In proton acceleration from laser-irradiated thin foil targets, adding foams on the front surface or connecting a helical coil on the rear surface of the foil has proven to be an effective scheme to enhance proton energy. In this paper, we make the first attempt to incorporate the above two enhancement schemes for laser-proton acceleration by simultaneously adding foams and connecting a helical coil to a thin foil target. By utilizing such integrated targets in the experiment, focused beams were generated. The maximum proton energy and the number of energetic protons are apparently enhanced. Moreover, quasi-monoenergetic peaks were formed at the high-energy end of the spectra. Particle-in-cell plasma simulations and electromagnetic beam dynamics simulations show that the double-layer target not only enhances the energy of protons but also leads to a multiple-fold increase in the number of escaped electrons, which results in an enhanced post-acceleration in helical coil subsequently.

Laser-driven ion acceleration has received extensive interest due to its unique ion beam characteristics. These characteristics, including small source size,1 short pulse duration,2 and ultrahigh peak current,3 make them highly advantageous for various applications such as FLASH radiotherapy,4 ion driven fast ignition,5 and warm dense matter generation.6 The primary acceleration mechanism for energetic ions is known as target normal sheath acceleration (TNSA).7 In TNSA, hot electrons are generated at the front surface of the target by absorbing the laser energy and then set up a space charge field to accelerate ions at the rear side of the target. The method has been recognized as a robust approach to generate proton beams with energies of tens of MeV.8 At present, it is capable of producing protons of up to 85 MeV through TNSA.9 However, theoretical and experimental studies10,11 show a scaling relationship between the energy of TNSA ion beams and laser intensity as EionsIlaser1/2. This indicates that achieving proton energies in the hundreds of MeV ranges with current laser facilities12 is highly challenging, if not infeasible. In addition, TNSA intrinsically generates ions characterized by a broad angular distribution13,14 (10°–20° half-angle) and exponential energy spectrum,7 which impose stringent limits for applications.

An effective approach to achieving higher-energy protons is to increase the energy conversion efficiency from laser to hot electrons for higher electrons' number and energies. Pre-pulse ablation lasers have been used to generate a pre-plasma, in which the absorption of the main laser is increased, so that the acceleration field at the target's rear side is strengthened and the proton energy is enhanced.15,16 Novel targets, which can enhance laser absorption and ion conversion efficiency, have been widely proposed and studied. These efforts encompass microstructure targets,17,18 isolated targets,19,20 near-critical-density (NCD) double-layer targets,21,22 and so on. Among them, double-layer targets composed of a nest-like carbon nanotube foam (CNF) layer and a thin foil have shown extensive advantages.23 The CNF layer, with an average electron density in the near-critical density (NCD) region, can be fully ionized and homogenized to plasma at the rising edge of the laser pulses,24 so that the laser can propagate into targets until completely absorbed. In the NCD layer, relativistic self-focusing25 and self-phase modulation26 can enhance laser intensity by a factor of 10 at the most. In addition, direct laser acceleration (DLA) in the NCD plasma can substantially boost both the electron energy and number as a result of the strong laser-plasma coupling.27 When applied to laser ion acceleration, CNF-based double-layer targets significantly improve proton cutoff energies and number by several times28,29 and achieve breakthroughs of heavy ion energy up to many tens of MeV/u.21,22

Another way to enhance the energy is to prolong the time in which protons are effectively accelerated. It has been recognized that several detrimental factors such as the self-generated magnetic field30 and the limited laser pulse duration10 would impede the long-term acceleration of protons. Multistage acceleration schemes were proposed and examined in experiments to prolong the acceleration time. A multi-stage TNSA acceleration scheme has been developed. This scheme uses multiple laser pulses to successively interact with a series of targets, thus repeatedly accelerating protons within the sheath field generated at each target's rear surface.31,32 The delay time between multiple laser pulses needs to be precisely controlled. Another cascade acceleration scheme uses a channel with a diameter of micrometers behind a thin foil.33,34 The laser interacts with the microchannel to create an electric field inside the channel that can focus and post-accelerate protons from the thin foil. These two methods require a very precise laser control and complex target structures. Kar et al. proposed a scheme that can realize the post-acceleration, energy selection, and ion collimation at the same time by incorporating a micro helical coil (HC) on the rear surface of the flat foil target.35 The laser-foil interaction first generates a proton beam and a positive charge on the foil. In sequence, a neutralizing current with an ultrahigh density of μCm−1 is driven to generate an electromagnetic pulse (EMP) traveling along the HC. This EMP can create an intense GV/m electric field in the center of HC to post-accelerate the proton beam. This scheme, performed with a 200 TW laser system, achieved an increase in ∼5 MeV in proton energy.35 

The EMP's strength is related to the charges escaped from the target due to the laser irradiation. Subsequent studies have shown that the charge (dominated by escaped electrons) is optimal at a laser pulse duration of a few 100 fs.36 In addition, the thinner the target, the more charge is released.37 These approaches are expected to enhance the post-acceleration in helical coil. However, there is limit to this decrease in target thickness. Thin targets may be susceptible to laser pre-pulse or amplified spontaneous emission (ASE), which can damage the target before the main pulse arrives, affecting the laser-plasma proton acceleration.38 Varying the pulse duration at a fixed laser energy can result in a reduction of intensity, leading to a decrease in the energy of the laser-driven protons.39,40 Therefore, it is a complex problem to increase both the escaped electron charge and to proton energy produced by interacting with the laser.

Double-layer targets have been experimentally demonstrated as an effective method, simultaneously enhancing the escaped electron charge and the proton energy. If we seamlessly attach a CNF layer to a thin foil's front surface and connect a helical coil to its rear surface. This kind of integrated target could achieve a synergistic effect, increasing the energy of the laser-driven protons and generating stronger EMP to improve the post-acceleration of the protons in the helical coil. Since only one laser pulse is required and the target is simple, such a scheme could easily be realized without intricate experimental operation, compared to other compact cascade accelerations.

This study explores the enhancement of proton acceleration by integrating a CNF-based double-layer target with a helical coil. The experimental results indicate that the integrated targets lead to an apparent increase in proton energy and number. We present a comparison of proton acceleration between single-layer and double-layer targets, highlighting the advantages of the double-layer targets in achieving higher-energy protons when combined with a helical coil. Particle-in-cell (PIC) laser-plasma simulations and electromagnetic beam dynamics simulations were performed to provide insights into enhanced acceleration processes.

The experiments were performed using the Compact LAser Plasma Accelerator (CLAPA) facility41 at Peking University. The CLAPA laser is based on Ti:sapphire with a central wavelength of λ=800nm and a duration of 40 fs. The laser pulses with an on-target energy of 1.2 J were focused by an f/2.5 off-axis parabola to a spot of 5 μm full-width at half-maximum. The peak intensity was 3.3×1019W/cm2. A single plasma mirror system was used to increase the temporal contrast of the laser to 1012 at 40 ps before the main pulse.42 As sketched in Fig. 1(a), the laser pulses were normally incident on the targets. The double-layer targets were composed of a CNF layer and a 4-μm-thick aluminum foil. The single-layer targets were bare 4-μm-thick aluminum foils. The thickness of the CNF layer was 40 μm, and its mass density was 1.1 mg/cm3, corresponding to an electron density of 0.2 nc22 if all the ions are fully ionized. HCs were normally placed a few millimeters behind the incident foils and connected to the edge of the foils by an aluminum wire (delay line). There is a controlled gap distance d between the HC and the foil. The configuration allowed precise control of the arrival time of the electromagnetic pulse at the HC relative to the arrival of the protons from the foil by adjusting the gap distance.43 HCs were made of a 0.1-mm-diameter aluminum wire, with a pitch of 0.22 mm, an internal diameter of 0.7 mm, and a length of 10.5 mm. All the double- or single-layer targets and HCs were supported by insulating ceramics to ensure that the target charge can form a circuit along the HC. As shown in Fig. 1, the helical coil axis is oriented to the X-axis and the target front surface at x = 0 mm.

FIG. 1.

(a) Experimental setup scheme. (b) SEM imagines the carbon nanotube foam. (c) Picture of the helical coil targets before and after the shot.

FIG. 1.

(a) Experimental setup scheme. (b) SEM imagines the carbon nanotube foam. (c) Picture of the helical coil targets before and after the shot.

Close modal

The ion energy spectra were measured by a Thomson parabola spectrometer (TPS) at 780 mm away along the normal direction of the target surface. The pinhole of the TPS was 200 μm in diameter, corresponding to a solid collection angle of 5.2×108sr. Radio chromatographic film stacks (RCFs) were placed 3 cm behind the target to detect the proton spatial distribution at different energies. The RCF stacks had 8 layers of HD-V2 RCFs and covered by a 10-μm-thick aluminum foil. Imaging plates (IPs) were positioned 4 cm behind the target for electron detection, consisting of five layers of BAS-IP SR, which were separated by five layers of a 1-mm-thick aluminum foil. Note that RCFs and IPs were not used at the same time in a single shot.

In the experiments, we performed multiple laser target shots on both single-layer and double-layer targets without helical coils. We adjusted the target position (relative to the focus position of the laser at low intensity) for each shot. The TPS was used to measure the spectra of each shots. The proton cutoff energies for different shots are shown in Fig. 2(a). Obviously, proton cutoff energies are higher for double-layer targets than for single-layer targets. The energy spectral distributions and raw TPS images of the two shots where the cutoff energies are close to the mean value are shown in Figs. 2(c) and 2(d). The double-layer targets significantly enhance the proton energy spectrum. The charge states from C1+ to C6+ can be ionized in single-layer targets, while C4+ to C6+ are dominant in double-layer targets. Previous studies have shown that ion charge states are related to laser intensity,42,44–46 which indicates that here self-focusing occurs and increases laser intensity in the CNF. It is notable that the number of protons increases significantly in double-layer targets. The total number of protons over 1.5 MeV of a double-layer target is 2.8 times that of a single-layer target.

FIG. 2.

(a) Proton cutoff energies for TPS of single-layer targets and double-layer targets for varying target positions. The lower axis shows the target position, where ± means the foils were placed before/after the laser focal plane. (b) Proton energy spectra of the two shots with the cutoff energies close to the mean value in (a). (c) and (d) are the raw images of TPS in (a).

FIG. 2.

(a) Proton cutoff energies for TPS of single-layer targets and double-layer targets for varying target positions. The lower axis shows the target position, where ± means the foils were placed before/after the laser focal plane. (b) Proton energy spectra of the two shots with the cutoff energies close to the mean value in (a). (c) and (d) are the raw images of TPS in (a).

Close modal

We investigated the enhancement effect of the integrated targets in the experiments. Figures 3(a)–3(e) illustrate the proton dose distributions on the RCF stacks for single-layer and double-layer targets, with and without HCs. The RCF data with distinguishable proton signals are shown in the zoom-in views. The seven RCF images on each row correspond to 1.0/3.1/4.5/5.5/6.5/7.3/8.0 MeV. The on-axis proton spectra were derived from RCF data using an iterative analytical method47,48 starting from the last exposed RCF (i.e., at the highest proton energy), considering on the center beam spots within 1°. The energy deposition in the RCF layers was calculated with SRIM simulation.49 The HD-V2 RCF's dose threshold is 10 Gy,50 higher than the TPS system's. Therefore, the RCF-detected cutoff energy is lower than the TPS results.

FIG. 3.

Dose distributions are measured by RCF stacks for (a) single-layer target, (b) double-layer target, (c) single-layer HC target with a 2 mm gap distance, (d) double-layer HC target with a 2 mm gap distance, and (e) double-layer HC target with a 3 mm gap distance. (f) The energy spectra for each target derived from dose distributions. The error bars were estimated considering the uncertainty in dose conversion.51 

FIG. 3.

Dose distributions are measured by RCF stacks for (a) single-layer target, (b) double-layer target, (c) single-layer HC target with a 2 mm gap distance, (d) double-layer HC target with a 2 mm gap distance, and (e) double-layer HC target with a 3 mm gap distance. (f) The energy spectra for each target derived from dose distributions. The error bars were estimated considering the uncertainty in dose conversion.51 

Close modal

One can see that the proton beam distribution is larger and more uniform for the double-layer target compared to the single-layer target, which is consistent with our previous results.42 The proton cutoff energy for single-layer targets is 5.5 MeV. With a double-layer target, the proton cutoff energy is boosted to 6.5 MeV, in agreement with the TPS results. Absolute space integration on the RCFs showed that the number of protons produced by the double-layer target was 7.5×109. This is five times higher than that of the single-layer target in the range from 1.1 MeV to 6.5 MeV. The enhanced proton flux of a double-layer target is advantageous to compensate the particle loss in the post-acceleration. For all the integrated targets, the divergence angle of protons, which is calculated considering the radius of the focused proton beam (∼1 mm) on the first layer of the RCF and the target to RCF distance (∼30 mm), is reduced (<2° half-angle) after post-acceleration. The proton flux after helical coil post-acceleration (HCPA) of the double-layer target is 1.5 times higher than that of the single-layer target at the central beam spots within a 1° angle. Post-acceleration does not increase the cutoff energy (5.5 MeV) for single-layer targets. In contrast, the proton energy spectra for double-layer targets with HC are clearly modulated and the cutoff energy increases to 7.3 and 8.0 MeV for the 2 and 3 mm gap distances, respectively. Moreover, the post-acceleration in the HC is evident in the quasi-monoenergetic peaks at 6.5 and 7.3 MeV, respectively. The clear modulation on the energy spectrum indicates that the double-layer targets not only provide the higher energy protons introduced to HCPA but can also enhance the effect of proton acceleration within HC.

We detected electron signals in the rear direction of the target in the case of single-layer targets and double-layer targets without helical coil post-acceleration. The front surface of the IP stacks was covered with a 1-mm-thick aluminum foil to block protons and heavy ions. Escaped electrons in the rear direction with energies above 0.5 MeV and protons above 14 MeV can cause signals on the IPs. As shown in Fig. 4, the electron signal for the double-layer target is stronger than that of the single-layer target. Figure 4(c) presents the response curves on each IP for electrons with different initial energies, obtained through the Monte Carlo simulation using FLUKA.52 The total count on each IP is shown in Fig. 4(d), which can be used to deconvolve the energy spectra based on the assumed spectra shape. Here, we adopt the Pukhov et al.53 Maxwellian function of dN/dE=N0eE/kBT, where N0 and T are the total number of electrons and the hot electron temperature, respectively. The values of N0 and T are obtained by iterating the parameter space according to the Levenberg–Marquardt algorithm.54 The fitted electron temperature is 0.6 MeV for the single-layer targets and 1.2 MeV for the double-layer targets. The total electron charge measured by the IP stacks is estimated by integrating the spectral profile in Fig. 4(d). We called the estimated electron charge as “detected charge.” The “detected charge” is 1.8 nC in a single-layer target. While in a double-layer target, the “detected charge” is 6.1 nC, which is 3.4 times of that in a single-layer target. It should be noticed that “detected charge” does not equate to the total charge of the escaped electrons. First, a significant portion of the escaped electrons are emitted from the front surface of the targets. Second, a large fraction of the escaped electrons with energies below 0.5 MeV37,55 cannot be detected by IP stacks. Without knowing the full energy spectra, although the enhancement of the high energy electrons with energies above 0.5 MeV in double-layer targets is clear, but the enhancement factor of the escaped electrons cannot be directly inferred.

FIG. 4.

PSL counts of IP stacks of (a) double-layer target and (b) single-layer target. (c) The response between mPSL counts and electrons (mPSL per electron) derived from FLUKA simulations. (d) The total count on each IP of the single-layer target (blue triangles) and double-layer target (red circles), related to the right y-axis. The peak energies of the response curves correspond to the electron energy on each IP. The corresponding deconvolved electron spectra, related to the left y-axis.

FIG. 4.

PSL counts of IP stacks of (a) double-layer target and (b) single-layer target. (c) The response between mPSL counts and electrons (mPSL per electron) derived from FLUKA simulations. (d) The total count on each IP of the single-layer target (blue triangles) and double-layer target (red circles), related to the right y-axis. The peak energies of the response curves correspond to the electron energy on each IP. The corresponding deconvolved electron spectra, related to the left y-axis.

Close modal

To illustrate the acceleration physics happening in the single-layer and double-layer targets, 2D PIC simulations were performed with the EPOCH code.56 The double-layer target consisted of a plasma slab of 0.2nc density and 40 μm thickness, representing CNF target, and a plasma slab of 400nc density and 4 μm thickness, representing aluminum foil, where nc is the critical density. For a single-layer target, a 4-μm-thick plasma slab with a solid density of 400nc represents the single-layer aluminum foils. A small-scale preplasma with the profile ne=n0exp(x/l), where n0=400nc and preplasma scale length l=4μm, is placed in front of the single-layer target, which mimicked the preplasma generated by the irradiated prepulse prior to the main pulse.57,58 A hydrogen plasma slab with a thickness of 20 nm and a density of 1.9nc was applied as a contamination layer after both the single-layer and double-layer targets. The initial temperature of the electrons was 1 keV. The simulation box measured 200λ in the laser direction (X) and 50λ transversely (Y) in 2D with a resolution of 100 cells/λ and 32 cells/λ in the respective directions. Each cell contained 28 macroparticles. A linearly polarized laser pulse, with peaked intensity I0=3.3×1019W/cm2, and a Gaussian envelope in both the spatial and temporal distributions with a diameter (FWHM) DL of 5.0 μm and an FWHM duration of 40 fs, was used to mimic the experimental parameters.

Figure 5(a) shows the laser electric field Ey in the double-layer target at 160 fs, before the laser pulse reaches the second layer. Due to relativistic self-focusing, NCD plasma acts as a positive lens,59 resulting in a smaller focal spot and a 1.9-fold increase in electric field strength. When the laser propagates through the NCD plasma, it forms a clearly defined plasma channel [Fig. 5(b)]. Electrons can be efficiently accelerated via DLA.27, Figure 5(c) shows the energy spectra of escaped electrons from the single-layer and double-layer targets at 640 fs; the time is chosen when the electron cutoff energy reaches a maximum in both cases. We consider electrons outside 2 μm of the target where the space charge electric field decays significantly, to be escaped electrons in the simulations. The double-layer target shows a much higher electron energy and number than that of the single-layer target. Electrons from the NCD plasma and Al layers are counted separately in the simulation. It turns out that 99.4% of the total escaped electrons are from the NCD plasma rather than the solid foil. This means that the NCD plasma absorbs and converts most of the energy of the laser pulse into electrons' kinetic energy. Here, we have simply estimated the total charge of the escaped electron in a realistic 3D case by multiplying the factor E3D/E2D=r0π/2h, representing the ratio between the laser energy injection to the box in 2D and in 3D.34 The r0 is the laser focal spot size, and h=1m, as the non-simulated direction is regarded as one unit length in the 2D EPOCH code. As a result, the total charge of escaped electrons is estimated to be 30 nC in the double-layer target and 10 nC in the single-layer target, respectively. The superponderomotive electron flow establishes an enhanced sheath field to accelerate protons.22,42 Figure 5(d) shows the proton energy spectra. The double-layer target exhibits enhancement both in the cutoff energy and in the number. The simulated maximum proton energy for double-layer and single-layer targets is 11.7 and 7.3 MeV, respectively.

FIG. 5.

2D PIC simulation results. (a) Normalized Ey distribution by E0=mecω/e at t = 160 fs. The NCD plasma is located in the range of 10–50 μm. (b) The energy density of the electrons from NCD plasma normalized by ncmec2 at t = 160 fs. (c) The escaped electron energy spectra at 640 fs (2 μm off-targets range). (d) The proton energy spectra from simulation at 640 fs (within 5° at rear target).

FIG. 5.

2D PIC simulation results. (a) Normalized Ey distribution by E0=mecω/e at t = 160 fs. The NCD plasma is located in the range of 10–50 μm. (b) The energy density of the electrons from NCD plasma normalized by ncmec2 at t = 160 fs. (c) The escaped electron energy spectra at 640 fs (2 μm off-targets range). (d) The proton energy spectra from simulation at 640 fs (within 5° at rear target).

Close modal

To demonstrate the double-layer target's contribution to the post-acceleration in the helical coils, we conducted PIC simulations using CST Particle Studio,60,61 where electromagnetic fields and particle dynamics are depicted as the equation scheme retains Maxwell's equations.62 Here, the generation of fast electrons and protons is simplified as the emission of particle sources with energy distributions derived from experimental data and EPOCH simulations. The double-layer target is simplified to a single-layer target with more escaped electrons. The simulation parameters are made to be as consistent with the experiment as possible, with spatial dimensions matching the experimental scale. The 4 μm thick aluminum foil target is attached to the delay line of HC with a wire diameter of 100 μm aluminum. All materials, modeled as lossy metals, have conductivity and resistance based on the database of the studio. The HC is defined by a radius of R=0.4mm, a pitch of P=0.22mm, and a length of L=10.5mm. The target, coil, and holder components are finely meshed with a cell size of Δx=Δy=Δz=10μm, encompassing a total simulation volume of 40 cm3. Electrons and protons are modeled with macroparticles to achieve the specified quantity. The number of protons in the simulation is determined based on the number obtained experimentally without the helical coil, as shown in Fig. 2. The cutoff energies of emission protons are 5.5 MeV for double-layer targets and 6.5 MeV for single-layer targets with the same temperature Tp=1.0MeV. The corresponding output energy spectra are derived by statistical calculations of all protons emitted from the helical coil.

In the target charging mode of post-acceleration in the HC,36,63 the energetic laser-driven electrons can escape into the vacuum after overcoming the electric potential barrier and cause residual positive charge on the target. The neutralizing current of the helical coil analogous to a charged capacitor being suddenly connected to a transmission line. The accelerating field inside the HC is directly proportional to the escaped electron charge,35,55,63 as ExQ, where Ex is the axial electric field in HC and Q is the escaped electron charge. We did not measure the exact number of escaped electrons or perform proton imaging to detect the current in the experiment. In the CST simulations, the escaped electron charges are adopted as 30 and 10 nC for double-layer and single-layer targets, respectively, which is obtained from the PIC simulations. The energy spectrum of the escaped electrons is set to be exponential.

Figure 6(a) shows the neutralizing currents at the inlet position of HC. Different total charges (Qtot) of escaped electrons, 10 and 30 nC, were simulated to represent single-layer and double-layer targets. The neutralizing current corresponding to 30 nC is three times that of the 10 nC case. The magnitude of the axial electric field for a charge of 30 nC is 0.4 GV/m, three times that of a 10 nC charge. For the single-layer target with a charge of 10 nC, the energy spectrum modulation is unremarkable, limited by the weak accelerating electric field (top layer). The cutoff energy for protons after post-acceleration is 5.5 MeV in the simulation, consistent with experimental data. An escaped electron charge of 30 nC, which is representative of double-layer targets, produces a stronger axial electric field, noticeably modulating the energy spectrum. After post-acceleration, protons achieve a cutoff energy of 7.4 MeV with a 2 mm gap distance and 7.9 MeV with a 3 mm gap distance, matching the experimental data. The increased escaped electron charge of double-layer targets leads to the enhancement of the electric field during post-acceleration and stronger modulation in the energy spectrum. The simulations show that the 30 and 10 nC charge settings for escaped electrons explain the modulation on the proton energy spectrum very well.

FIG. 6.

(a) The current distribution at the entrance of the helical coil with different gap distances and escaped electron charges. The charges of 30 nC and 10 nC correspond to double-layer and single-layer targets, respectively. (b) The axial electric field distribution within the helical coil at 300 ps. The target front surface is at x = 0 mm, and the particle emission time is t = 0 ps. (c) Experimental energy spectra (solid lines) and simulated energy spectra (dashed lines) after post-acceleration.

FIG. 6.

(a) The current distribution at the entrance of the helical coil with different gap distances and escaped electron charges. The charges of 30 nC and 10 nC correspond to double-layer and single-layer targets, respectively. (b) The axial electric field distribution within the helical coil at 300 ps. The target front surface is at x = 0 mm, and the particle emission time is t = 0 ps. (c) Experimental energy spectra (solid lines) and simulated energy spectra (dashed lines) after post-acceleration.

Close modal

By adjusting the length of the gap distance, protons can be selectively enhanced within specific energy ranges, thus achieving a more versatile modulation of the energy spectrum. Figure 7(a) illustrates the energy gain for different input proton energies. At a pitch of 0.22 mm and a gap distance of 2 mm with Qtot=10nC, protons with the input energy of 4.2 MeV experience the most significant acceleration, achieving an energy gain of 2.9 MeV. Changes in the gap distance can cause the electric field to facilitate protons at different positions. The axial electric field shifts 1 mm forward with a 3 mm gap distance. Protons with an input energy of 4.8 MeV can be most effectively enhanced by 3 MeV.

FIG. 7.

(a) The energy gain for various input proton energies, as obtained from simulations at different pitch and gap distances of the helical coil, and the escaped electron charges are 10 nC and 30 nC. (b) The simulated energy spectrum under optimized settings of 0.25 mm pitch and 3.5 mm gap distance. The blue line is the input proton spectrum, and the red line is the output spectrum with an escaped electron charge of 30 nC. The black line is the experimental spectrum of single-layer targets with HC.

FIG. 7.

(a) The energy gain for various input proton energies, as obtained from simulations at different pitch and gap distances of the helical coil, and the escaped electron charges are 10 nC and 30 nC. (b) The simulated energy spectrum under optimized settings of 0.25 mm pitch and 3.5 mm gap distance. The blue line is the input proton spectrum, and the red line is the output spectrum with an escaped electron charge of 30 nC. The black line is the experimental spectrum of single-layer targets with HC.

Close modal

To achieve a higher cutoff energy through post-acceleration, the proton with an input energy of 6.5 MeV should be efficiently accelerated. This corresponds to the proton cutoff energy of double-layer targets. Simulations were performed to investigate the optimal post-acceleration of protons with a cutoff energy of 6.5 MeV. First, the proton velocity of 6.5 MeV should match the speed of the axial electric field propagation along HC, described as60,64 vp=vE=1.2P2πRc, where vp is the proton velocity, and vE is the axial electric field velocity with current dispersion. Here, the pitch and radius are set to be 0.25 and 0.4 mm, respectively, to achieve velocity matching. In the simulations, varying the length of the gap distance, we have observed that the protons with an input energy of 6.5 MeV are optimally accelerated with a gap distance of 3.5 mm. Figure 7(b) shows the energy spectra of the proton after HCPA in the optimized setting. Compared with the experimental results of single-layer targets with post-acceleration, the cutoff energy of protons has the potential to increase from 5.5 MeV to over 10 MeV.

The experimental results demonstrate that the protons after HCAP are pencil straight with a divergence angle of only 2°. Figure 8(a) shows the energy-dependent divergence angle of the proton beams. The proton's divergence angle slightly decreases with energy. To study the influence of the helical coil on the divergence of the protons, we set a uniform distribution with a constant divergence angle of 8° for all the protons in the CST simulation at the beginning. Other simulation conditions are the same as those described above for the double-layer targets with HC and a 2 mm gap distance. Figures 8(b) and 8(c) show the distribution of protons at different times. When ejected from the HC, most protons are restricted by the HC structure and their transverse distribution is consistent with the HC's internal diameter. Protons with energies of 4–6 MeV are well focused, and the beam spot is significantly smaller than the HC diameter. As protons continue to propagate and reach the RCF position, the beam spot expands and exceeds the HC diameter. The protons that were previously focused will also spread out. Figures 8(d)–8(g) show the number density distribution of protons with different energies at the RCF position. The divergence angles of the protons are close to the HC projection angle 1.8° and are larger at lower energies, which agrees with the experimental results. However, it is worth noting that the density distribution in the simulations exhibits a central convergence. The beam spots of protons in the experiment are more uniform. This may be due to the simplification of the proton beam parameters in our simulations. For example, the initial divergence angle of protons is not uniformly distributed but a Gaussian,14,65 and there is angular chirp in the energy spectra.66,67 Deeper studies need to be done in the future.

FIG. 8.

(a) Experimental results of the proton divergence angle (half angel) after HCPA for single-layer and double-layer targets at a gap distance of 2 mm. (b) The spatial distribution of proton beam after HCPA for double-layer targets at t = 500 ps. The blue dotted line indicates the HC region, and the black dotted line indicates the HC projection angle 1.8°, which means the angle from the emission spot to the end edge of the HC. (c) Spatial distribution of the proton beam after HCPA for double-layer targets at t = 900 ps; (d)–(g) normalized number density distributions of protons with different energies reaching at the RCF position.

FIG. 8.

(a) Experimental results of the proton divergence angle (half angel) after HCPA for single-layer and double-layer targets at a gap distance of 2 mm. (b) The spatial distribution of proton beam after HCPA for double-layer targets at t = 500 ps. The blue dotted line indicates the HC region, and the black dotted line indicates the HC projection angle 1.8°, which means the angle from the emission spot to the end edge of the HC. (c) Spatial distribution of the proton beam after HCPA for double-layer targets at t = 900 ps; (d)–(g) normalized number density distributions of protons with different energies reaching at the RCF position.

Close modal

In previous works, protons with energies close to 60 MeV were experimentally obtained by double-layer targets at higher laser intensity,22 and the number of electrons was enhanced by several times with the double-layer targets.29 We envision that the integrated targets can be used in a petawatt-class femtosecond laser to generate high-energy protons for radiotherapy applications. As shown in Fig. 9(a), the scaling for escape electron charge as a function of incident laser intensity can be obtained from the reference model.63 In that model, we adopt a laser pulse with a duration width of 40 fs, a focal spot radius of 6 μm, and an absorption coefficient of 40%. When the laser interacts with single-layer targets, it is hoped that a total escaped electron charge of 300 nC will be generated by a petawatt-class laser with an intensity of 3×1021W/cm2 (marked by the red circle). In double-layer targets, the heating of electrons can be multiplied. We assume that a 600 nC escaped electron charge will be generated (marked by the red star). Protons with an exponential spectrum of 60 MeV cutoff energy are injected into HCs. As shown in Fig. 9(b), the cutoff energy of a proton with an initial energy of 60 MeV can be increased to 90 MeV with the escaped electron charge of 300 nC. In double-layer targets with a charge of 600 nC, the cutoff energy can be increased to 115 MeV after post-acceleration, which is sufficient to treat shallow-seated tumors.68 

FIG. 9.

(a) Expected target charge of escaped electrons calculated from the model as a function of laser intensity. The red circle shows 300 nC charge from single-layer targets; the red star shows 600 nC charge from double-layer targets. (b) Spectrum of input protons in simulations with a petawatt laser (black line); post-acceleration spectrum with a charge of 300 nC (blue line); post-acceleration spectrum with a charge of 600 nC (red line). HC radius 0.4 mm, pitch 0.65 mm, gap distance 7 mm, HC length 32.5 mm.

FIG. 9.

(a) Expected target charge of escaped electrons calculated from the model as a function of laser intensity. The red circle shows 300 nC charge from single-layer targets; the red star shows 600 nC charge from double-layer targets. (b) Spectrum of input protons in simulations with a petawatt laser (black line); post-acceleration spectrum with a charge of 300 nC (blue line); post-acceleration spectrum with a charge of 600 nC (red line). HC radius 0.4 mm, pitch 0.65 mm, gap distance 7 mm, HC length 32.5 mm.

Close modal

In conclusion, we conducted experiments with integrated targets combining CNF-based double-layer targets with helical coils, in which we observed a focused and quasi-monoenergetic proton beam with a cutoff energy of 8 MeV. The proton flux is increased by 1.5 times. 2D PIC simulations show that laser self-focusing and DLA electrons in NCD plasma contribute to enhanced TNSA acceleration and the charge of escaped electrons is more than three times that of the single-layer target. As a result of the boosted injection energy and the enhanced post-acceleration, the energy of protons is synergistically enhanced. This compact synergistic enhancement scheme of laser-proton acceleration can be applied to terawatt and petawatt lasers, promising high-energy and quasi-monoenergetic proton beams, which can be highly beneficial for the application of oncological therapy.4 

This work was supported by the following projects: NSFC Innovation Group Project (Grant No. 11921006) and the National Grand Instrument Project (Grant No. 2019YFF01014402). W. Ma acknowledges support from the National Science Fund for Distinguished Young Scholars (No. 12225501). The PIC simulations were carried out on High-performance Computing Platform of Peking University.

The authors have no conflicts to disclose.

Zhipeng Liu: Investigation (equal); Visualization (equal); Writing – original draft (equal). Ying Gao: Funding acquisition (lead); Supervision (lead); Writing – original draft (lead); Writing – review & editing (lead). Qingfan Wu: Investigation (equal). Zhuo Pan: Investigation (equal). Yulan Liang: Investigation (equal). Tan Song: Investigation (equal). Tianqi Xu: Investigation (equal). Yinren Shou: Investigation (equal). Yujia Zhang: Investigation (equal). Haoran Chen: Investigation (equal). Qihang Han: Investigation (equal). Chenghao Hua: Investigation (equal). Xun Chen: Investigation (equal). Shirui Xu: Investigation (equal). Zhusong Mei: Investigation (equal). Pengjie Wang: Investigation (equal). Ziyang Peng: Investigation (equal). Jiarui Zhao: Investigation (equal). Shiyou Chen: Investigation (equal). Yanying Zhao: Investigation (equal); Resources (lead). Xueqing Yan: Resources (lead); Supervision (lead); Writing – original draft (lead). Wenjun Ma: Funding acquisition (lead); Investigation (equal); Supervision (lead); Writing – review & editing (lead).

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

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