Electronic Stopping Power Research Articles

Study of modulation in complex refractive indices induced by ultrafast relativistic electrons using infrared and THz probe pulses.

Objective 
Achieving ultra-precise temporal resolution in ionizing radiation detection is essential, particularly in positron emission tomography, where precise timing enhances signal-to-noise ratios and may enable reconstruction-less imaging. A promising approach involves utilizing ultrafast modulation of the complex refractive index, where sending probe pulses to the detection crystals will result in changes in picoseconds (ps), and thus a sub - 10 ps coincidence time resolution can be realized. Towards this goal, here, we aim to first measure the ps changes in probe pulses using an ionizing radiation source with high time resolution.
Approach 
We used relativistic, ultrafast electrons to induce complex refractive index and use probe pulses in the near-infrared (800 nm) and terahertz (THz, 300 µm) regimes to test the hypothesized wavelength-squared increase in absorption coefficient in the Drude free-carrier absorption model. We measured BGO, ZnSe, BaF2, ZnS, PBG, and PWO with 1 mm thickness to control the deposited energy of the 3 MeV electrons, simulating ionization energy of the 511 keV photons. 
Main results 
Both with the 800 nm and THz probe pulses, transmission decreased across most samples, indicating the free carrier absorption, with an induced signal change of 11% in BaF2, but without the predicted Drude modulation increase. To understand this discrepancy, we simulated ionization tracks and examined the geometry of the free carrier distribution, attributing the mismatch in THz modulations to the sub-wavelength diameter of trajectories, despite the lengths reaching 500 µm to 1 mm. Additionally, thin samples truncated the final segments of the ionization tracks, and the measured initial segments have larger inter-inelastic collision distances due to lower stopping power (dE/dx) for high-energy electrons, exacerbating diffraction-limited resolution. 
Significance
Our work offers insights into ultrafast radiation detection using complex refractive index modulation and highlights critical considerations in sample preparation, probe wavelength, and probe-charge carrier coupling scenarios.

Prediction of electron-solid interaction parameters using machine learning.

Electron backscattering coefficient and electron-stopping power are essential concepts in many disciplines, from radiation to materials science, semiconductor manufacturing, and space exploration. They enable precise calculations, measurements, and simulations of electron interactions with matter, which contribute to advancing science, technology, and safety in a variety of applications. The availability of these data is fundamental to scientific research to validate hypotheses, conduct experiments, and explore new theories. A relatively novel machine learning approach has demonstrated notable success in enhancing data quality and completeness, significantly contributing to the facilitation of data discovery. Using fundamental material property data, the stacking ensemble machine learning (EML) technique was established in this study to generate electron-solid interaction parameters for any target material over a wide range of energies. The final stacking EML was built using the base and meta learners bagging regressor (BR), K-nearest neighbors (k-NN), random forest (RF), support vector regression (SVR), and eXtreme Gradient Boosting (XGB). In this study, two publicly available databases with a total of 4030 data points were used. Training datasets have 785 and 525 data points for electron backscattering coefficient and stopping power, respectively, whereas testing datasets contain 262 and 175 data points. Fivefeatures were used as input variables to train different individual algorithms and their combinations. On both the training and test datasets, the model was evaluated using different error metrics, including R-squared (R2), mean-absolute-error (MAE), root-mean-squared-error (RMSE), and mean-absolute-percentage-error (MAPE). Our model evaluation tests revealed that combining RF and XGB with a k-NN meta-learner outperformed other algorithms. The analysis of error metrics demonstrated a very close fit to all samples in each training dataset. Furthermore, predictions made by the model on unseen test data indicated accurate estimations of new backscattering and stopping power data. The developed model achieved high prediction accuracy for various target materials across the broad electron energy spectrum. The outcomes demonstrate the effectiveness of machine learning methodology and the chosen models' suitability for addressing substantial physics challenges.

Accelerating multiscale electronic stopping power predictions with time-dependent density functional theory and machine learning

Knowing the rate at which particle radiation releases energy in a material, the “stopping power,” is key to designing nuclear reactors, medical treatments, semiconductor and quantum materials, and many other technologies. While the nuclear contribution to stopping power, i.e., elastic scattering between atoms, is well understood in the literature, the route for gathering data on the electronic contribution has for decades remained costly and reliant on many simplifying assumptions, including that materials are isotropic. We establish a method that combines time-dependent density functional theory (TDDFT) and machine learning to reduce the time to assess new materials to hours on a supercomputer and provide valuable data on how atomic details influence electronic stopping. Our approach uses TDDFT to compute the electronic stopping from first principles in several directions and then machine learning to interpolate to other directions at a cost of 10 million times fewer core-hours. We demonstrate the combined approach in a study of proton irradiation in aluminum and employ it to predict how the depth of maximum energy deposition, the “Bragg Peak,” varies depending on the incident angle—a quantity otherwise inaccessible to modelers and far outside the scales of quantum mechanical simulations. The lack of any experimental information requirement makes our method applicable to most materials, and its speed makes it a prime candidate for enabling quantum-to-continuum models of radiation damage. The prospect of reusing valuable TDDFT data for training the model makes our approach appealing for applications in the age of materials data science.

The electronic stopping power of self-irradiated molybdenum in different charge states

Molybdenum is not only an excellent photovoltaic material but also a crucial component in semiconductors. However, its high bandgap restricts its application in optoelectronic devices. This limitation arises primarily because the energy barrier between photogenerated electron-hole pairs cannot be directly overcome by sunlight. Self-irradiation can overcome these barriers, allowing efficient separation of photogenerated electrons and holes, making molybdenum an excellent light-absorbing material. By altering the charge state of molybdenum-based materials, their light absorption can be adjusted. This project aims to systematically study the optical properties and electronic stopping power of molybdenum-based materials in different charge states through theoretical calculations and experiments.

Response of a high-pressure 4He scintillation detector to nuclear recoils up to 9 MeV

Helium-4-based scintillation detector technology is emerging as a strong alternative to pulse-shape discrimination-capable organic scintillators for fast neutron detection and spectroscopy, particularly in extreme gamma-ray environments. The 4He detector is intrinsically insensitive to gamma radiation, as it has a relatively low cross-section for gamma-ray interactions, and the stopping power of electrons in the 4He medium is low compared to that of 4He recoil nuclei. Consequently, gamma rays can be discriminated by simple energy deposition thresholding instead of the more complex pulse shape analysis. The energy resolution of 4He scintillation detectors has not yet been well-characterized over a broad range of energy depositions, which limits the ability to deconvolve the source spectra. In this work, an experiment was performed to characterize the response of an Arktis S670 4He detector to nuclear recoils up to 9 MeV. The 4He detector was positioned in the center of a semicircular array of organic scintillation detectors operated in coincidence. Deuterium–deuterium and deuterium–tritium neutron generators provided monoenergetic neutrons, yielding geometrically constrained nuclear recoils ranging from 0.0925 to 8.87 MeV. The detector response provides evidence for scintillation linearity beyond the previously reported energy range. The measured response was used to develop an energy resolution function applicable to this energy range for use in high-fidelity detector simulations needed by future applications.

Theoretical Study to Calculate the Radiation Stopping Power for Electrons in Human Tissues

Theoretical Study to Calculate the Radiation Stopping Power for Electrons in Human Tissues

Highly accurate ab initio electronic stopping power results for protons in Al material: a Lindhard stopping theory investigation

The main goal of this work is to enhance theoretical precision evaluations for the random electronic stopping power (RESP) of protons in solid targets across a wide range of energies, including low, intermediate, and high energies. The RESP of protons is investigated in different crystalline forms of Al material: FCC and two theoretical build structures (hexagonal and tetragonal). Initially, we divide the RESP calculations of protons in Al material into two individual contributions: one for the valence electrons and the other for the core electrons. Using this approach, we introduce a combination method that defines the total RESP as the sum of these contributions. We estimate the core electrons’ contribution to the RESP results within the local density approximation (LDA) based on the Lindhard stopping theory, where we calculate the density of Al material within the density functional theory (DFT) framework. We employ the RESP contribution of valence electrons as determined in our previous study within the linear response time-dependent density functional theory. We produce high-quality RESP results with the assistance of the combination method with low computational cost compared to other theoretical works. We test the accuracy of using the LDA based on Lindhard’s stopping model in calculating the RESP of protons in the Al target. In addition, within this approach, we investigate the influence of the crystal structure on core electrons’ contribution to the RESP.

Temperature Effects of Nuclear and Electronic Stopping Power on Si and C Radiation Damage in 3C-SiC.

Silicon carbide has been considered a material for use in the construction of advanced high-temperature nuclear reactors. However, one of the most important design issues for future reactors is the development of structural defects in SiC under a strong irradiation field at high temperatures. To understand how high temperatures affect radiation damage, SiC single crystals were irradiated at room temperature and after being heated to 800 °C with carbon and silicon ions of energies ranging between 0.5 and 21 MeV. The number of displaced atoms and the disorder parameters have been estimated by using the channeling Rutherford backscattering spectrometry. The experimentally determined depth profiles of induced defects at room temperature agree very well with theoretical calculations assuming its proportionality to the electronic and nuclear-stopping power values. On the other hand, a significant reduction in the number of crystal defects was observed for irradiations performed at high temperatures or for samples annealed after irradiation. Additionally, indications of saturation of the crystal defect concentration were observed for higher fluences and the irradiation of previously defected samples.

Time-dependent density-functional theory study on nonlocal electron stopping for inertial confinement fusion

Understanding laser–target coupling is of the utmost importance for achieving high performance in laser-direct-drive (LDD) inertial confinement fusion (ICF) experiments. Thus, accurate modeling of electron transport and deposition through ICF-relevant materials and conditions is necessary to quantify the total thermal conduction and ablation. The stopping range is a key transport quantity used in thermal conduction models; in this work, we review the overall role that the electron mean free path (MFP) plays in thermal conduction and hydrodynamic simulations. The currently used modified Lee–More model employs various physics approximations. We discuss a recent model that uses time-dependent density functional theory (TD-DFT) to eliminate these approximations in both the calculation of the electron stopping power and corresponding MFP in conduction zone polystyrene (CH) plasma. In general, the TD-DFT calculations showed a larger MFP (lower stopping power) than the standard modified Lee–More model. Using the TD-DFT results, an analytical model for the electron deposition range, λTD−DFT(ρ,T,K), was devised for CH plasmas between ρ=[0.05−1.05] g/cm3, kBT=[100−1000] eV. We implemented this model into LILAC, for simulations of a National Ignition Facility-scale LDD implosion and compared key physics quantities to ones obtained by simulations using the standard model. The implications of the obtained results and the path moving forward to calculate this same quantity in conduction-zone deuterium–tritium plasmas are further discussed, to hopefully close the understanding gap for laser target coupling in LDD-ICF simulations.

BEB-based models for ionisation cross sections of electron and positron impact with diatomic molecules

The ionising interactions of high-energy particles with molecules have applications in many areas. Despite this, some areas, including positron scattering, lack experimental data due to difficulties in performing experiments. Here, quick and simple methods for computing direct electron and positron impact ionisation cross sections are presented. These calculations, performed using the open-source software RAPID-CS, can provide a complete data set as a first approximation for when experimental, or more detailed computational work is not available. The cross-sectional data set includes the total, partial/fragment-specific, single-differential, average secondary electron energy and stopping power cross sections. The molecules N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}, O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and CO were chosen to study due to the availability of positron scattering data. An overall good agreement with experimental and other computational results is presented.Graphical abstractDirect electron (left) and positron right) impact partial ionisation cross sections for N2. Total cross section: red, N2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N^{+}_{2}$$\\end{document} partial cross section: blue, N+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+}$$\\end{document} partial cross section: green.electron: solid lines: BEB, experimental measurements by Lindsay and Mangan [36]:Ürosses, Straub et al. [37]: stars, Opel et al. [39]: squares. Positron: solid lines: BEB0, Dashed lines: BEBA, Marler and Surko [23]: red crosses, Bluhme et al. [24]: stars

Efficient computational modeling of electronic stopping power of organic polymers for proton therapy optimization

This comprehensive study delves into the intricate interplay between protons and organic polymers, offering insights into proton therapy in cancer treatment. Focusing on the influence of the spatial electron density distribution on stopping power estimates, we employed real-time time-dependent density functional theory coupled with the Penn method. Surprisingly, the assumption of electron density homogeneity in polymers is fundamentally flawed, resulting in an overestimation of stopping power values at energies below 2 MeV. Moreover, the Bragg rule application in specific compounds exhibited significant deviations from experimental data around the stopping maximum, challenging established norms.

Mechanisms of ion irradiation induced ordering in amorphous TiO2 nanotubes: Effects of ion mass and energy

Amorphous TiO2 nanotubes were irradiated in-situ in a transmission electron microscope (TEM) with Kr+ ions at energies of 46 keV, 150 keV, and 1 MeV and with 46 keV Xe+ ions, to investigate the structural and morphological evolution of the nanotubes under irradiation. At all irradiation conditions, amorphous TiO2 nanotubes exhibited significant morphological instability, and tended to undergo volumetric swelling with increasing ion counts, often until collapse of the original nanotube structure. Molecular dynamics (MD) simulations confirmed that irradiation-induced defects can explain the observed swelling. Structurally, nanotubes remain amorphous following all Kr+ irradiation conditions, but irradiation with 46 keV Xe+ leads to the formation of anatase nanocrystallites. Importantly, through systematically varying ion energy and ion species, we try to elucidate the influence of nuclear and electronic stopping power on ion irradiation induced changes. By contextualizing these results within the existing literature, we propose that the observed changes in TiO2 nanotube morphology and structure could be due to a competition between two mechanisms: (1) disorder-induced swelling and (2) irradiation-induced amorphous-to-crystalline transformation.

Modification of Cu Oxide and Cu Nitride Films by Energetic Ion Impact

We have investigated lattice disordering of cupper oxide (Cu2O) and copper nitride (Cu3N) films induced by high- and low-energy ion impact, knowing that the effects of electronic excitation and elastic collision play roles by these ions, respectively. For high-energy ion impact, degradation of X-ray diffraction (XRD) intensity per ion fluence or lattice disordering cross-section (YXD) fits to the power-law: YXD = (BXDSe)NXD, with Se and BXD being the electronic stopping power and a constant. For Cu2O and Cu3N, NXD is obtained to be 2.42 and 1.75, and BXD is 0.223 and 0.54 (kev/nm)−1. It appears that for low-energy ion impact, YXD is nearly proportional to the nuclear stopping power (Sn). The efficiency of energy deposition, YXD/Se, as well as Ysp/Se, is compared with YXD/Sn, as well as Ysp/Sn. The efficiency ratio RXD = (YXD/Se)/(YXD/Sn) is evaluated to be ~0.1 and ~0.2 at Se = 15 keV/nm for Cu2O and Cu3N, meaning that the efficiency of electronic energy deposition is smaller than that of nuclear energy deposition. Rsp = (Ysp/Se)/(Ysp/Sn) is evaluated to be 0.46 for Cu2O and 0.7 for Cu3N at Se = 15 keV/nm.

The IAEA electronic stopping power database: Modernization, review, and analysis of the existing experimental data

We review the electronic stopping power data within the IAEA database, assessing the abundance and scarcity of available data as a function of energy and collisional systems. Our analysis includes an examination of the experimental values, their evolution in time, the dispersion among data, and trends of the more recent measurements. Additionally, we provide comparisons with SRIM-2013 calculations for select cases of interest. Notably, we identify sparsely measured systems and energy regions, emphasizing the pressing need for new, reliable data and independent theoretical predictions.

Reproducibility of real-time time-dependent density functional theory calculations of electronic stopping power in warm dense matter

Real-time time-dependent density functional theory (TDDFT) is widely considered to be the most accurate available method for calculating electronic stopping powers from first principles, but there have been relatively few assessments of the consistency of its predictions across different implementations. This problem is particularly acute in the warm dense regime, where computational costs are high and experimental validation is rare and resource intensive. We report a comprehensive cross-verification of stopping power calculations in conditions relevant to inertial confinement fusion conducted using four different TDDFT implementations. We find excellent agreement among both the post-processed stopping powers and relevant time-resolved quantities for alpha particles in warm dense hydrogen. We also analyze sensitivities to a wide range of methodological details, including the exchange-correlation model, pseudopotentials, initial conditions, observable from which the stopping power is extracted, averaging procedures, projectile trajectory, and finite-size effects. We show that among these details, pseudopotentials, trajectory-dependence, and finite-size effects have the strongest influence, and we discuss different strategies for controlling the latter two considerations.

Simulations of stand-off runaway electron beam termination by tungsten particulates for tokamak disruption mitigation

Stand-off runaway electron termination by injected tungsten particulates offers a plausible option in the toolbox of disruption mitigation. Tungsten is an attractive material choice for this application due to large electron stopping power and high melting point. To assess the feasibility of this scheme, we simulate runaway collisions with tungsten particulates using the MCNP program for incident runaway energies ranging from 1 to 10 MeV. We assess runaway termination from energetics and collisional kinematics perspectives. Energetically, the simulations show that 99% of runaway beam energy is removed by tungsten particulates on a timescale of 4–9 µs. Kinematically, the simulations show that 99% of runaways are terminated by absorption or backscattering on a timescale of 3–4 µs. By either metric, the runaway beam is effectively terminated before the onset of particulate melting. Furthermore, the simulations show that secondary radiation emission by tungsten particulates does not significantly impact the runaway termination efficacy of this scheme. Secondary radiation is emitted at lower particle energies than the incident runaways and with a broad angular distribution such that the majority of secondary electrons emitted will not experience efficient runaway re-acceleration. Overall, the stand-off runaway termination scheme is a promising concept as a last line of defense against runaway damage in ITER, SPARC, and other future burning-plasma tokamaks.

Asynchronous propagation of atomic force and excited electronic charge in GaAs under proton irradiation

The studies for the interaction of energetic particles with matter have greatly contributed to the exploration of material properties under irradiation conditions, such as nuclear safety, medical physics and aerospace applications. In this work, we theoretically simulate the non-adiabatic process for GaAs upon proton irradiation using time-dependent density functional theory, and find that the radial propagation of force on atoms and the excitation of electron in GaAs are non-synchronous process. We calculated the electronic stopping power on proton with the velocity of 0.1–0.6 a.u., agreement with the previous empirical results. After further analyzing the force on atoms and the population of excited electrons, we find that under proton irradiation, the electrons around the host atoms at different distances from the proton trajectories are excited almost simultaneously, especially those regions with relatively high charge density. However, the distant atoms have a significant hysteresis in force, which occurs after the surrounding electrons are excited. In addition, hysteresis in force and electron excitation behavior at different positions are closely related to the velocity of proton. This non-synchronous propagation reveals the microscopic dynamic mechanism of energy deposition into the target material under ion irradiation.

Design Aspects of the Emittance Diagnostic for the Scorpius Accelerator

A multi-pulse linear induction accelerator, Scorpius, will be constructed at the NNSS U1A facility for use in radiographic experiments. One of the many diagnostics, the injector emittance diagnostic, will provide information on the quality of the beam emanating from the injector and therefore the quality of the beam in the accelerator. A slit-harp design was chosen for the emittance diagnostic. We have modeled the performance of the diagnostic for various simulated Scorpius beams, using several computational tools depending on the physics of the effects under investigation. Additional modeling of electron stopping power, energy deposition, heat dissipation, and x-ray attenuation drove material choices for the collimator jaws and harp wires. The signal chain is designed around constraints of signal extraction, biasing to suppress crosstalk between harp wires via secondary electron emission, and multi-pulse record capability. The ensemble of materials, electrical, and mechanical aspects of the design to reconstruct the emittance from the injector of the accelerator are described.

Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions

The autoionization states formation due to MO promotion during collisions of keV-energy ions with solids produces a dominant contribution to inelastic energy losses and, accordingly, to the electronic stopping powers dE/dx. The correlations of emitted electron numbers δ with the values of inelastic energy losses Q are shown. When corresponding distances of closest approach are reached, the MO orbital promotion produces a stepwise increase in values of Q and δ. Based on the measured ionization cross-sections and Q values, electronic stopping powers can be calculated. For the case when such measurements are not available, the scaling for the ionization cross section in the case of K, L and M shell excitation can be used.We have proposed a new model for calculating electronic stopping power in which the formation of autoionization states in atomic collisions makes a dominant contribution to the inelastic energy loss and ionization of colliding atoms. Using data on the values of energy losses and ionization cross sections, it is possible to calculate the values of electronic stopping. The model predicts the threshold character of the dE/dx dependence versus the collision velocity and an increase in inelastic energy losses at the collision energies at which the threshold for the corresponding MO promotion occurs.

Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions

The autoionization states formation due to MO promotion during collisions of keV-energy ions with solids produces a dominant contribution to inelastic energy losses and, accordingly, to the electronic stopping powers dE/dx. The correlations of emitted electron numbers δ with the values of inelastic energy losses Q are shown. When corresponding distances of closest approach are reached, the MO orbital promotion produces a stepwise increase in values of Q and δ. Based on the measured ionization cross-sections and Q values, electronic stopping powers can be calculated. For the case when such measurements are not available, the scaling for the ionization cross section in the case of K, L and M shell excitation can be used.We have proposed a new model for calculating electronic stopping power in which the formation of autoionization states in atomic collisions makes a dominant contribution to the inelastic energy loss and ionization of colliding atoms. Using data on the values of energy losses and ionization cross sections, it is possible to calculate the values of electronic stopping. The model predicts the threshold character of the dE/dx dependence versus the collision velocity and an increase in inelastic energy losses at the collision energies at which the threshold for the corresponding MO promotion occurs.