Study of the transfer and matching line for a PWFA-driven FEL

The development of compact accelerator facilities providing high-brightness beams is one of the most challenging tasks in the field of next-generation compact and cost affordable particle accelerators. Recent results obtained at SPARC_LAB show evidence of the FEL laser by a compact (3 cm) particle driven plasma-based accelerator. This work is carried out in the framework of the SPARC_LAB activities concerning the R&D on plasma wakefield accelerators for the realization of new compact plasma based facilities, i.e EuPRAXIA@SPARC_LAB. The work here presented is a theoretical study demonstrating a possible scheme concerning the implementation of an innovative array of discharge capillaries, operating as active-plasma lenses, and one collimator to build an unconventional transport line for bunches outgoing from plasma accelerating module. Taking advantage of the symmetric and linear focusing provided by an active-plasma lens, the witness is captured and transported along the array without affecting its quality at the exit of the plasma module. At the same time the driver, being over-focused in the same array, can be removed by means of a collimator.


Introduction
Compact accelerator facilities development, providing high-brightness beams, is one of the most challenging tasks in the field of next generation compact and cost affordable particle accelerators.Particular attention is given to plasma-driven particle facilities due to their possibility to integrate high-gradient accelerating plasma modules with a short wavelength Free Electron Laser (FEL).Extremely strong electric fields (up to hundreds of GV/m) generated in the plasma allow accelerating gradients much higher than in conventional accelerators and set the basis for achieving very high final energies in a compact space.The plasma-based accelerator scheme is considered an efficient alternative to the current RF accelerators capable of ensuring compact structures [1].The EuPRAXIA (European Plasma Research Accelerator with eXcellence In Applications) preparatory phase aims at designing of the world's first accelerator facility based on advanced plasma-wakefield techniques to deliver 1-5 GeV high brigthness beams as required for users applications.This project foresees the realisation of a user facility based on both laser-driven and beam-driven plasma acceleration.For the beam-driven scenario the LNF-INFN laboratories in Frascati (Italy), with its EuPRAXIA@SPARC LAB projects, represents one of the pillars for the experimental activities.Indeed, at SPARC LAB, recent experimental results represented a first proof-of-principle demonstration of FEL lasing by a compact (3 cm) particle beam-driven plasma accelerator [2,3].

Motivation
The work presented here is in the framework of the EuPRAXIA@SPARC LAB project [4] and aims to demonstrate the feasibility of realising a transport line for beams outgoing from a plasma module preserving beam parameters.In plasma-based acceleration, either driven by ultra-short laser pulses [5] or electron bunches [6] the plasma is used as an energy transformer in which the driver pulse energy is transferred to the plasma through the excitation of plasma wakes and, in turn, to a witness bunch externally [7] or self-injected [8].A common issue to both the laser and particle beam-driven methods is represented by the extraction of the accelerated witness bunch that can lead to a large degradation of its emittance.When exiting the plasma the accelerated bunch has a large angular divergence, of several mrad, that is some orders of magnitude larger with respect to beams accelerated by conventional (RF) photo-injectors.For non-negligible energy spreads σ E , such a large divergence also leads to a rapid increase of the normalized emittance that, in a drift of length s, is given by the following formula: where E is the bunch energy and ε g the geometrical emittance [9].It is thus mandatory to catch the accelerated witness as soon as possible.In addition because of the high energy spread, the electron bunch coming from plasma accelerators suffers of strong chromatic effects that quickly degrade the emittance.An analytical description of the beam emittance degradation in free space propagation is given by the chromatic length parameter σ E ε 0 where γ is the Lorentz factor, σ E the relative energy spread, σ 0 x and ε 0 are the initial values of bunch transverse size and geometric emittance.L c shows how normalized emittance dilution is driven both by high energy spread and a small ratio between beam size and divergence [10].

EXTRACTION SYSTEM
In this paper, an innovative extraction system based on active plasma lenses will be presented.Two active-plasma lenses (APLs) [11] provide the capture and the focusing of the witness while a collimator is used to remove the driver.An APL essentially consists of a current-carrying cylindrical conductor whose axis is parallel to the beam.Here the plasma, produced after the ionization of the gas confined within the capillary, only acts as a conductor while the net focusing effect is produced by the flowing discharge current.Indeed, according to Ampere's law, the bunch is focused by the azimuthal magnetic field, B ϕ generated by the discharge current : where µ 0 is the vacuum permeability and J(r ′ ) the current density within the aperture (r< R with R the capillary radius).If we considered the focusing strength of an APL, given by K = ∂B ϕ (r) ∂r e 0 m 0 cγ , it can be understood how these elements are innovative.Infact, their focusing is symmetric like in solenoids but the resulting force scales as F ∝ γ −1 (with γ the relativistic Lorentz factor) like in quadrupoles.Moreover the focusing can reach several tens of kT/m, i.e., orders of magnitude larger than the strongest available quadrupoles (≃ 600 T/m).The tunability of the system is obtained by adjusting the external discharge current I D = S J • dS.Driver removal is based on the different focusing provided by the first APL to the accelerated witness bunch and the energy-depleted driver: the witness is focused exactly at the entrance of a collimator so as not to cut its charge while the driver is over-focused to have a spot size larger than the collimator aperture.
Starting from a recent work [12], the simulation analysis, which led to the definitive choice of the characteristics of the elements along the line, was conducted by using several simulation tools linked each other.The plasma acceleration process was simulated with Architect code, a hybrid code that works as a Particle-In-Cell (PIC) for the electron bunches while treating the plasma as a fluid [13].With Architect code a driver of 170 pC followed by a witness of about 30 pC are simulated downstream the PWFA module.Witness and driver bunches parameters at the exit of the accelerating module are in the Table 1.The dynamics of the two bunches from the exit of the PWFA module is simulated by General Particle Tracer (GPT) code, while MATLAB (MATrix LABoratory) is used for the analysis of beam propagation in plasma lenses.
The first code takes into account space charge effects, while the second code reproduces the magnetic field generated by the discharge-current in APL.Moreover, MATLAB code is used to simulate beam interaction with the plasma considering plasma wakefields acting on the beam itself by the use of the equation reported in [14].Thanks to the use of these tools a possible scheme concerning the implementation of an array of active plasma lenses and a collimator were simulated to design a transfer line capable to extract and transport the accelerated and highly divergent witness bunch and, at the same time, to reduce the driver to 1.4% of its initial charge.The witness cut is not significant infact it is 0.07 % of its initial charge.radius.The focusing is obtained applying a discharge current I D of 1 kA in the first and 400 A in the second lens.The position of the first lens respect to the PWFA module has been carefully chosen to preserve the witness normalized emittance taking into account different contributions and seeking a compromise between them.Infact, as shown in the Eq.1, short drifts would be preferable to avoid emittance degradation due to the large divergence of the beam.At same time, small drifts would produce a small witness spot at the APL entrance i.e., a larger bunch density.As demonstrated few years ago [15] large bunch densities produce non negligible plasma wakefields in the APL that, being nonlinear, would increase the beam emittance during the lens focusing.The current of the first lens is larger than that of the second to ensure greater focusing in the first centimeters of the line and to cut more driver at the entrance of the second lens that, in this case, also acts as a collimator.
Taking advantage of the focusing of the first lens, a collimator 3 cm long with an aperture of 150 µm is located at 62.5 cm from the accelerating module.At this position the witness is focused exactly at the entrance of the collimator, without losing any charge, while the driver is cut because it is overfocused to a spot size much larger than the collimator aperture almost in its entirety (see Fig 2).
From studies conducted by varying the parameters of the elements, this configuration appears to be a good compromise to guarantee transport of the witness in a very compact length (73.5cm), as highlighted in Fig. 3. Figure 4 shows that witness normalized emittance along beamline grows from 0.5 mm mrad to 0.8 mm mrad.As expected this increase is in the initial drift downstream the PWFA module and in APLs.Beam envelope and emittance trend change, respectively in Fig. 3 and Fig. 4, is due to the 0.07% charge degradation of the witness after the collimator.Evolution of the witness normalized emittance along the beam line.Such a solution is tunable changing the parameters of the elements along the line and can be implemented in a future facility based on plasma acceleration where the compactness represents the mail goal.

CONCLUSION
Plasma-based acceleration, either driven by ultra-short laser pulses or electron bunches, has proven the feasibility to drive a high gain FEL.The focus of the research now concerns on one side on the reproducibility and stability of the acceleration, mandatory to pilot a user-facility and, on the other side, the proper extraction and capture of the accelerated beam to avoid its quality degradation, which might prevent FEL generation.This work proposes a possible scheme concerning the implementation of an innovative array of discharge capillaries, operating as active-plasma lenses to build an unconventional transport line for bunches outgoing from plasma accelerating module.Taking advantage of the symmetric and linear focusing provided by an active-plasma lens and a use of a collimator, this compact and tunable configuration appears to be a good compromise to guarantee transport of the witness and the driver removal in a 73.5 cm length.This beam line involves a 60% increase in witness emittance compared to the initial value but, despite this increases, it represents a valid alternative to a conventional transfer line.Indeed, dogleg or chicane beam lines requires longer spaces (of the order of tens of meters) and, due to a finite energy spread, might strongly affect the beam longitudinal phase space, requiring small deflection angles and non-trivial methods to limit and compensate the bunch elongation due to the dispersion introduced by each bending.Parametric studies are on going to show the system tunability by varying the energy and the energy spread of the beams.In addition, the system can be tuned by varying the current and position of the lenses.The proposed solution represents a good compromise to guarantee transport of the witness and the driver removal in a very short length that could be implemented in the future plasma acceleration facility.

Figure 1 .
Figure 1.Layout, not in scale, of the extraction system consisting of two active-plasma lenses (in yellow) and a collimator between them (in green).

Figure 1 4 Table 2 .Figure 2 .
Figure1shows the layout of the extraction system, while the optimized parameters are listed in Table2.The lenses are 3 and 1 cm respectively long and both have a 500 µm hole

Figure 3 .
Figure 3. Witness envelope along the beam line.

Figure 4 .
Figure 4.Evolution of the witness normalized emittance along the beam line.

Table 1 .
Bunches parameters at the exit of the PWFA module.* Witness core parameters are rms value referring to the 80% of the whole bunch.