Laser-induced acceleration of Helium ions from unpolarized gas jets

An RCF wrap-around detector was used in order to cover a wide angular range around the plasma target. The self-made wrap-around holder, shown in figure 2, was built of aluminum. Rolled endwalls were welded on a ground plate with circular cross-section area (diameter of 104 mm). In order not to clip the focusing/diverging laser beam, an entrance/exit gap was given between the endwalls: s_entr = 26.2 mm (entrance), and s_exit = 20 mm (exit). Hence, at each side an angular range of 11.1–165.4° relative to the laser axis could be covered by the RCFs. The RCF wrap-around holder could be mounted directly on the valve holder without disassembling the setup. This is important since the previously defined nozzle position had not to be lost in any case. At the right side with respect to the laser axis, a bore hole in the well wall allowed to simultaneously operate the TPS at −90° during the wrap-around RCF measurements. Gafchromic HD-V2 RCF wrapped in 5 μm thick Al foil were used (dimensions of the RCFs: l_rcf × h_rcf = 140 × 40 mm²). These RCFs do not possess any protective layer on top of the active radiation-sensitive medium which would filter out incoming helium ions. The Al shielding is important in order to block side-scattered laser light and to protect the RCFs from arising plasma temperatures. According to Srim [24], 5.09 μm corresponds to the range of 1.6 MeV ⁴He²⁺ ions in aluminum. Thus, ions with an energy >1.6 MeV could reach the RCF's active layer. For the sake of convenience, the RCF detectors were fixed with paper-clips at the endwalls.

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The RCF wrap-around measurements were conducted for the first laser shots in order to experimentally obtain the main ion-emission angles and to compare them to the EPOCH-simulation data being described in section 3 (laser-beam energy after compression 43.8 J, pulse duration 3.2 ps, which leads to a focus intensity of I_L = 2. 65 × 10¹⁸ W cm⁻²). The original yellow RCF-dye color turns green when exposing the RCF to ionizing radiation. Due to the protective Al shielding, only x-rays and laser-accelerated He ions with energies >1.6 MeV could reach the active RCF layer, but no scattered laser light. Hence, the color change is due to ions and x-rays. It becomes obvious that a nearly homogeneous color change is present (exposure to x-rays, background (BG) signal) which is interspersed with more intense regions (laser-accelerated ⁴He^1+,2+ ions). A 'horizontal' lineout at the height of the laser focus provides the angular ion distribution in the laser-target interaction plane: see figure 3. Here, the BG-corrected RCF data is plotted against the angle relative to the laser-propagation direction (the insert in the top right corner illustrates the RCF scan in pseudo colors from the left side with respect to the laser direction). A sharp peak in ion signal (both ion species) around ±90° with respect to the laser-propagation direction with a FWHM of 23° is given. This result is in line with the EPOCH-simulated data. Furthermore, both in forward and in backward direction intense ion signals could be detected in the angular ranges of $23.4^\circ \leqslant \varphi \leqslant 42.9^\circ$ and $143.4^\circ \,\leqslant \varphi \leqslant 165.4^\circ$, respectively. In both cases, the helium ions got a vertical momentum component, i.e. ion signals could be detected above the focal plane. Moving from both RCF boundaries to the RCF center, the ion distribution narrows with increasing height. In order to investigate the ion distribution also in larger heights above the laser-target interaction region, a second RCF wrap-around measurement was conducted with Gafchromic HD-V2 RCFs with a height of 100 mm (same length as before). The basic shape of the angular distribution was comparable to the prior data. It became obvious, that with increasing height the narrowing in ion signal continues but peters out, i.e. the RCFs were exposed to less dose. Either the number of laser-accelerated ${}^{4}{\mathrm{He}}^{1+,2+}$ ions decreases for these angular ranges, or the particle energies do (and since the 5 μm Al shielding filters low-energy ions, less dose will be absorbed by the RCF). The occurance of negative gray scale values is due to the BG subtraction.

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Due to the fact that it is not possible to distinguish between singly and fully-ionized helium ions, this measurement served as qualitative investigation of the predominant ion-acceleration directions in the focal plane. The ion species as well as their energies cannot be extracted from the raw data. Therefore, attendant TPS measurements were conducted around −90° relative to the laser direction (see section 2.3). Here, the TPSs were aligned in the height of the laser focus.

Within the PHELIX experiment, a modified TPS was used which is based on a novel design [25, 26]. In contrast to the conventional concept, a wedge-shaped capacitor replaces the parallel electric plates. By applying HV to the modified capacitor, a gradient electric field is built up which results in an increased particle deflection. Furthermore, for the sake of a compact design, the wedge-shaped capacitor is inserted into the magnetic field.

Following the experimental results from the angular ion measurements, the three TPSs were mounted at −80°, −90°, and −100°. In the further course of this paper, the TPSs are denoted as follows: TPS-80, TPS-90, and TPS-100, respectively. The pinhole diameters (entrance into each TPS) were chosen according to the angular distribution of the accelerated ions: TPS-90 was equipped with a 200 μm pinhole (≃170 nsr), while TPS-80 and TPS-100 with less signal compared to the center TPS got a 350 μm one (≃356 nsr and ≃370 nsr, respectively). A HV of 3 kV was applied to the capacitor plates and a maximal magnetic field of 0.5 T was given.

The TPS measurements for extracting the energy spectra for both helium-ion species were performed with Agfa md4.0 IPs. These IPs are not equipped with any protective layer on top of the sensitive detector surface. Such a layer would block incoming helium ions. Due to the lack of a proper ³He-ion source as well as slitted CR-39 detector plates, the IPs could not be calibrated with ${}^{\mathrm{3,4}}{\mathrm{He}}^{1+,2+}$ ions. Therefore, the obtained IP signals did not yield any credible quantitative information about the ion number, but the achieved ion energies could be determined for various laser-target parameters. The ion-energy spectra, i.e. the normalized signal intensity (per MeV and sr, log₁₀-scale) against the ion energy (in MeV, lin.-scale), could be extracted from the IP scans. A TPS-analysis Matlab code was used for this purpose. Here, the zero order had to be defined manually (oversaturated single pixels), while the ion-species properties (charge, mass) as well as the field parameters (length, strength) had to be set. According to these input parameters, the code simulates the corresponding particle parabola along which the image data, i.e. the gray scale values, are extracted, and henceforward, related to the particle energies. Furthermore, the BG values are instantly subtracted. In addition, the obtained ion energies were also compared to CST(Particle Studio)-simulated data regarding the energy-deflection dependencies. For each TPS and each helium-ion species an energy-deflection fit function ${ \mathcal E }({y}_{\mathrm{tps}})={{ay}}_{\mathrm{tps}}^{-2}+b$ (a, b = const, a in keV m², b in keV) could be extracted. In case of TPS-90, the parameters are a = 2.317 keV m² and b = 24.57 keV. With the help of the CST-simulated energy-deflection fit parameters, any desired vertical deflection y_tps (on the ion parabolas from the IP raw images) of a specific helium-ion species in a particular TPS directly could be transformed into the corresponding ion energy. The normalized uncertainty in energy $\left|{\rm{\Delta }}{ \mathcal E }/{ \mathcal E }\right|$, i.e. the energy resolution of a specific TPS, is determined by the size of the TPS pinhole d_ap at an adjusted distance l₀ from the laser-target interaction region. Due to the ion 'imaging', a broadening in width of the TPs, δ_tp, on the detector is caused, which can be calculated via ${\delta }_{\mathrm{tp}}={d}_{\mathrm{ap}}({l}_{0}+{l}_{\mathrm{tps}}){l}_{0}^{-1}$, where l_tps is the distance between the pinhole and the detector plane inside the TPS [27, 28]. Now, the intrinsic spectrometer resolution is given by $\left|{\rm{\Delta }}{ \mathcal E }/{ \mathcal E }\right|=\left({\rm{d}}{ \mathcal E }/{\rm{d}}{y}_{\mathrm{tps}}\right){\delta }_{\mathrm{tp}}\,{{ \mathcal E }}^{-1}$ which leads to $\left|{\rm{\Delta }}{ \mathcal E }/{ \mathcal E }\right|=2{\delta }_{\mathrm{tp}}\,{y}_{\mathrm{tps}}^{-1}\,\propto \sqrt{{ \mathcal E }}$ [29].

Simultaneously to the RCF wrap-around measurement during the first laser shot (${{ \mathcal E }}_{{\rm{L}}}\approx 44\,$J, τ_L = 3.2 ps, n_max = 0. 06 n_c), TPS-90 was armed with an Agfa md4.0 IP detector. 23 min after exposure, the IP was scanned. Figure 4(c) illustrates the IP scan in pseudo colors (originally, the 16 bit .tif-files were saved in gray scale values). One pixel corresponds to 25 μm. The {x, y}_tps-axes, i.e. the E–and B-deflection directions, were added to the plot. The right side of the image actually is the top side of the IP within the TPS. Two sharp TPs were recorded. Directly after having extracted the scanned data, the signals, i.e. the deflection parameters in x_tps- and y_tps-direction, were roughly analyzed and cross-checked with the CST-simulated data for ${}^{4}{\mathrm{He}}^{1+,2+}$ ions in order to verify the experimental outcome regarding the accelerated ion species. Additional information: the BG level is increased for y_tps ≳ 4.5 cm (top side of the IP) so that the low-energy branch of the ion TPs smears. The high BG signal was due to an insufficient lead shielding of the TPS housing at the beginning of the experimental beamtime. Therefore, the thickness of the attached lead sheath was doubled from 2 mm to 4 mm so that the disturbing BG signal could be suppressed. In figure 4(a) the corresponding ${}^{4}{\mathrm{He}}^{1+,2+}$ ion-energy spectra are illustrated. The normalized gray scale values from the TPs are plotted against the ion energies. It has to be considered that in case of ⁴He¹⁺ the minimal energies are not plotted due to the aforementioned BG issue. Therefore, energies between 0.24 and 0.5 MeV had to be cut. In case of fully-ionized He, the signal was much stronger, and thus, it was distinguishable from the BG signal. Taking into account that the gray scale values depend on the ion dose (particle number and ion energy), then roughly speaking a larger gray scale value corresponds to a larger particle number at a constant energy. The normalized energy uncertainties for a specific TP (Thomson parabola) broadening (in case of TPS-90: ${\delta }_{\mathrm{tp}}^{90}=(360\pm 5){\rm{\mu }}{\rm{m}}\approx 365$ μm) are exemplified in figure 4(b). The high-energy cut-offs are given with ${{ \mathcal E }}_{\mathrm{cut} \mbox{-} \mathrm{off}}=4.65\,$MeV for ⁴He²⁺ (${\rm{\Delta }}{ \mathcal E }/{ \mathcal E }=0.033$) and ${{ \mathcal E }}_{\mathrm{cut} \mbox{-} \mathrm{off}}=3.27\,$MeV for ⁴He¹⁺ (${\rm{\Delta }}{ \mathcal E }/{ \mathcal E }=0.055$).

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For the subsequent laser shots, the RCF wrap-around holder was removed and the ion-energy spectra were obtained with TPS-80 to TPS-100. The highest signals regarding signal intensity and ion energy were recorded in TPS-90 which is in good agreement with the RCF measurements for the angular ion distribution. Both in TPS-80 and TPS-100, the signal intensities as well as the achieved ion energies were lower compared to the transversal acceleration direction. Furthermore, it could be measured that the signal intensity in TPS-80 was lower than in TPS-100 (which is in good agreement to the experimental data presented in [12]). In the further course of this paper, the focus is set on the main ion-emission angle.

During the PHELIX beamtime, laser energies between ∼40 and 120 J were available. Within the first laser shots, the optimal laser parameters for the whole experiment could be determined. Of course, the maximal laser energy was applied which led to a high ion dose on the TPS IPs (high signal intensity and an ion energy of ∼11 MeV). But, accelerating helium ions to maximal ion energies was not the goal in this feasibility study. Furthermore, laser energies between 60 and 120 J came along with a couple of disadvantages: on the one hand, the BG level regarding disturbing x-rays increased, followed by parasitic proton signals from impurities on the nozzle surface in the TPS spectra (the nozzle was cleaned with acetone beforehand—it is recommended to use isopropanol instead). On the other hand, the arising plasma temperatures caused dramatic material damage in the nozzle throat. It turned out that brass is not a suitable nozzle material for higher laser-energy shots. Instead of brass, titanium is a more temperature-resistant processible material. In the laser-energy range of 40–60 J, these problems did not occur. Instead, stable and clean IP signals could be extracted and the helium-ion energies were in the right range regarding future spin-polarization measurements of laser-accelerated ³He ions from a pre-polarized ³He gas-jet target. Thus, the further laser shots were conducted with these lower laser energies. Figure 5 illustrates ${}^{4}{\mathrm{He}}^{1+,2+}$ ion-energy spectra for the maximal available laser-energy (119 J) as well as for laser energies of about 40 J. The neutral particle density within the gas jet was constant (0.06 n_c). In case of fully-ionized helium, the high-energy cut-off is 10.9 MeV, i.e. a factor of about 3 times (${{ \mathcal E }}_{\mathrm{cut} \mbox{-} \mathrm{off}}=3.6\,$MeV for ${{ \mathcal E }}_{{\rm{L}}}=38\,$J) and 2.3 times (${{ \mathcal E }}_{\mathrm{cut} \mbox{-} \mathrm{off}}=4.6\,$MeV for ${{ \mathcal E }}_{{\rm{L}}}=44\,$J) larger than in the lower laser-energy regime. For singly-ionized helium, the high-energy cut-offs are comparable to each other. Only the signal intensity is about one order of magnitude enlarged in case of the high-energy laser shot. It is obvious, that independently from the laser and density parameters (0.06 or 0.03 n_c) the ⁴He¹⁺ spectra were shaped in a similar vein: thermal spectrum with high-energy cut-offs of ∼2–3 MeV. In former publications, such a result (and even the presence of He¹⁺ ions) was explained with the assumption that fully-ionized helium recombines during the propagation through the gas-jet regions, loses energy due to collisions and can pick up an electron from neutral helium atoms [12, 14]. Furthermore-regarding the high laser intensities—a nearly fully-ionized plasma would be expected. In a perfect environment this argument is true. But, regarding the ion energies as well as the gas-jet densities, the acceleration of singly-ionized atoms cannot be explained only with recombination processes. Additionally, also the contrast ratio of the attached laser pulse as well as its focusing into the gas-jet region has to be considered. Single ionization caused by the pre-pulse as well as taking place in the outer (lower-)intensity regions are a stronger explanation for the He¹⁺-ion yield. The high-energy data are in good agreement to the experimental data in [14].

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The ion-energy spectra (fully-ionized ^4,3He) for different maximal particle densities in the gas-jet target as well as different laser parameters are plotted in figure 6. In total, three different particle densities were applied: 0.06 n_c and 0.03 n_c for ⁴He, and 0.02 n_c for ³He. The attached laser parameters vary for each shot (${{ \mathcal E }}_{{\rm{L}}}\sim (40\,\ldots \,60)$ J, τ_L = (0. 3 ... 3.2) ps). The largest high-energy cut-off and highest normalized signal intensity was achieved for the highest pulse duration of 3.2 ps in combination with the largest target density of 0.06 n_c. On the other hand, the ion fluxes are drastically reduced at the lowest target density of 0.02 n_c.

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When comparing the ion-energy spectra in figures 5 and 6 with regard to the applied laser and density parameters, diversities in the flux and high-energy cut-offs become obvious. To further discuss the experimentally obtained data and to systematically scan the target density-pulse duration parameter space, extensive EPOCH simulations were conducted (see section 3).

In order to get an impression about the ion numbers, TPS-80 was armed with a Tastrak CR-39 detector for one laser shot. In order not to run the risk of oversaturating the SSNTD, TPS-80 was chosen according to the EPOCH simulations as well as according to the RCF measurements. Furthermore, within this laser shot a decreased helium backing pressure was applied in order to ensure a decreased particle density within the gas-jet target. TPS–80 was equipped with a 350 μm pinhole which corresponds to a solid angle of 355.8 nsr. The laser-target parameters were set to: ${n}_{\mathrm{He}}^{\max }=0.03\,{n}_{{\rm{c}}}$, ${{ \mathcal E }}_{{\rm{L}}}=39\,$J, and τ_L = 0.3 ps leading to a focus intensity of I_L = 2. 5 × 10⁻¹⁹ W cm⁻². After the etching procedure, two sharp helium-ion TPs became visible on the CR-39 SSNTD. Furthermore, also the zero order which defines the origin of the TP-coordinate system was visible as a milky white spot. From the ⁴He ion-energy spectra the high-energy cut-offs could be determined to 3.28 MeV (${\rm{\Delta }}{ \mathcal E }\,{{ \mathcal E }}^{-1}\,=0.045$) for ⁴He²⁺ ions and 2.48 MeV (${\rm{\Delta }}{ \mathcal E }\,{{ \mathcal E }}^{-1}=0.077$). Within the covered 355.8 nsr, the total number of ⁴He²⁺ was 2.02 × 10⁴ and 4.92 × 10⁴ in case of ⁴He¹⁺ ions. With this He²⁺-ion number (for 0.03 n_c at 80°) a lower limit for the polarimetry reaction can be estimated. For the polarimetry, the fusion reaction D(³He,p)⁴He with a Q-value of 18 MeV can be used. In the polarized case (³He²⁺ is polarized and fuses with deuterium in a CD₂ foil), a polarization transfer from the ions to the fusion protons is given which is measurable in the angular distribution of the fusion protons. Thus, an asymmetric distribution in the proton signal is expected (for instance, one receives a left-right or top-bottom asymmetry). The number of protons on each detector can be calculated by n_p = L × dσ(dΩ)⁻¹ ΔΩ = N_3He2+ × ρ_A,CD2 × dσ(dΩ)⁻¹ ΔΩ, with the luminosity $L={N}_{3\mathrm{He}2+}\,\times {\rho }_{A,\mathrm{CD}2}$, the total number of ³He²⁺ ions N_3He2+=17.84 × 10⁶ entering the polarimetry setup and hitting the CD₂ foil with areal density of ρ_A,CD2 = 2. 7 × 10²⁰ cm⁻², the resonance value of the differential cross section of the fusion reaction of dσ (dΩ)⁻¹ = 60 mb sr⁻¹, and the covered solid angle inside the polarimetry (between CD₂ and proton detector) ΔΩ = 6.25 sr. This leads to a proton number of 1800 per detector per laser shot which is a useful value for a polarization measurement. It has to be noted that this is the lower limit for the estimated proton yield: for the main ion-emission angle (±90°), a longer pulse duration (3.2 ps), and a higher gas-jet density (in case of polarized ³He gas: 30 bar which corresponds to 0.06 n_c), this proton number will be enhanced.

Simultaneously to the TPS monitoring, CR-39 SSNTDs were mounted in different distances to the laser-target interaction region. After etching the additional CR-39 SSNTDs for data anlysis, a color change from translucent to milky/cloudy white became apparent on the target-facing surface. These colored CR-39 plates could not be analyzed with a microscope scanner since a clear transmission of light was not possible and no ion tracks were visible. The color change after etching was due to x-ray radiation from the laser-plasma interaction.