We have investigated space and astrophysical phenomena in nonrelativistic laboratory plasmas with long high-power lasers, such as collisionless shocks and magnetic reconnections, and have been exploring relativistic regimes with intense short pulse lasers, such as energetic ion acceleration using large-area suspended graphene. Increasing the intensity and repetition rate of the intense lasers, we have to handle large amounts of data from the experiments as well as the control parameters of laser beamlines. Artificial intelligence (AI) such as machine learning and neural networks may play essential roles in optimizing the laser and target conditions for efficient laser ion acceleration. Implementing AI into the laser system in mind, as the first step, we are introducing machine learning in ion etch pit analyses detected on plastic nuclear track detectors. Convolutional neural networks allow us to analyze big ion etch pit data with high precision and recall. We introduce one of the applications of laser-driven ion beams using AI to reconstruct vector electric and magnetic fields in laser-produced turbulent plasmas in three dimensions.
I. INTRODUCTION
We have been working on laboratory astrophysics where space and astrophysical phenomena are experimentally investigated by using non-relativistic large laser facilities, such as collisionless shocks1–4 and magnetic reconnections.5–8 In space plasmas, one obtains local magnetic field and plasma distribution functions with in situ measurements by spacecraft, and thus, it is difficult to obtain global structures of, for instance, a collisionless shock. In contrast, astrophysical objects are far distant and never be accessible, and therefore, one obtains global information about the objects with telescopes, but no local or microscopic information.9 Laboratory astrophysics can connect these two completely different methodologies investigating the same physical subjects, such as collisionless shocks. For example, in the early days of laboratory astrophysics, we started to obtain the global shock structures using imaging for both plasma density and emission,1 and electric and magnetic field structures.2 We have extended these to include local plasma information using Thomson scattering measurements.3,4
Since we started up the laboratory astrophysics project relevant to the collisionless shock10 more than a decade ago, there have been more and more researchers have started working on laboratory astrophysics on many new topics.11 However, the nanoseconds kilojoule class large laser facilities open for basic science are limited: LULI2000 at the Ecole Polytechnique, Vulcan at the Rutherford and Appleton Laboratory, Gekko XII at the Osaka University, Shenguang II at the Shanghai Institute of Optics and Fine Mechanics, and OMEGA at the Rochester University, and there have been two increments megajoule (MJ) class laser facilities NIF at the Lawrence Livermore National Laboratory and LMJ at Bordeaux. They are all single-shot bases, and the number of shots is also limited; for instance, users of MJ class laser facilities can normally have a few shots a year, even though they have to go through high competition to obtain the machine time. The lack of statistics is a serious issue in laboratory astrophysics with large laser facilities, and we have been extending laboratory astrophysics by using intense femtoseconds to picoseconds lasers.
Intense short-pulse laser technologies enable us to access relativistic plasmas in laboratories with much higher repetition rates than those large laser facilities, and there are many more short-pulse laser facilities over the world.12 We have been exploring relativistic regimes, such as electron acceleration by turbulent wakefield,11,13 energetic ion acceleration using large-area suspended graphene,14–16 and the Weibel instability in the sub-relativistic counterstreaming plasmas.17 Increasing the intensity and repetition rate of the lasers, we have to handle large amounts of data from the experiments as well as the control parameters of laser beamlines. Artificial intelligence (AI) such as machine learning (ML) and neural networks (NNs) may be essential in optimizing the laser and target conditions for efficient laser ion acceleration.
Data science and ML have recently been implemented in dealing with such big data in laser plasma physics.18 To optimize laser-driven ion acceleration, laser wavefront and target position are automatically controlled with ML.19 AI and data science are going to be essential research tools to investigate plasma physics such as theory, simulation, and experiment. We have been implementing AI in laser-driven ion acceleration experiments to stabilize the ion beam quality and energies using the above-mentioned beam line information and online diagnostics. To this end, as an example and as the first step, we have recently implemented ML to etch pit analyses measured with solid-state nuclear track detectors (SSNTDs),20 where tremendous manual efforts had been required without ML.20 We further develop this by implementing NNs, and we also discuss the application of the big data of ion etch pits on the reconstruction of vector electric and magnetic fields in three dimensions (3D) in laser-produced plasmas. Note that there is an attempt to reconstruct a 3D magnetic field from proton radiography using radio chromic films (RCFs).21 However, it is still challenging to distinguish an electric field from a magnetic field using the dose level detected on RCFs. We use big data obtained from ion etch pits recorded on SSNTDs.20 In addition to machine learning, a data-driven method can be another way to automate ion etch pit analyses recorded on SSNTDs.22 We start with machine-aided turbulent field reconstruction using NNs.
In this paper, we report our recent efforts on laser ion acceleration, diagnostics, and the applications of laser-driven quantum beams using AI. In Sec. II, we describe the practical problem in laser-driven ion acceleration experiments and our motivations for the optimization of laser ion acceleration with AI, together with the implementation of AI in numerical simulations and data analyses. In Sec. III, we develop the convolutional neural network (CNN) to develop the ion etch pit analyses with ML as an example of AI implementation in laser ion acceleration experiments. In Sec. IV, we introduce applications of a large dataset of ion etch pits automatically collected by CNN. As an example, we discuss machine-aided vector electric and magnetic field reconstruction in 3D. Finally, we give a summary and discussions in Sec. V.
II. DATA DRIVEN OPTIMIZATION OF LASER ION ACCELERATION WITH ARTIFICIAL INTELLIGENCE
Figure 1 shows a typical workflow of laser-driven ion acceleration, corresponding to the J-KAREN experiment for ion acceleration.16 In order to conduct an experiment, we need a laser, targets, and diagnostics [Fig. 1(a)]. Then, we analyze the obtained data [Fig. 1(b)] and perform simulations to understand the data [Fig. 1(c)]. In a relatively large laser facility, laser alignment and operation are supported by the facility, and regardless of the scale of the facility, targets and diagnostics have to be prepared by users. In most cases, unless the numerical simulation is more difficult than conducting the experiment, we perform numerical simulations to design the experiment to determine the target and laser parameters. Particle-in-cell (PIC) simulations are often used for laser-driven ion acceleration to determine the target thickness, focusing F-number, and pulse duration relevant to the laser facility. There is a maximum laser energy for a certain laser facility, and one may reduce the energy to obtain the energy scaling otherwise fixed to the maximum energy. Since the laser energy is fixed, once the focusing optics are settled, one can change the laser intensity by elongating the pulse duration and moving the target away from the best focus position; in both cases, one can reduce the laser intensity. The contrast is the prepulse-to-peak intensity ratio, which is difficult to calculate by the PIC simulations, but can alter the ideal experimental conditions. The PIC simulations predict the results, but normally, there are some deviations from the experimental results. These come from the effects not included in PIC simulations, and the prepulse is one of the essential factors not included in PIC simulations.
Current workflow of laser-driven ion acceleration experiment. (a) Experiment, (b) data analyses, and (c) numerical simulations support each other.
Current workflow of laser-driven ion acceleration experiment. (a) Experiment, (b) data analyses, and (c) numerical simulations support each other.
For example, we developed the thinnest targets using graphene, large-area suspended graphene (LSG),14 with the thickness of a single atomic layer to multilayer graphene. Graphene is the strongest 2D material, stronger than diamond at the extremely thin target regime,23 however, can be destroyed by the prepulse prior to the main laser peak. In order to investigate this, we are developing the combined simulation of PIC and molecular dynamics for prepulse. The deviation between the prediction and the results is a seed of new research topics.
Simulations can be used to design the experiment, predict the results, and provide a better understanding together with the experimental results since the simulations can provide us the data that cannot be obtained from experiments such as the time evolution of laser and plasmas as in Fig. 1(c). During the experiment, one can obtain the preliminary energy distribution functions from online diagnostics such as the Thomson parabola spectrometer,16,24 and one may change some controlling parameters for laser as shown in Fig. 1(a). Off-line diagnostics such as a stack of solid-state nuclear track detectors (SSNTDs) provide complemental data and reliability.25–27
There are fluctuations in laser focus and pointing and targets resulting in the fluctuation of ion energies. As mentioned above, the laser energy and optics are fixed, and we try to align the laser best focus at the targets, shortest pulse duration, and lowest prepulse level to achieve the laser intensity as high as possible, which is considered to result in the higher ion energies. Thus, the fluctuations normally reduce the ion energies. For example, our previous experiments using LSG show relatively stable ion acceleration with energy fluctuations also relatively small when the laser contrast is good.16 However, some cases show completely different results. Figure 2 shows the Thomson parabola images together with the target images before and after the shots. In Fig. 2(a), both protons and carbons are accelerated up to high energies close to the zero deflection point in the x-ray signal corresponding to the infinite ion energy. The target images before and after the shot in Fig. 2(d) show that not only the graphene but also the substrate burned out by the laser making a much larger hole in the substrate, where the white dashed circle represents the original hole on the substrate. In Fig. 2(b), only the proton parabola is clear, but the carbons are not clear. Furthermore, the proton energy is much lower than that of Fig. 2(a), and as seen in Fig. 2(e), the laser burned the substrate out, making a hole larger than the original hole but much smaller than that of Fig. 2(d) after the shot. These two shots are nominally identical with the same laser and the same targets. In Fig. 2(c), there is no ion signal, but only a weak x-ray signal is recognized even with the thicker target considered to be more stable. Note that both in Figs. 2(d) and 2(e), the suspended graphene and the graphene on the substrate, which appear darker in color, burned out, and the substrate burned out, making the larger holes. However, in Fig. 2(f), one can see that just the suspended graphene burned out, but the graphene on the substrate still survived. This indicates that the laser surely reaches the target and also the energy meter just before the target chamber shows the laser energy of 14.5 J; however, the laser target interaction is extremely weak. Shot-by-shot fluctuations are extremely large and cannot be explained by the laser energy or target thickness. There are hidden parameters governing ion acceleration. One of the solutions to suppress the shot-by-shot fluctuations is a plasma mirror reducing the prepulse.28 Another solution can be artificial intelligence (AI).
Thomson parabola images with (a) 16-layer LSG with 17.3 J, (b) 16-layer LSG with 17.8 J, and (c) 32-layer LSG with 14.5 J. All the shots are taken at 10° from the target normal on the same day. (d)–(f) Corresponding microscope images of the LSG targets before and after the laser irradiations, respectively, with the same scale indicated in (d), which is taken with lower magnification to capture the entire image of the laser burn mark.
Thomson parabola images with (a) 16-layer LSG with 17.3 J, (b) 16-layer LSG with 17.8 J, and (c) 32-layer LSG with 14.5 J. All the shots are taken at 10° from the target normal on the same day. (d)–(f) Corresponding microscope images of the LSG targets before and after the laser irradiations, respectively, with the same scale indicated in (d), which is taken with lower magnification to capture the entire image of the laser burn mark.
We are currently implementing AI such as ML and NN into the workflow as shown in Fig. 3. By implementing AI, we have three more bridges between (1) simulation and AI, (2) experiment and AI, and (3) data analysis and AI.
Workflow of laser-driven ion acceleration experiment with artificial intelligence.
Workflow of laser-driven ion acceleration experiment with artificial intelligence.
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Without considering the realistic constraints, in numerical simulations, there are still many governing parameters for laser-driven ion acceleration: laser energy, pulse duration, waist size or F-number, contrast, polarization, chirp, incident angle to the target, and intensity by changing the target position, and also target material, state, shape, density, temperature, thickness, and further one may combine multiple species of targets and/or may combine multiple laser beams with multiple targets.29 The parameter space is huge, and a comprehensive understanding of the physics of laser ion acceleration has not been realized yet. Currently, we are working on simple 1D simulations focusing on the phase-stable radiation pressure acceleration30 to investigate the optimum condition with the aid of NN.31 We will generalize this in 2D for more realistic cases in the future.
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Based on the numerical prediction of the optimized laser-driven ion acceleration with the aid of AI, we will conduct a laser experiment. Here we also want to implement AI into the laser system by including the real-time monitoring of laser beam lines as shown in Fig. 3. There are many components to deliver a laser beam to the experimental area, such as optical parametric chirped pulse amplification (OPCPA), many stages of amplification, beam pointing, and phase at each step.32 So far, there are monitors at each step to operate the J-KAREN laser, but not online and connected. We are going to use all the beamline data as inputs for the neural network to maximize the ion energy. We have also developed real-time, scintillator-based relativistic ion diagnostics for the output of the neural network.33,34 As a middle- or long-term goal, we will implement these online and optimize the laser system in real-time to stabilize and maximize the laser-driven ion acceleration in the future.
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As mentioned above, intense short lasers can be operated at high repetition rates, and the experimental data can be much more than that of single-shot-based large laser facilities. Data science and informatics are crucial to deal with these big data. We have been implementing AI to automate data analyses on huge amounts of experimental data. For practice and practical purposes, we have started this with the ion etch pit analyses detected on plastic nuclear track detectors (PNTDs) from laser-driven ion acceleration experiments with the aid of conventional not deep ML.20 A widely used PNTD is CR-39, which is sensitive to stopping protons and all the heavier ions but less sensitive to electrons and photons. Therefore, PNTD is considered to be the most reliable ion diagnostics in laser-driven ion acceleration experiments, where a number of ions, electrons, and photons (x-rays and γ-rays) are simultaneously generated. Moreover, since different kinds of PNTDs have different sensitivities to ions, one can distinguish ion species with the same charge-to-mass ratio; for example, C6+ and O8+ can be identified using polycarbonate (PC) and polyethylene terephthalate (PET),27 which cannot be distinguished with Thomson parabola spectrometer.16 However, PNTDs require chemical etching and microscope scanning to recognize the ion etch pits. To analyze the ion species and the energies, one has to repeat this process multiple times.27 So far, ion etch pit analyses demand tremendous time and effort by hand and require an expert to distinguish which signals actually come from the laser-target interactions and some other particles from the environment and secondary thermal neutrons. ML can assist in automating ion pit detection and recognition. In Sec. III, we briefly review our recent paper on the implementation of ML into the ion etch pit analyses,20 discuss the problems of the ML, and introduce one of the solutions by a convolutional neural network (CNN).
III. ION ETCH PIT ANALYSES WITH CONVOLUTIONAL NEURAL NETWORK
As mentioned above, data analyses of ion etch pits detected on PNTDs require tremendous time and effort; it has been a practical problem to secure enough researchers to analyze the data. We normally use five to ten PNTDs to compose a stack detector for laser-driven ion diagnostics, for instance, five pieces of CR-39 with the dimension of 5 × 5 cm2 are used in J-KAREN experiments.16 A single piece of CR-39 with this size corresponds to about 10 000 images with a fast-scanning optical microscope. For a high repetition rate laser experiment, we accumulate the ion data on the stack for nominally identical targets, such as eight-layer LSG.16 We may change the stack once or twice a day, and we have 4 shot days a week and 3 weeks of an experiment a year, resulting in about 106 microscope images.20 Conventional statistical analyses can pick up ion pits with eccentricity and darkness of the objects'; however, it is still difficult to exclude noises, and we used to analyze the ion etch pit with human eyes eventually.27
We have implemented ML to automate the ion etch pit analyses.20 We used two datasets from a conventional accelerator (HIMAC, QST) and laser experiment (LFEX, Osaka University), and the details of the experiments are found in Ref. 20. While the former provides known energy and known species of ions (carbons), the latter does unknown energy and unknown species of ions (protons, carbons, oxygens, golds, and so on). The PNTDs used in the experiment were CR-39 and Kapton for HIMAC and LFEX, respectively. As mentioned above, CR-39 is sensitive to stopping protons and all the heavier ions with a relatively clean surface, and Kapton is sensitive to heavier ions than aluminum or silicon but with a much more noisy surface. Figure 4 shows samples of microscope images of (a) CR-39 from the HIMAC experiment and (b) Kapton from the LFEX experiment used as a detector for the Thomson parabola spectrometer.20 Here we also use CR-39 from the LFEX experiment for comparison purpose. We confirmed our methodology works using the calibration experiment data with the known ion species and energies.20
(a) A microscope image of etched CR-39 from the conventional accelerator (HIMAC, QST) with known ion energy and known ion species, i.e., all the signals come from carbon and the pit size is the same with a clean surface. Microscope images of (b) etched Kapton from laser experiment, where a gold mounted on large-area suspended graphene is irradiated with LFEX laser resulting in unknown ion energy and unknown ion species, i.e., the ion etch pits are different sizes depending on the ion species and energies.
(a) A microscope image of etched CR-39 from the conventional accelerator (HIMAC, QST) with known ion energy and known ion species, i.e., all the signals come from carbon and the pit size is the same with a clean surface. Microscope images of (b) etched Kapton from laser experiment, where a gold mounted on large-area suspended graphene is irradiated with LFEX laser resulting in unknown ion energy and unknown ion species, i.e., the ion etch pits are different sizes depending on the ion species and energies.
Each microscope image goes through smoothing, binarization, and outline extraction, and then we classify the extracted images into ions and noises by eyes. For instance, we use 604 ion etch pits and 582 noises for Kapton data, and for CR-39, similar numbers of ion etch pits and noises are used.20 Using these as training data for machine learning (ExtraTreesClassifier), all the microscope images are examined to pick up the ion etch pits.20, Figure 5 shows examples of machine-aided automatic ion etch pit detections of (a) CR-39 from HIMAC and (b) Kapton from LFEX. As discussed in Ref. 20, since a conventional accelerator provides nominally the same energy and single species of ions with a well-controlled ion fluence, we can control the overlapping of ion etch pits as seen in Fig. 5(a). Furthermore, since the surface of CR-39 is clean or less noisy, automatic ion detection is relatively easy: both precision (predicted true ion pits/all the predictions) and recall (predicted true ion pits/all the true ion pits) are almost perfect. The precision and recall are evaluated from randomly selected 20 microscope images.20 For the LFEX experiment, there are many kinds of particles with various energies without control of fluence. We use various types of PNTDs to select ion species and Thomson parabola to separate energies and charge to mass ratio and to reduce the ion fluence.20,27 Although the Kapton surface is much noisier than that of CR-39, we can automatically identify ion etch pit with a precision of 95%. The recall is lower than that of CR-39 from HIMAC; nevertheless, we analyze huge amounts of microscope images and thus a number of ion pits.
Machin learning on ion etch pit detection: (a) CR-39 HIMAC data using the training data from HIMAC. About 105 ion pit detection from more than 5000 microscope images with a precision of 98% and recall of 98%, and (b) Kapton LFEX data using training data from LFEX. About 105 ion pit detection from more than 17 000 microscope images with a precision of 95% and recall of 76%. The cropping margin was 3 pixels.
Machin learning on ion etch pit detection: (a) CR-39 HIMAC data using the training data from HIMAC. About 105 ion pit detection from more than 5000 microscope images with a precision of 98% and recall of 98%, and (b) Kapton LFEX data using training data from LFEX. About 105 ion pit detection from more than 17 000 microscope images with a precision of 95% and recall of 76%. The cropping margin was 3 pixels.
Although ML in ion etch pit analyses provides us with huge amounts of data with high precision, there are still practical problems. Figure 6(a) shows an example of CR-39 from the LFEX experiment, but the training data are from the HIMAC experiment. Even though the etching conditions are nominally identical with CR-39 clean surfaces and the etched pits are very similar to those in Fig. 5, ML cannot detect the ion pits well, only one is detected out of four ion pits. The only minor difference between Figs. 5(a) and 6(a) is the background darkness, which might be difficult to recognize here, but the background of the laser experiment tends to be slightly brighter than that of the calibration experiment. Although we still do not understand why training data from the calibration experiment do not work for the laser experiment, Fig. 6(a) indicates that we have to make training data for each experiment.
Machine learning on ion etch pit detection: (a) CR-39 LFEX data using the training data from HIMAC and (b) Kapton LFEX data using the training data from LFEX but with a cropping margin of 5 pixels.
Machine learning on ion etch pit detection: (a) CR-39 LFEX data using the training data from HIMAC and (b) Kapton LFEX data using the training data from LFEX but with a cropping margin of 5 pixels.
Figure 6(b) shows the same Kapton data from LFEX with the training data from LFEX but with the cropping margin slightly larger than that of Fig. 5(b). The precision is still high (93%), but the recall is reduced to 31%. We need to optimize the cropping margin of the outline extraction. Since the larger margin means that more noise signals and other pits can be included in the selected rectangle regions, i.e., unwanted noise and overlapping can be trained as ion pits. Since an ion fluence cannot be known a priori in laser experiments, when an ion fluence is high and many ion pits overlap each other, we need to pick up un-overlapped ones by adjusting the cropping margin.
Another important parameter affecting the result is the binarization threshold before the outline extraction,20 which is not directly relevant to ML. We can find the optimum parameters and algorithm for some cases as in Ref. 20; however, if we have to investigate the optimization of the ML for each energy of ions, each species of ions, and each experiment, it is simply replacing the problem; we take times to adjust the parameters and algorithms instead of looking at ion etch pits by eyes. Our goal is not just to implement AI in laser experiments, but to find a solution with the aid of AI. We need a robust methodology to automate ion etch pit analyses.
Image recognition such as our face recognition to log into our computers and automatic identification of dog pictures from photo libraries is ubiquitous nowadays, which is based on deep learning using artificial neural networks, a subset of machine learning. Deep learning can solve more complicated problems than ML. Here we use a convolutional neural network (CNN), a type of artificial neural network that is well-developed in image recognition. A CNN is composed of convolution layers and pooling layers, and the essential difference between CNN and ExtraTreesClassifier, which is not deep, conventional ML, is that the CNN can treat 2D images as is while the ExtraTreesClassifier converts the 2D images into 1D text data. Thus, CNN keeps the spatial information during the image recognition and is considered to be more robust than conventional not deep ML. We use VGG16, a widely used algorithm for image recognition with 16-layer CNN, without weight. We use the same training data as ML and set the test and train size to 20% and 80%, respectively, and the batch size to 128. We set the learning rate to and evaluate the loss with binary cross entropy and metrics with accuracy. Figure 7 shows typical (a) accuracy and (a) loss in terms of epoch number. The ion etch pits are simple form, black circular images, and thus accuracy and loss quickly converge.
Typical convergence of (a) accuracy and (b) loss in terms of the number of epochs.
Typical convergence of (a) accuracy and (b) loss in terms of the number of epochs.
Figure 8 shows the CNN etch pit detection with the same data as in Fig. 6. Although the conventional ML (ExtraTreesClassifier) cannot recognize most of the ion pits on CR-39 LFEX data using the training data from HIMAC in Fig. 6(a), the deep machine learning or CNN (VGG16) properly recognizes all the ion pits on the same data from laser experiment with the training data from the calibration experiment. Figure 8(b) clearly shows more ion etch pits are recognized by CNN. The precision and recall are 95% and 83%, respectively; especially the recall is improved significantly with CNN.
CNN on ion pit detection with the same data as in Fig. 6. (a) CR-39 LFEX data using the training data from HIMAC and (b) Kapton LFEX data using the training data from LFEX but with a cropping margin of 5 pixels.
CNN on ion pit detection with the same data as in Fig. 6. (a) CR-39 LFEX data using the training data from HIMAC and (b) Kapton LFEX data using the training data from LFEX but with a cropping margin of 5 pixels.
Figure 9 shows another example of CNN robustness using the same data from CR-39 used as a detector of Thomson parabola spectrometer, predicted ion etch pit distribution (a) with ExtraTreesClassifier and (b) with VGG16. Although one may recognize a few parabolae in Fig. 9(a), there are many parabolae in Fig. 9(b). It is evident that CNN is more robust.
A comparison of ion etch pit analyses with (a) conventional ML with (b) CNN on the same CR-39 used as a detector of Thomson parabola spectrometer.
A comparison of ion etch pit analyses with (a) conventional ML with (b) CNN on the same CR-39 used as a detector of Thomson parabola spectrometer.
Table I summarized the results of automatic ion etch pit detections with ML and CNN with various conditions. Note that the precision and recall with * are calculated from Figs. 6(a) and 8(a); as seen in Fig. 9, the predicted ion etch pits with ML in Fig. 9(a) are too less to choose the statistical sample randomly. Except these, for instance, the best performance in terms of precision and recall for Kapton data is obtained with ML when the proper training data and cropping margin are used. However, ML is more sensitive to the training data and cropping margin than CNN. Since various species of ions with widespread energy spectra are accelerated in the laser experiments, CNN can be used in many cases without fine-tuning the conditions of data selection and training data.
Automatic ion etch pit detection with ML and CNN.
Algorithm . | ML . | ML . | ML . | ML . | CNN . | CNN . |
---|---|---|---|---|---|---|
Training data | CR-39 HIMAC | Kapton LFEX | CR-39 LFEX | Kapton LFEX | CR-39 LFEX | Kapton LFEX |
Test data | CR-39 HIMAC | Kapton LFEX | CR-39 HIMAC | Kapton LFEX | CR-39 HIMAC | Kapton LFEX |
Crop margin (pixels) | 3 | 3 | 3 | 5 | 3 | 5 |
Precision (%) | 98 | 95 | 100* | 93 | 100* | 95 |
Recall (%) | 98 | 76 | 25* | 31 | 100* | 70 |
Algorithm . | ML . | ML . | ML . | ML . | CNN . | CNN . |
---|---|---|---|---|---|---|
Training data | CR-39 HIMAC | Kapton LFEX | CR-39 LFEX | Kapton LFEX | CR-39 LFEX | Kapton LFEX |
Test data | CR-39 HIMAC | Kapton LFEX | CR-39 HIMAC | Kapton LFEX | CR-39 HIMAC | Kapton LFEX |
Crop margin (pixels) | 3 | 3 | 3 | 5 | 3 | 5 |
Precision (%) | 98 | 95 | 100* | 93 | 100* | 95 |
Recall (%) | 98 | 76 | 25* | 31 | 100* | 70 |
IV. APPLICATION OF BIG ION ETCH PIT DATA
Machine-aided ion etch pit analyses allow us to access a large amount of ion data, which cannot be available by hand. Using this big ion etch pit data, there are many possible applications such as exploring energy frontier in laser-driven ion acceleration with stack detector of PNTDs and laser nuclear physics by combining PNTDs and Thomson parabola spectrometer. So far, although a PNTD can detect ions one by one, it has been difficult to exclude the environmental particles recorded on the PNTD together with the laser-accelerated ions. In order to exclude these background ion etch pits, one has to precisely measure the background level using blank PNTDs not used in the shots but with the same manufacture lot as the ones used in the stack detectors. As mentioned above, we normally obtain about 106 microscope images from PNTD stack detectors, and to statistically analyze those small number of background particles, we have to analyze millions of microscope images. This is not practical by hand, but the machine-aided analyses allow us to handle this.
Another important application of the big ion etch pit data is the reconstruction of electric and magnetic fields in laser-produced plasmas. Ion radiography is a key diagnostic often used in laser plasma experiments.35 For instance, we have investigated collisionless shock formation in laser-produced plasmas and tried ion radiography to measure shock electric/magnetic field.2, Figure 10 shows a schematic image of the experimental setup relevant to the collisionless shock experiment.2 A double parallel planar target is irradiated with a high-power laser, where the laser coming from the right and the right targets is thin enough for the laser to burn through it and irradiate the left target, forming counterstreaming plasmas. In the counterstreaming plasmas, two collisionless shocks are excited. Since the laser is focused on the right target and defocused on the left target, the plasma from the right (left) is faster (slower) and more like point source (one-dimensional) expansion. These asymmetric plasmas excite asymmetric shock waves, and thus, there will be shear flows along the contact surface.2 The shear flows excite the Kelvin–Helmholtz (KH) instability downstream of the shocks and evolve into turbulence. To determine the experimental conditions shot by shot, in this experiment, we used a stack of radio chromic films (RCFs) for the ion detector as shown in Fig. 10, since RCFs change color when they are exposed to radiations, such as proton beams. The white regions in the RCF in Fig. 10 correspond to the absence of ions; the most left feature is the shadow of the left target, which is massive in the line of sight direction, and the electric/magnetic fields of a pair of shocks. The transverse modulations correspond to KH vortices, and we assumed a turbulent electric field downstream of the shocks to account for the observed features in the RCF with the support of numerical simulations.2 However, this can be a magnetic field.36
An RCF provides a dose level as a color scale, and it is difficult to distinguish a magnetic field from an electric field. We are planning to replace RCF with PNTD, such as CR-39. As shown in Fig. 11(a) when an ion goes through a single cell homogeneous electric and magnetic field , the ion trajectory will be deflected by the field. By using PNTD, a single ion measured as an ion pit has three to five observable variables, namely, the position in the PNTD detector and the energy , or the position and the velocity that can be measured from the eccentricity of the ion etch pit with the aid of machine learning.37 To mathematically reconstruct the vector electric and magnetic field, corresponding to six unknown field variables, we need two ions as shown in Fig. 11(a). Mathematically, the ion response to the electric field is different from that to the magnetic field. Therefore, more data would be better to reconstruct the more complex electromagnetic field. In the same manner, when there are two cells, we need four ion etch pits to reconstruct the vector electric and magnetic fields as shown in Fig. 11(b). As shown in Fig. 11(c) when there are n ion etch pits, we can reconstruct three-dimensional (3D) vector electric and magnetic fields with the resolution of by by .
Schematic images of ion radiography with the information of ion etch pits detected on a PNTD detector. (a) A single-cell homogeneous electric and magnetic field require two ion etch pits and to mathematically resolve the field. (b) To reconstruct two cells with 12 unknown variables, we need 4 ion etch pits – corresponding to 12 measurable quantities. (c) Using big ion etch pit data with 3n known variables, we can reconstruct three-dimensional three-vector electric and magnetic fields in laser-produced plasmas.
Schematic images of ion radiography with the information of ion etch pits detected on a PNTD detector. (a) A single-cell homogeneous electric and magnetic field require two ion etch pits and to mathematically resolve the field. (b) To reconstruct two cells with 12 unknown variables, we need 4 ion etch pits – corresponding to 12 measurable quantities. (c) Using big ion etch pit data with 3n known variables, we can reconstruct three-dimensional three-vector electric and magnetic fields in laser-produced plasmas.
Figure 12 shows our conceptual image of three-vector electric and magnetic field reconstructions in 3D with the aid of AI. By replacing the RCF in Fig. 10 with the PNTD detector, we can obtain big ion etch pit data with ML or CNN. If the electric and magnetic field is known, then it is straightforward to calculate the ion trajectories [Fig. 12(a)]. However, we have to solve the inverse problem by using big ion etch pit data from the ions to reconstruct the unknown electric and magnetic field [Fig. 12(c)]. In general, this is not trivial. Here we are also implementing a neural network (NN) as shown in Fig. 12(b). At first, we numerically calculate ion trajectories under the influence of a known electric and magnetic field as in Fig. 12(a). Then, we train an NN with the ion information on the detector plane as inputs and the field information as outputs as in Fig. 12(b). We are planning to use Maxwell's equations and the equation of motion to evaluate the loss values.38 Finally, we apply the NN to the unknown field by providing the known ion etch pit information as in Fig. 12(c).
Schematic images of machine-aided reconstruction of vector electric and magnetic fields in three dimensions. (a) When and fields are known, it is easy to calculate ion trajectories (scattering problem). (b) Using known and fields and the relevant ion deflections, a neural network is trained to enforce the loss values by physical restrictions such as Maxwell's equations and the equation of motion. (c) Using the neural network, we reconstruct and fields in 3D from a large amount of ion etch pit data also obtained with the aid of AI (inverse scattering problem).
Schematic images of machine-aided reconstruction of vector electric and magnetic fields in three dimensions. (a) When and fields are known, it is easy to calculate ion trajectories (scattering problem). (b) Using known and fields and the relevant ion deflections, a neural network is trained to enforce the loss values by physical restrictions such as Maxwell's equations and the equation of motion. (c) Using the neural network, we reconstruct and fields in 3D from a large amount of ion etch pit data also obtained with the aid of AI (inverse scattering problem).
In order to realize this, we have started to implement NN for simplest cases.39 When we analyze ion radiographs with RCFs, we have to assume an electric field or magnetic field considering a simple geometry, such as a shock wave, and often obtain a specific component of electric or magnetic field in 2D. As discussed in Ref. 39, we are now able to determine a uniform electric or magnetic field using the data from two-ion etch pits. This means that we can reconstruct a 2D three-vector electric or magnetic field using ion etch pits. Furthermore, we are also able to distinguish uniform vector electric and magnetic fields using five-ion etch pits in 2D.39 A 2D, three-vector electromagnetic field reconstruction is already possible by assuming an average field along the ion trajectories. There are more data necessary to reconstruct the fields than that of mathematical prediction; however, since we can obtain large amounts of data using ML and CNN, this will not be a practical problem.
As the next step, we use 2D hydrodynamic (HD) or magnetohydrodynamic (MHD) simulations to produce shock waves and then produce 3D cylindrical symmetric numerical data from the 2D results. By using test particle simulations to calculate the particle deflection, we make a numerical ion radiograph providing relevant ion etch pit data. Using the numerical ion etch pits, i.e., the 2D positions and velocities at the detection plane, with the known electric or magnetic field from the HD or MHD simulations, we train NNs and inspect the vector electric and magnetic field relevant to the shock waves in 3D in the future. For example, we calculate laser–matter interaction with radiation (magneto)hydrodynamic [R(M)HD] simulations and map the results into (M)HD simulations with high resolutions to investigate KH (Richitmeyer–Meshkov) instabilities.2,40,41 In many laboratory experiments using nanosecond-long large laser facilities, it is still difficult to directly calculate the plasma generation via laser–matter interactions and hydrodynamic instabilities using particle-in-cell (PIC) simulations. A possible way to calculate more realistic electromagnetic fields is RHD simulations for laser–matter interactions and mapping the RHD results into a PIC simulation to calculate various types of instabilities. We are extending laboratory astrophysics using intense femtosecond-lasers to access relativistic regimes, where PIC can simulate through the plasma generation to the kinetic instability.17 We will apply the 3D three-vector electromagnetic field reconstruction using the PIC data, where we can directly calculate the electric and magnetic fields relevant to the instability.
Finally, by confirming the methodology works for synthetic numerical ion radiography, we will apply the NNs to experimental ion etch pits to reconstruct the 3D three-vector electric and magnetic fields in laser-produced plasmas. In experiments, one cannot confirm if the NN predictions are correct since there is no way to measure the 3D three-vector electromagnetic turbulence in laser-produced plasmas. As mentioned above, we will apply physics-informed neural networks (PINNs) where the loss values are evaluated by the physical laws, Maxwell's equations, and equations of motion.
As described in Sec. II, although a short-pulse laser can be unstable, a few megaelectron volt protons required for ion radiography are relatively stable. We can take a reference shot to measure the angular distribution, energy distribution, and velocity of ions easily.20 Then, we can trace back all the ion trajectories to find the initial conditions. We may assume an ideal initial condition as a point or region source representing most of the ion origins. This will be a future problem, but it is not an essential problem; we can assume statistically relevant initial conditions. The essential challenge is solving the inverse problem with huge data of ion trajectories with fully connected NNs. This is also a future issue.
V. DISCUSSIONS AND SUMMARY
We have been investigating space and astrophysical phenomena from nonrelativistic to relativistic regimes using intense short-pulse lasers. Intense lasers have typically a higher repetition rate than large, nanosecond-long, high-power lasers, and consequently, we have to analyze large amounts of data. Furthermore, although intense lasers can have many more shots than high-power lasers, intense lasers are less stable compared with long high-power lasers. To stabilize the intense laser system itself, we have started to implement artificial intelligence (AI) in laser experiments.
As the first step, we have introduced AI in laser-driven ion diagnostics with plastic nuclear track detectors (PNTDs).20 Even though machine learning provides us with much more data with high precision, there are still essential controlling parameters affecting prediction precision and recall, such as the training data from calibration experiments cannot be applied to data from laser experiments. In this paper, we introduce a convolutional neural network to solve this problem, where the prediction is more robust than that of conventional machine learning.
We introduce one of the applications using the resultant big ion data to reconstruct vector electric and magnetic fields in laser-produced plasmas in three dimensions with machine-aided ion radiography with PNTDs. So far, we have to assume a relatively simple geometry of electric or magnetic field to estimate, for example, shock electric field,2 and cannot distinguish the electric field from the magnetic field by single proton beams. A large number of ion etch pit data allows us to address this with the aid of a neural network.39 The machine-aided vector electric and magnetic field reconstruction in 3D will be a unique tool to investigate space and astrophysical phenomena in laboratories.
Finally, we discuss training data for CNN under various transforms such as rotation, translation, interpolation, and coarsening. Since the training data used to analyze the ion etch pit data are circular images, i.e., straight incident of ions into the PNTDs, the rotation of the training data does not affect the results. However, it would be important when we use the ion etch pit data for the reconstruction of 3D, three-vector electric and magnetic fields, since we have to analyze the deflected ion etch pit. To this end, we have to include the obliquely incident ions in the training data, requiring a conventional accelerator to control the incident angle. In this case, we need to rotate the images of the oblique incident ion etch pits to make the training data more robust. As mentioned in Ref. 20, the size of ion etch pits depends on the ion energy and species. The interpolation of the training data would be useful to automatically pick up various ion species with various energies. Up to now for the calibration experiments and laser ion acceleration experiments, we have to pick up specific ion species and energies to remove the background ions. Thus, we do not want to include a variety of ion etch pit sizes in training data, although it can be controlled depending on the applications. As explained in Sec. III, since the CNN treats the 2D images as 2D while the ML converts the data into 1D text and has pooling layers to extract the 2D characteristics of the 2D images, the CNN is more robust in terms of translation of the objects. As described in Ref. 20, we also apply a smoothing or blurring filter to coarsen the images to make the training data more robust for CNN. Automation of ion etch pit analyses for laser ion acceleration and its applications still needs trial and error; nevertheless, the CNN can be a solution for many ion acceleration experiments with intense lasers.
ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI (Grant Nos 19K21865, 19H00668, JPJSBP120203206, 20KK0064, JPJSBP120229940, 24H01816, and 22H01195), Core-to-Core Program (Nos. JPJSCCA2019002 and JPJSCCA20230003), the National Science and Technology Council of Taiwan (Grant Nos. 109-2628-M-008-004-MY3, 111-2111-M-006-005-MY2, 112-2811-M-006-009, 111-2112-M-006-011-MY3), the NINS program of Promoting Research by Networking among Institutions (Grant Nos. 01422301 and 102050NINS000312), and the Sumitomo Foundation, the Research Foundation For Opto-Science and Technology.
Nima Bolouki acknowledges that he was supported by the project LM2018097, funded by the Ministry of Education, Youth and Sports of the Czech Republic. Sadruddin Benkadda acknowledges financial support from the French Federation for Magnetic Fusion Studies (FR-FCM) and the Eurofusion Consortium, Search and Training Programme under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Y. Kuramitsu: Conceptualization (lead); Data curation (equal); Formal analysis (supporting); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Software (supporting); Supervision (lead); Validation (supporting); Visualization (lead); Writing – original draft (lead). T. Taguchi: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Visualization (lead). F. Nikaido: Data curation (equal); Formal analysis (equal); Validation (equal); Visualization (equal). T. Minami: Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Validation (lead); Writing – review & editing (equal). T. Hihara: Data curation (lead); Formal analysis (lead); Investigation (equal); Validation (equal). S. Suzuki: Data curation (equal). K. Oda: Data curation (equal). K. Kuramoto: Data curation (equal). T. Yasui: Data curation (equal). Y. Abe: Data curation (lead); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Supervision (equal). K. Ibano: Investigation (equal); Resources (equal). H. Takabe: Investigation (equal); Writing – review & editing (equal). C. M. Chu: Data curation (equal); Investigation (equal); Resources (equal). K. T. Wu: Data curation (equal); Investigation (equal); Resources (equal). W. Y. Woon: Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Supervision (equal). S. H. Chen: Investigation (equal). C. S. Jao: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal). Y. C. Chen: Investigation (equal); Methodology (equal); Resources (equal). Y. L. Liu: Funding acquisition (equal); Investigation (equal). A. Morace: Data curation (equal); Investigation (equal); Resources (equal). A. Yogo: Data curation (equal); Resources (equal). Y. Arikawa: Data curation (equal); Investigation (equal); Resources (equal). H. Kohri: Data curation (equal); Investigation (equal); Resources (equal). A. Tokiyasu: Data curation (equal); Investigation (equal); Resources (equal). S. Kodaira: Data curation (equal); Investigation (equal); Resources (equal); Supervision (equal). T. Kusumoto: Investigation (equal). M. Kanasaki: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal). T. Asai: Data curation (equal); Investigation (equal); Resources (equal). Y. Fukuda: Data curation (equal); Funding acquisition (lead); Investigation (equal); Supervision (equal). K. Kondo: Data curation (equal); Investigation (equal). H. Kiriyama: Data curation (equal); Investigation (equal). T. Hayakawa: Investigation (equal). S. Tanaka: Investigation (equal). S. Isayama: Investigation (equal). N. Watamura: Methodology (equal); Validation (equal). H. Suzuki: Conceptualization (equal); Methodology (equal). H. S. Kumar: Investigation (equal). N. Ohnishi: Investigation (equal); Supervision (equal). T. Pikuz: Investigation (equal). E. Filippov: Investigation (equal). K. Sakai: Data curation (equal); Investigation (equal). R. Yasuhara: Investigation (equal). M. Nakata: Investigation (equal). R. Ishikawa: Investigation (equal). T. Hoshi: Conceptualization (equal); Methodology (equal). A. Mizuta: Investigation (equal). N. Bolouki: Investigation (equal). N. Saura: Investigation (equal); Methodology (equal). S. Benkadda: Funding acquisition (equal); Investigation (equal); Supervision (equal). M. Koenig: Investigation (equal). S. Hamaguchi: Funding acquisition (lead); Investigation (equal); Methodology (equal); Supervision (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.