PERLE. Powerful energy recovery linac for experiments. Conceptual design report

There has been much progress in SRF cavity design and processing in recent years, stimulated by projects like ILC, XFELs, factory-type colliders, light sources and ADS. This has triggered a diversification of designs, materials, techniques, and applications and no longer does any project have to depend on a set frequency or cell design just because of history or convenience. There now exist in many places around the world the knowledge, experience and tool sets to design, build, test and integrate fully customised and optimised SRF designs for new and exacting requirements. Recent examples include crab cavities for short pulse x-ray sources and colliders, HOM-damped cavities for ${e}^{+}{e}^{-}$ colliders, high power proton linacs for ADS, etc. The cavity shape optimisation for ERLs is somewhat different than for high-gradient pulsed linacs. The CW operation and potential for high circulating currents require careful attention to heat load (both from RF losses and field emission) and beam break up (BBU). In this regard a balance needs to be found between peak electric and peak magnetic fields while maintaining good efficiency and, very importantly, keeping HOMs well away from strong harmonics of the beam current. Because the ERL beam current spectrum depends strongly on the filling pattern and recirculation time, some assumptions must be made about machine operation when examining the HOM spectrum. This is discussed further in this article. An important parameter in maintaining good HOM damping is to have strong cell-to-cell coupling. This allows HOMs to propagate easily to the end cells, where the dampers are typically located, and makes the cavity less sensitive to tuning and fabrication errors. In particular it minimises the possibility for HOMs to become trapped in the cavity centre or tilted away from HOM couplers. Stronger cell-to-cell coupling implies a larger iris between cells, whereas efficiency is favoured by a smaller iris, so a compromise must be reached. Dangerous HOMs can be detuned if necessary by altering the profile of the cell. The gradient and impact energy of the cell multipacting barrier can be calculated and it is prudent to avoid operating close to this gradient. The impact energy can be minimised by flattening the cell profile in the equator region to make the barrier softer and easier to transition or process away.

The cryostat is the less glamorous cousin of the cavity and is often something of an afterthought, despite being the major share of the cost of the cryomodule. Previous SRF ERLs have used or adapted cryostats from other projects, in some cases converting them from pulsed to CW operation. Some important considerations are pressure code compliance, static heat load, maintainability and operability and cost. The number of magnetic and thermal shields and intercepts, the mechanical support and alignment scheme and whether the linac is continuous (like ILC) or segmented (like CEBAF and SNS) are all variables. For a large machine like LHeC it is worth performing a careful evaluation or even a new, clean sheet design optimised for this purpose, however, for a test machine like PERLE it is advantageous to use an existing well proven design. For this study we have used the SNS style cryostat as it can easily accommodate the 805 MHz 5-cell beta = 1 cavities with very minimal modifications, has plenty of heat load capacity, is a segmented design allowing phased construction of the facility and ease of maintenance, and has existing tooling and operational experience. More details are presented in section 3.3

The purposes of the PERLE ERL demonstrator are to provide flexible test beams for component development, low energy physics experiments, and also to demonstrate and gain operational experience with low-frequency HC SRF cavities and cryomodules of a type suitable for scale up to a high-energy machine. Since the cavity design, HOM couplers, fundamental power coupler (FPC's) etc will be all new or at least heavily modified, PERLE will serve as a technology test bed that will explore all the parameters needed for a larger machine. There is no other HC ERL test bed in the world that can do this. PERLE will also feature emittance preserving recirculation optics and this will also be an important demonstration that these can be constructed and operated in a flexible user-facility environment. The machine must run with high reliability to provide test beams for experimenters or ultimately provide Compton or FEL radiation to light source users. This demonstration of stability and high reliability will be essential for any future large facility.

Understanding the quench levels of superconducting cables and magnets is important for an efficient design and the safe and optimal operation of an accelerator using superconducting magnets. Quench levels are used as an input to define requirements for controlling beam losses, therefore influencing e.g. beam cleaning and collimation, beam loss monitor positions and thresholds, interlock delays etc.

The quench level defines the maximum amount of energy that can be deposited locally in a superconducting magnet or cable to cause the phase change from superconducting to normal-conducting state. The quench level is a function of the energy deposition distribution and the duration of the impact, the local temperature before the impact, the cooling capacity, and the local magnetic field.

State of the art electro–thermal solvers, which are used to predict the quench levels of superconducting cables and magnets, are mainly based on lab experiments without beam. To verify their predictions in case of beam impact, quench levels have been extensively studied with beam in the LHC at the end of Run 1 in February 2013. The results for short duration ($\lt 50\,\mu {\rm{s}}$) and steady state ($\gt 5\,{\rm{s}}$) energy deposition are in good agreement with predictions based on electro–thermal simulation codes like QP3 [15] and THEA [16]. For intermediate duration energy depositions the electro–thermal models predict a factor 4 lower quench levels than found during the experiment [17], which still needs to be understood.

Currently the LHC is the only accelerator at CERN, where quench tests with beam can be performed for all relevant time scales. Nevertheless, the LHC is not an adequate test bed to perform quench tests as: (i) only magnets installed in the LHC can be tested, (ii) non-trivial beam dynamic studies are required to interpret experimental results and (iii) the LHC is a sophisticated accelerator which is ultimately optimised to deliver luminosity to the particle physics experiments. The other facilities at CERN either lack the availability of cryogenics (PS, HiRadMat) or the particle beams (SM18). Furthermore, using the fast extraction from the SPS the HiRadMat facility could only cover the regime of short duration energy deposition. Therefore, a dedicated facility equipped with cryogenics to perform quench tests is required.

2.2.1.1. Energy deposition studies

Figures 1, 2 show the energy deposition per primary electron in a solid copper target for 150 MeV and 1 GeV electrons, respectively. For the simulations an emittance of 50 μm and a beta-function at extraction of 5 m was considered. The bin size was 1 mm³. Combining the peak energy deposition with the quench levels for the LHC main dipoles, as calculated by QP3, the number of primary particles required to reach quench levels for different durations of the energy deposition can be derived. Figure 3 summarises the required number of primary particles in case of different particle energies and pulse length durations.

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Comparing these numbers to the baseline beam parameters shows that PERLE can provide sufficient beam to perform quench tests during all stages of its construction. It is important to assure in a subsequent detailed design process that the facility can provide fast and slow extracted beams to the quench test experiments, to allow for experiments in all energy deposition duration regimes.

2.2.1.2. Quench test facility

PERLE is described below in a default configuration including cavities at 801.58 MHz in up to 4 cryomodules and a bunch spacing of 25 ns. To gain flexibility and widen its potential as a development facility for testing cavities and cryomodules with beam, PERLE may, however, also be configured to a number of different frequencies, especially those which are commonly used in accelerator facilities worldwide, i.e. 352 MHz (Linac4, ESS), 401 MHz (LHC, FCC), 704 MHz (ESS), the PERLE default 802 MHz (LHC, FCC and LHeC) and 1300 MHz (ILC, XFEL, ...). To make this possible, the injector must be based on a photocathode with a laser pulser that can be operated at ${f}_{0}=12.146\,\mathrm{MHz}$ with a buncher/booster system adjusted to a harmonic of f₀. The frequency of 12.146 MHz is chosen as a joint sub-harmonic of these commonly used frequencies. The exact harmonic frequencies accessible as PERLE's main RFs are given in table 1, assuming the possibility to tune the subharmonic f₀ by moderate variations of $\pm 4$ kHz. This assumption translates to certain tuning range, for example at 801.58 MHz of ±0.26 MHz, which would have to be implemented in the buncher/booster.

Table 1.  Main RF ranges for selected harmonics, in MHz, accessible to PERLE with an injector pulsed at ${f}_{0}=12.146\,\mathrm{MHz}$, a configuration suitable for beam based RF developments at most commonly used frequencies with this facility.

h	29	33	58	66	107
h $\cdot \,({f}_{0}$ − 4 kHz)	352.118	400.686	704.236	801.372	1299.19
h $\cdot \,({f}_{0}$ + 4 kHz)	352.350	400.950	704.700	801.900	1300.05

Referring to the description of source and injector in section 4.1 below, it is clear that a bunch repetition frequency of 40.1 MHz (25 ns) is not compatible with most of the above frequencies and should be adapted to either 12.146 MHz, where it could be used with all mentioned frequencies, with the caveat that a larger bunch charge would have to be generated for a similar average current (challenging 1 nC for 12 mA). For tests at 401 and 802 MHz, however, a bunch repetition frequency of 36.438 MHz can be chosen, which would be close enough to the LHeC parameters to be relevant. It would produce 12 mA of beam current with 329 pC bunch charge. The filling scheme and bunch recombination pattern, see section 3.4 (figures 16, 17) would have to be adapted ${mutatis}\,{mutandis}$ (the harmonic 20 becoming harmonic 22) with individual bunch spacings $7\lambda$–$8\lambda$–$7\lambda$. The buncher/booster system described in section 4.1 remained unchanged. It is noteworthy that for a bunch repetition frequency of 12.146 MHz, captured and accelerated in this booster at 801 MHz, the frequency of the cavities in the ERL might still be 704 and 1300 MHz, and even the simultaneous operation at different frequencies in the same linac would not be impossible.

For a given electron beam of energy, E, scattered off a fixed proton target, the elastic ep cross section depends only on the polar angle θ of the scattered electron. This determines both the negative four-momentum transfer squared, Q², and the energy $E^{\prime}$ of the scattered electron through the relations

$$\begin{eqnarray}&&{Q}^{2}=\displaystyle \frac{2{{ME}}^{2}(1-\cos \theta )}{M+E(1-\cos \theta )}\,\,\,\,\,\,\,\,\,\,E^{\prime} =\displaystyle \frac{E}{1+\tfrac{E}{M}(1-\cos \theta )},\end{eqnarray} \tag{ 2.1 }$$

where M is the proton mass. The cross section, in its Born approximation, is given as the product of four factors, the Rutherford formula, the Mott electron spin modification, a correction, equal to $E^{\prime} /E$, for the proton recoil and finally a function $f({G}_{E},{G}_{M},\theta )$, which characterises the spin and the spatial extension of the proton

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{d}}\sigma }{{\rm{d}}{\rm{\Omega }}}=\displaystyle \frac{{\alpha }^{2}}{{[E(1-\cos \theta )]}^{2}}\cdot {\cos }^{2}\displaystyle \frac{\theta }{2}\cdot \displaystyle \frac{1}{1+\tfrac{E}{M}(1-\cos \theta )}\cdot f({G}_{E},{G}_{M},\theta ),\end{eqnarray} \tag{ 2.2 }$$

with α the fine-structure constant. With the convention $\tau ={Q}^{2}/4{M}^{2}$ the form factor term is given by

$$\begin{eqnarray}&&f({G}_{E},{G}_{M},\theta )=\displaystyle \frac{{G}_{E}^{2}+\tau {G}_{M}^{2}}{1+\tau }+2\tau {G}_{M}^{2}{\tan }^{2}\displaystyle \frac{\theta }{2}.\end{eqnarray} \tag{ 2.3 }$$

To some first approximation, one has ${G}_{M}={\mu }_{p}{G}_{E}$ and ${G}_{E}=1/{(1+{Q}^{2}/0.71{\mathrm{GeV}}^{2})}^{2}$, with the anomalous magnetic moment ${\mu }_{p}$ of the proton. The two form factors G_E and G_M can be separated through a variation of the energy following Rosenbluth. This should be an advantage of PERLE as with its variable energy it may cover a large range from a few hundreds of MeV to almost 1 GeV. The formulae above are sufficient for practical estimates of counting rates, but neglect all the physics which is contained in corrections to equation (2.2) as arise from electroweak, BSM and higher order QED effects.

The luminosity of a facility like PERLE is obtained as $L=\rho {{lN}}_{A}{N}_{e}$. For a hydrogen target of density $\rho =0.07$ g cm⁻³ and length l = 10 cm one gets $L=4.3\times {10}^{23}$ cm⁻² N_e. For a source delivering 320 pC of charge and a 25 ns bunch spacing one obtains a current of 12.8 mA corresponding to about $8\times {10}^{16}$ e s⁻¹, or a number of electrons per bunch of ${N}_{e}=2\times {10}^{9}$. As a consequence the luminosity for elastic ep scattering can be expected to be as high as $3\times {10}^{40}$ cm⁻² s⁻¹ with a 10 cm proton target.

The unification of the electromagnetic and weak interactions within the SU(2)_L × U(1) theory is expressed by the Weinberg angle ${\sin }^{2}{\theta }_{W}$, which has a strong characteristic dependence on the momentum scale ($\sqrt{{Q}^{2}}$ in ep scattering) due to loop corrections [23] to the tree-level expressions, see figure 4.

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The most precise ${\sin }^{2}{\theta }_{W}$ measurements so far were performed at the Z pole at LEP and SLC, leading to an unresolved discrepancy of about three standard deviations. Various measurements of so far limited precision were performed at low scales, with a departure from theory observed by the NuTeV Collaboration in $\nu N$ scattering which caused a multitude of subsequent considerations as on the amount of strange quarks in the nucleus and the behaviour of nuclear corrections. Measurements of the mixing angle are very complex challenges and lead to new insight often beyond the genuine intention to determine ${\sin }^{2}{\theta }_{W}$. Measurements with the LHeC (FCC-he), as presented in the LHeC CDR [1], will be based on very large electroweak asymmetry effects and determine the electroweak mixing angle precisely for a range below the Z mass up to high scales of 1 (3) TeV.

With PERLE one can access effects from Z-boson exchange with polarised electron scattering, as well as with charge asymmetry measurements, for $\sqrt{{Q}^{2}}$ between about 0.1 and 1 GeV. The intensity of a polarised electron source is probably an order of magnitude higher than that of a positron source. This makes the measurement of a polarised electron scattering asymmetry, ${A}^{-}$, more likely than that of a charged or combined charge and polarisation asymmetry, B. Both have been discussed in [24]. The polarisation asymmetry can be expressed as

$$\begin{eqnarray}&&{A}^{-}(P,P^{\prime} )=\displaystyle \frac{\sigma (P)-\sigma (P^{\prime} )}{\sigma (P)+\sigma (P^{\prime} )}=-\kappa \displaystyle \frac{P-P^{\prime} }{2}\cdot ({v}_{e}A-{a}_{e}V),\end{eqnarray} \tag{ 2.4 }$$

where $\kappa ={Q}^{2}G/\sqrt{2}2\pi \alpha$ determines the size of the asymmetry to be O(${10}^{-4}{Q}^{2}/$GeV²). Here v_e and a_e are the weak neutral current (NC) couplings of the electron and V and A are combinations of the form factors G_E and G_M with interference form factors, g_E and g_M, which depend on the quark NC couplings v_q and a_q ($q=u,\,d$), as well as the charged current axial vector form factor g_A. Evidently, the asymmetry ${A}^{-}$ is different from zero through parity violation. With PERLE, ${A}^{-}$ enables a measurement of the mixing angle in a particularly interesting range of scale, as is illustrated in figure 4.

The measurement accuracy depends on the beam energy and scattering kinematics. This is illustrated in figure 5. Since the asymmetries vanish at small angles while the cross section decreases towards larger angles, an optimum is observed, with striking variations. One finds for a beam energy $E\sim 1\,\mathrm{GeV}$ that asymmetry measurements at $\theta \sim 30^\circ \mbox{--}90^\circ$ can be expected to be especially precise.

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The interpretation of the asymmetry measurement in terms of ${\sin }^{2}{\theta }_{W}$ requires to control the nucleon form factors which enter V and A. Following [24] one can write the hadronic vector contribution to the asymmetry, V, as

$$\begin{eqnarray}&&V=2\displaystyle \frac{{G}_{E}{g}_{E}+f(\tau ,\theta ){G}_{M}{g}_{M}}{{G}_{E}^{2}+f(\tau ,\theta ){G}_{M}^{2}},\end{eqnarray} \tag{ 2.5 }$$

and the axial vector part A as

$$\begin{eqnarray}&&A=2\displaystyle \frac{2(1+\tau )(\tau -E/M){\tan }^{2}\theta /2\cdot {G}_{M}{g}_{A}}{{G}_{E}^{2}+f(\tau ,\theta ){G}_{M}^{2}},\end{eqnarray} \tag{ 2.6 }$$

with the kinematic function $f=\tau (1+2(1+\tau ){\tan }^{2}\theta /2)$. For a rough estimate of the requirements one may choose a working point where the ${A}^{-}$ asymmetry is well measurable, choosing a polar angle $\theta =90^\circ$ and a beam energy E = 1 GeV, which leads to a momentum transfer squared of ${Q}^{2}=1$ GeV². A measurement of ${\sin }^{2}{\theta }_{W}$ to 0.5% precision at only this point required an ${A}^{-}$ measurement accuracy of 1%. Variations of the five form factors, ${G}_{E},\,{G}_{M},\,{g}_{E},\,{g}_{M},\,{g}_{A}$, described in [24], by ±1% lead to ${A}^{-}$ changes of $\pm 0.26 \% ,\pm 0.74 \% ,\mp 0.03 \% ,\,\mp 0.93 \% ,\,\mp 0.05 \%$, respectively. The very small influence of the weak electric form factor g_E is caused by the smallness of the vector coupling combination $2{v}_{u}+{v}_{d}=0.03$. Similarly, since the weak mixing angle is close to 1/4, the electron vector coupling is nearly zero which implies that the contribution to the asymmetry ${v}_{e}A$ (see equation (2.4)) is practically negligible with respect to ${a}_{e}V$, and therefore g_A has only a very weak influence on the mixing angle measurement. The dominant influence of the form factors is seen to be due to the magnetic form factors G_M and g_M, which when known to 1% accuracy cause an uncertainty each of 0.5% to ${\sin }^{2}{\theta }_{W}$. As is shown in the subsequent section 2.4.3, the G_M factor is already known to within 1%. Therefore one expects the ${A}^{-}$ measurement to basically need to control g_M, via the kinematic dependencies on θ and E and its theoretical relation to G_E, when deriving ${\sin }^{2}{\theta }_{W}$. Beyond these leading order considerations one has to care for higher order electroweak and hadronic effects as have been extensively studied in the preparations of the low energy MESA experiment [25].

Besides providing a measurement of ${\sin }^{2}{\theta }_{W}$, with ep scattering asymmetries, one accesses also new combinations of quark couplings. Following [24] one sees, for example, that the hadronic axial vector factor A determines a combination of ${a}_{d}+3.55{a}_{u}$ which can be compared with ep scattering at HERA and the LHeC where $A={a}_{d}-2{a}_{u}$.

The measurement of the weak mixing angle at small scales is an area of vigorous activity, because of the new level of precision anticipated in a coming generation of tests of its predicted scale dependence, as at Mainz and Jefferson Lab, and because of the relation these measurements have to new physics such as rare Higgs decays and dark Z bosons, see [26] and references therein. The salient potential of the here presented ERL facility consists in its potential large energy coverage and particularly high luminosity which make further studies of the possibility to measure that process with PERLE interesting indeed.

The proton electromagnetic form factors, G_E and G_M, which have been studied for many decades, have become the focus of recent research mainly due to the proton radius puzzle, recognised even in the popular press [27]. It is the more than $7\sigma$ discrepancy between the determination of the proton radius with electrons (${r}_{E}=0.8775(51)\ {\mathsf{fm}}$ [28]) and using muon spectroscopy (${r}_{M}=0.84087(39)\ {\mathsf{fm}}$). Since its observation in 2010, the discrepancy has sparked large work efforts on both the experimental and theoretical side, but no widely accepted explanation has yet been found.

On the electron side, both spectroscopy and scattering experiments agree. In the latter, the radius is extracted from the slope of the form factors at ${Q}^{2}=0$. Since data can only be taken at finite Q², the form factors have to be extrapolated to 0. Currently, the most precise data set from scattering experiments [29–31] has been measured by the A1 collaboration in Mainz at the MAMI accelerator. It contains more than 1400 measured cross sections and reaches closest to the static limit with ${Q}_{\min }^{2}\approx 0.003\ {({\mathsf{GeV}}/c)}^{2}$. While there are no structures/changes of curvature expected below this point, it is not possible to rule them out. Such structures would invalidate the extrapolation and may resolve part of the puzzle.

This data set also found an interesting structure in G_M at low Q², shown in figure 6. The magnetic form factor, divided by the standard dipole, exhibits two local extrema. While the minimum is found in earlier extractions, the maximum has not been seen and is in fact below the resolution of previous data. This leads to a significantly different magnetic radius compared to earlier findings. The strength of the maximum is strongly affected by radiative corrections and could be a statistical aberration. An external validation is important as the existence of structures like this points to corresponding length scales in the physics inside the proton.

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Fits to the world data set exhibit a cusp around ${Q}^{2}=1.5\ {({\mathsf{GeV}}/c)}^{2}$ in G_M, shown in figure 7, again pointing to underlying length scales in the internal structure of the proton. However, the cusp is only visible in the combination of multiple data sets and could be an artefact.

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PERLE could provide crucial new high-precision data to study these three phenomena using different experimental approaches:

• Possible structures below Q²_min and their influence on the proton radius could be studied with a single, low beam energy and forward scattering experiment, similar to the PRad experiment [32]. At lower energies and higher beam currents than planned for PRad, an ERL beam with a point-like target (e.g. a gas jet) could provide higher rates and smaller systematic uncertainties. An alternative approach is to exploit initial state radiation, measuring deep into the radiative tail to probe Q²-values that are orders of magnitude smaller than directly accessible. This approach is described in more detail e.g. in [33].
• The low-Q² structure in G_M could be studied in an experimental setup similar to [29]. The interesting region in Q² would be covered by performing an angular scan of the cross section and multiple energies up to 300 MeV. Such an experiment would benefit substantially from a point-like target without target walls, which are the main background of [29]. It would produce an electric radius with similar uncertainties, and a magnetic radius with substantially improved precision compared to current results. Additionally, with a polarised beam and target, an asymmetry measurement, sensitive to the ratio ${G}_{E}/{G}_{M}$, could be performed. Such a measurement would help to disentangle G_E and G_M from the cross-section measurement and would make it possible to study whether the structure is related to imperfect radiative corrections.
• The high-Q² structure could be studied with high precision using beam energies of 1 GeV and up, possibly with just one angular scan of the cross section at a fixed energy around 1.3 GeV. Without a good connection to lower beam energies, the precision of the absolute normalisation is not likely to better than a few percent, however the cusp structure is large enough that a good relative normalisation of the data points, e.g. using a detector at forward angles as a luminosity monitor, is enough to extract a meaningful result.

Using virtual photon tagging, it is possible to study confinement-scale QCD. In photo-production, the photon tagger sets the rate limit and only a small fraction of the tagged photons interact with the target, leading to low data-taking efficiency. At forward angles, the virtual photons are almost real, so that a forward scattering electron tagger can be used as a highly efficient substitute. Because of the high efficiency and high beam currents, it is possible to use pure, thin targets and detect low energy recoil particles which would not escape traditional, thick targets. It is thus possible to measure the reactions $\gamma p\to {\pi }^{0}p,{\pi }^{+}n$, $\gamma n\to {\pi }^{0}n,{\pi }^{-}p$ and $\gamma D\to {\pi }^{0}D$. Coherent ${\pi }^{0}$ production in D and ³He measure relative signs of the $\gamma p\to {\pi }^{0}p$, $\gamma n\to {\pi }^{0}n$ amplitudes.

Such an experiment requires beam energies of 300 MeV or more. Depending on the target, beam current and polarisation capabilities, different experiments are possible:

• With about 1 mA unpolarised beam, a measurement with a thin, windowless, unpolarised gas target, detecting either the ${\pi }^{+}$ or the recoiling proton, could be performed. This would allow a test of ${a}_{{nn}}={a}_{{pp}}$ and few-body calculations via $\gamma D\to {nn}{\pi }^{+}$, and also check a_np with $\gamma D\to {np}{\pi }^{0}$. It would further be possible to test isospin conservation by testing
  $$\begin{eqnarray*}&&A(\gamma p\to {\pi }^{+}n)+A(\gamma n\to {\pi }^{-}p)=\sqrt{2}[A(\gamma n\to {\pi }^{0}n)-A(\gamma p\to {\pi }^{0}p)].\end{eqnarray*}$$
• At about 10 mA unpolarised beam, with a windowless transverse polarised gas target, one could test isospin breaking through a measurement of $\gamma N\to {\pi }^{0}N$ near threshold.

For more information, see e.g. [34].

The search for new physics beyond the Standard Model is a major focus of the nuclear and particle physics community. A simple extension of the SM Lagrangian [35, 36] leads to new 'dark' Abelian forces with a new dark gauge field ${A}^{{\prime} }$. Among many others, a possible production mechanism is ${e}^{-}p\to {e}^{-}{{pA}}^{{\prime} }(\to {e}^{-}{{pe}}^{+}{e}^{-})$, i.e. the elastic scattering with a radiated 'dark' photon, and the possible subsequent decay of the radiated ${A}^{{\prime} }$ into a lepton pair ('visible decay'). The DarkLight experiment [37], planned to be run at the Jefferson Lab ERL, aims to search for these visible decays in the region preferred by the muon g-2 results, detecting all four outgoing particles. A variant also looking for invisible decays is planned [38]. The PERLE facility could be an option for a version 2 of the experiment, with increased luminosity.

Alternatively, with high-precision, high-rate detectors measuring just the recoiling proton and electron, it should be possible to mount a competitive search sensible to both visible and invisible decays. More work is needed to study this further.

At Q² above 1 GeV², determinations of the form factor ratio from unpolarised and polarised measurement do not agree. This has been attributed to two-photon exchange, whose size is directly tested in current experiments [39–41]. At lower Q², this effect is believed to be small, but could explain part of the proton ratio discrepancy. A positron source would make it possible to measure the effect directly at small Q², validating theoretical calculations.

The experiments described so far require a fixed target. Colliding beams open additional interesting possibilities. Head-on collisions with a high-momentum proton beam can probably not help with the physics described, however, if it could be arranged that the beam collide almost collinearly, i.e. essentially with the same, not opposite, direction, one would access the fixed-target equivalent of backward scattering at very low Q², accessing the magnetic form factor at unprecedentedly small four-momentum transfer. Similar, a collision of a muon and electron beam in this way would test lepton universality, a further possible explanation for the radius puzzle.

Gamma-rays with energies up to 30 MeV can induce a variety of photonuclear reactions. Photoinduced nuclear excitations below the nuclear separation energy will decay by subsequent re-emission of γ-radiation. When this reaction proceeds via a nuclear resonance it is addressed as nuclear resonance fluorescence (NRF). The NRF process may populate an excited low-lying nuclear isomer which may decay by β-decay processes addressed as internal photoactivation.

Photodisintegration reactions become possible when a nucleus is photo-excited above the separation threshold. Then either neutrons or charged nuclear constituents such as protons or even α-particles can be emitted. Photodisintegration reactions that result in a daughter nucleus which is radioactive are called external photoactivation. An extreme mode of photodisintegration is photofission where a nuclear fission process occurs once the nucleus has been activated by the absorption of the γ-ray. The various photonuclear reactions are sketched in figure 8.

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The field of nuclear structure physics addresses the investigation of the nuclear many-body problem and its understanding in terms of effective nucleon–nucleon interactions that emerge from QCD as the effective interaction between hadrons. Since the electromagnetic interaction is understood quantitatively, photonuclear reactions enable the separation of the photonuclear reaction mechanisms from the nuclear properties and thus nuclearmodel-independent measurements. Due to the clean reaction mechanism of γ-rays with the nucleus, its iso-vector and one-step character, the field of nuclear structure physics has tremendously profited from photonuclear research since the seminal works of Bothe and Gentner in 1937 [44].

2.5.2.1. Nuclear single-particle structure

2.5.2.2. Collective nuclear structures

2.5.2.3. Nuclear photofission

Due to our understanding of the unified electroweak interaction, the electromagnetic reaction processes of photons with nuclei are closely related to nuclear reactions involving the weak interaction [48]. Consequently, photonuclear studies can, at least partly, shed light on weak interactions in materials that are employed in detectors for weak-interaction processes such as detectors for searching for neutrinoless double-beta decay or for neutrino signals from supernovae.

2.5.3.1. Nuclear matrix elements for $0\nu \beta \beta$-decay

2.5.3.2. Detector response to stellar neutrinos

Energetic γ-rays belong to the thermal environment in stars. Understanding of nuclei in the variety of stellar conditions requires a detailed knowledge of photonuclear reactions. Research opportunities for photonuclear reactions in nuclear astrophysics are numerous. We will mention only two examples.

2.5.4.1. Stellar capture reactions

2.5.4.2. Nuclear synthesis

PLACET2 is a tool that allows to describe the whole machine without unrolling the lattice and computes the element phases according to the beam time of flight. The β functions and the energy profile shown in figure 18 are obtained following a test bunch into the lattice from the injector to the dump. The energy profile shows that the lengths of the arcs are properly tuned to obtain the maximum acceleration and deceleration. The regularity and the symmetry of the β functions, validate the matching of all the arcs in the presence of strong RF-focussing from the linacs.

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Figure 19 shows the transverse phase space at 900 MeV: the plots show the emittance preservation, and in particular the absence of nonlinearities. Collective effects such as CSR and short-range wake fields are not included, however analytical computations predict a small impact.

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Comparing the longitudinal phase space at injector and at dump (see figure 20) one can note that the bunch length is well preserved, proving the isochronicity of the whole lattice. A small energy chirp is present at the dump, which shall be removed with a fine tuning of the arc lengths. Figure 20 (right) shows the longitudinal phase space at 900 MeV. While the curvature induced by the RF can be seen, the total energy spread remains extremely contained (below $0.01 \%$).

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PLACET2 is capable of tracking many bunches simultaneously in the lattice preserving their time sequence everywhere in the machine. This allowed us to verify the bunch recombination pattern and to assess the multi-bunch effects in a realistic operational scenario.

Estimates of the BBU threshold current have been performed using the major 26 dipole modes of the SPL cavity design, scaled to 802 MHz and collected in table 5. The Q-values are all set to $1\times {10}^{5}$, as followed from preliminary studies with both coaxial and waveguide dampers which are expected to suppress the HOM impedance to satisfying levels and reduce the Q-values of the most crucial modes to less than $1\times {10}^{5}$, although other Q-values can be higher.

A 6D distribution of hundred macro-particles per bunch has been used and tens of thousand of bunches have been tracked, simulating several milliseconds of continuous operation. The statistical fluctuations of the positions of the bunch centroids as they propagate through the lattice, excite the HOMs without the need of further perturbations.

The plots in figure 21 show the amplitudes of the HOMs in one of the cavities as many bunches pass by. When the bunch charge is increased from 1.6 to 1.9 nC a mode starts to build up in the vertical plane leading to an instability. Note that this bunch charge is more than 5 times larger than the one foreseen for operation.

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3.5.2.1 HOM detuning

In order to investigate the impact of the detuning, the frequency of each mode has been altered in the following way:

$$\begin{eqnarray*}&&{f}_{i}^{{\prime} }={f}_{i}+G({{Df}}_{i})\end{eqnarray*}$$

where $G(\sigma )$ is a random number drawn from a zero-centred Gaussian distribution with variance $\sigma ={{Df}}_{i}$, with D being a detuning factor typically of the order of $1\times {10}^{-3}$.

The tracking studies for the detuning analysis relied on single particle bunches carring the nominal charge. The machine was initially filled with zero-action bunches, without any perturbation of the modes. A bunch carrying some action was then injected, exciting all the modes. The propagation of this exitation was studied by continuing the injection of several thousands of zero-action bunches and checking their action at the dump. After the initial perturbation, the logarithm of the outcoming actions quickly assumes a linear behaviour and the decay slope can be fitted.

The results of this analysis are shown in figure 22, where each histogram is computed for a specific detuning value and collects the excitation slopes resulting from several random seeds. Very small detuning factors create a broad spread, with few seeds showing a behaviour worse than the case without detuning. More realistic values of the detuning around $1\times {10}^{-3}$ produce sharper distributions where almost all the different seeds show a faster damping of the perturbation.

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Physical parameters of the beam, delivered by the photocathode, are essentially defined by the gun. It also dictates the parameters of the drive laser. Photocathodes are typically characterised by their QE, defined as the ratio of extracted electrons to incident photons, its dependence on the energy of incident photons and characteristics of photocathode material. The last parameter defines the laser wavelength which should be used to extract the beam. Difference between energy of incident photons and work function defines initial energy of emitted electrons. In combination with the angular distribution of emitted electrons it determines the initial beam emittance [62].

Originally, in DC guns for ERL application, GaAs photocathodes were used illuminated with laser light with a wavelength of 532 nm [63, 64]. These photocathodes are usually activated to the surface state close to negative electron affinity (NEA) in the gun with Caesium dispensers. This procedure was difficult to properly control and thus does not allow reaching high QE, typically few percent. Another problem of GaAs photocathodes is the requirement to ensure high vacuum conditions in the gun and poor lifetime due to back ion bombardment which does not allow reaching high average current for reasonable long time. More recent designs at Cornell University, Daresbury Laboratory [65] and JAEA-KEK [66] proposed activation of the photocathodes in a dedicated preparation facility directly connected to the gun and to replace photocathode in the gun as operating photocathode degrades. GaAs photocathodes prepared separately following this approach reached maximum QE of 20% at operational wavelength, but did not solve the problem of lifetime.

More robust photocathodes based on Sb are less sensitive to vacuum conditions and to back ion bombardment. Pioneering experiments at Boeing [67], and the University of Twente [68], at Brookhaven Laboratory [69], TJNAF [70], and Cornell University [59] demonstrated the possibility to obtain a reasonable QE for Sb-based photocathodes at a level of 5%–10% and, most importantly, their ability to deliver a HC for a substantial period of time.

For delivery of polarised electrons, GaAs based photocathodes still remain the only choice. So far, maximum demonstrated current of polarised electrons is at the level of 5 mA [71] while the possibility to reach level of 20 mA needs to be investigated. Main parameters of photocathode families principally applicable for PERLE are shown in table 6. It can be seen that if the requirements to the laser for unpolarised beam are modest, the production of polarised electrons demands a yet high laser power. However, this higher laser power leads to thermal desorption resulting in a deterioration of vacuum and reduction of the photocathode lifetime. Cooling down of the photocathode during operation should be taken into account at the gun design.

The main decisive parameter of a DC photocathode gun is its operational voltage. It defines the energy of electrons at the exit of the gun and the 'rigidity of the beam'. This operational voltage also dictates the electric field on the photocathode which defines maximum emission density and, as a result, the beam emittance which may be estimated as

$$\begin{eqnarray}&&{\epsilon }_{n}=\sqrt{\displaystyle \frac{{qkT}}{2\pi {\epsilon }_{0}{E}_{c}{{mc}}^{2}}}.\end{eqnarray} \tag{ 4.1 }$$

Here, q denotes the bunch charge, T the photocathode effective temperature, with kT referred to as the photocathode's intrinsic energy, E_c is the electric field on the photocathode surface at bunch launching and m the mass of the electron. The traditional approach to design guns for ERLs for driving FELs demands that the gun operation voltage should be as high as possible to a reach minimal beam emittance. Maximum operational voltage of 500 kV with a field of 10 MV m^–1 has been demonstrated at the gun developed at JAE for the cERL project at KEK [72]. However, a very high voltage in the gun implies the risk of field emission from the gun electrodes leading to electron stimulated gas desorption and vacuum deterioration. This leads to a degradation of the QE of photocathodes, especially those with low work function materials like GaAs activated to NEA state. A lower voltage is also more convenient for spin manipulation. The optimal values of gun voltage and cathode field should therefore be properly selected at the design stage. A dual operation mode of the gun, at high voltage for unpolarised photocathodes and at low voltage for polarised photocathodes, may not be excluded. Practically, the operational voltage of the gun will be optimised taking into account all effects which have an impact on the gun performance such as photocathode lifetime, beam polarisation, beam emittance etc. Considering these aspects, as well as a demonstrated stable operation at other facilities [58, 65, 69], a choice of the maximum operation voltage of 350 kV for the unpolarised regime and of 200 kV for the polarised regime seems reasonable.

In order to get preliminary estimates required on the drive laser system to deliver beam with parameters required for PERLE, the performance is calculated of a 350 kV gun with a JLAB-DL electrode system operating with Cs3Sb photocathode (figure 24). Simulations have shown that an optimal beam emittance of 2 πmm mrad can be obtained with illumination of the photocathode with a laser pulse with top hat spatial distribution with a diameter of 3 mm and a flat top laser pulse with a length of 80 ps. The RMS bunch length at 1 m from the photocathode is 8.5 mm (36 ps) which only slightly depends on the laser pulse length.

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Once emerged from the gun, the electron beam begins to elongate due to the space charge repulsion. To longitudinally compress the bunch to the required 3 mm a compensation energy chirp should be introduced which is typically done with an RF buncher. In order to provide linear energy modulation the frequency of the buncher should be selected to have bunch flight time at the buncher shorter than 10° of its RF phase. For the bunch charge of 320 pC which has an RMS buncher flight time of 36 ps the required frequency should be less than 775 MHz. Further increase of the bunch charge leads to an increase of the bunch flight time and may require even lower buncher frequency. Practically attractive is 400.8 MHz—the first sub-harmonic of the PERLE default frequency. Further gradual beam compression and acceleration can be provided with a booster consisting of a series of single cell 801.6 MHz cavities with individual coupling and control of amplitude and RF phase. As the energy transferred to the beam in the injector booster to reach 5 MeV is 60 kW and is not recovered, the precise number of cavities is defined by the maximum power which may be loaded into a single cavity with the coupler. Assuming that maximum coupler power is 20 kW the booster should consist of at least four cavities. Taking into account that the first two cavities are operated essentially off-crest and at low field as well as a required contingency in case of increasing injector energy, the number of the cavities should be increased to five.

An analysis of the current scientific and technological level of the high average current electron sources for ERLs allows us to conclude that an unpolarised electron source with beam parameters required for PERLE may be built in a relatively short time. This would best be based on a 350 kV DC photocathode gun operated with Sb-based photocathodes followed by a buncher and superconducting booster consisting of five independently fed and controlled RF cavities. A design of a HC polarised electron source requires more investigation but is considered to be a second step for PERLE. A baseline scheme, delivering an average current 2–4 times less than in the unpolarised regime may be realised on the basis of an unpolarised source operating with a family of GaAs photocathodes and reduced DC gun at an operational voltage to 200 kV.

The choice of frequency and gradient is important for any project and depends on a range of factors. It is definitely not a one-size-fits all situation. For large projects, the total cost is dominated by a few competing items such as RF power, cryogenics, structure costs (e.g. modules) and conventional facilities (tunnel, surface buildings, penetrations, etc). Each of these has a frequency and gradient dependence and depends on the choice of underlying technology assumed. In general the overall cost optimum is a balance between linear costs (such as structure and tunnel) which increase as the gradient is lowered and the machine gets longer, and quadratic terms such as RF power and cryogenic capacity, which increase as the gradient is increased but result in a shorter machine. The result is a rather broad cost minimum allowing some flexibility in the choice of frequency and gradient to accommodate other factors. There are various cost models in use or under development but in general the optimum frequency for this type of machine is somewhere between a few hundred MHz and one GHz. Below this range the structures become very expensive and above this range RF power costs increase. As has been extensively studied in the conceptual design of the LHeC the frequency needs to be significantly below a GHz also for avoiding adverse effects due to BBU instability [1]. For compatibility with the LHC, a harmonic of 200 MHz is highly desirable. A frequency of 801.58 MHz is a convenient harmonic¹² that is close to the estimated cost optimum and also compatible with other systems currently in use or under development at CERN [73–75]. The optimum gradient range is also quite wide, ranging from around 10 to 20 MV m^–1 depending on assumptions about the temperature and Q₀ that can be reliably expected. In general for a large machine the lowest reasonable gradient should be adopted to maximise reliability and minimise the chances of field emission. However, for a small machine like PERLE, at least in the first phase, the cost optimum may favour a higher gradient.

The maximum accelerating gradient is primarily limited by the CW power dissipated on the cavity walls. Due to the quadratic dependence, a medium accelerating gradient with the lowest surface resistance (high Q₀) at moderate to high gradients is required. The number of cells per cavity is a compromise between a reasonable 'real estate gradient' while reducing the probability of trapped modes.

The salient feature of an energy recovery linac, at least in CW operation, is the continuous transfer of stored energy from the cavity to the accelerated beam and simultaneously the transfer of (almost equal) energy from the decelerated beam back into the cavity. To first order, the power fed into the cavity through the FPC from the power source is equal to the power losses in the cavity walls, which can be extremely small. Another formulation of this feature is that the net beam loading at the fundamental frequency is zero in spite of a large beam current. As a consequence, the excitation of HOMs, notably at frequencies where accelerated and decelerated beam currents are not in anti-phase, will be dominating the design.

4.2.2.1. Initial design choices

The choice of five cells per cavity is retained from technical arguments derived in [75]. The standard parameterisation for elliptical cavities is used [76]. Figure 25 shows the envelope of the scaled five-cell cavity with a large iris aperture diameter of 150 mm, scaled from an existing 704 MHz design.

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Detailed parametric scans were carried out to further optimise the aperture choice from the scaled version [77]. Some key RF parameters such as the ratio of B_p/E_p, R/Q, cell-to-cell coupling for the fundamental and higher order modes, frequency dependence of the fundamental mode and HOMs were studied. A first optimisation aimed at minimising the integrated longitudinal loss factor, which is a measure for the power lost into well-damped HOMs for very short bunches; for a beam current of 40 mA, the 150 mm diameter aperture (version 1) would result in a total HOM power of the order of 35 W.

The geometrical scans performed are used as guidance considering both fundamental mode and HOMs. An increase in aperture to 160 mm from version 1 and adapting the other geometrical parameters leading to an optimum B_p/E_p ratio, is a reasonable choice. This design will be referred to as version 2. An alternative 'low-loss' like design was also considered; it is described below in section 4.2.3.

Relevant RF parameters for the mid-cell and five-cell geometries are listed in table 8 and compared to the initial scaled version.

Table 8.  RF parameters of five-cell geometry for version 2 compared to that of the scaled initial version.

Parameter	Ver 1 (Scaled)	Ver 2
Frequency (MHz)	801.58	801.58
Number of cells	5	5
Active cavity length (mm)	935	935
Voltage (MV)	18.7	18.7
Ep (MV m–1)	45.1	48.0
Bp (mT)	95.4	98.3
R/Q (Ω)	430	393
Cell-cell coupling (mid-cell)	4.47%	5.75%
Stored energy (J)	154	141
Geometry factor (Ω)	276	283
Field flatness	97%	96%

4.2.2.2. Impedance spectra

The longitudinal impedance spectrum calculated in time domain for both versions are shown in figure 26. This first two to three monopole pass-bands pose the highest impedance and do not easily propagate into the beam pipes requiring targeted HOM couplers to damp them to sufficiently low values. In the transverse plane, see figure 27, a few passbands of interest with primarily the two first bands (TE₁₁ and TM₁₁) being at least an order of magnitude higher than the rest. Similar to the longitudinal plane, transverse impedances at frequencies above 2.8 GHz are significantly smaller in impedance and above the cutoff of the beam tube.

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Detailed simulations with loop-like coaxial HOM couplers are underway to determine the level of damping achieved for the lowest order HOMs which pose the highest risk.

4.2.2.3. Loss factors and HOM power

The very small bunch length can excite frequencies well up to 50 GHz or above. This is characterised by the longitudinal loss factor ${k}_{| | }$. Figure 28 shows the frequency dependence of the integrated loss factors for the initial two versions of the cavity.

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In addition to HOM damping, the induced HOM power from the short bunches is of the order of 35 W for the nominal bunch charge of 0.32 nC and average beam current of 40 mA, for three passes. This level of power can easily be handled by loop-coupled couplers. However, resonant excitation of a HOM can easily lead to powers in the 1–2 kW range (assuming $R/Q=50$ Ω and ${{Q}}_{{\rm{ext}}}={10}^{4}$). Therefore, the couplers will have to be designed to handle this power and impose the condition of HOM impedance to not exceed 500 kΩ for the longitudinal modes. For transverse modes, single and multi-bunch simulations have to be carried out to determine the acceptable damping levels. The effect of the transition sections using tapers and bellows is already discussed in [75].

4.2.2.4. External Q and power requirements

Considering the steady state condition of recirculating beams and energy recovery only, the beam loading can be assumed to be small. Then the input RF power required to maintain the cavity voltage is directly proportional to the peak detuning, see figure 29.

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A realistic ${Q}_{{\rm{ext}}}\sim {10}^{7}$ with a corresponding power of 50 kW will allow for sufficient margin during transients. At these power levels and frequency range, standard UHF television IOTs become an attractive and robust option.

The cavity cell shape should be carefully optimised to balance accelerating mode efficiency with HOM damping needs (loaded ${Q}^{\prime}$ s) and HOM power extraction (HOM frequencies relative to the HC lines in the beam spectrum), as well as mechanical and cleaning considerations. Shapes such as the JLab ERL HC profile [78] and BNL3 ERL [79] cavity are good examples. Starting from these so-called 'Low-Loss' shapes, which feature cavity shapes with a steep wall angle down to 0°, led to the cavity optimisation described here. The low-loss type profile (vertical wall) and contoured irises produce moderate surface magnetic and electric field enhancements normalised to the accelerating gradient; the vertical walls also are the main difference compared to the initial designs with larger inner diameter describe above. This is a one-die design, meaning all the cell cups are produced from the same profile with the end cells simply being trimmed shorter to tune for field flatness.

Extracting HOM power from the cavities to room temperature absorbers must be considered in the cryomodule design (see below). Very effective HOM damping can be achieved by absorbers on the beamline either side of the cavity, providing the beam pipe is sufficiently enlarged to allow the dangerous HOMs to propagate. These, however, consume valuable space and the absorbers must be thermally isolated from the cold beamline components. The JLab waveguide damping scheme [78] avoids this by taking the HOM power out sideways to warm loads but is probably overkill for the LHeC requirements. As already indicated above, loop-coupled HOM dampers, possibly similar to the LHC type mounted on the ends of the cavity close to the end cell, will be sufficient. An example of the implementation of these couplers is described in detail in section 4.3 below. Many other configurations are of course possible. For this type of coupler, the HOM power is removed via a cable to a warm termination. This also allows easy monitoring of the HOM signals for diagnostic purposes.

Figure 30 shows a potential candidate cavity shape optimised for the PERLE and LHeC applications, it uses a median iris diameter (=tube) of 130 mm. The main parameters of the selected shape are listed in table 9, comparing it to a subset of the shapes investigated in this study with iris diameters varying from 115 to 160 mm and limited to solutions with equal iris and tube diameters.

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Table 9.  Parameters of a subset of cavity shapes studied during the cavity optimisation. Each cavity has 5 cells and a nominal effective voltage of 18.7 MV.

Parameter	Unit	Jlab1	Jlab2	CERN1	CERN2
Iris	mm	115	130	150	160
Frequency	MHz	802	802	801.58	801.58
Lactive	mm	922.14	917.911	935	935
$R/Q={V}_{{\rm{eff}}}^{2}/(\omega W)$	Ω	583.435	523.956	430	393
Integrated kloss	V pC–1	3.198	2.742	2.894	2.626
(R/Q)/cell	Ω	116.687	104.7912	86	78.6
G	Ω	273.2	274.717	276	283
(R/Q) · G/cell	${{\rm{\Omega }}}^{2}$	31877	28788	23736	22244
Equator diameter	mm	323.1	328.0	350.2	350.2
Wall angle	°	0	0	14	12.5
${E}_{{\rm{pk}}}/{E}_{{\rm{acc}}}$		2.07	2.26	2.26	2.40
${B}_{{\rm{pk}}}/{E}_{{\rm{acc}}}$	${10}^{-9}\,{\rm{s}}\,{{\rm{m}}}^{-1}$	4.00	4.20	4.77	4.92
kcc	%	2.14	3.21	4.47	5.75
${N}^{2}/{k}_{{\rm{cc}}}$		1168	778	559	435
cutoff TE11	GHz	1.53	1.35	1.17	1.10
cutoff TM01	GHz	2.00	1.77	1.53	1.43
Eacc	MV m–1	20.3	20.4	20.0	20.0
Epk	MV m–1	42.0	46.1	45.1	48.0
Bpk	mT	81.1	85.5	95.4	98.3

Normalised to λ, the beam tube and iris diameter of the selected solution are slightly larger than the TESLA or CEBAF upgrade (LL) shapes, but smaller than the original CEBAF or JLab HC. This allows good cell-to-cell coupling for HOM damping and reduced sensitivity to fabrication errors, while preserving high shunt impedance for the operating mode for good efficiency. The outer part of the cell profile is tuned to keep harmful HOMs far away from beam harmonics. Figure 31 shows the monopole spectrum of the cavity calculated from a long-range wakefield simulation with matched terminations on the beam pipes but no other HOM absorbers (similar to figure 26 above). Note that modes below the beam tube cutoff are unresolved and their final amplitudes and their Q's will depend on the HOM damping configuration, but all modes are well separated from the RF harmonics. Figure 32 shows the dipole spectrum, which is similarly well separated from harmful frequencies. The low-loss type profile (vertical wall) and contoured irises produce moderate surface magnetic and electric field enhancements, normalised to the accelerating gradient.

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The first scaled version of the 802 MHz ERL cavity was further optimised. Moderate improvement of the HOM performance was obtained with a small increase in aperture with the consequence of about 10% decrease in the fundamental mode R/Q. Given the short bunches and moderately HC, version 2 (Jlab₂ in table 9) is considered as a baseline towards realising a first prototype. Detailed studies including the FPC and HOM couplers are ongoing to finalise the cavity geometry and the optimum placement of the couplers.

Two options are investigated for the operational beam dump. In the first case no additional magnet has to be installed in the main lattice. A 0.66 m long dipole (SBEND) with a 0.906 T magnetic field acts as a spectrometer and separates vertically the different energy beams to direct them towards the respective superimposed arc (figure 47).

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This magnet can be used to deflect the 5 MeV beam towards a vertical beam dump as shown in figure 48. A C-shaped dipole has to be used to host a T-shaped vacuum chamber. The 5 MeV beam gets a deflection of about 90° in 3 cm and is extracted from the magnetic field region. Due to the strong edge effects and the low energy, the beam size increases rapidly and the 3 σ envelope has a radius of 65 mm (for a normalised emittance of 10 mm mrad) at a height of 10 cm from the Linac axis; here the vertical dump has to be installed (figure 48). Due to the low energy no window can be installed at the entrance of the dump system. The beam continues diverging in vacuum before hitting the dump material. A low Z material, like carbon, can be used to limit the backscattering and the weight of the dump block which has to have a size of indicatively 0.4 m × 0.1 m × 0.1 m (length, width and thickness respectively). For an incident energy of 5 MeV, about 1%–1.5% of the electrons are scattered back from carbon. The corresponding fraction of energy (or power) which is backscattered is a bit less as the electrons deposit part of their energy before being scattered back. For a 64 kW electron beam one can estimate roughly 0.6 kW backscattered from the carbon dump. To further reduce the backscattering towards the recirculating beam, a thin layer of a heavier material should be installed at the entrance of the dump, provided that a free hole is left for the passage of the beam. Detailed studies are needed to assess the feasibility of the proposed design (including a cooling system and additional shielding), evaluate potential integration conflicts (especially for the replacement of the underneath dipole) and the real impact of the backscattering on the recirculating beam quality. Moreover detailed tracking studies in a real 3D field have to be performed to check the effect of the strong fringe fields on the electron beam.

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The second option foresees the installation of three additional small dipoles in the 1.42 m drift between the end of the Linac and the start of the vertical spreader (k1, k2 and k3 in figure 49). The first dipole has a magnetic length of 0.2 m, a magnetic field of 0.044 T and kicks the 5 MeV beam by $30^\circ$ to extract it horizontally towards the beam dump. After a 5 m drift line the beam is dumped against a cylinder of graphite (20 cm radius and 10 cm long). Also in this case a cooling system and a surrounding shielding have to be foreseen. A clearance of  2 m is obtained between the main lattice and the shielding assuming a shielding transverse size of 1 m. Since k1 is operated in DC mode, all the beams are slightly affected by its magnetic field. The two remaining magnets are thus used to bring the other energy beams back on to the reference trajectory before the vertical spreader (figure 50). All three magnets have the same magnetic length, and the magnetic field is 0.088 T (with opposite polarity) and 0.044 T for k2 and k3 respectively. Preliminary studies were performed to check the impact of the proposed bump on the optics. The horizontal dispersion can be closed to $1.6\times {10}^{-7}$ m while the β functions at the entrance of the first dipole of the vertical spreader differ by 15% with respect the nominal optics; no further optimisation was attempted.

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During the commissioning period of PERLE, and in general during the beam setup, it is important to be able to dump the beam at the different energies. The easiest solution is to keep switched off the first horizontal dipole of the arc corresponding to the energy of interest and let the beam go straight towards the dump (figure 49). This dipole has to have a C-shape to allow the installation of a Y chamber for the recirculating and the extracted beam. The minimum bending angle of 22.5° guarantees enough clearance between the next dipole and the vacuum chamber of the extracted beam. If the dipoles of the arc are powered in series they can all be switched off during the setup period. Also in this case the line to the dump, one per each energy, corresponds to a 5 m drift. The β function at the dump is about 50 m corresponding to a minimum beam size for the most energetic beam of 238 μm. In order to limit the energy deposition and the activation of the dump materials, the setup should be performed with a reduced intensity. In table 11, the current corresponding to a power deposition of 64 kW at the different energies is shown.

The dump system will consist of three superimposed blocks of graphite with a radius of 20 cm and a maximum length of 1.2 m (for the 950 MeV beam) to absorb also the secondary showers. Additional shielding has to be envisaged and a total occupancy of 2 m × 3 m has to be considered around the dump blocks.

Up to now only DC magnets have been considered. In the eventuality that the setup dumps have to be also used as emergency dumps, fast kickers have to be included in the lattice. The CW operation mode and the 25 ns bunch spacing require a rise time t_m = 23 ns to allow for some jitter. A system impedance Z of 25 Ω is assumed, and a rather conservative system voltage U of 60 kV. Assuming a full horizontal and vertical opening of 40 mm, the magnetic length of the fast kickers has to be 0.46 m and the gap field 0.038 T. One extraction system per each each energy has to be installed after the vertical spreader when the beams are fully separated. Preliminary studies were carried out only for the 905 MeV beam but analogous considerations hold for the other energies. A fast horizontal kicker is installed between the last two quadrupoles before the arc (q3S6 and q4S6 in figure 49). The beam is deflected outwards by the kicker and goes through the 40 mm diameter of the defocusing quadrupole (q4S6) getting an additional kick. A horizontal Lambertson septum, placed 0.5 m before the first arc dipole (ba6), extracts the beam towards the dump line (figure 51). A clearance of 6 mm between the recirculating and the extracted beam envelope is obtained at the septum with the proposed configuration. The ba6 dipole has to be C-shaped (the present H-shaped design and the size of the magnet are not compatible with a fast extraction system due to the limited available space in the lattice) and the magnetic field free region is assumed to start at 70 mm from the main axis. Additional 30 mm are considered for the beam pipe of the extracted beam. A 0.5 m long septum with a 1.1 T magnetic field provides a kick of 174 mrad and thus an offset of 108 mm at the ba6, in agreement with the specifications.

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In order to limit the energy deposition at the emergency dumps, the interlock system has to stop the injector and pulse the kickers of all the different arcs simultaneously. This limits the maximum number of dumped bunches to 7 (bunches contained in one arc and one Linac). A kicker flattop of 166 ns is needed to fit all the bunches in and a fall time of 23 ns is assumed.

The energy and power deposition at the dumps for different energies are summarised in table 12. The TL to the dump have to be ∼10 m long and a defocusing quadrupole has to be installed at ∼4 m in order to increase the beam size at the dump and reduce the energy density (for the 905 MeV beam, a 0.6 mm × 0.4 mm beam size can be achieved using a quadrupole identical to q4S6). A block of superimposed kickers can be envisaged to align vertically the different energy beams at the dumps and reduce the transverse occupancy of the dump/shielding block.

The possibility of using the PERLE TL to perform quench and damage tests of superconducting magnets and cables is explored. The fast extraction system of the emergency dumps is used to extract only the number of needed bunches in the shadow of the nominal ERL operation. The length of the kicker waveform has to be extended up to 0.1 s (the risk of flashovers has to be carefully evaluated) to fulfil the test requirements.

In this case the lines have to include a triplet to vary the focal point and the beam size at the focal point. The different energy lines are recombined and a system analogous to the one used at the entrance of the Linacs is used. Steering magnets and a matching insertion are included as well. In total the line can be up to 30 m long and additional 10–20 m have to be considered for the test samples and the downstream beam dump. The parameters in table 12 are used for the dump design. It is assumed that the beam setup is done with a reduced intensity, the full intensity beams will then be dumped on the samples. For further analysis, more detailed optics studies have to be performed, the dynamic range of the magnets and potential RP issues to be evaluated.

Depending on the electron-beam time-structure, various optical systems capable to produce high gamma-ray fluxes are nowadays available. On the one hand, for bunch trains of low repetition rate, nonlinear [85] or passive [86] optical recirculators may be used (e.g. ELI-NP-GS [87]: trains of 32 bunches separated by 16 ns at a repetition rate of 100 Hz). The related laser system has to provide the maximum pulse intensity allowed by the foreseen spectral density (e.g. ELI-NP-GS: 400 mJ at 100 Hz for green 515 nm light, 14 μm transverse spot size of the intensity profile and 3 ps longitudinal pulse width). On the other hand, for CW electron bunches of repetition rate $\gtrsim 10\,\mathrm{MHz}$, Fabry–Perot cavities [88] (i.e. optical resonators) may be used [89–92]. This is the technical solution envisaged for the PERLE photon beam facility.

Fabry–Perot cavities consist of a sequence of high reflectivity mirrors (see figure 52). When the laser beam frequency satisfies resonance conditions (see [93] for pulsed beams), the power is enhanced at most by a factor $G=F/\pi$ inside the cavity (in practice laser/cavity spatio-temporal mode mismatches can reduce this factor by several dozens of percent). The cavity finesse F depends on mirror losses and reflection coefficients. However, the higher the cavity enhancement factor the narrower the optical resonance ${\rm{\Delta }}\nu /\nu =\lambda /({LF})$, where $\nu =c/\lambda$ is the laser frequency and L the cavity optical round-trip length. Dedicated laser cavity feedback is needed to preserve the resonance conditions [93, 94]. Experimentally, a cavity with $F\approx 28000$ ($G\approx 9000$) for picosecond pulses and with L = 4 m was demonstrated by some of us in [95].

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The power that can be stored inside the cavity is limited by thermal effects and mirror coating damage threshold. An average power of 670 kW (for 10 ps pulses and 250 MHz repetition rate) was obtained [96] for intra-cavity high-harmonic attosecond pulse experiments [97]. Concerning Compton experiments, 50 kW was recently demonstrated by some of us on the ATF electron ring of KEK [98]. A 35.68 MHz cavity ($L\approx 8.4$ m) designed for storing 10 ps pulses of average power above 600 kW is presently under development at LAL by some of us for the Compton x-ray machine ThomX [99]. This is a similar optical cavity that is needed for the PERLE photon beam facility. Besides, a CW laser beam of 700 kW will also be stored in the VIRGO interferometer in a near future [100]. There is thus a global effort to achieve stable and routinely operating cavities in high average power regime. One should also mention that developments on long $L\approx 30$ m monolithic and high finesse cavity are also on-going [101].

Mode properties (wave front profile, polarisation) of optical cavities solely depend on their geometries. Specific optical designs must then be supplied to fulfil the requirements of Compton experiments [102, 103]. Following the arguments of [103], one must consider planar four-mirror cavities made of at least two concave reflective surfaces for the ERL SCRF photon beam facility (see figure 52). The distance between the two planar mirrors (M₁ and M₂) can be adjusted to lock the cavity round-trip frequency to the accelerator radio-frequency while the distance between the two concave mirrors (M₃ and M₄) can be varied to tune the laser beam spot size at the IP. This geometry has been successfully tested at the ATF [92]. Eventually, with a careful design of the high reflectivity mirror coating, the mode polarisation of a planar four-mirror cavity can be freely tuned.

The laser source is of prior importance for high finesse cavities. One must start from a low phase noise mode-locked oscillator and then amplify the signal using the chirped pulse amplification technique [104]. The laser amplifier system is also of prior importance because it must not induce additional phase noise (e.g. AM/PM coupling via nonlinear processes) while providing stable and long term operations. Considering a repetition rate of 40 MHz and picosecond pulses, the most mature and powerful technology is based on ytterbium-doped diode-pumped fibres. Reasonably low noise laser mode-locked oscillators are commercially available at this wavelength (around 1030 nm) and amplifiers with up to an average power of 830 W [105] (and more recently 2 kW [106]) was demonstrated on a table top experiment. Besides, a fully connectorised and compact Yb doped fibre amplifier system providing 50 W has been operated over days at ATF/KEK [92] in gamma ray production experiments. This system has been recently upgraded to 200 W at CELIA for the ThomX project. This is what is needed for the PERLE photon beam facility. Using a LBO crystal, the laser beam frequency can finally be doubled with more than 50% efficiency before entering the optical cavity to provide a high average power beam at a wavelength close to 515 nm. Eventually one can also parallelise two fibre amplifiers to compensate for the second harmonic generation limited efficiency [107–109].

To reach a stored average power of more than 300 kW, the cavity finesse must be $\approx 30\,000$ leading to ${\rm{\Delta }}\nu /\nu \approx 2\times {10}^{-12}$. A strong feedback between laser and cavity is clearly required to keep the system on resonance. However, it should be mentioned that such a high average power has never been demonstrated for a wavelength of 515 nm. Apart from higher absorption in SiO₂, one of the dielectric dioxide used for high reflective coating, one does not expect tremendous differences for the cavity finesse foreseen here, experimental tests could be done at LAL and CELIA. The laser beam and cavity parameters are summarised in table 13.

Table 13.  Expected laser beam and cavity parameters.

	$\lambda =1030\,\mathrm{nm}$	$\lambda =515\,\mathrm{nm}$
Laser beam average power (W)	200	100 (200)
Laser beam time FWHM (ps)	1–10	1–10
Cavity beam waist (μm)	60	60
Cavity beam intensity spot size (μm)	30	30
Cavity beam Rayleigh length (mm)	22.0	11.0
Cavity finesse	28000	28000
Cavity stacked average power (kW)	$\gt 600$	$\gt 300(\gt 600)$

For other laser beam wavelengths one could also use gain media doped with the other rare earth elements Er (1.5 μm) or Tm (1.9 μm) [110]. Performances would be reduced with regard to Yb but still useful. Using quarter wave stack cavity mirror coatings one could also consider filling a single cavity with λ and $\lambda /3$ (e.g. doubled Yb: 515 nm and Er: 1545 nm) to provide a gamma frequency together with its third harmonic.

There is freedom in choosing the cavity geometry. Here a trade-off is proposed between a small laser-electron crossing angle, small enough laser beam spot size at the IP while ensuring reasonably large spot sizes on the mirror surfaces. To calculate the cavity mode one considers a planar four-mirror cavity (see figures 52 and 53 for a possible implementation) with L = 7.5 m seeded with a 40 MHz pulsed laser beam of wavelength 515 nm. Assuming a quasi symmetric geometry we set the distance between the concave mirrors D close to ${D}_{0}=2$ m and the distance h = 35 mm to avoid beam vignetting effects induced by the 15 mm inner diameter beam pipe (see figure 53(b)). The concave mirror radius of curvature is fixed to D₀ and the mirror diameters to 1 inch. The laser beam waist w₀ is shown as a function of ${\rm{\Delta }}D=D-{D}_{0}$ in figure 54(a). Small waist values are thus obtained for the very mechanically stable confocal geometry (D ≳ D₀) [103] though very close to the modal instability region. We choose ${w}_{0}=60\,\mu {\rm{m}}$ (i.e. 30 μm Gaussian intensity spot size). As expected [111], the transverse mode profile is elliptical and the main radii are shown as a function of the optical path length in figure 54(b). From this figure one sees that the mode is collimated between the two plane mirrors with a beam radius of approximately 2.7 mm on the mirror surfaces. Such beam radius leads to negligible diffraction losses induced by the 1 inch mirror edges. We obtain a crossing angle between the laser beam and the electron bunch of $1.2^\circ$. With $h/D=0.017$, the incident angle on the concave mirror is $0.53^\circ$ leading to a small mode ellipticity of roughly $2.4 \%$ and negligible polarisation instabilities [102]. As for the mechanical mirror mounts, motion actuators and vacuum vessel, we propose to adopt the technical solutions tested successfully over years at ATF/KEK [92, 99]. It is noticeable that these elements were recommissioned without any difficulty after the 2011 earthquake, and the design can thus be considered as robust.

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