In this report, an efficient hybrid laser technique, nanosecond laser rear-side processing and femtosecond laser-assisted selective etching (FLSE) for the manufacturing of high-density gas capillary targets, is demonstrated. Cylindrical capillary nozzles for laser betatron X-ray sources were numerically simulated, manufactured from fused silica by 3D laser inscription and characterized using interferometry and gas density reconstruction. The dependence of gas concentration profiles on the wall roughness of cylindrical channels is presented.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The need of modest scale research facilities, and the demand of higher X-ray energy for the investigation of warm dense matter  increase the interest in advanced X-ray sources, driven by laser-accelerated electrons. Such sources require manufacturing and characterization of tailored gas targets with micrometric dimensions. Confining the laser field inside the plasma bubble can act as an effective wiggler to produce betatron X-ray radiation with harmonics peaking in the range of tens and hundreds of keV . The betatron critical frequency ωc can be calculated from the relation (1), where γ is the relativistic factor of the accelerated electrons, n is the plasma concentration and rβ - the amplitude of the betatron orbit :4]. The operation at near critical plasma densities and sharp focusing to the smaller target dimensions decrease the dephasing length of the laser wakefield acceleration (LWFA). It is difficult to maintain the optimal LWFA conditions to get the maximum energy of accelerated electrons and increase the energy of betatron radiation and rβ via transverse laser direct acceleration. Tailored concentration profiles [3,5,6], gas nozzles with different ionization energies , colliding laser pulses , two LWFA stages with lower plasma density for electron acceleration and higher density for optimized betatron radiation  are used to control the injection of the electrons, increase the energy of the accelerated electrons and raise the efficiency of betatron radiation. Implementation of short pulses and high plasma densities decreases the LWFA intensity threshold and opens the way of design of femtosecond table top medical grade ultrashort X-ray sources with lower laser energy of tens of millijoules and pulse duration of 7-20 fs at 1 kHz repetition rate [10–12].
In this report, we demonstrate a new method of 3D laser formation of tailored gas targets using micrometric nozzle arrays manufactured in fused silica. Depending on required plasma density profile, focus length and laser power, several stages of the accelerator with different nozzle geometry can be implemented to ensure the electron injection, acceleration and increased efficiency of betatron radiation on a single chip.
Gas jet nozzles for laser wakefield acceleration may be fabricated from various materials using various subtractive and additive technologies. The nozzle materials should be resistant to the harsh operational conditions. The conventional method of CNC machining from metals is time-consuming and is not suitable for fabricating complex structures with a high aspect ratio (structure depth to width ratio). Stereolithography-based methods allow rapid manufacturing from plastics of custom-shaped nozzles down to 100 µm size at a low cost . However, additional post-processing is required to open the blocked nozzle, and the materials are of moderate resistance. Also, in the sub-millimeter scale, the printed holes fail in maintaining the circular shape, and the achievable aspect ratio is close to one . Taking into account the hardness of material and manufacturing flexibility, glassy materials seems to be an appealing alternative.
Conventional mechanical drilling of glass suffers from limitations in hole aspect ratio (typically up to 10:1), achievable minimum hole diameter (on the order of 100 µm), relatively slow processing speed and low machining quality . The performance of direct laser ablation is limited in the case of thick samples. Plasma shielding, scattering from kerf sidewalls, debris accumulation are serious challenges, preventing fabrication of deep and taper-less structures . One of the solutions is to remove the material from the rear side of a sample, which is usually referred to as the rear-side processing, back-side ablation or bottom-up technique [17–23]. The overview and comparison of various micro-hole drilling techniques in glass could be found in .
Liquid-assisted femtosecond laser drilling of high aspect ratio holes (50:1) at the speed of several of µm/s from the rear side of the glass was already demonstrated more than a decade ago . The drilling depth was mainly limited by the accumulation and redeposition of the processing debris . The redeposition and accumulation effects can be reduced by tightly focusing nanosecond laser pulses, which induce micro-cracks in the glass. By choosing a proper pulse overlap, the material can be removed as large particles with the size up to hundreds of microns [19,21]. This technique is energy-efficient and could be applied for large-scale applications. However, it has limitations regarding the minimum hole diameter and surface quality. Nevertheless, in this paper, we demonstrate the hybrid 3D fabrication technique, in which the large volume of glass is removed by nanosecond pulses and the final micro-holes are manufactured by the femtosecond laser-assisted selective chemical etching technique (FLSE) [25–28].
In this report, we present results on the simulation, fabrication and characterization of cylindrical micronozzles with the diameter of 100-500 μm and length of several millimeters to produce high-density gas targets for laser wakefield acceleration. Nozzles were fabricated using the nanosecond laser rear-side processing approach alone and the hybrid 3D fabrication technique.
2. Numerical simulation
The concentration, velocity, pressure and temperature of gas jets, ejected by micronozzles, were simulated using OpenFOAM  compressible steady-flow solver rhoSimpleFoam. The Reynolds-averaged Navier–Stokes (RANS) k-𝜔 Shear Stress Transport (SST) turbulence model describing turbulence using two transport equations and 2 transported variables - turbulent kinetic energy k and 𝜔 - the specific rate of dissipation of the turbulence kinetic energy k into internal thermal energy was applied. A general thermo-physical model of calculation was based on internal energy and compressibility parameter ψ = 1/RspecT, where Rspec is the specific gas constant and T is the temperature. The viscosity of the fluid μ was calculated according to the Sutherland viscosity model as a function of the temperature T from the Sutherland coefficient As and Sutherland temperature Ts, according to:
Material properties used in the simulation are given in Table 1. The actual values of the density, the speed of sound and refraction index were recalculated in the simulation based on the local values of pressure and temperature.
Nitrogen gas was implemented as the main modelling media to define optimal geometries of the nozzles during their manufacturing. The results are applicable also to helium frequently used as a laser wakefield acceleration media. The concentration differences at the nozzle output for nitrogen and helium are in the range of 7-10% only. The refractive index of nitrogen is higher by order of magnitude compared to helium and allows much easier and precise interferometric measurements of the gas target distribution. The simulation area comprises the length of microcapillary of 2.8 mm and 6 x 4 mm simulation area of expansion of the gases. Because of the high aspect ratio 1:18 (150 µm and 2.8 mm) only the part of simulation – 600 x 600 µm close to the output of the nozzle is shown. Simulated images of gas concentration and Mach number of nitrogen and helium at the backing pressure of 60 bar of a cylindrical nozzle with the output diameter of 300 μm are presented in Fig. 1. The concentrations at the output of the nozzle for nitrogen and helium are similar because the gas density ρ depends on the Mach number M being close to critical to both of gases :
The higher deviations of Mach number between nitrogen and helium at larger distances depend on the gas temperature and speed of sound being inverse proportional to the square root of the mass of gases. Helium having lower molecular mass expands quicker, and the local temperature drops to the lower values compared to nitrogen. It results in higher Mach numbers of helium defined as a ratio of gas flow velocity and local speed of sound.
The capillary nozzles were manufactured from fused silica using the nanosecond rear-side processing approach alone and the hybrid 3D laser machining technique. The sketch of the nozzle is presented in Fig. 2(a). The nozzle consisted of the 35 mm-diameter holder with a frustum of a cone and microcapillaries, fabricated along the element axis. The commercially-available 150 x 150 mm2 and 76 mm-diameter fused silica plates with the thicknesses of 6.3 mm and 12.7 mm, respectively, were used as raw material.
3.1 Nanosecond laser processing
The processing setup with a nanosecond laser is presented in Fig. 2(b). Gas jet nozzles were fabricated using the second harmonics (532 nm) of a diode-pumped solid-state (DPSS) laser (from Ekspla). The pulse duration, measured at full-width at half-maximum, was 4.5 ns. The laser system provided the maximum average laser power of 18 W at the 200 kHz pulse repetition rate. The galvanometer scanner intelliSCAN 14 (from SCANLAB) was used to guide the laser beam in the XY plane, focused by the telecentric f-theta lens with the focal length of 80 mm. The diameter of the focused beam at the 1/e2 level equalled to 10.5 µm. Typical pulse energy and laser fluence was 90 µJ and 210 J/cm2, respectively. Samples were mounted on the translational stage with a stepper motor 8MT167-100 (from Standa) for vertical positioning. The drilling and milling of fused silica were conducted using the spiral-mode cutting technique, presented in , with variable inner and outer diameters, depending on the desired structure. Initially, the laser beam was focused below the rear surface, and then the positioning stage was moved down at a fixed vertical speed, which depended on the area of the milled surface. The removed volume of glass was divided by the processing time to calculate the material removal rate (mm3/s). The material removal rate was divided by the average laser power to obtain the energetic efficiency of processing (mm3/J).
The nozzle was fabricated by two stages. In the first stage, the frustum of a cone and screw holes were fabricated. The material removal rate for such high-volume milling reached 2.34 mm3/s with the 18 W average laser power.
The energetic efficiency at such conditions was 0.13 mm3/J. Therefore, it took a few dozen minutes to manufacture a 35 mm-diameter nozzle holder with the 2 mm height of the frustum of a cone. The average roughness Ra of the milled surface, measured in the horizontal direction by the stylus profiler Dektak 150 (from Veeco), was in the range of 4-6 µm.
In the second stage, the nozzle holder was turned upside down and the intrinsic structure, consisting of a microchannel and an adapter, was fabricated with reduced average laser power and pulse repetition rate to achieve high-quality drilling and milling. The minimum diameter of the hole was 100 µm in the 6.3 mm-thick glass plate. For smaller diameters, processing debris was trapped inside a hole, and the process stopped. The achieved aspect ratio of 63:1 was comparable with the liquid-assisted femtosecond drilling technique . However, the processing speed was significantly enlarged. It took only 15 s, 30 s, 60 s, 160 s to drill 100 µm, 200 µm, 300 µm and 500 µm-diameter holes, respectively, in the 6.3 mm-thick glass sheet with the 0.48 W average laser power. Therefore, the material removal rate and processing energetic efficiency where 3.3 × 10−3 mm3/s and 6.9 × 10−3 mm3/J, respectively, calculated for the 100 µm-diameter hole and approximately 15 × 10−3 mm3/J for other holes. The front-side scanning electron microscope (SEM) images of drilled holes are presented in the Fig. 3. The maximum surface chipping, which is typical for nanosecond laser processing of glass, was around 100 µm. For examination of the surface roughness, the sample was cut through an array of holes and polished to open a channel. An SEM image of opened channels is given in Fig. 4(a). It is clearly seen that the fabricated channels are taper-less and maintain their cylindrical shape for the entire thickness of the glass. The rough surface, visible in Fig. 4(b), occurs due to the nature of the process. The surface topography of 500 µm-diameter channel, measured by the stylus profiler, is presented in Fig. 4(c). The measured average surface roughness Ra of a channel in the vertical direction was 1.4 µm, the average peak-to-valley distance Rz was 8 µm.
The nanosecond laser rear-side processing approach is a flexible technique, which allows us to fabricate the 2.5D structures in the bulk of glass. For instance, capillaries with variable diameters, as shown in the Fig. 4(d).
3.2 Hybrid 3D machining technique
Initially, samples were shaped using the DPSS nanosecond laser with a high material removal rate. In this step, a nozzle holder and an adapter without a microchannel, similar to the one presented in Fig. 4(d), were fabricated. The 0.8 mm-diameter adapter with a conical tip was required to reduce the thickness of laser-untreated volume to 2 mm for the further processing step.
Then, micro-capillaries were inscribed using the femtosecond laser direct writing technique and etched in the potassium hydroxide (KOH) of 10M concentration for 22 hours. In such way, the manufacturing showed no chipping on the microchannel entrance surface, shown in Fig. 5(b), and the diameter accuracy control has been improved up to +/− 2 μm, depending on the channel size precompensation. For the channel fabrication, the femtosecond Yb:KGW Pharos laser (from Light Conversion) operating at the 515 nm wavelength and ~300 fs pulse duration was used. The repetition rate was set to 500 kHz, and the processing speed was 0.5 mm/s to ensure the 1000 pulses/µm density. The laser beam was focused with a 100x microscope objective (from Mitutoyo, NA = 0.5) to achieve ~2 µm spot size.
The vertical channel was formed according to the fabrication geometry, demonstrated in the Fig. 5(a). The whole channel length was divided into the 9 sections with a single section length of ~230 µm. The section was composed of the layers consisting of a set of concentric circles, which increased the etched cavity size. The concentric circles were manufactured by translating the sample relative to the laser focus with the XY positioning system that allows the accuracy of ~300 nm (Aerotech ANT150). The single layer was not entirely filled by the circles to minimise the fabrication time. The z step between the layers in the single section was defined experimentally and was 4-5 µm. Each section was terminated by the end sections, composed of the few layers, fabricated by the same processing parameters. However, in this case, the whole area of the layer was filled entirely by concentric circles. The circle's radius in the layer was changed by the 1.5 µm step. This sectional fabrication minimised the saturation during the etching as the etched section was separated and fall out. Therefore the clear etchant could achieve deeper and deeper sections. Due to the aberrations , for the deeper focusing the pulse energy dissipated, and higher energy was needed to induce the required modifications. In this way, ~300 nJ pulse energy was used for the first section and ~800 nJ pulse energy for the last section. The vertical channel shape was precompensated by changing the maximum section radius to achieve the taper-less microchannel. The total laser fabrication time of 100 µm diameter channel was ~21 min. SEM images of an opened channel are shown in Fig. 6. The magnified etched microchannel and adapter images demonstrate a significant difference in the surface morphology. The adapter, drilled using the nanosecond laser and etched for 22 h, shows the rough worm-like surface. The surface profile, measured with a stylus profiler, is given in Figs. 7(a) and 7(b).
The surface roughness of the microchannel, fabricated with the FLSE technology, was Ra = 120 nm (Rz = 568 nm). For comparison, the surface roughness of the adapter, drilled with the nanosecond laser and etched for 22 hours, was Ra = 3.5 µm (Rz = 18.8 µm). Note that etching further increased the roughness of channels, fabricated using nanosecond laser.
The FLSE technology significantly improves the average surface roughness Ra (~12 times) and average peak-to-valley distance Rz (~14 times) of the microchannel; however, due to the long fabrication time, it is less competitive in the processing of high-volume parts. The minimum diameter that can be achieved in the 2 mm thick fused silica was ~30 µm, which is ~3 times smaller compared to the nanosecond laser drilling. Therefore, the FSLE technology can be preferred where the low surface roughness and small < 100 µm diameter microchannels are required. Images of the fabricated nozzle with the 2 mm-length capillaries are given in Fig. 8.
4. Characterization of nozzles
The gas density profiles were measured using nitrogen, Mach-Zehnder interferometer, continuous wave 632.8 nm He-Ne laser and subsequently filtered using Fourier transformation . The gas nozzles were tested in a vacuum chamber at the vacuum level of 10−5 mbar. The laser was operated, and the interferometer was installed outside of the vacuum chamber with one of the interferometer arms crossing the vacuum chamber through the windows of the optical quality of λ/10. The diagram of the Mach-Zehnder interferometer is presented in Fig. 9(a) and the images of measured phase interferograms of the gas jet at the backing pressure of 60 bar of the cylindrical nozzle with an output diameter of 300 μm for helium are given in Fig. 9(b) and for nitrogen in Fig. 9(c). The nozzles were driven by the Parker 9 series microvalve with the 0.8 mm orifice, actuated by a specialised pulse driver enabling millisecond operation. The operation of the microvalves and CCD cameras were synchronised and triggered by the master oscillator.
Nitrogen was used for the determination of the gas density profiles because of the sufficiently higher refractive index relative to the helium. The Abel transformation was performed to get the 3D map of the nozzle gas density. The phase was retrieved, and the density profiles were reconstructed using the interferometric data evaluation algorithms (IDEA) . The simulated integral phase profiles of nitrogen gas at 60 bar of cylindrical nozzles with the output diameter of 100 μm, 200 μm, 300 μm and 500 μm are presented in Figs. 10(a), 10(c), 10(e) and 10(g), respectively.
The reconstructed integral phase profiles are presented in Figs. 10(b), 10(d), 10(f) and 10(h). Integral phase φ was calculated from the OpenFOAM concentration simulations with following integration of the phase change while the interferometer beam was crossing the nozzle gas jet. The measured profiles of integral phase were reconstructed from measured interferograms using IDEA software package. In Figs. 11(a) and 11(b), the simulated and reconstructed transversal concentration profiles of gas at 60 bar of cylindrical nozzles with the output diameter of 200 μm and 300 μm, respectively, are presented. Solid lines correspond to the concentration simulations of nitrogen and dashed of helium. Markers represent the experimental data. In Fig. 11(c), the simulated and reconstructed longitudinal concentration profiles of gas at 60 bar of cylindrical nozzles with output diameter 300 μm (line 1, marker 6), 200 μm (line 2, marker 7) and 100 μm (line 3) are given. In Figs. 11(d) and 11(e), the reconstructed integral phase profiles of Mach-Zehnder interferometer of nitrogen gas at 60 bar of cylindrical nozzles with the output diameter of 100 μm and Rz = 568 nm and Rz = 8 µm, respectively, are shown.
5. Results and discussion
The calculated and measured integral phase φ, presented in Fig. 10, and gas concentration profiles, presented in Fig. 11, are in good correspondence for the nozzles with the diameter of 100, 200 and 300 μm. The measured phase profiles of the nozzle with the output diameter of 500 μm were 15% lower relative to the predicted by numerical simulation because of the low removal rate of the residual gas by the vacuum pump system. Depending on the valve backing pressure of 20 to 60 bar, the achieved concentration of the gas density at the exit of micronozzles was in the range of 2-6 × 1020 cm−3. The concentration profiles were parabolic, and the concentration dropped by orders of magnitude at the distance of 4-5 diameters from the output. At these distances, the concentration depends linearly on the backing pressure of the valve. The density at the output of the nozzle is close to the critical density of subsonic flow inside of the capillary, and the Mach number of the gas jet is in the range of 1.3-1.4. Leaving the capillary, the gas expands quickly, and at the distance of the diameter of the nozzle, reaches the velocity of 2-3 Mach. At a distance, being equal of 0.5-0.7 diameters of the nozzles from the output, the concentration profile is relatively flat, and the concentration changes 20-30% within the focused beam of 10-20 μm at FWHM of accelerating laser. The gas concentration of cylindrical nozzles with the diameter of 200-300 μm at 60 bar of backing pressure is 1.8-2.2 × 1020 cm−3. This value is higher relative to Laval nozzles with the throat of the same size as cylindrical nozzle because the output area of Laval nozzles is typically several times greater than the critical area. The concentration can be raised by increasing the backing pressure several times. The maximal pressure is limited by the mechanical characteristics of the valve and strength of the material. Cylindrical nozzles have advantages where high-density and short gas target are required, and the laser beam is focused close to the nozzle output area. The supersonic Laval nozzles have advantages where more extended flat profiles with modest gas concentration and long focusing length of the laser beam are implemented.
The gas concentration of cylindrical nozzles with the diameter of 100 µm, measured at the distance of 50 μm from the output of the nozzle was 25% lower in the channel with the higher wall roughness of Rz = 8 µm relatively to the channel with the wall roughness of Rz = 568 nm. The corresponding gas concentrations were 2.2 × 1020 and 3 × 1020 cm−3, respectively. The difference of the gas concentration of the channels decreased with the distance from the nozzle output and reached similar values of 0.8-1 × 1020 cm−3 at the distance of 150 μm from the nozzle output. The SEM images of wall roughness and integral phase of FLSE and rear-side technique are presented correspondingly in Fig. 6(c), Figs. 4(c) and 4(d), Figs. 11(d) and 11(e).
6. Conclusions and outlook
The combination of the 7-12 fs laser pulses and plasma targets of the size of 100-200 μm and the gas density of 1-3 × 1020 cm−3 allows to reach the laser strength parameter a0 >2 and accelerate the electrons with lasers having several terawatt of power. It opens the opportunity to benefit from the generation of ultrashort X-ray pulses with a high repetition rate of 1 kHz. At the distance of the diameter of the channel, the concentration profile is relatively flat and changes 20-30% within the focused beam of 10-20 μm at FWHM of accelerating laser. Higher gas density will result in shorter dephasing length and lower the energy of accelerated electrons. The decreased energy will be partially compensated by higher plasma field. Additionally, to increase the dephasing length, a periodical nozzle array with modulation of the density with high and low concentrations regions can be implemented. The described manufacturing technique can be used for manufacturing of Laval nozzles and combinations of cylindrical, slit and Laval nozzle arrays on a single chip to produce tailored gas concentration profiles.
The nanosecond laser rear-side processing approach allows rapid fabrication of gas jet nozzles with the minimum 100 µm-diameter capillaries in a 6.3 mm-thick fused silica. The maximum material removal rate for high-volume parts is 2.34 mm3/s with the 18 W average laser power. However, due to the nature of the process, the channel roughness is on the order of several micrometers. The FLSE technology significantly improves the average surface roughness (~12 times) and average peak-to-valley distance (~14 times) of the microchannel; however, due to the low fabrication time, it is less competitive for processing of high-volume parts. The limitations above can be eliminated by the hybrid 3D machining technique, when high-volume parts, which do not require high quality, are removed by nanosecond pulses, and high-quality capillaries are fabricated by the laser-assisted chemical etching. Such a technique allows achieving both - high processing speed and quality.
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