Dual stage approach to laser-driven helical coil proton acceleration

Helical coil accelerators are a recent development in laser-driven ion production, acting on the intrinsically wide divergence and broadband energy spectrum of laser-accelerated protons to deliver ultra-low divergence and quasi-monoenergetic beams. The modularity of helical coil accelerators also provides the attractive prospective of multi-staging. Here we show, on a proof-of-principle basis, a two-stage configuration which allows optical tuning of the energy of the selected proton beamlet. Experimental data, corroborated by particle tracing simulations, highlights the importance of controlling precisely the beam injection. Efficient post-acceleration of the protons with an energy gain up to ∼16 MeV (∼8 MeV per stage, at an average rate of ∼1 GeV m−1) was achieved at an optimal time delay, which allows synchronisation of the selected protons with the accelerating longitudinal electric fields to be maintained through both stages.


Introduction
Proton acceleration using high power laser drivers has shown progress at a significant pace over the past two decades, motivated by the vision of delivering a compact and cost-effective alternative to conventional accelerators. Laser-driven sources, moreover, possess a unique ultra-short burst duration, enabling beam delivery at exceptionally high currents and dose rates [1]. In this context, target normal sheath acceleration [2] (TNSA) has been the most widely studied mechanism of ion acceleration from an intense laser pulse, where ions are accelerated by the space charge field set up by a hot electron sheath at the rear side of foil targets irradiated by intense lasers. This mechanism produces a proton burst that has a relatively wide angular spread (∼10 • -20 • half-angle), with a broadband, exponentially decaying spectrum, thus limiting the proton flux at high energies. The development of helical coil (HC) accelerators, as first proposed in [3,4], has therefore shown promise to mitigate these inherent disadvantages of the TNSA mechanism, and potential as a laser driven alternative to conventional radio frequency (RF) accelerators for medical applications [5][6][7][8], production of secondary radiation sources [9][10][11], and high energy density physics [12]. The energy selection characteristic of the HC scheme is advantageous for the aforementioned applications, as, for instance, accurate control of the proton bunch energy is essential for applying Bragg peak penetration for targeted hadron therapy. Furthermore, high brilliance beams are also highly desirable for these applications, and the HC scheme delivers the large particle flux of TNSA at the desired proton bunch energy by chromatic focusing.
The HC accelerators [3,4,13,14] consist of a helix of wire perpendicular to the rear surface of a typical flat foil (FF) target. Irradiating the foil generates simultaneously a proton beam at its rear surface and a positively charged unipolar electromagnetic (EM) pulse, tens of ps in duration, which flows along the helix wire at v EM ≃ 0.98c [3,[15][16][17]. The travelling EM pulse along the helical path produces a strong EM field region within the HC, with strong radial and longitudinal components, the former of which acts to focus and collimate protons directed along the helix axis, while the latter accelerates them further, resulting in a quasi-monoenergetic, highly collimated proton bunch emerging from the end of the HC. The specific proton energy which is synchronised with the velocity of the EM pulse along the helix axis can be selected by careful control of the HC diameter and pitch. Pencil beams of energies of up to 50 MeV have recently been demonstrated using a single HC at a petawatt-class laser facility [13].
While the beam energies can be further improved by optimising the HC design and using ultra-high intensity laser drivers, the same outcome can be achieved by multi-staging HCs while using multiple high intensity laser pulses. A proof-of-principle demonstration of multi-staging HC modules is reported in this article, where the proton bunch generated from one HC is further accelerated in a second HC driven by a separate laser. Under optimum injection conditions, the resulting energy gain of the proton bunch was double that of a single stage. This method also addresses the issue of the accelerated proton bunch outrunning the electric field in a HC [18], which limits energy gain to the initial ∼10 mm of HC [13,18]. A systematic temporal scan demonstrates that the spectral peak energy in a dual stage HC configuration is highly sensitive (on the ps scale) to the delay between the driving laser pulses, which is further corroborated by particle tracing simulations elucidating the injection dynamics of a TNSA seed beam of broad spectral profile.

Experiment
The experiment was performed using the Vulcan laser at the Rutherford Appleton Laboratory in the UK [19,20]. A dual laser configuration was employed to drive the first and second stage HCs with separate irradiations as shown in figure 1. The first stage was driven by a (2.5 ± 0.3) ps pulse containing ∼50 J (henceforth CPA1) and the second stage by a (3.4 ± 0.9) ps pulse containing ∼60 J (henceforth CPA2), where laser energy is quoted post-compressor. Both beams were focussed after wavefront corrections, by f/3 off-axis parabolic mirrors to ∼5 µm full-width at half-maximum (FWHM) spots on target, each containing 35% of the delivered energy within the FWHM. This resulted in both beams delivering peak intensities of ∼ 3 × 10 19 W cm −2 . The first stage HC (henceforth called HC1) had an inner diameter d 1 = 700 µm and pitch p 1 = 500 µm, while the second stage HC (henceforth called HC2) had a smaller inner diameter d 2 = 500 µm and pitch p 2 = 425 µm. The increased pitch to diameter ratio of HC2 was chosen to synchronise higher energy protons with the objective of accelerating further the protons accelerated by HC1. Both HCs were constructed from stainless steel wire of diameter d w = 125 µm and were 8.0 ± 0.3 mm long, separated by 3.5 ± 0.6 mm to minimise the influence of the EM pulse in one HC on the other. The lasers irradiated 2 × 2 mm FFs of 25 µm thick Au. The Au foil in the first stage (henceforth called FF1) was directly attached to HC1, seeding a proton beam within the HC. The second stage Au foil (henceforth called FF2) was attached to HC2 via a 125 µm diameter stainless steel connecting wire, manufactured to the specification shown in figure 1. This arrangement allowed the protons emitted from HC1 to be injected directly into HC2, avoiding any disruption due to the laser interaction with FF2, as well as the possibility of on-shot self-proton probing of the HC2 charge pulse interaction with the proton beam generated from FF2. In addition to the dual stage helical coil (DSHC) configuration shown in figure 1, several shots were taken in a single stage helical coil (SSHC) configuration were HC2 was removed and only CPA1 employed. The proton beams emitted from HCs were observed on stacks of radiochromic film (RCF) [21][22][23][24] at 75 mm from the proton source, as shown in figure 1.
The delay, τ , between the peak of the EM pulses entering HC1 and HC2, was controlled by varying the arrival of the laser pulses at their respective targets using optical delay lines built into the laser system. The delay incorporates the time taken for the EM pulse to flow from FF2 to HC2 along the connecting wire, which was calculated assuming a nominal speed of the EM pulse v EM ≃ 0.98c, as measured in [3,[15][16][17] and the wire length measured from the photographs of the target taken before irradiation. The uncertainty in the calculation of τ is mainly a combination of the error in measuring the length of the connecting wire (±0.5 mm) and the error in synchronising CPA1 and CPA2 (±4 ps) using a fast photodiode connected to an oscilloscope.

Results
A selection of SSHC produced proton beams observed on RCF are shown in figure 2(a). As expected, the SSHC produced an ultra-low divergence proton beam (0.5 • HWHM) at ∼24 MeV, with the beam divergence increasing to HC1's 2.5 • half-angle aperture at lower and higher energies (figure 2(a)). The energy band of the collimated part of the beam represents the protons which have remained synchronised with the electric field throughout the HC and therefore have received maximum energy gain. As shown in figure 2(d) the  Note lower sensitivity HD-V2 type RCF is shown in (a1-5) and (c1-3) while higher sensitivity EBT-3 type RCF is shown in (b1-5) and (c4-5). White solid (dotted) circles represent the 2.5 • (0.7 • ) half-angle cone of the SSHC (DSHC) apertures. The green (red) circles encompass 0.45 • (0.37 • ) half-angle cones for SSHC (DSHC) targets as the divergence is calculated from the HC exit opposed to the divergence scale which is calculated from the proton source at FF1. (d) Energy spectra extracted from dose converted RCF for a 0.5 • half-angle cone from the HC exit (red solid and dotted circles) in (a)-(c) are shown in comparison to a typical proton spectra obtained from a flat foil (FF) for the same angular cone. A 0.5 • half-angle cone was chosen as this is approximately the half-width at half-maxima (HWHM) of the most tightly focussed proton beams in HC shots, as seen in (a3), (b5) and (c4). A FF spectrum for a 2.5 • half-angle cone is also shown for comparison. Spectra obtained from PTRACE simulations are over-plotted as solid lines. SSHC spectrum exhibits a peak at ∼24 MeV corresponding to the optimal focussing seen on RCF. The SSHC provides a significant enhancement in proton flux, compared to the reference FF shot, over a broad energy range of 20-30 MeV due to the focussing, and post-acceleration of lower-energy, higher flux TNSA protons. The observed broad spectral profile of the HC-driven proton bunch is typical of the case where the HC is attached directly to the proton generating foil and the electric field pattern acts on a broadband proton energy range close to their source before they are significantly dispersed along the HC axis [3,18,25]. Such a broad spectral peak with moderately good collimation was chosen as a suitable candidate to study beam injection into a second stage, as discussed later, for the intended temporal scan covering a range of proton energies.
A systematic scan of the DSHC configuration was followed by varying the time at which protons from HC1 were injected into HC2. Figures 2(b) and (c) show a selection of RCF data obtained from two DSHC shots taken for τ ≃ 142 ps and τ ≃ 179 ps. As shown in figure 2(d), the proton spectra from the DSHC targets exhibit narrow-band spectral peaks at the maximally collimated energies. Although the second HC reaccelerates a part of the spectral peak delivered by the first stage, the number of particles delivered by the DSHC case within the spectral peak are significantly higher than that from the FF and the SSHC targets at similar energies. For example, 10 7 protons in the energy range 39-41 MeV would result in a dose deposited in water of 5 Gy, assuming a pencil beam width of 1 mm, which is high enough for therapeutic applications. Unlike the broad spectral peak obtained from the SSHC with coils attached to the FF, the spectral peaks from the DSHCs were significantly narrower, most likely as a result of the smaller bandwidth able to be selected by the HC2 due to temporal and spatial dispersion of protons along the HC axis during their time of flight across the length of HC1. Spectral bunches with a narrower bandwidth have also been observed in HC targets when including a delay line between the foil and the coil entrance [13]. The gap between the FF and the coil allows spatial dispersion of the TNSA protons, resulting in the charge pulse synchronising with a narrower energy range, similar to what occurs in the DSHC.
As expected, τ plays a crucial role in the DSHC configuration, controlling the spectral window selected by the HC2. Figure 3 shows the systematic temporal scan over ∼100 ps range as carried out in the experiment to study the dynamics of beam injection in DSHCs. Spectral peaks (with ultra-low divergence) are produced at higher energies by reducing τ , i.e. when higher energy protons from HC1 are injected into HC2 synchronously with the EM pulse. For instance, τ = 142 ps and 179 ps, for the cases shown in figures 2(b) and (c), represent, as discussed later with the help of particle tracing simulations, timely injection of ∼26 MeV and ∼16 MeV protons from the FF1 in the HC2. The spectral peaks at ∼40 and ∼32 MeV observed for the two cases represent a significant (∼14 MeV and ∼16 MeV respectively) net gain in proton energy due to the DSHC configuration. The rapid drop in energy observed for shorter delays (τ < 140 ps) is due to the lack of protons beyond 40 MeV produced by the first stage. In this scenario protons are injected into HC2 after the arrival of the peak of the EM pulse and experience a decelerating electric field.

Discussion
To interpret more accurately the experimental observations, the experiment was modelled in the particle tracing code PTRACE [26]. The input proton beam in the simulations was given a small 2.5 • divergence cone and a Boltzmann-like TNSA spectral distribution with a 10 MeV temperature in the 10-30 MeV region of interest, as produced in experimental FF shots ( figure 2(d)). The EM pulses produced at both stages were measured during the experiment employing the self-probing technique [17], where the proton beam produced by the interaction is deployed to probe the EM pulse generated from the same laser interaction. Firstly, the EM pulses produced by CPA1 and CPA2 were diagnosed independently by using an FF attached to a wire, arranged in a square wave pattern (SWP) facing the foil's rear side and in the line of sight of the TNSA protons. Proton deflection by the EM pulse propagating along the SWP wires led to depleted regions of dose surrounding the wire shadow on the RCF. The magnitude of the EM pulse travelling along a wire can typically be represented in terms of a linear charge density, which allows for numerical modelling of the EM pulse's radial electric fields in the simulations. By comparing the deflection of the protons at a given point on a given RCF layer to that caused by a charged wire modelled in PTRACE, one can reconstruct the linear charge density associated with the EM pulse at that point. Repeating this process for different points on each RCF layer, the velocity and temporal profile of the EM pulse along the SWP wire can be obtained [17]. The velocity of the EM pulse flowing along the wire was measured as v EM ≃ 0.98c, in agreement with earlier works. The EM pulse temporal profiles were found as asymmetric Gaussians with t r ≃ 5 ps half width at half maximum (HWHM) rise for both stages and t d ≃ 20 ps (30 ps) HWHM decay time for first (second) stages. The measured rise and decay times are broadly in line with those measured previously at other laser systems [3,4,13]. Although a detailed study of the EM pulse profile was not feasible during the campaign, the longer decay times measured in the current experiment may be attributed to the longer pulse durations of the interaction laser pulses. The interaction of CPA1 with the first stage produced a peak linear charge density measured as λ 1 ≃ 23 ± 3 µC m −1 . Although the SWP setup showed similar peak linear charge density for CPA2 as CPA1, on-shot self-proton probing of HC2 in a few shots indicated this stage's peak linear charge density to fluctuate in the range of λ 2 ≃ (10 ± 3) − (15 ± 3) µC m −1 . Since the CPA2 energy remained relatively stable between shots, the fluctuation in λ 2 may be arising from factors such as shot to shot variations in CPA2 pulse duration and alignment of the CPA2 on FF2, or suboptimal coupling of EM pulse to the coil in HC2 due to its complex geometry and fabrication.
A SSHC simulation with λ 1 = 23 µC m −1 produced a similar spectral profile as the experimental data, as shown in figure 2(d), for the focussed part of the beam. The residual discrepancy at lower energies arises due to highly non-uniform and diffused profile of the beam obtained in the experiment, most likely due to non-uniformity in the input beam profile not being focused effectively by the tailing part of the electric field region within the HC. Subsequently a series of DSHC simulations were performed in the parameter space of τ = 120 − 230 ps and λ 2 = 5 − 20 µC m −1 with a fixed λ 1 = 23 µC m −1 . As shown in figure 2(d), simulated spectra obtained for τ = 140 ps with λ 2 ≃ 20 µC m −1 and τ = 180 ps with λ 2 ≃ 10 µC m −1 are in good agreement with the experimental spectra obtained from their respective shots. The simulated peak energy for the full parameter space is plotted in figure 3(a) incorporating a colour scale representing the input energy (energy at FF1) corresponding to the spectral peak. As can be seen, the simulation indicates the synchronization of higher energy protons for lower τ , and the required proton energy beyond 35 MeV to achieve a net gain for τ < 140 ps. Figures 4(a) and (b) give a detailed account of the proton dynamics in the DSHC based on the τ = 140 ps and τ = 180 ps simulations, while using the same value of λ 2 ≃ 20 µC m −1 for a one-to-one comparison. Other simulation parameters were kept the same as those shown in figure 1(d). As can be seen in figures 4(a) and (b), HC1 in both cases accelerates seed protons above 14 MeV propagating within the positive longitudinal electric field region, while the <14 MeV seed protons propagating within the negative field region are decelerated. From figure 4(c) it can be seen that 15-16 MeV seed protons experience optimal focussing and acceleration in the HC1, which leads to the spectral peak observed at ∼24 MeV for the SSHC shown in figure 2(d).
Comparing figures 4(a1) and (b1) we see that altering τ translates the second stage electric field along the time axis, effectively synchronising the HC2 with a different energy band of the proton beam emerging from HC1. For τ = 180 ps the accelerating electric field of HC2 synchronises with >15 MeV seed protons that have efficiently accelerated in the first stage. In particular, the ∼16 MeV seed protons receive near-maximum energy gain in both stages, leading to a highly efficient double-stage acceleration as shown in figure 4(c). Comparing this with the experimental data taken at τ = 180 ps, as shown in figure 2(d), a net energy gain of ∼16 MeV (∼8 MeV per stage) is estimated to be produced in the DSHC target. On the other hand, in the τ = 140 ps case the electric field at HC2 is formed significantly sooner than the arrival of the ∼ 16 MeV seed protons which are optimally accelerated by the HC1. Therefore, HC2 accelerates the highest energy protons produced by the HC1, although these emerge less collimated from the HC1 ( figure 2(a)). The maximum energy gain in this case is obtained for ∼26 MeV seed protons, as seen in figure 4(c), which enter the HC2 with ∼35 MeV after acceleration in HC1. These protons are injected into the HC2 at ∼150 ps, slightly behind the EM pulse reaching the HC2 at 140 ps, and experience a small deceleration over the first few mm inside the HC2 before they penetrate into the accelerating positive field region as shown in figure 4(a1). Figure 4(c) shows dynamics in energy gain vs seed energy for various τ , highlighting the accuracy in time of injection required to achieve an optimal energy gain in a multi-stage configuration. At the same time, figure 4(c) also indicates the flexibility of tuning optically the output energy in a given set of HCs. The majority of the temporal scan indicates substantial acceleration in HC2, though the energy gain varies due to the highly dynamic interaction between the protons and the electric fields within the DSHC targets. The maximum energy gain across the τ range was observed for τ = 180 ps, although this produced a lower spectral peak than the case with τ = 140 ps. In this experiment shown here, we chose to have a broadband seed beam into the second stage, and chose to select narrowband in the second coil. However, we can minimise transmission losses through appropriate coil designs, and any subsequent coil stages that could be added may not incur significant transmission losses if the coils are designed to collect the entire exit flux from the preceding stage, thus resulting in a significant proton flux even after multiple stages of acceleration. Future work aimed to explore the feasibility of operating the HC targets at high repetition will be crucial to envisage a pragmatic approach towards developing a compact beam delivery system for the aforementioned applications.

Conclusion
In conclusion, we have demonstrated successful deployment of HC targets in a double stage configuration, which is a promising first step towards building a miniature, modular, all-optical accelerator. Due to the short duration of the EM pulses driving the HCs, the experimental data highlights the requirement for precise timing on the ps-scale for an optimum performance, which offers tunability of output energy. A modular approach not only provides better control over beam parameters, but also may offer an alternative route to reaching proton energies of therapeutic relevance (i.e. above 60 MeV) by using multiple pulses at more moderate power, rather than a single laser pulse at PW power or above. The multi-stage approach also addresses the issue of desynchronisation in HC accelerators as highlighted in earlier works [13,18], which hinders the continuous acceleration of a desired proton bunch to high energies. This data serves as a proof of principle work for further exploration on multi-PW, multi-beam systems which will become available in coming years [27][28][29][30].

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.