rate</th><th>life time</th></tr></thead><tbody><tr><td>Gas jet</td><td>&lt; 20 self-foc.</td><td>10<sup>18</sup></td><td>multiple jets</td><td>turbulent flow</td><td>10 Hz</td><td>&gt; 24 h</td></tr><tr><td>Gas cell</td><td>&gt; 1 self-foc.</td><td>10<sup>17</sup>–10<sup>19</sup></td><td>machining</td><td>gas feed dependent</td><td>10 Hz</td><td>laser quality dependent</td></tr><tr><td>Plasma channel HE</td><td>&lt; 30 guiding</td><td>(1–5) × 10<sup>18</sup> parabolic</td><td>similar to gas jet</td><td>laser quality dependent</td><td>10 Hz</td><td>&gt;24h</td></tr><tr><td>Plasma channel discharge</td><td>10–90 guiding</td><td>5 × 10<sup>17</sup>–10<sup>19</sup> parabolic</td><td>multiple gas feed</td><td>discharge dependent</td><td>10 Hz</td><td>laser quality dependent</td></tr><tr><td>Cap tube</td><td>10–1000 guiding</td><td>(0–5) × 10<sup>17</sup> homogeneous</td><td>multiple gas feed</td><td>gas feed static</td><td>10 Hz</td><td>laser quality dependent</td></tr></tbody></table>

Although current operation of experiments is lower than 10Hz, the listed targets have the capability, in terms of gas feed, to operate at 10 Hz provided an adequate evacuation system is used to minimise the gas load inside the interaction chamber. Gas jets and gas cells can be used in a range of gas length and density, and laser power where self-focussing is effective, otherwise the distance of high intensity interaction is limited to the diffraction length. Consequently gas jets and gas cells are better suited for injectors. The comparison of gas cell and gas jets for similar conditions of plasma density shows that gas cells are more stable, essentially due to a smoother gas feed system.

Gas jets exhibit an open geometry interesting for diagnostics, and provides robustness against laser beam defects in quality of instability. Heavy gas load may prevent large repetition rate. Plasma channels HE, formed by hydrodynamic expansion, are able to guide intense pulses over a moderate distance at intermediate density, and have the advantage of open geometry, similar to gas jets. Plasma channels created by discharge and grazing incidence capillary tubes are the two main types of wave-guides adequate for intense laser guiding in the 10 cm range, scalable to longer lengths. They can operate in the quasi-linear regime and are suited for accelerator structures. Multiple gas feeds along the propagation axis could be used to tailor the density profile for controlled acceleration. 10Hz repetition rate should not be an issue in terms of gas load. Energy deposition and flow in the waveguides should be studied to determine if cooling systems should be implemented.

A critical issue for the lifetime of gas cell and waveguides is the laser beam quality and stability. As the laser properties also play a crucial role in the reproducibility of the acceleration process, this seems to be an absolutely necessary requirement for the design of the laser system.

Finally, systematic studies of the stability of the gas/plasma density should be performed for each type of target: it is a parameter which is not well documented although it is crucial for the stability of the acceleration process. Figure 32.5
<figure><img src="image_281.png" /><figcaption>**Fig. 32.5.** Comparison of published results with EuPRAXIA injector parameters. Operation points of published results are indicated in 3 parameter spaces: energy spread vs energy (a), energy spread vs charge (b), and energy spread vs divergence space (c); symbols indicate different injection mechanisms; the two EuPRAXIA baseline injectors are indicated as grey area for 150 MeV and red area for 1 GeV.</figcaption></figure>

summarises the properties of published electron beams for four parameters relevant for the EuPRAXIA design.

It shows that among the examined results for all injection schemes, none has all four parameters within the range of EuPRAXIA design. It indicates that more efforts are necessary in particular to reduce the beam divergence of the injector. However we can see that reference [843] is close to EuPRAXIA target parameters for an injector at 150 MeV. We can also see that reference [832] presents parameters within the range of EuPRAXIA target but produced too low charge electron bunches.

## 32.3 Enabling Laser Design and Optimisation

### 32.3.1 Introduction

The EuPRAXIA infrastructure relies on a range of laser systems to drive plasma acceleration in a set of different configurations, including the 150 MeV injector, and
the 1 and 5 GeV accelerators. The “Laser Design and Optimisation” Work Package (WP4) has delivered the design of the laser systems and all required subsystems to fulfil the specifications starting from the “Benchmarking of existing technology and comparison with the requirements” (EuPRAXIA Deliverable Report D4.1, see also Sect. 7.2), where a major effort was dedicated to the identification and definition of the most promising approaches. This process of selection was also strongly driven by some of the physics specifications requiring pulse duration as short as 30 fs to be available. Indeed, this requirement, combined with the significant energy per pulse needed by the three LPA schemes, made Ti:Sa emerge as the most suitable technology, with main components featuring a high TRL.

Based on the foreseen temporal constraints, the design of the main EuPRAXIA lasers could be delivered using Ti:Sa laser technology and exploiting the dramatic ongoing developments in pump lasers, i.e. lasers capable of delivering ns pulses with ≈100 J level energy per pulse at a 100 Hz pulse repetition rate. An overview of the full conceptual design is given in Chapter 10.

Conceptual laser design and optimisation was driven by the physics specifications set by the acceleration schemes.

Here we further discuss main issues behind the conceptual laser design that concern enabling key components.

The first issue concerns the thermal management of the main amplifier heads. Here a combination of conductive cooling through the crystal mounts and convective cooling in air of the amplifying crystal, the most commonly used cooling techniques in low repetition rate systems, may be found to be in-sufficient for high repetition rate operation at the required energy levels. Other more aggressive cooling strategies must then be envisaged, such as fluid (i.e. liquid or gas) forced flow cooling. Indeed, for these reasons, the amplifying crystals considered are not monolithic, but are divided into two identical sub-crystals face-cooled by a liquid flow, to increase the available cooling surface. This fractioning of the crystal has no impact on the overall energy amplification performances. A quantitative evaluation is given in Chapter 10 for such a configuration with water cooling. Preliminary simulations indeed show that this scheme may provide the appropriate heat extraction with a manageable wavefront aberration. More detailed, full-scale simulations are however needed in combination with a set of validation experiments on real samples to reduce design uncertainties and support the technical design.

Beam transport from the final amplifier to the target final focus includes a set of issues currently still under quantitative evaluation. An overview of these important issues is included in Chapter 10. The main challenges are certainly the thermal and spectral issues in the compressor, and the pointing stability at the interaction plane. Regardless of the grating technology, cooling of the gratings will most likely be necessary. While numerical modelling is being implemented and preliminary small-scale experiments are just emerging, a reliable compressor design with cooled gratings will require full-scale components tests at the required average power level. Moreover, depending on the laser beamline, wide bandwidth acceptance will be needed. New grating technologies are emerging, like hybrid gratings with metal and multilayer dielectric coatings or new configurations for pure multilayer dielectric gratings. Among these issues, compressor grating performance at high average power levels is certainly of concern and grating cooling technology will be necessary to control the impact on beam quality.

Regarding the pointing stability, in general, the requirements depend on the specific application, involving possibly super-position of two laser focal spots or a laser focal spot and an electron beam in the focal region. These specifications will require a major design effort, still under investigation. In general, pointing stability will be
affected by the whole system and several strategies can be considered. Active sta-
bilisation of PW-scale lasers using closed loops between stability detection on the
interaction point and crucial transport optics is being considered. At the same time,
passive stabilisation adopting self-stabilizing optics mounts, is also being considered.

32.3.2 Pump Laser Technology

The availability of the required pump laser power is a critical issue in the design. It
should be noted that the diode laser pump units considered in our design currently use
commercially available diode laser technology, either directly or with small changes
in use condition. These pump sources use low-cost passively cooled arrays of 1-cm
diode laser bars, which were developed for low repetition rate and low duty cycle use
and have limited cooling capacity by design (for low cost and compactness). The low
heat extraction rate leads to restrictions in either duty cycle, output power, spatial
brightness or power conversion efficiency, meaning that in general the diode laser
pumps are marginal in performance for the EuPRAXIA system. In the solutions
presented here, these limitations are proposed to be overcome by accepting reduced
performance or by interleaving many sources at the expense of substantially increased
cost. Alternative solutions without these performance restrictions are also available,
but these are either research prototypes that require technology transfer to industry
[Platz, 2018] or require the use of microchannel cooling of bars, which is not preferred
on cost and reliability grounds.

DIPOLE-Like Technology

DiPOLE is a diode-pumped, solid state laser amplifier architecture developed at the Central Laser Facility. It is based on an end-pumped stack of ceramic Yb:YAG slabs, cooled by a flow of low-temperature, high-pressure helium gas [Ertel 2011]. This technology was recently demonstrated at the 1kW level with the DiPOLE100 system (STCF, UK, HiLASE, CZ), showing 100 J output energy @ 10 Hz, 1030 nm with > 60 J expected conversion @ 515 nm [Mason 2017]. This architecture and gain material exhibit reduced reabsorption loss and increased absorption and emission cross-sections in Yb:YAG, with a low quantum defect due to the very close pump and emission wavelengths being 940 nm and 1030 nm, respectively. These advantages enable efficient energy extraction and potential scalability to high average power. A scaled version of this architecture has already been considered as a pump source for the 30 J, 30 fs, 10 Hz Gemini upgrade at STFC (EPAC project). The main specs of the Gemini upgrade are very relevant to the Laser 2 (P0) of EuPRAXIA and will constitute an extremely interesting reference system in view of the final design.

At this stage we can envisage a possible schematic approach to the main
EuPRAXIA amplifier module, (AMP3(P0)) where, scaling the DiPOLE system to the
150 J level (IR), we can consider up to three pumping units, delivering the required
280 J each (@0.5 µm) on the final Ti:Sa crystal. This will be discussed in more details
in the following paragraph.

P60-Like Technology

The P60 is a commercial system produced by Amplitude Technologies as a part of
the P-series systems, using an improved “active mirror” configuration, the so-called
Disk Amplifier Heads (DAH), based on Nd:YAG. Currently operated with flash lamp
pumping, conversion to diode pumping has been developed by Amplitude and a preliminary design has been produced. The general architecture of the P60 includes a seeder, followed by 6 identical Nd:YAG DAH amplifiers. The main features of the system are 1) enhanced and simple thermal management without cryogenic cooling. Longitudinal liquid cooling in gain/heat load distributed disks; 2) compatibility with diode pumping, 3) compact footprint 1.5 x 4.8 m and beam specifications suitable for Ti:Sa pumping.

The demonstrated performances include >70J at 1064nm with a 0.41% RMS shot-to-shot stability and 75% SHG efficiency with 5-6ns Gaussian temporal pulse @ 2.8J/cm² incident fluence with a 65 mm diameter and 18 mm thick LBO type I crystal. These values indicate that an array of a limited number of P60-like systems could deliver the required pump energy for Laser1 and Laser2. Laser3 will require additional development to reach the >100 J level after SHG so that an array of up to 4-5 units would provide sufficient pump energy.

The DPSSL version of the P60 is envisaged to operate at an ultimate rep. rate of 100 Hz. However, current heat load performances would already enable 3.5 kW average power with 75 J per pulse (IR) at 50 Hz with no risk. In fact, the thermal load extraction capability demonstrated in disk amplifiers with flashlamps pumping is similar to the heat load at 50 Hz with diode pumping. Moreover, diodes with required brilliance and power supplies are existing and qualified. One important issue concerns the lifetime of diodes for high rep rate. Assuming a diode lifetime of 2 billions shots at a 2% duty cycle, diodes should be replaced every 700/230 days at 8/24H operation at 100 Hz rep-rate and every 1400/460 days at 8/24H operation at 50 Hz rep-rate.

## HAPLS-Like Technology

The HAPLS system was developed by the LLNL for ELI Beamlines (Prague). The system is based on a diode pumped, He cooled Nd:APG-1 glass with cooled ASE edge cladding and currently can operate at >100 J output energy demonstrated @ 3.3 Hz, 1053 nm, with 0.7% RMS stability and 80 J SHG energy @ 526.5 nm. Ramping up to 10 Hz, 200 J (IR) the design limit is currently in progress. In the HAPLS system, the diode pumped system is used to pump a Ti:Sa system to deliver 30 J in 30 fs at 10 Hz. This technology is derived from Inertial Fusion Energy Laser architectures and can be aperture scaled to single aperture, kilojoule, >100kW output. For the HAPLS preamplifier, LLNL took a first step towards increasing the repetition rate of J-class Ti:sapphire lasers by working with Northrup Grumman Cutting Edge Optronics (NG CEO) to produce a green pump laser that is fully diode-pumped and capable of producing 2J at 10Hz. Based on this experience and the data obtained from the design, construction, and operation of this laser system, increasing the repetition rate by 10× to 100Hz is straightforward. This design is compatible with the mandatory (P0) requirements for AMP1 and AMP2, possibly even at 100 Hz (P1).

## 32.3.3 Pump Array Layouts

The two systems P60 and DiPOLE described above have been considered as the main building blocks for the pump laser system for the Ti:Sapphire laser chain. An analysis was then carried out to determine the most efficient arrangements of the pump arrays fitting the pump energy requirements, minimizing the number of required devices and the energy in excess which is lost. In this analysis further assumptions were made, that is:

- For the Amplitude P60 system, it was assumed possible to scale down the system to lower energy levels, taking advantage of the modularity of the system;
- The DiPOLE 100 was considered capable to readjust the rep rate and the pulse energy at the same average power (e.g. running at 20 Hz with 50 J of pulse energy in the infrared)

Regarding the operation at the P1 performance level, a diode pumped version of the P60 system was considered, capable to operate at 50 Hz at the same output pulse energy.

## P0 Performance Level

The P0 operation regime has a pulse repetition rate of 20 Hz. The two pump sources considered above feature a repetition rate of only 10 Hz. To circumvent this problem (in view of the development of devices operating at higher rep rate) we consider the use of two (or two sets) of pump sources operating in interleaved mode. In this way the repetition rate of the pump pulses arriving to the amplifiers is effectively doubled.

Moreover, pump energies higher than about 60 J (as needed by the AMP3 module) require the use of more than a single pump source. In turn, this calls for specific arrangements to multiplex the input from several pump units to the amplification crystals.

## P1 Performance Level

The P1 operation regime considers a pulse repetition rate of 100 Hz, along with higher energies than P0. Currently no solutions for pump sources are available to meet these requirements and will have to be developed for the purpose. Speculatively, we have considered the availability of a system similar to Amplitude P60 but operating at 50 Hz, resulting from the conversion to diode laser pumping of the available P60 (which is flashlamp pumped), with an output energy of 60 J/pulse in the second harmonic. Again, reaching 100 Hz requires the time interleaving of a pair of twin sources. This analysis did not include the DiPOLE 100 system, as no developments are currently planned toward a high energy, high rep rate system.

## 32.3.4 Conclusive Remarks

The requirement of 20/100 Hz of repetition rate respectively at the P0/P1 performance level has a very significant impact on the pump laser arrays: as the available/foreseen pump devices have a repetition rate of 10Hz/50Hz; this requires the doubling of the pump sources to achieve the required repetition rate by temporally interleaving the shots. As a secondary point, the pump pulses must be routed to the amplifying crystals using angular multiplexing of the input directions. This introduces some complexity in the design of the optical layout of the amplifiers. Also, shot to shot energy stability issues can become more critical when the pump pulses are delivered alternatively by two different sets of devices. It is clear that the availability of pump sources natively operating at 20 Hz / 100 Hz would introduce a large simplification in the architecture of the whole laser amplifier.

Summarising the current and expected performances of kW-scale DPSSL pumping systems currently available, we can say that the three selected systems are in a highly advanced development stage. All of them have demonstrated performances required to fulfil part of the pumping needs of the main EuPRAXIA laser P0 specifications. Some of these technologies are being considered independently for scaled
operation at higher rep rate and higher energy per pulse, making them good candidates for pump lasers to reach the P1 specifications. However, a significant targeted development will be needed to address scaling of candidate systems at the desired 100 Hz repetition rate. In view of this, a dedicated de-risking activity is foreseen as discussed in Chapter 10.

## 32.4 Outreach and Liaison

The EuPRAXIA consortium has established an Outreach and Liaison group based at the University of Liverpool/Cockcroft Institute. The group holds weekly online meetings with the Management Support Team at DESY to ensure that communication activities are always on the agenda and to continuously monitor progress.

### 32.4.1 Resources

#### The EuPRAXIA Brand

The group produced a collection of materials to assist the partners with the dissemination of the project and its objectives, creating a visual language to facilitate the prompt identification of the EuPRAXIA brand.

In order to ensure a consistent message the group created some informative slides about the project and made them available to all project partners. A template for presentations was also created and all partners were encouraged to use it in order to reinforce the project branding.

Following the same visual identity idea, the group produced a poster template to advertise all EuPRAXIA-related events and a series of roll-up banners that were displayed prominently at project meetings, workshops and conferences around the world.

#### Website and social media

The project website www.eupraxia-project.eu is the main portal of information of EuPRAXIA for the external world. It is regularly updated with news and upcoming events. Relevant news about EuPRAXIA are also promoted via social media, using the Facebook pages of the Cockcroft Institute and the Quasar group as well as the corresponding twitter accounts @cockcroft_news and @QUASAR_6group, with the hashtags #EuPRAXIA, #plasma, and #accelerator.

#### Intranet

A repository of documents was set up in the University of Liverpool's Sharepoint system to facilitate the internal exchange of documents among the project partners. The intranet is linked to the website and all participants in the project have been provided with a password to access the information. Apart from the repository of documents, Sharepoint offers a news blog and a collaborative work space (wikipraxia).
<figure><img src="image_282.png" /><figcaption>Fig. 32.6. EuPRAXIA leaflet.</figcaption></figure>

## Leaflets

The group produced an informative leaflet about EuPRAXIA which can be downloaded from the website (http://www.eupraxia-project.eu/downloads.html). All partners were encouraged to use the leaflet for promoting the project among colleagues, national authorities, policy makers, and the public in general. In order to facilitate the local promotion, the leaflet was translated to German, French, Portuguese, Italian, and Spanish. Moreover a non-technical version of the leaflet was produced to assist in the communication of the project objectives to non-scientific audiences.

## Brochure

A glossy 28-page brochure of the EuPRAXIA project was prepared and focuses on the key technologies to be developed by EuPRAXIA (high-power lasers, accelerator technology, free-electron lasers, high-energy physics and other applications) highlighting their challenges and potential for innovation, and includes information about the project and its partners in general.

The brochure was designed to appeal to a very broad audience. Its primary targets are members of the technology industry, but it also addresses European policy makers, potential users, broader scientific community and the general public.

The brochure informs members of the technology industry of the opportunities offered by EuPRAXIA for innovation and business. It is particularly relevant for the laser industry, manufacturers of accelerator components (magnets, vacuum systems, etc.), feedback and control software developers, and system engineers. It also informs potential users of free-electron lasers and the high-energy physics community of the unique opportunities presented by EuPRAXIA. The brochure was distributed to all project partners and at international conferences and workshops. It is also available for download via the project website and available in electronic form via ISSUU (https://issuu.com/quasar-group/docs/eupraxia_brochure_web/2) for easy access by various device platforms. Several A0 posters were also produced on the basis of the brochure and used to communicate the challenges across the different scientific work packages.
<figure><img src="image_283.png" /><figcaption>Fig. 32.7. EuPRAXIA brochure.</figcaption></figure>

<figure><img src="image_284.png" /><figcaption>Fig. 32.8. Demonstration of the *Surfatron* game at a past outreach event.</figcaption></figure>

## Video

A short video clip about EuPRAXIA, styled as an action movie trailer, was produced. The aim of the video was to create a sense of anticipation for the potential impact of plasma accelerators on society. The video has been shown at numerous outreach events, scientific conferences and meetings, and it is available on Youtube (https://www.youtube.com/watch?v=vDkkKtlMUvs). It also features on the European Commission's "EU-funded R&I projects" playlist.
## The Surfatron

A computer game called *Surfatron* was created to demonstrate the concept of wakefield acceleration. The game simulates the motion of a particle in a travelling wave, likened to the motion of a surfer riding a wave at sea.

The player can control the parameters of the wave (amplitude, wavelength, and frequency), as well as the injection velocity of the particle into the wave.

By finding the optimum parameters and releasing the particle at the right time, the aim is to obtain maximum acceleration for the particle. The game also includes some information about the science of EuPRAXIA. The *Surfatron* attracted large crowds at outreach events and international conferences where a leaderboard and prizes helped audience engagement.

### 32.4.2 Publications

#### Feature articles

A number of feature articles about EuPRAXIA have been published on websites and magazines around the world. This included for example:

- EuPRAXIA Design Study comes of age, Accelerating News (October 2018)

- Plasma accelerators could overcome size limitations of LHCarge Hadron Collider, Horizon (July 2018)

- EuPRAXIA@SPARC_LAB: verso la prima generazione di acceleratori da tavolo, SIF Prima Pagina (July 2018).

- Charting a course for advanced accelerators, CERN Courier (November 2017)

- Boosting the electron beam brightness: NeXsource, Accelerating News (September 2017)

- Acceleration re-defined once again in Pisa, INFN News (July 2016)

- EuPRAXIA consortium paves way for next generation laser technology, Accelerating News (July 2016)

- Three million euros for European Plasma Research Accelerator with eXcellence In Applications (EuPRAXIA) project, Laserlab Newsletter (June 2016)

- Consortium sets out to build European laser plasma accelerator, Physics World (April 2016)

- World's first high energy plasma-based accelerator to be built, Electro Optics (April 2016)

- What will the world's first plasma accelerator look like?, Design Products & Applications (April 2016)

- Innovation news in brief: Scientists to build world's first plasma accelerator, The Maven (April 2016)

- Compact modern accelerators for big science, Accelerating News (November 2015)

- EU consortium to develop plasma accelerator, Horizon 2020 Projects (November 2015)

- EU launches plasma particle accelerator, Semiconductor Engineering (November 2015)

- EU funds design study for European plasma accelerator, Deutsches Wissenschafts- und Innovationshaus (November 2015)

- EU funds design study for European plasma accelerator, phys.org (November 2015)
## Newsletter

The Outreach and Liaison group created a newsletter called *EuPRAXIA Files* to reinforce the sense of community, help with the work of the EuPRAXIA researchers, and strengthen the links with other communities. *EuPRAXIA Files* is a collection of abstracts from published papers that are relevant to the EuPRAXIA study. The newsletter has become a platform for all the research articles generated within the project. *EuPRAXIA Files* is produced every four months and sent by email to all project partners and associate partners. It is also made available for download from the website (http://www.eupraxia-project.eu/the-eupraxia-files.html).

## 32.4.3 Activities

### Active promotion

The Outreach and Liaison group has contributed actively to the promotion of the project by participating in industrial exhibitions associated to major conferences of accelerator science and technology. Using a booth sponsored by the University of Liverpool, they distributed informative material and answered questions about EuPRAXIA in the *International Particle Accelerators Conference – IPAC*, the world’s largest conference in the field, in Busan, South Korea (2016), Copenhagen (2017), and Vancouver (2018) as well as in the *International Beam Instrumentation Conference – IBIC* in Barcelona (2016) and Grand Rapids, USA, (2017).

Individual members of the consortium have also been very active in the promotion of EuPRAXIA with contributions at a large number of conferences, for example *Lab Innovations* in Birmingham, UK (2018).

The project brochure and leaflets actively distributed among national authorities, policy makers and the wider scientific community with a focus on Germany, UK, Portugal, Italy and France.

### Outreach events

The EuPRAXIA Consortium has been strongly committed to public engagement and endeavours to communicate its objectives and results to the general public through the organisation of outreach events. By communicating the specific research challenges and opportunities of plasma accelerators, this has helped increase the attractiveness of the field overall.

#### Marie Curie Day 2017

On 7 November 2017, an event was organised to celebrate the 150th birth anniversary of Marie Skłodowska Curie, as well as the EU funding program that bears her name. This pan-European event was held simultaneously at the University of Liverpool, CERN, and the Ludwig Maximilian University in Munich. All talks were recorded and are available via the event website (https://marie-curie-day-2017.org/).

In Liverpool, almost 100 local high school students attended a series of activities at the University: an introductory talk by an actress playing the role of Madame Curie, a live connection with CERN where Dr Marco Silari presented the impact of MSCA on research at CERN, a set of hands-on demonstrations on radioactivity, and a poster session about our research and training. The children also participated in a poster competition about “Women in Science”. The event next featured a talk by Prof Carsten Welsch about “Accelerating Researcher Training” that was live streamed for
<figure><img src="image_285.png" /><figcaption>Fig. 32.9. Outreach activities on the “Physics of Star Wars” in Nov 2017.</figcaption></figure>

world-wide access. Among other topics, it covered the physics challenges and opportunities of the EuPRAXIA project. An evening talk at LMU Munich by Professor Katia Parodi on “Research in ion beam cancer therapy” concluded the event.

### Physics of Star Wars

The University of Liverpool team organised a “Physics of Star Wars” event on 27 November 2017 at the University’s Central Teaching Laboratory. The aim of the event was to introduce cutting-edge science to hundreds of secondary school children, undergraduate and PhD students, as well as university staff. The day started with a lecture which first presented iconic scenes from the movies to then link them to the group’s research projects on particle acceleration.

After the lecture, all attendees were given the opportunity to understand the science behind Star Wars through numerous hands-on activities. This was then linked to ongoing research activities, including EuPRAXIA. Laser and beam-driven acceleration were motivated through the enormous acceleration “gradient” achieved when spacecraft in the famous films jump to hyperspeed.

### Symposium

The symposium “Quantum Leap towards the Next Generation of Accelerators” took place at the Liverpool Arena Convention Centre on 6 July 2018 as part of the 3rd EuPRAXIA Collaboration Week. Its aim was to bring together scientists, industry, and policy makers involved in the development of novel accelerators, and to raise the public profile of the project through widespread coverage in the media.

Over 120 high school students were invited to the symposium which offered them an excellent opportunity to learn about the societal impact of particle accelerators, while meeting and interacting with scientists.

The event featured talks from research leaders about accelerators and their applications in an accessible and entertaining way. The talks were streamed live over the internet and are now available on YouTube. The talks were followed by a two-hour long interactive session with scientists and engineers, featuring a poster session showcasing the main results from EuPRAXIA, and hands-on demonstrations for the students, illustrating the concepts of wakefield acceleration.

The Symposium was the occasion to bring together for the first time the scientists of the consortium with members of relevant companies. The symposium included an industry exhibition with 20 exhibitors. The afternoon session was especially addressed
to the industry and it presented the main technological challenges and innovation opportunities offered by EuPRAXIA. Representatives from more than 40 companies were present at the event.

## *Audiences and impact*

The outreach events organised by the University of Liverpool have been targeted mostly at local high school students (ages 14 – 17). The participation of girls was encouraged by targeting girls’ schools and ensuring a balanced representation of female demonstrators and speakers.

Apart from the direct participation in the events listed above, which for logistical reasons is limited to a few hundred people, the reach and scope of the activities has been greatly multiplied by intensive dissemination campaigns before, during, and after each of the events.

Traditional media coverage (press, radio, and TV), as well as social media (Twitter, Facebook and Instagram) have made it possible for the EuPRAXIA outreach activities organised from Liverpool to have an international impact.

The *Marie Curie Day* was an international success: more than 500,000 people read about the event via the internet, social media and wider press coverage, and the *Physics of Star Wars* event reached more than one Million people. The total reach of communication about the Symposium in 2018 was also in excess of 100,000.

## **32.5 Experience from PWFA Test Experiments**

Plasma-based technology promises a tremendous reduction in size of accelerators used for research, medical, and industrial applications, making it possible to develop tabletop machines accessible for a broader scientific community. In addition to the acceleration purposes, plasmas are very useful to shape the beam longitudinal phase space and can be used also as strong focusing devices. In both cases the required structures are very compact and allow for a wide tunability. In the following sections, the main results obtained from beam-plasma interaction at the INFN’s SPARC_LAB facility and a number of DESY experiments will be presented and discussed.

### **32.5.1 Active Plasma Lenses**

While overcoming the limits of conventional accelerators and pushing particles to higher energies, plasma-based accelerators usually produce beams of large angular divergence. Rapid and degradation-free capture of such bunches requires strong and tunable focusing optics. Active plasma lenses (APLs) represent a compact and affordable tool to generate radially symmetric magnetic field gradients, several orders of magnitude larger than what conventional quadrupoles and solenoids can provide. Originating at the Berkeley Radiation Lab in 1950 [399], the technology was not widely adopted until its recent resurrection by the same laboratory [38,181] in the context of advanced accelerators. INFN and DESY have recently taken lead in this research with a number of recent results.

Two previous works from SPARC_LAB [305,844] show that APL focusing can be highly non-linear and induce a dramatic emittance growth. Starting from these findings we have studied in detail the problem and developed an improved system with which we obtained experimental results showing how these non-linearities can be minimised and lensing improved [845]. These achievements represent a major breakthrough toward the miniaturisation of next-generation focusing devices.

At SPARC_LAB, the APL consists of a 3 cm-long sapphire tube with 500 µm hole radius. The capillary is filled at 1 Hz with H₂ gas (produced by an electrolytic
<figure><img src="image_286.png" /><figcaption>**Fig. 32.10.** Beam spot on a screen downstream of the lens with the discharge turned off (a) and on (b) [845] (copyright 2018 by the American Physical Society).</figcaption></figure>

generator) through two inlets. The two capillary electrodes are then connected to a discharge circuit fed by a 20 kV pulser. To test the APL focusing we varied the bunch transverse spot size at the capillary entrance from 35 µm up to 160 µm. This is the argest spot size that ensures to transport the entire beam charge across the capillary clear aperture.

Figure 32.10 shows the resulting focused and unfocused beams after the APL. What we found is that to improve the focusing and preserve the beam emittance the discharge-current flowing through the capillary must be high enough to fully ionise the gas and produce a more linear magnetic field. In addition to this, the interaction with plasma generates beam-driven wakefields that can strongly affect the bunch dynamics. In this context, passive plasma lenses are able to produce a net beam focusing through the plasma neutralisation of the space-charge fields. When dealing with active plasma lenses we have therefore to consider their combined effect. The non-linearities of the overall focusing can be minimised by manipulating both the bunch shape and the capillary-discharge setup.

Figure 32.11 shows the bunch emittance measured downstream of the capillary as a function of the spot size at its entrance. Each point is obtained for the minimum spot provided by the APL on the first screen downstream. According to simulations, the best compromise in terms of resulting emittance is obtained by entering into the plasma with a transverse spot size of 110 µm. We thus followed this expectation and tuned the magnetic optics along the photo-injector to achieve an experimental spot size at capillary entrance of 115 µm. When the discharge is turned on and its delay adjusted to provide the minimum spot size on such a screen (70 Å), the beam is squeezed down to 17.5 µm. These conditions corresponded also to the best results in terms of beam emittance (0.9 µm), which is almost preserved with respect to the unperturbed beam.

Plasma lens studies at DESY are broad and diversified. The discharge capillaries, with varying length (15–195 mm) and diameter (300 µm to 1.5 mm) are manufactured centrally, then installed and tested across several laboratories: at the Mainz Microtron (MaMi), at CERN’s CLEAR User Facility and on site at the FLASHForward facility.

First results came from MaMi [846], where a 30 mm long, 1 mm diameter capillary milled from two sapphire slabs was used to demonstrate stable APL operation with magnetic field gradients up to 823 T/m. These experiments were done using hydrogen, and found evidence of a radial field non-linearity towards the capillary walls [847].
<figure><img src="image_287.png" /><figcaption>**Fig. 32.11.** Resulting emittance as a function of beam spot size at capillary entrance. The black square and red circle data points refer to the experimentally measured emittances. The blue dash-dotted line represents the expected emittance from numerical simulations. The grey dashed line shows the unperturbed (X) beam emittance without APL [845] (copyright (2018) by the American Physical Society).</figcaption></figure>

<figure><img src="image_288.png" /><figcaption>**Fig. 32.12.** Direct measurements of the radial magnetic field profile in an APL. A non-linearity is observed in the helium-filled APL (a), caused by a radial plasma temperature non-uniformity, which leads to aberration and emittance growth. This aberration is suppressed in an argon-filled APL (b) [849].</figcaption></figure>

This problem was further investigated and eventually overcome by a series of experiments at the CLEAR User Facility [848], which utilised a similar 15 mm long, 1 mm diameter sapphire capillary. By using a tightly focused electron beam and offsetting the capillary transversely, the local magnetic field could be measured by observing the angular deflection of the 200 MeV electron beam [849]. Figure 32.12 shows high-precision measurements of the full radial magnetic field profile.

Crucially, this measurement was performed in both helium (expected to behave exactly like hydrogen) as well as in argon – a much heavier gas species. The measurements show that the field non-linearity in helium is consistent with theoretical prediction, whereas in argon, the field is linear to within the precision of the measurement.
<figure><img src="image_289.png" /><figcaption>Fig. 32.13. Emittance measurements from a series of quadrupole scans in both (a) helium and (b) argon. The beam emittance is observed to grow in the helium-filled APL, as expected from the non-linear fields, whereas in the argon-filled APL no emittance growth is observed [849].</figcaption></figure>

This finding suggests that the aberration and consequent emittance growth can be fully suppressed by an appropriate choice of gas species, given that a sufficiently low beam current to avoid plasma wakefields is used. This prediction was confirmed by measuring the beam emittance before and after lensing in both a helium and argon lens (see Fig. 32.13), successfully demonstrating emittance preservation in the argon-filled APL.

At FLASHForward, plasma density profile of the APL is carefully characterised, both longitudinally and transversely, using two independent techniques: laser interferometry and Stark broadening. This, together with magnetohydrodynamical (MHD) simulations, has lead to an increased understanding of the complex evolution of the plasma over µs timescales, from initial ionisation and heating to the eventual diffusion and recombination.

### 32.5.2 Plasma Dechirper

The wakefield structure in a plasma-based particle accelerator offers distinct advantages for future free-electron laser (FEL) and high energy physics (HEP) applications, such as strong intrinsic focusing and high accelerating gradients. These, in principle, allow for the stable propagation and acceleration of an injected bunch to required energies over distances orders of magnitude shorter than those possible in conventional accelerator designs. A challenge of plasma-based concepts, however, is the development of the longitudinal phase-space (LPS) of the beam, accelerated in an environment that may imprint a large linear energy-time dependency – the so-called “chirp” – on the beam up to the GeV/mm level. Upon exit of the plasma section this large negative remnant chirp will halt FEL gain or lead to a beam size increase limiting luminosity in HEP experiments. Ideally the chirp ought to be mitigated in order to utilise plasma wakefield acceleration techniques in future facilities. At SPARC_LAB we have developed a new plasma-based device that allows tuning of the beam LPS by using the wakefields excited in a plasma channel [305]. Such a solution is based on the use of the wakefields created by the beam in the plasma and can be employed both to remove the energy chirp (acting like a dechirper) or tune it by adjusting the plasma density. The basic idea of the LPS manipulation is shown in Figure 32.14, where the LPS and computed plasma wakefield (red line) produced by a 200 pC bunch in a plasma whose density is $10^{14} \text{cm}^{-3}$ are shown. In such a configuration, the tail of the beam experiences a decelerating electric field and loses its energy, while the head moves along an unperturbed plasma, keeping its energy constant.
<figure><img src="image_290.png" /><figcaption>**Fig. 32.14.** LPS of the beam and longitudinal plasma wakefield $W_z$ (red line) produced in a plasma channel by a moving electron bunch (blue dots) [613] (copyright (2019) by the American Physical Society).</figcaption></figure>

To measure the effect on the energy spectrum of the beam induced by the plasma, the beam was transported to the magnetic spectrometer downstream of the capillary and several measurements were made at different plasma densities. Once the $H^2$ is ionised it takes almost 10 µs to recombine. During this time, the plasma density slowly decreases. Thus by choosing the time of arrival by delaying the beam the plasma density observed by the electron bunch was varied. Figure 32.15a shows the unperturbed energy spectrum when there is no plasma in the capillary. In this case the overall energy spread is 0.6 MeV. When the plasma is turned on and its density tuned to $np~10^{14}~cm^{-3}$ (corresponding to a delay on the order of 4.5 µs), a maximum reduction of the beam energy spread was observed, reduced to 0.1 MeV as shown in Figure 32.15b.

Because of the high flexibility of the plasma dechirper by manipulating the parameters of the system (e.g. plasma density) and parameters of the beam (by changing its density with focusing), the system can be tuned in order to remove the given correlated energy spread. It represents an essential feature in order to make the plasma-accelerated beams usable with conventional magnetic optics and for applications involving the generation of FEL radiation.

The FLASHForward experiment [850], attached to the FLASH FEL facility, is designed to generate the characteristically high accelerating fields in the wake of FLASH electron beams interacting with a plasma. This setup was used to perform a proof-of-principle experiment in which the correlated energy spread of a chirped FLASH electron bunch was completely removed by the electric fields generated in plasma. This world-first demonstration was shown to generate dechirping strengths orders of magnitude higher than competing state-of-the-art techniques [851,852] and strengths much larger than subsequent plasma-based dechirping examples [613].

In this experiment an electron bunch, with length 63 µm and a linear chirp of 60.5 MeV/mm, was transported from FLASH to the FLASHForward beamline. Once in FLASHForward the chirped bunch was injected into a 33 mm-long plasma, generated by firing a high-voltage discharge through pumped argon gas. After the discharge pulse ends the density of the plasma electrons exponentially decays due to plasma recombination and expansion into vacuum. The plasma density can, therefore, be controlled by delaying the arrival time of the electron beam relative to the discharge,
<figure><img src="image_291.png" /><figcaption>**Fig. 32.15.** Energy spectrum of the electron beam after the capillary without (a) and with (b) plasma in the channel. A significant reduction in energy spread is observed [613] (copyright (2019) by the American Physical Society).</figcaption></figure>

<figure><img src="image_292.png" /><figcaption>**Fig. 32.16.** A series of energy spectra, as recorded by the optical system surrounding the dipole spectrometer (shown in (a)), for no interaction with plasma as well as two dechirping plasma densities. The standard deviation for each energy slice – an average over 50 consecutive shots – is shown by the error ranges. The simulated energy spectra for the corresponding plasma densities are shown in (b) [850] (copyright (2019) by the American Physical Society).</figcaption></figure>

with the electron beam experiencing lower densities – and therefore lower dechirping gradients – at ever longer times after discharge.

An electron spectrometer located downstream of the plasma capillary was used to disperse the bunch in energy and record the dechirping effect. The energy spectrum of the chirped bunch without interaction with plasma, as well as two cases after interaction with plasma, can be seen in Figure 32.16.
The experimentally derived parameters were used to simulate the dechirping effect using a particle-in-cell code. The plasma density was varied with the maximum dechirping effect observed at a plasma density of $2 \times 10^{15} \text{ cm}^{-3}$. The spectra and dechirping effect in these two cases show good agreement. In addition, the fluctuation of the spectra over 50 consecutive shots with and without plasma interaction is consistent, suggesting that the plasma dechirper does not decrease the stability of the incoming beam, increasing the technique's applicability to future FEL and HEP facilities.

Simulations of the chirped bunch interacting with plasma over the full discharge delay time can be seen in Figure 32.17. A comparison between the profile and absolute values of dechirping for both the experimental and simulated data sets shows excellent agreement. The incoming 60.5 MeV/mm chirp is fully compensated 7.9 µs after discharge, implying a dechirping strength of 1.8 GeV/mm/m; two orders of magnitude greater than competing state-of-the-art techniques, with the potential to compensate even greater chirps in shorter distances in future experiments. As such, this principle may be used to mitigate the large energy chirps of electron bunches generated in plasma, thus drastically improving the applicability of plasma wakefield schemes to future experiments where a negligible correlated energy spread is required.

### 32.5.3 Plasma Sources

The parallel development of plasma sources is another essential area of research for the development of practical plasma accelerators. A region of plasma in which the species, density, ionisation state, uniformity, length and longitudinal and/or transverse profile of the plasma density are all well defined is required for both PWFAs and LWFAs. Additionally, the plasma source will need to be reproducible and highly reliable.

For the 1 GeV case, we foresee a single stage of plasma acceleration, 40 cm long (1 mm in diameter), coupled with the RF linac operating at about 500 MeV. Such a goal can be obtained with a plasma density around $1 \times 10^{16} \text{ cm}^{-3}$ (corresponding to a wave breaking field $E_0$ around 13 GV/m), that can be used to produce electric fields of 1–2 GV/m and characterised by a plasma wavelength of $\lambda_p \approx 300$ µm. In our plasma module, these operating conditions will be obtained by producing a neutral gas pressure around 50 mbar, that will be ionised by using a voltage around 25–27 kV, corresponding to a plasma current pulse through the capillary of 500 A. The maximum allowed voltage in this design is around 40 kV, which can be used to ionise up to 70-cm long capillaries.

For the 5 GeV case, if we maintain the plasma density around $1 \times 10^{16} \text{ cm}^{-3}$, the structure of the capillary plasma source has to be changed with respect to the previous case. In fact, this value of density allows to reach accelerating gradients around 1–2 GV/m, that entails the use capillaries up to 2–3 m in length in order to achieve 5 GeV. In this operating conditions, the requested breakdown voltage for a conventional single stage capillary could become larger than 100–150 kV. This high voltage may damage the capillary surface, therefore using a trigger discharge which will reduce the breakdown threshold as well as the jittering time of the discharge is planned.

This proposed scheme is based on the gas filled capillary discharge in which we pre-ionise the gas with a preformed plasma prior to the main discharge. Similar mechanisms have been studied in the past for different purposes, such as cold cathode thyratron [853], trigatron [854] and segmented laser trigger ablative capillaries [781].

With this scheme, which may be referred as segmented capillary discharge, we aim to combine the advantages of the segmented discharge with gas-filled capillary
<figure><img src="image_293.png" /></figure>

**Fig. 32.17.** The FWHM of the chirped bunch energy as a function of discharge time relative to the arrival time of the electron bunch. The standard deviation, representing the shot-to-shot fluctuations per delay step, is plotted. Simulated FWHM of the chirped bunch energy spectra as a function of electron plasma density over the identical range are shown for comparison [850] (copyright (2019) by the American Physical Society).

technology to produce long plasma channel (m-scale) for plasma-based acceleration schemes of the EuPRAXIA project.

The segmented capillary discharge proposed for this project will use a trigger discharge obtained with a pulsed high voltage signal to overcome the limits of the Paschen’s law. The scheme in Figure 32.18 shows a possible implementation of this technique. A voltage of few kVs is imposed between the two external electrodes. The voltage is not enough to ignite the discharge because is still lower than the breakdown threshold obtained with the Paschen’s curves. The initial plasma, instead, is formed in a short primary capillary (first stage). Part of this plasma and free electrons expand into the long capillary (the second stage) being accelerated by the potential of the last electrode. The electrons then gain in a short distance enough energy to ionise the neutral molecules, producing an avalanche-like effect in the neutral gas which lets the discharge to ionise the entire gas column. The proposed technique led to produce m-scale plasma channel with reasonable applied voltage. Due to the reduced requirement on the breakdown voltage, the basic structure of the segmented capillary discharge can be repeated to create a multi-stage capillary without particular attention on the high voltage generator. The multistage capillary is then just a chain of few assembled segmented capillaries.

A single segmented capillary unit can be extended by adding more units obtaining up to m-scale capillaries homogeneously ionised and controlled independently one to each other, leading to the desired length of plasma with the proper density (1 × 10¹⁶–1 × 10¹⁷ cm⁻³) required for this project. The possible interference between the electrodes is avoided by the use of the stripline in the discharge circuit, which allows to carry high voltage without crosstalk.
<figure><img src="image_294.png" /><figcaption>**Fig. 32.18.** Scheme of the segmented capillary: in the first stage the trigger discharge starts the ionisation of the entire gas confined into the capillary (second stage). This single unit can be extended by adding more units to reach m-scale capillaries.</figcaption></figure>

### 32.5.4 Beam-Driven Plasma Wakefields

One of the main goals of DESY’s FLASHForward facility is to accelerate an externally injected witness bunch without degrading the longitudinal and transverse beam quality (i.e., while preserving charge, energy spread and emittance). This challenging task has seen significant progress in recent experiments. While much of this work is currently on-going, one particularly striking preliminary result is shown in Figure 32.19, demonstrating fine control over the longitudinal phase space resulting in very low-energy spread acceleration – on the sub-per-mille level.

Reaching this result involved finding the sweet spot in a large parameter space of beam- and plasma parameters. It should be emphasised that performing a multi-dimensional scan over thousands of shots demands ultra-stable beams and plasmas and a high level of machine tunability.
<figure><img src="image_295.png" /></figure>

**Fig. 32.19.** Sample shots showing energy spectrum of a two-bunch beam, with a driver (left) and a witness bunch (right), with no interaction (top) and after passing through 33 mm of plasma (bottom). This working point was the result of an optimisation procedure to preserve energy spread. In fact, the initial (correlated) energy spread was approximately halved during acceleration, from 0.09% RMS to 0.05% RMS (spectral peak).

## 32.6 Use of Other Novel Technologies

### 32.6.1 Possible Alternative Injector Concepts

One of the objectives of the non-EU-funded EuPRAXIA work package WP10 is to monitor the world-wide efforts on the alternative injector concepts. This survey is performed as part of EuPRAXIA in order to present a complete picture of the competing advanced acceleration schemes and to evaluate if one of these concepts may serve as an alternative external injector in the future. This CDR-chapter lists some of the most prominent efforts in this field and shows some simulation and experimental results. While the efforts on ultra-cold electron sources will also be covered here, the current world-wide efforts can be split into two main directions:

- Dielectric laser acceleration (DLA)

- THz acceleration in dielectric loaded wave-guides

It must be noted that beam-driven dielectric wakefield accelerators are not within the scope of this report.

### 32.6.2 Ultra-Cold Electron Source

Electron sources are the basic components for many applications from electron diffraction and electron microscopy systems to state-of-the-art scientific research facilities utilizing particle accelerators, such as X-ray free-electron lasers, injector for laser-plasma based accelerators and high-energy electron-positron colliders, e.g. the International Linear Collider (ILC) and the Compact Linear Collider (CLIC). Here a brief description of the preliminary results undertaken at the University of Manchester is given.
<figure><img src="image_296.png" /><figcaption>**Fig. 32.20.** Sketch and photo of the experimental setup for the ultra cold electron source at Manchester University.</figcaption></figure>

<figure><img src="image_297.png" /><figcaption>**Fig. 32.21.** The first electrons measured on 2nd March 2017 at Manchester University.</figcaption></figure>

Cold atom electron source (CAES) have been proposed as an alternative to conventional photo-injectors or thermionic electron guns, which are widely used in today's particle accelerators. The CAES can produce electron beams with temperatures as low as 10 K ($\Delta E \approx 1$meV), which is several orders of magnitude lower than for both thermionic and photo-emitter sources. The resultant beam emittance (which is a measure of beam quality in position and momentum phase space) is hence markedly improved, allowing ultra-high brightness electron bunches to be produced. These features are crucial for the next generation particle accelerators, e.g. free-electron lasers, plasma-based accelerators and the future high luminosity linear colliders, and for structure studies using high resolution electron diffraction. Figure 32.20 shows a schematic of the cold atom electron source and a picture of the setup.

First electrons were measured in spring 2017 (see Fig. 32.21) with the further characterisation of the source still ongoing.

Given the very experimental stage of this concept, it cannot be seen as a viable alternative for use at EuPRAXIA at the moment.

### 32.6.3 Dielectric Laser Acceleration (DLA)

Dielectric laser-driven acceleration (DLA) refers to the acceleration of electrons in photonic micro-structures made of dielectric and semiconductor materials which are
<figure><img src="image_298.png" /><figcaption>**Fig. 32.22.** Example of the modulation of the transverse beam size due to the phase-dependence of the focusing field. For more details see [859]</figcaption></figure>

driven by lasers in the 0.8µm–10µm range. A good review can be found in [855]. Compared to laser plasma acceleration (LWFA), each individual laser is very low power, but the goal is to stage multiple DLAs with each powered by a dedicated laser at high repetition rate (MHz). First steps towards staging of these accelerators have been shown e.g. by the University of Erlangen, Germany. While the overall acceleration length achieved experimentally so far is still very limited (sub-cm length, sub-MeV overall energy gain), significant acceleration gradients (hundreds of MeV/m) have been observed [856].

Multiple leading groups have recently joined in the “Accelerator on a Chip International Program” (ACHIP) to combine the efforts on this topic. This program covers all aspects of building such an accelerator, thus not only acceleration, but also electron guns, transverse focusing, diagnostic and light generation [857]. With the transverse focusing of the electron beam also being performed by DLAs, Figure 32.22 shows a result of the simulation of an externally injected beam with a length of multiple laser-periods. Due to the phase-dependent transverse focusing, the transverse beam size gets modulated. While most of the studied concepts are driven by side-coupled lasers, currently studies on longitudinally coupled structures are being revitalised aiming to make use of the recent progress in manufacturing technology [858].

Given the current limitation of experimentally achieved energy gain of ≤ 1MeV, it cannot be seen as a viable alternative for use at EuPRAXIA at the moment.

## THz Acceleration in Dielectric Lined Waveguides

A different concept of dielectric acceleration is the acceleration of electrons by THz lasers in dielectric loaded waveguides. Lasers are used to create THz fields, e.g. by optical rectification, which are then coupled into the waveguides. These structures consist of metallic waveguides which are lined with suitable dielectric material (e.g quartz) to slow down the phase-velocity in the structures. Given the high frequency and the dielectric material, field levels of the order of several hundred MeV should be achievable without breakdown. As suitable THz sources are only currently being developed, only proof of principle experiments have been done so far [860]. At DESY, the AXSIS [861] project currently aims to set up the required laser and accelerator infrastructure to develop an all-THz driven light source.

All-optical solutions require the development of corresponding electron sources such as described in e.g. [862]. First experimental steps towards this goal have been achieved [863] but are still very limited in energy as well as beam quality. While these results are still far from fulfilling the requirements, they are an important stepping stone. On the other hand, simulation studies on the combination of a conventional S-band RF-gun with a THz linac also show promising results [864].
Given the current limitation of experimentally achieved energy gains of few 10ns of MeV, it cannot be seen as a viable alternative for use at EuPRAXIA at the moment. This may be revised if more powerfull THz sources should become available.

### 32.6.4 State of the Art in Fibre Optics Lasers

Another main task of WP10 is to monitor the progress of fiber lasers (FL) and to judge their applicability to the EuPRAXIA project. Currently almost all LWFA experiments are performed using Ti:Sa laser systems. While these systems are capable to deliver the required laser parameters for single shots, they feature the following main disadvantages:

- Low repetition rate. PW-class Ti:Sa systems are currently limited to the few Hz range, mainly limited by thermal issues.

- Low efficiency. PW-class Ti:Sa systems have a very poor conversion efficiency from wall plug power to laser power.

In fiber lasers, optical fibers doped with rare earth ions (e.g. ytterbium) are used as gain materials. These lasers are wide spread in industry use due to their robustness, high repetition rate (CW possible) and high efficiency [865-869]. There are efforts ongoing to increase the power obtained from a single fiber, e.g:

- double clad fibers to allow increasing the pumping power

- large core fibers. If used, one loses the advantage of having a single mode fiber and additional tricks must be applied to compensate the associated disadvantages (e.g. strong coiling of the fibers, asymmetric fiber designs, ...).

Still, the power from a single fiber is limited to the mJ level. Several groups worldwide pursue efforts to combine multiple FL to reach higher laser power. In the next section some of this concepts are described.

While most currently used fiber lasers today operate in CV or short pulse mode, ultra-short pulse generation from fiber lasers is possible and was demonstrated using e.g. rare-earth-doped fibers providing the required bandwidth.

In summary FL feature the following key advantages:

- very high ratio of surface to volume and thus a well controllable cooling of the gain material.

- Ability to use materials with low quantum defect

- Laser guiding effect.

- The fibers guides the laser and pump light and thus a good laser quality is obtained. (up to 90% for kW systems)

- This allows using the very efficient diode lasers as pump lasers.

- high efficiency. (due to low intrinsic losses, usability of materials with low quantum defect)

The applicability of fiber lasers to LWFA has been studied e.g. in [870,871]

### Combination Methods

In order to increase the maximal power obtainable from a fiber laser based system, there are multiple options to combine the power from multiple fibers.

- The possibility to resonantly drive the plasma wake with multiple comparably low-power lasers pulses spaced in time has been studied e.g. in [607]. While this is an interesting concept, it does not bring down the power per pulse to the level achievable by today's fiber laser systems and the rep-rate is also not suitable.
- The use of incoherently combined laser pulses has been studied in [872]. While the presented results achievable by the incoherent combination are better than one may expect, the disadvantages are too dominant.

- There are currently several groups worldwide trying to coherently combine the power of multiple fiber lasers. The central issues are the required high control over the individual fibers and the fast feedback [873–876] and e.g. the Jena group managed to combine multiple rod-type fiber lasers [877,878]. In France, the X-CAN project (which is a follow-up of the ICAN-project) is using thin fibers and is currently aiming to combine 64 fibers. While these concepts can in principle scaled to much more fibers, still significant engineering work must be done.

## Conclusion

While the fiber lasers have very promising results, their individual power is too small for LWFA applications. While they may be used as pumps for TiSa systems, the world-wide development of the coherent combination of multiple fibers has not yet achieved the required level and must be monitored for further developments. On the long run, the high rep-rate of fiber lasers will be crucial to the success of LWFA, not only because of the obvious benefits for the users, but also as it will allow to implement kHz-feedback concepts around the laser and LWFA.

## 32.7 Experience from FEL Test Experiments

As discussed in Chapter 1, there are currently three experimental projects towards an LWFA-based FEL – SOLEIL-LOA, CFEL-DESY (Lux) and KIT-FSU. The first two programs involve the longitudinal beam decompression, and KIT-FSU collaboration aims at the transverse gradient undulator scheme. The scientific programs of these projects are very different from each other, and therefore, they provide different experiences and teach us different lessons.

### SOLEIL-LOA

The SOLEIL-LOA project has FEL amplification as its final goal, and the intermediate steps include equipment commissioning, beam dynamics and incoherent radiation studies, weak and high-gain FEL processes. In this experiment, the regime with moderate electron energies of 150-200 MeV, and UV-XUV radiation 200-300 nm is explored in order to relief the amplification constraints which become more challenging as the radiation wavelength becomes shorter. The beamline is designed to provide tight and sophisticated control of the beam properties.

During the commissioning runs, different regimes of LWFA were explored, including usage of different target designed – a variable-length gas cell and super-sonic gas nozzle. For the further work the preference was given to the nozzle target, as it allows more flexibility for the setup and alignment. The nozzle setup was tested in the different regimes, using the pure low-Z gas (helium), or a mixture of low- and high-Z gases (helium + 1–2% nitrogen) for ionisation injection, with and without a plastic wafer for the shock-injection. For the final work the nozzle with gas mixture was chosen as a most straightforward and repeatable way of operation.

In this project a strong accent is made on the electrons manipulation beamline and it starts with the three specially designed variable strength quadrupoles (QUAPEVA) placed only a few millimetres downstream the LWFA nozzle. These
quadrupoles were shown to play a major role in the beam dynamics and manipu-
lation of the beam transverse phase space. Due to the plasma effects on the laser
propagation, LWFA beam intrinsically acquires some angle with the laser axis, which
was shown to be reproducible along the session of shots. This effect may deviate from
session-to-session and practically represents an important problem for the beamline
alignment. It was shown that controlling the positions of QUAPEVA quadrupoles it
is possible to separately correct orbit mis-steerings and minimise beam dispersion.
This correction technique was realised with a help of a specially developed procedure
of beam pointing alignment compensation (BPAC), which takes advantage of the
motorised translations of the QUAPEVA quadrupoles. Performing this procedure at
the beginning of each shooting session has proven to be a very useful tool for the
dynamics control of the beamline alignment and beam transverse dispersions.

This manipulation of the longitudinal electron phase space is realised via a mag-
netic chicane. Besides the longitudinal beam decompression, the chicane allows to
use a tuneable slit in the dispersive section for electron energy range selection. This
part was essential for the photon observation, as it allows to select a single percent
energy window and correlate it to the undulator radiation spectral features.

Therefore the beamline has proven to provide a tight and sophisticated control
of the beam properties, and is able to correct the intrinsic limitations of the LWFA
beam, such as relatively low pointing stability, emmitance growth and energy spread.
The matched electron beam leads to the successful observation of undulator syn-
chrotron radiation after an 8 m transport path. In the experiments targeting the
photon generation it was shown, that the proper advance beam manipulation is
essential for the successful studies of the amplification. Several of the most relevant
recent results are presented in [879–882].

CFEL-DESY

The scientific programme of CFEL-DESY projects covers a wide range of tasks. It goes from the development of the plasma target and high-repetition-rate LWFA, to the spontaneous X-ray emission and FEL amplification, also including some aspects of software development.

A first challenging part of this work is the development of the dedicated LWFA
scheme using a multi-inlet gas-cell with the tailored pressure profile and pulsed dis-
charge. Such a scheme should allow the separate injector and accelerator stages and
it targets the high-energy 600 MeV and high quality electron beams. The compatibil-
ity of the *Lux* beamline with the *Regae* linac machine also requires a dedicated gas
evacuation system and limits the size of the interaction chamber.

As an intermediate step on the way to FEL amplifier, the *Lux* projects, also
targets generation of the keV-level X-rays at a moderately high repetition-rate of
5 Hz.

KIT-FSU

The KIT-FSU project aims – as a major milestone on the path towards a LWFA-
driven transverse gradient undulator (TGU)-FEL – at demonstrating and investigat-
ing the TGU scheme for the case of spontaneous undulator radiation. Besides the
continuous work on improving the LWFA performance at the JETI laser facility in
Jena, it encompasses the development and realisation of a well-adapted beam trans-
port line, the design, realisation and characterisation of a superconducting TGU and
the theoretical and experimental investigation of the beam dynamics inside the TGU
and subsequently the characteristics of the generated radiation.
The TGU scheme requires a beam transport line with adjustable dispersion at the entrance of the TGU for matching the electron energy to the TGU's magnetic flux density amplitude. That is achieved by a dogleg chicane, composed of a quadrupole triplet for beam capture and an achromat-like cell, in the first experimental approach consisting of two dipole magnets with a quadrupole triplet centred between them. Similar to the SOLEIL-LOA approach, the pointing uncertainty of the LWFA is coped with in particular by making the quadrupole magnets positionally adjustable and applying a beam-based alignment scheme. For this purpose dedicated in-vacuum quadrupole electromagnets have been designed and built. The described linear transport line and alignment procedure were successfully experimentally demonstrated. Our concept for the beam transport is currently being expanded to a non-linear scheme allowing for chromatic correction and proper matching of a wide electron energy distribution in order to take full advantage of the TGU scheme.

On the side of the TGU, various options of realising such a device had been investigated before a 40-period superconducting TGU with cylindrical pole shape was built. The device has been successfully quench-tested in a liquid Helium bath and is currently under commissioning in its own, conduction cooling-based cryostat. Two complementary experimental tests of the TGU are planned in order to gain a comprehensive understanding of the beam dynamics inside the TGU as well as of the TGU radiation properties: (1) A test with a well-defined electron beam at a conventional accelerator to be performed at the ARES linac which is a part of the SINBAD test facility in collaboration with DESY, Hamburg, and (2) a test at the laser wakefield accelerator at the JETI laser facility in Jena. While with the former "analytical" experiment the properties of the TGU in terms of beam dynamics and generated radiation will be mapped out in detail, the latter "synthetic" experiment will be the actual proof of principle for a LWFA-driven TGU light source.

## 32.8 Accelerator Prototyping – Report on Test Experiments

### 32.8.1 Introduction

In this chapter we report on the prototyping and experimental activity that some of the EuPRAXIA partners pursued to get information relevant for the present Conceptual Design Report (CDR). At the moment of writing the CDR, some of the experiments have already shown interesting results, others have been approved and already assembled; this chapter accounts for all of them with some examples. The experiments we cover here are focused on improving the plasma accelerated beam quality in terms of beam parameters, reproducibility and reliability.

One of these experiments will test advanced plasma cells to assess the sensitivity of the electron beam quality and reliability on impinging laser pulse and plasma parameters. This is a critical issue for EuPRAXIA as the dependencies of electron beam parameters on the driving laser and plasma conditions need to be understood fully.

The second experiment proposes a single shot, compact, non-destructive bunch length measurement. The electron bunch length is a crucial parameter in generating the plasma bubble typical of particle driven plasma accelerators; indeed, the driver bunch length needs to be finely tuned to trigger the plasma acceleration of the witness beam. Moreover, the high brightness beam of EuPRAXIA relies on high current, that is short bunch length. The single shot feature can be particularly useful for monitoring the reproducibility of plasma accelerated beams helping in adjusting the many key parameters. At the same time, having compact diagnostics is mandatory if one wants to build a compact accelerator.
The third experiment addresses the issues of capillary manufacturing to minimise mainly aging problems in all the schemes using capillaries (both laser- or beam-driven as well as in staged plasma accelerators). The multiple discharge may damage the capillaries affecting the plasma distribution and thus the accelerated beam parameters.

### 32.8.2 Testing Laser Wakefield Accelerator Sources for EuPRAXIA

A joint experiment, involving different institutes of the EuPRAXIA consortium, have been proposed; its mail goal is to examine the electron beam quality and reproducibility from laser-driven plasma wakefield acceleration in a double gas cell. This is a key component of the development work required for EuPRAXIA, aiming to deliver compact, high quality, high rep-rate electron beam sources based on plasma acceleration technology.

Recent progresses in Laser Wakefield Acceleration (LWFA) have demonstrated acceleration of electron beams to > GeV energies. However, in order to build a facility based on LWFA-driven beams, their stability, reproducibility, energy spread, etc. need to be improved further. In LWFA, an intense laser pulse propagates through an underdense plasma and drives a plasma wave. It leads to large longitudinal and transverse fields, which are capable of accelerating and focusing electrons.

Typically, the plasma is formed by ionisation of a gaseous medium provided by a supersonic gas jet, a gas-filled capillary or a gas cell. Along with the stability of the driving laser, the properties of the plasma medium and its stability affect the beam quality in LWFA. In order to produce stable, high-quality electron beams for applications, it is essential to delineate the effects of the laser driver from that of the plasma medium. The determination of tolerances in the variation of several key parameters is crucial for designing an accelerator such as EuPRAXIA and is poorly documented: such an experiment may provide data which are much needed to benchmark simulations and speed up LWFA development.

The experiment will investigate the influence of laser parameters on controlling the electron beam parameters for given tailored plasma profiles; this is of paramount importance to EuPRAXIA.

The experiment will be hosted in the Lund Laser Centre (LLC). In order to have a meaningful test, it is important that the drive laser is well characterised for all its parameters, including energy, pulse length, spectrum, wave-front and pointing fluctuations on every shot in order to delineate the driver effects from those induced by the plasma. The 20TW laser at the LLC is ideal for this test in this regard as it not only fields all the necessary diagnostics for this experiment but also employs fast pointing control in order to stabilise the laser pointing from shot to shot.

The experiment will use the 20TW laser facility at LLC. The high-power laser beam will be focused using an F/20 parabolic mirror to a spot size of ~20 µm yielding a normalised vector potential in vacuum of 1.4. The gas cell will be pressurised through two separate fill tubes to ≤1bar to give electron densities in the range 0–2 × 10¹⁹ cm⁻³. One tube will be used to fill the first cell with a helium (or hydrogen)-nitrogen mix, and the second tube will fill the second cell with pure helium (hydrogen). This will allow to investigate the performance of the acceleration under different injection conditions.

A short pulse transverse probe will be used to diagnose the performance of the gas cell (plasma density) and to characterise online the plasma profile with a Mach-Zehnder interferometer. The stability of the gas cell during the acceleration will be monitored shot-to-shot. The transmitted laser pulse will be sampled onto a spectrometer to measure the effects on the laser spectrum due to the plasma wave formation.
A magnetic spectrometer with scintillator-based detectors will measure the produced electron spectrum and angular distribution.

The experimental team is composed of researchers from Imperial College London, CNRS, CEA, INFN and CLF. Each collaborator has proven expertise in LWFA and gas cell design and is actively involved with the EuPRAXIA design project.

The proposal will be partially funded by the ARIES network and 4 weeks of access at the laser facility in Lund has been planned. The highly characterised, pointing-stabilised laser in the Lund Laser Centre is of fundamental importance for this experiment.

### 32.8.3 Non-Destructive Bunch Length Measurement Based on Smith-Purcell Radiation

Non-destructive bunch measurements are a very important diagnostics in a plasma accelerator to improve reliability and repeatability by tuning the (many) parameters affecting the acceleration process. The experiment aims to measure the bunch length at the SPARC_LAB linear accelerator by using Coherent Smith-Purcell radiation and comparing the results with other diagnostic tools. The innovative Smith-Purcell detectors are designed by the LAL group.

Smith-Purcell radiation is emitted when an electron bunch is traveling close to a corrugated planar device; from the peculiarity of the emitted radiation spectrum it is possible to measure the bunch length. The beam trajectory is a fundamental parameter and the beam axis will be adjusted with two BPMs, one upstream and one downstream as well as a charge monitor that is installed downstream. Downstream optical transition radiation (OTR) screens will be used as well.

The installed detectors are described in Figure 32.23, since there is a correlation between the Smith-Purcell radiation angle and its frequency, it is possible to measure the whole emitted radiation spectrum in one single shot.

To look for the signal, the accelerator was delivering the maximum possible charge (to minimise the signal noise) and the beam axis was set as close as possible to the grating. Afterwards the grating position has been moved to understand the background and it has been changed to measure the signal with different dynamic ranges. The bunch profile could also be changed using the low energy bunch compressor (first two Linac sections). The results are being analyzed and compared to standard bunch length measurements with an RF deflector.

The fully coherent signal due to the very large pitch grating has been observed. The measurement of the fully coherent signal is always coupled with the measurement of the background by replacing the grating by a blank plane (grating without teeth). Measuring the partially coherent signal with several gratings having different pitches allows a measurement of the signal yield on a large dynamic range. By comparing this signal yield with the fully coherent signal the form factor of the bunch can be extracted while eliminating most theoretical uncertainties on the description of the single electron yield.

### 32.8.4 3D-Printed Capillary for a Hydrogen-Filled Discharge for Plasma Acceleration

Plasma-based acceleration experiments require capillaries with a radius of a few hundred microns to confine plasma up to a centimetre scale capillary length. A long and controlled plasma channel allows to sustain high fields which may be used for the manipulation of the electron beam or to accelerate electrons. The production of these capillaries is relatively complicated and expensive since they are usually made with hard materials whose manufacturing requires highly specialised industries. Fine
<figure><img src="image_299.png" /><figcaption>**Fig. 32.23.** The SPARC_LAB experimental apparatus (right) and conceptual drawing (left), as seen after its installation in 2018.</figcaption></figure>

<figure><img src="image_300.png" /><figcaption>**Fig. 32.24.** Discharge current profile and averaged density along the entire capillary length acquired every 100 ns of delay from the discharge trigger. Each point is averaged over 10 shots and over the entire capillary length. The error bars represent the standard deviation around the mean value [883] (reprinted with permission of AIP Publishing).</figcaption></figure>

variations of the capillary shape may significantly increase the cost and time needed to produce them.

SPARC_LAB demonstrated the possibility of using 3D printed polymeric capillaries to drive a hydrogen-filled plasma discharge up to 1 Hz repetition rate in an RF-based electron linac [883]. The plasma density distribution has been measured after several shot intervals, showing the effect of the surface ablation on the plasma density distribution. This effect is almost invisible in the earlier stages of the discharge. After more than 55,000 shots (corresponding to more than 16 h of working time), the effects of the ablation on the plasma density distribution are not evident and the capillary can still be used.

The use of these capillaries may significantly reduce the cost and time for prototyping, allowing us to easily manipulate their geometry, laying another building block for future cheap and compact particle accelerators.

The effects of the ablation of the capillary can be observed by measuring the average electron plasma density variation after thousands of shots, as shown in Figure 32.24. The density has been acquired by varying the trigger of the Intensified Charge-Coupled Device (ICCD) with respect to the discharge trigger with 100
<figure><img src="image_301.png" /><figcaption>**Fig. 32.25.** Plasma electron density distribution along the capillary measured at the maximum density value for an increasing number of shots [883] (reprinted with permission of AIP Publishing).</figcaption></figure>

<figure><img src="image_302.png" /><figcaption>**Fig. 32.26.** Entrance of the capillary after the print (left) and after more than 55,000 shots (right). The burns on the entrance are probably caused by the electrons impinging on the plastic during the alignment [883] (reprinted with permission of AIP Publishing).</figcaption></figure>

ns steps. Each point is averaged over 10 shots, and each density value is averaged over the entire capillary length. The error bars represent the standard deviation around the mean value. As can be seen from the earliest measurements taken after 10,000 shots, the electron density in the earlier shots reached its maximum of $\simeq 10^{17} \text{ cm}^{-3}$ around 500 ns after the discharge, and then it started to decrease exponentially at 600 ns. By increasing the number of shots, the electron density peak moves to an earlier time (almost 400 ns after the trigger), but its value does not change.

Due to the burns caused by the earlier discharges, when the thermal conduction is higher and the heat flux can penetrate more easily into the capillary walls, the capillary surface becomes harder and it changes its thermal conductivity reducing the possibility to be ablated and increasing the heat transfer to the gas letting it be ionised faster. The shot-to-shot error on the averaged plasma density around the maximum, i.e. between 300 and 600 ns, is lower than 7% even for the measurements obtained
at 50,000 shots. The plasma density profiles along the capillary acquired when the plasma density reached its maximum, i.e., at 500 ns delay for the earlier shots and 400 ns for the latest, have been plotted in Figure 32.25. After more than 50,000 shots (corresponding to more than 16h of working time), no significant degradation of the longitudinal plasma distribution has been revealed.

The high plasma temperature which heats the capillary surface also altered the optical properties of the capillary. The optical transmission in the range between 400 and 700 nm has been measured before and after 55,000 shots. The burns caused by the discharges reduce the transmission of light, especially at the lower wavelengths, possibly due to surface modification because of hardening. This is not pronounced enough to prevent the observation of the plasma emitted light, but the transmittance of the Balmer beta line is reduced by almost 17%. The changes in the transmittance may also be caused partly by the electrons of the accelerated beams which during the alignment have hit the capillary surface or by the ablation caused by the plasma itself. The different transmittance of the light has been taken into account during the spectroscopic analysis.

The picture of the entrance hole of the capillary has been acquired before and after more than 55,000 shots (Fig. 32.26) by using a microscope with a magnification of 12.5. On the left side of Figure 32.26, it is possible to see the capillary before its use. The entrance of the capillary has a 1 mm diameter, and the internal surface is not perfectly smooth due to the printing process. On the right, the figure shows the same hole after 55,000 shots placed in high vacuum and exposed to electron bunches. The radius of the capillary has been changed during the operation, and it is larger by $79\pm8$ µm than in the left image. A microscope was also used to observe the transverse profile of the capillary. From the comparison between the edge (on the right of the picture) and the middle part of the capillary, it was observed that the ablation affects the capillary uniformly. The radius gets larger by 1.4 pm per shot, which is comparable with the values obtained with sapphire capillaries.

## 32.9 CAD Model of the Conceptual EuPRAXIA Facility Layout

Some example screenshots of the CAD model of the proposed EuPRAXIA facility layout are shown below. The current model is conceptual, but will form a basis for the detailed technical layout to be developed in the next phase of EuPRAXIA. The full CAD model is available upon request.

<figure><img src="image_303.png" /><figcaption>**Fig. 32.27.** Screenshot of the CAD model of the proposed EuPRAXIA facility layout. Here, the laser-driven plasma acceleration construction site is shown in a perspective view.</figcaption></figure>
<figure><img src="image_304.png" /><figcaption>**Fig. 32.28.** Screenshot of the CAD model of the proposed EuPRAXIA facility layout. Here, the laser-driven plasma acceleration construction site is shown in a top view.</figcaption></figure>
## 33 EuPRAXIA Publications and Conference Contributions

The following list provides an overview of the journal publications and conference proceedings published as part of the EuPRAXIA design study. Many more papers were published and presented in the past four years on topics and results related to the project, these could not all be included here but are mentioned in many cases as references throughout this report.

### 33.1 List of EuPRAXIA Peer-Reviewed Publications

1. Xia G., Bonatto A., Pizzato Nunes R., Liang L., Jakobsson O., Zhao Y., Williamson B., Davut C., Wang X. Plasma Beam Dumps for the EuPRAXIA Facility. Instruments 4(2) 10 (2020). 10.3390/instruments4020010

2. Ghaith A., Loulergue A., Oumbarek-Espinos D., Marcouille O., Valleau M., Labat M., Corde S., Couprie M.-E. Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser. Instruments 4 1 (2020). doi:10.3390/instruments4010001

3. Nguyen F., Bernhard A., Chance A., Couprie M.-E., Dattoli G., Lechner C., Marocchino A., Maynard G., Petralia A., Rossi A.R. Free electron laser performance within the EuPRAXIA facility. Instruments 4(1) 5 (2020). doi:10.3390/instruments4010005

4. Siders C.W., Galvin T., Erlandson A., Bayramian A., Reagan B., Sistrunk E., Spinka T., Haefner C. Wavelength Scaling of Laser Wakefield Acceleration for the EuPRAXIA Design Point. Instruments 3(3) 44 (2019). 10.3390/instruments3030044

5. Toci G., Mazzotta Z., Labate L., Mathieu F., Vannini M., Patrizi B., Gizzi L.A. Conceptual Design of a Laser Driver for a Plasma Accelerator User Facility. Instruments 3(3) 40 (2019). 10.3390/instruments3030040

6. Huebner M., Will I., Koerner J., Reiter J., Lenski M., Tuemmler J., Hein J., Eppich B., Ginolas A., Crump P. Novel High-Power, High Repetition Rate Laser Diode Pump Modules Suitable for High-Energy Class Laser Facilities. Instruments 3(3) 34 (2019). 10.3390/instruments3030034

7. Ghaith A., Oumbarek D., Kitegi C., Valleau M., Marteau F., Couprie M.-E. Permanent Magnet Based Quadrupoles for Plasma Acceleration Sources. Instruments 3(2) 27 (2019). doi:10.3390/instruments3020027

8. Ghaith A. et al. Tunable High Spatio-Spectral Purity Undulator Radiation from a Transported Laser Plasma Accelerated Electron Beam. Scientific Reports 9 19020 (2019). 10.1038/s41598-019-55209-4

9. Tomassini P., Terzani D., Labate L., Toci G., Chance A., Nghiem P.A.P., Gizzi L.A. High quality electron bunches for a multi-stage GeV accelerator with the Resonant Multi-Pulse Ionization injection. Physical Review Accelerators and Beams, in press (2019).

10. Weikum M. et al. EuPRAXIA – a compact cost-efficient particle and radiation source. AIP Conference Proceedings 2160 040012 (2019). 10.1063/1.5127692

11. Terzani D., Londrillo P. A fast and accurate numerical implementation of the envelope model for laser-plasma dynamics. Computer Physics Communications 242 49–59 (2019). 10.1016/j.cpc.2019.04.007

12. Ferran Pousa A., Martinez de la Ossa A., Brinkmann R., Assmann R.W. Compact Multistage Plasma-Based Accelerator Design for Correlated Energy Spread Compensation. Physical Review Letters 123 (5) 054801 (2019). 10.1103/PhysRevLett.123.054801
13. Kokurewicz K., Brunetti E., Welsh G. H., Wiggins S. M., Boyd M., Sorensen A., Chalmers A. J., Schettino G., Subiel A., DesRosiers C., Jaroszynski D. A. Focused very high-energy electron beams as a novel radiotherapy modality for producing high-dose volumetric elements. Scientific Reports 9 10837 (2019). 10.1038/s41598-019-46630-w

14. Hidding B., Beaton A., Boulton L., Corde S., Doepp A., Habib F. A., Heinemann T., Irman A., Karsch S., Kirwan G., Knetsch A., Manahan G. G., de la Ossa A. M., Nutter A., Scherkl P., Schramm U., Ullmann D. Fundamentals and Applications of Hybrid LWFA-PWFA. Applied Sciences-Basel 9 (13) 2626 (2019). 10.3390/app9132626

15. Hidding B., Foster B., Hogan M. J., Muggli P., Rosenzweig J. B. Directions in plasma wakefield acceleration. Philosophical Transactions of The Royal Society A – Mathematical Physical and Engineering Sciences 377 (2151) 20190215 (2019). 10.1098/rsta.2018.0215

16. Panetta D., Labate L., Billeci L., Di Lascio N., Esposito G., Faita F., Mettivier G., Palla D., Pandola L., Pisciotta P., Russo G., Sarno A., Tomassini P., Salvadori P. A., Gizzi L. A., Russo P. Numerical simulation of novel concept 4D cardiac microtomography for small rodents based on all-optical Thomson scattering X-ray sources. Scientific Reports 9 8439 (2019). 10.1038/s41598-019-44779-y

17. Brandi F., Gizzi L. A. Optical diagnostics for density measurement in high-quality laser-plasma electron accelerators. High Power Laser Science and Engineering 7 e26 (2019). 10.1017/hpl.2019.11

18. Shalloo R. J., Arran C., Picksley A., von Boetticher A., Corner L., Holloway J., Hine G., Jonnerby J., Milchberg H. M., Thornton C., Walczak R., Hooker S.M. Low-density hydrodynamic optical-field-ionized plasma channels generated with an axicon lens. Physical Review Accelerators and Beams 22 (4) 041302 (2019). 10.1103/PhysRevAccelBeams.22.041302

19. Alejo A., Walczak R., Sarri G. Laser-driven high-quality positron sources as possible injectors for plasma-based accelerators. Scientific Reports 9 5279 (2019). 10.1038/s41598-019-41650-y

20. Mehrling T. J., Fonseca R. A., Martinez de la Ossa A., Vieira J. Mechanisms for the mitigation of the hose instability in plasma-wakefield accelerators. Physical Review Accelerators and Beams 22 (3) 031302 (2019). 10.1103/PhysRevAccelBeams.22.031302

21. Shpakov V. et al. Longitudinal Phase-Space Manipulation with Beam-Driven Plasma Wakefields. Physical Review Letters 122 (11) 114801 (2019). 10.1103/PhysRevLett.122.114801

22. Wilson T. C., Li F. Y., Weng S. M., Chen M., McKenna P., Sheng Z. M. Laser pulse compression towards collapse and beyond in plasma. Journal of Physics B-Atomic Molecular and Optical Physics 52 (5) 055403 (2019). 10.1088/1361-6455/ab0132

23. Balerna A. et al. The Potential of EuPRAXIA@SPARC LAB for Radiation Based Techniques. Condensed Matter 4 (1) 30 (2019). 10.3390/condmat4010030

24. Biagioni A. et al. Temperature analysis in the shock waves regime for gas-filled plasma capillaries in plasma-based accelerators. Journal of Instrumentation 14 C03002 (2019). 10.1088/1748-0221/14/03/C03002

25. Hussein A. E. et al. Laser-wakefield accelerators for high-resolution X-ray imaging of complex microstructures. Scientific Reports 9 3249 (2019). 10.1038/s41598-019-39845-4

26. Li X., Chance A., Nghiem P.A.P. Preserving emittance by matching out and matching in plasma wakefield acceleration stage. Physical Review
Accelerators and Beams 22 (2) 021304 (2019). 10.1103/PhysRevAccelBeams. 22.021304

27. Tomassini P., De Nicola S., Labate L., Londrillo P., Fedele R., Terzani D., Nguyen F., Vantaggiato G., Gizzi L. A. **High-quality GeV-scale electron bunches with the Resonant Multi-Pulse Ionization Injection**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 1–4 (2018). 10.1016/j.nima.2018.03.002

28. Couprie M.-E. **Towards compact Free Electron-Laser based on laser plasma accelerators**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 5–15 (2018).

29. Chiadroni E. et al. **Overview of plasma lens experiments and recent results at SPARC LAB**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 16–20 (2018). 10.1016/j.nima.2018.02.014

30. Li X., Mosnier A., Nghiem P.A.P. **Design of a 5 GeV laser-plasma accelerating module in the quasi-linear regime**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 49–53 (2018). 10.1016/j.nima.2018.02.104

31. Rossi A. R., Petrillo V., Bacci A., Chiadroni E., Cianchi A., Ferrario M., Giribono A., Marocchino A., Conti M. Rossetti, Serafini L., Vaccarezza C. **Plasma boosted electron beams for driving Free Electron Lasers**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 54–57 (2018). 10.1016/j.nima.2018.02.092

32. Gizzi L.A., Koester P., Labate L., Mathieu F., Mazzotta Z., Toci G., Vannini M. **A viable laser driver for a user plasma accelerator**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 58–66 (2018). 10.1016/j.nima.2018.02.089

33. Romeo S., Chiadroni E., Croia M., Ferrario M., Giribono A., Marocchino A., Mira F., Pompili R., Rossi A. R., Vaccarezza C. **Simulation design for forthcoming high quality plasma wakefield acceleration experiment in linear regime at SPARC LAB**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 71–75 (2018). 10.1016/j.nima.2018.02.081

34. Svystun E., Assmann R. W., Dorda U., Ferran Pousa A., Heinemann T., Marchetti B., Martinez de la Ossa A., Walker P.A., Weikum M.K., Zhu J. **Beam quality preservation studies in a laser-plasma accelerator with external injection for EuPRAXIA**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 90–94 (2018). 10.1016/j.nima.2018.02.060

35. Walker P. A., Assmann R. W., Brinkmann R., Chiadroni E., Dorda U., Ferrario M., Kocon D., Marchetti B., Pribyl L., Specka A., Walczak R. **Layout considerations for a future electron plasma research accelerator facility EuPRAXIA**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 111–113 (2018). 10.1016/j.nima.2018.02.028

36. Vantaggiato G., Labate L., Tomassini P., Gizzi L. A. **Modelling of pulse train generation for resonant laser wakefield acceleration using a delay mask**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 114–117 (2018). 10.1016/j.nima.2018.02.024
37. Costa G., Anania M. P., Bisesto F., Chiadroni E., Cianchi A., Curcio A., Ferrario M., Filippi F., Marocchino A., Mira F., Pompili R., Zigler A. Characterization of self-injected electron beams from LWFA experiments at SPARC LAB. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 118 – 122 (2018). 10.1016/j.nima.2018.02.008

38. Ferrario M. et al. EuPRAXIA@SPARC LAB Design study towards a compact FEL facility at LNF. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 134 – 138 (2018). 10.1016/j.nima.2018.01.094

39. Pompili R. et al. Recent results at SPARC LAB. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 139 – 144 (2018). 10.1016/j.nima.2018.01.071

40. Giribono A., Bacci A., Chiadroni E., Cianchi A., Croia M., Ferrario M., Marocchino A., Petrillo V., Pompili R., Romeo S., Conti M. Rossetti, Rossi A. R., Vaccarezza C. RF injector design studies for the trailing witness bunch for a plasma-based user facility. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 229 – 232 (2018). 10.1016/j.nima.2018.01.042

41. Scifo J. et al. Nano-machining surface analysis and emittance measurements of a copper photocathode at SPARC LAB. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 233 – 238 (2018). 10.1016/j.nima.2018.01.041

42. Diomede M. et al. Preliminary RF design of an X-band linac for the EuPRAXIA@SPARC LAB project. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 243 – 246 (2018). 10.1016/j.nima.2018.01.032

43. Biagioni A. et al. Wake fields effects in dielectric capillary. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 247 – 251 (2018). 10.1016/j.nima.2018.01.028

44. Giribono A., Bacci A., Chiadroni E., Cianchi A., Croia M., Ferrario M., Marocchino A., Petrillo V., Pompili R., Romeo S., Conti M. Rossetti, Rossi A. R., Vaccarezza C. EuPRAXIA@SPARC LAB: The high-brightness RF photo-injector layout proposal. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 282 – 285 (2018). 10.1016/j.nima.2018.03.009

45. Villa F., Cianchi A., Coreno M., Dabagov S., Marcelli A., Minicozzi V., Morante S., Stellato F. Design study of a photon beamline for a soft X-ray FEL driven by high gradient acceleration at EuPRAXIA@SPARC LAB. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 294 – 297 (2018). 10.1016/j.nima.2018.02.091

46. Vaccarezza C. et al. EUPRAXIA@SPARC LAB: Beam dynamics studies for the X-band Linac. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 314 – 317 (2018). 10.1016/j.nima.2018.01.100

47. Delbos N., Werle C., Dornmair I., Eichner T., Huebner L., Jalas S., Jolly S. W., Kirchen M., Leroux V., Messner P., Schnepp M., Trunk M., Walker P. A., Winkler P., Maier A.R. Lux – A laser-plasma driven undulator beamline. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 318 – 322 (2018). 10.1016/j.nima.2018.01.082
48. Cianchi A., Andreani C., Bedogni R., Festa G., Sans-Planell O., Senesi R. A **complementary compact laser based neutron source**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 323–326 (2018). 10.1016/j.nima.2018.01.052

49. Filippi F., Anania M. P., Biagioni A., Brentegani E., Chiadroni E., Cianchi A., Deng A., Ferrario M., Pompili R., Rosenzweig J., Zigler A. **Tapering of plasma density ramp profiles for adiabatic lens experiments**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 339–342 (2018). 10.1016/j.nima.2018.04.037

50. Filippi F., Anania M. P., Biagioni A., Brentegani E., Chiadroni E., Cianchi A., Ferrario M., Marocchino A., Zigler A. **Plasma ramps caused by outflow in gas-filled capillaries**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 346–349 (2018). 10.1016/j.nima.2018.02.102

51. Cianchi A. et al. **Conceptual design of electron beam diagnostics for high brightness plasma accelerator**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 350–354 (2018). 10.1016/j.nima.2018.02.095

52. Marongiu M., Castellano M., Chiadroni E., Cianchi A., Franzini G., Giribono A., Mostacci A., Palumbo L., Shpakov V., Stella A., Variola A. **Energy measurements by means of transition radiation in novel Linacs**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 355–358 (2018). 10.1016/j.nima.2018.02.093

53. Audet T. L., Lee P., Maynard G., Dufrenoy S. Dobosz, Maitrallain A., Bougeard M., Monot P., Cros B. **Gas cell density characterization for laser wakefield acceleration**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 383–386 (2018). 10.1016/j.nima.2018.01.053

54. Bisesto F. G., Anania M. P., Botton M., Chiadroni E., Cianchi A., Curcio A., Ferrario M., Galletti M., Henis Z., Pompili R., Schleifer E., Zigler A. **Evolution of the electric fields induced in high intensity laser-matter interactions**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 398–401 (2018). 10.1016/j.nima.2018.03.040

55. Brentegani E., Anania M. P., Atzeni S., Biagioni A., Chiadroni E., Croia M., Ferrario M., Filippi F., Marocchino A., Mostacci A., Pompili R., Romeo S., Schiavi A., Zigler A. **Numerical studies on capillary discharges as focusing elements for electron beams**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 404–407 (2018). 10.1016/j.nima.2018.03.012

56. Marocchino A., Chiadroni E., Ferrario M., Mira F., Rossi A. R. **Design of high brightness Plasma Wakefield Acceleration experiment at SPARC_LAB test facility with particle-in-cell simulations**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 408–413 (2018). 10.1016/j.nima.2018.02.068

57. Lee P., Audet T. L., Lehe R., Vay J.-L., Maynard G., Cros B. **Investigation of the dynamics of ionization induced injected electrons under the influence of beam loading effects**. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 428–432 (2018). 10.1016/j.nima.2018.02.004
58. Mira F., Ferrario M., Londrillo P., Marocchino A. Characterisation of beam driven ionisation injection in the blowout regime of plasma acceleration. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 441 – 445 (2018). 10.1016/j.nima.2018.01.019

59. Bisesto F. G. et al. The FLAME laser at SPARC LAB. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 452 – 455 (2018). 10.1016/j.nima.2018.02.027

60. Shpakov V., Chiadroni E., Curcio A., Fares H., Ferrario M., Marocchino A., Mira F., Petrillo V., Rossi A.R., Romeo S. Plasma acceleration limitations due to betatron radiation. Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment 909 463 – 466 (2018). 10.1016/j.nima.2018.02.058

61. Brandi F., Marsili P., Giammanco F., Sylla F., Gizzi L.A. Measurement of the particle number density in a pulsed flow gas cell with a second-harmonic interferometer. IOP Conf. Series: Journal of Physics: Conf. Series 1079 012006 (2018) doi:10.1088/1742-6596/1079/1/012006

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63. Pompili R. et al. Focusing of High-Brightness Electron Beams with Active-Plasma Lenses. Physical Review Letters 121 (17) 174801 (2018). 10.1103/PhysRevLett.121.174801

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## 33.2 List of EuPRAXIA Conference Proceedings

1. Nghiem P.A.P. et al. EuPRAXIA, a step toward a plasma-wakefield based accelerator with high beam quality. 10th International Particle Accelerator Conference (IPAC) May 19 – 24 2019 Melbourne, Australia. Proceedings of IPAC’19 WEZZPLS2 (2019). doi:10.18429/JACoW-IPAC2019-WEZZPLS2

2. Ferran Pousa A., Assmann R., Martinez de la Ossa, A. WAKE-T: A fast particle tracking code for plasma-based accelerators. 10th International Particle Accelerator Conference (IPAC) May 19 – 24 2019 Melbourne, Australia. Proceedings of IPAC’19 THPGW012 (2019). doi:10.18429/JACoW-IPAC2019-THPGW012

3. Weikum M.K. et al. Status of the HORIZON 2020 EuPRAXIA Conceptual Design Study. 10th International Particle Accelerator Conference (IPAC) May 19 – 24 2019 Melbourne, Australia. Proceedings of IPAC’19 THPGW026 (2019). doi:10.18429/JACoW-IPAC2019-THPGW026

4. Walker P.A. Facility Considerations For A European Plasma Accelerator Infrastructure (EuPRAXIA). 10th International Particle Accelerator Conference (IPAC) May 19 – 24 2019 Melbourne, Australia. Proceedings of IPAC’19 THPGW025 (2019). doi:10.18429/JACoW-IPAC2019-THPGW025

5. Zhu J., Assmann R.W., Ferran Pousa A., Marchetti B., Walker P.A. Simulation study of an RF injector for the LWFA configuration of EuPRAXIA. 9th International Particle Accelerator Conference (IPAC) April 29 – May 4 2018 Vancouver, Canada. Proceedings of IPAC’18 THPAF032 (2018). doi:10.18429/JACoW-IPAC2018-THPAF032

6. Ferran Pousa A., Assmann R.W., Martinez de la Ossa, A. Beam quality limitations of plasma-based accelerators. 9th International Particle Accelerator Conference (IPAC) April 29 – May 4 2018 Vancouver, Canada. Proceedings of IPAC’18 TUXGBE4 (2018). doi:10.18429/JACoW-IPAC2018-TUXGBE4

7. Ferran Pousa A., Assmann R.W., Martinez de la Ossa, A. VisualPIC: A New Data Visualizer and Post-Processor for Particle-in-Cell Codes. 8th International Particle Accelerator Conference (IPAC) May 14-19 2017 Copenhagen, Denmark. Proceedings of IPAC’17 TUPIK007 (2017). https://doi.org/10.18429/JACoW-IPAC2017-TUPIK007

8. Kokurewicz K., Welsh G. H., Brunetti E., Wiggins S. M., Boyd M., Sorensen A., Chalmers A., Schettino G., Subiel A., Desrosiers C., Jaroszynski D. A., Ledingham K.W.D. Laser-plasma generated very high energy electrons (VHEEs) in radiotherapy. MEDICAL APPLICATIONS OF LASER-GENERATED BEAMS OF PARTICLES IV: REVIEW OF PROGRESS AND STRATEGIES FOR THE FUTURE. Proceedings of SPIE 10239 UNSP 102390C (2017). Conference on Medical Applications of Laser-Generated Beams of Particles IV – Review of Progress and Strategies for the Future APR 24-25 2017 Prague CZECH REPUBLIC. 10.1117/12.2271183

9. Brunetti E., Yang X., Li F. Y., Reboredo Gil D., Welsh G.H., Cipiccia S., Ersfeld B., Grant D.W., Grant P.A., Islam M.R., Shahzad M., Tooley M.P., Vieux G., Wiggins S.M., Sheng Z.M., Jaroszynski D.A. Wide-angle electron beams
**from laser-wakefield accelerators.** LASER ACCELERATION OF ELECTRONS PROTONS AND IONS IV. Proceedings of SPIE 10240 UNSP 102400P (2017). Conference on Laser Acceleration of Electrons Protons and Ions IV APR 24-26 2017 Prague CZECH REPUBLIC. 10.1117/12.2269314

10. Tomassini P., Labate L., Londrillo P., Fedele R., Terzani D., Gizzi L.A. **High-Quality electron bunch production for high-brilliance Thomson Scattering sources.** LASER ACCELERATION OF ELECTRONS PROTONS AND IONS IV. Proceedings of SPIE 10240 UNSP 102400T (2017). Conference on Laser Acceleration of Electrons Protons and Ions IV APR 24-26 2017 Prague CZECH REPUBLIC. 10.1117/12.2266938

11. Macleod A.J., Noble A., Jaroszynski D.A. **On the energy-momentum tensor of light in strong fields: an all optical view of the Abraham-Minkowski controversy.** RELATIVISTIC PLASMA WAVES AND PARTICLE BEAMS AS COHERENT AND INCOHERENT RADIATION SOURCES II Proceedings of SPIE 10234 UNSP 102340F (2017). Conference on Relativistic Plasma Waves and Particle Beams as Coherent and Incoherent Radiation Sources II APR 27 2017 Prague CZECH REPUBLIC. 10.1117/12.2269630

12. Yoffe S.R., Noble A., Macleod A.J., Jaroszynski D.A. **Electron beam cooling in intense focussed laser pulses.** RELATIVISTIC PLASMA WAVES AND PARTICLE BEAMS AS COHERENT AND INCOHERENT RADIATION SOURCES II Proceedings of SPIE 10234 UNSP 102340E (2017). Conference on Relativistic Plasma Waves and Particle Beams as Coherent and Incoherent Radiation Sources II APR 27 2017 Prague CZECH REPUBLIC. 10.1117/12.2265812
Acknowledgements

Open access funding enabled and organized by Projekt DEAL. The completion of the EuPRAXIA design study and this Conceptual Design Report has been possible only because of the efforts and hard work of many people.

We would in particular like to thank the Scientific Advisory Committee:

Caterina Biscari (ALBA)

Franck Falcoz (Amplitude Technologies)

Luca Giannessi (FERMI)

Edda Gschwendtner (CERN)

Constantin Haefner (LLNL)

Knut Michel (Trumpf Scientific)

Christophe Simon-Boisson (Thales)

Thomas Tschentscher (European XFEL)

We also thank the EuPRAXIA Steering Committee (SC) and Collaboration Board (CB):

Ralph Assmann (CB,SC)

Reinhard Brinkmann (CB)

Antoine Chancé (CB,SC)

Enrica Chiadroni (SC)

Alessandro Cianchi (SC)

Jim Clarke (CB,SC)

Marie-Emmanuelle Couprie (CB,SC)

Brigitte Cros (SC)

Giuseppe Dattoli (SC)

Nicolas Delerue (SC)

Ulrich Dorda (SC)

Massimo Ferrario (chair CB,SC)

Leonida Antonio Gizzi (CB,SC)

Florian Grüner (SC)

Bernhard Hidding (CB,SC)

Simon Hooker (CB)

Dino Jaroszynski (CB,SC)

Roger Jones (CB,SC)

Luca Labate (SC)

Agustin Lifschitz (SC)

Andreas Maier (CB,SC)

Victor Malka (SC)

Barbara Marchetti (SC)

Alberto Martinez de la Ossa (SC)

François Mathieu (SC)

Alban Mosnier (CB)

Andrea Mostacci (CB,SC)

Zulfikar Najmudin (CB,SC)

Phu Anh Phi Nghiem (SC)

Federico Nguyen (CB)

Jens Osterhoff (SC)

Rajeev Pattathil (CB,SC)

Zheng-Ming Sheng (SC)

Luís Silva (SC)

Arnd Specka (CB,SC)

Ricardo Torres (CB)

Cristina Vaccarezza (SC)

Jorge Vieira (CB,SC)

Roman Walczak (CB,SC)

Carsten Welsch (CB,SC)

Mark Wiggins (SC)

Guoxing Xia (CB,SC)

The efforts of the Work Package leaders and co-leaders in coordinating the detailed technical design work have been essential to the success of this project.

Further special thanks go to

- the technical, scientific and administrative staff as well as the many early career researchers at our partner institutions who contributed to the conceptual work and organisation;

- the groups and researchers at our associated partners who dedicated their time and resources entirely as in-kind contributions to EuPRAXIA;

- the DESY EU Office, in particular Tom Minniberger and Ute Krell, for their continued support in funding and reporting matters;

- and the many colleagues and researchers who offered their advice in fruitful discussions - the editors would like to name in particular J. Collier, H. Dosch, G. Mourou, W. Sandner, T. Tajima, C.-G. Wahlström and O. Wiestler.

Finally, we would like to acknowledge with much appreciation the European Union's Horizon 2020 programme for our funding of this design study. Some of this work was also partially funded by the Center of Advanced Systems Understanding (CASUS)
which is financed by Germany’s Federal Ministry of Education and Research (BMBF) and by the Saxon Ministry for Science, Culture and Tourism (SMWK) with tax funds on the basis of the budget approved by the Saxon State Parliament.

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 653782. The information herein reflects only the views of its authors and the European Commission is not responsible for any use that may be made of the information contained.

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**Open Access** This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Publisher’s Note** The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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