Stopping Power Calculations Research Articles

Nanodosimetric investigation of the track structure of therapeutic carbon ion radiation part 1: measurement of ionization cluster size distributions

At the Heidelberg Ion-Beam Therapy Center, the track structure of carbon ions of therapeutic energy after penetrating layers of simulated tissue was investigated for the first time. Measurements were conducted with carbon ion beams of different energies and polymethyl methacrylate (PMMA) absorbers of different thicknesses to realize different depths in the phantom along the pristine Bragg peak. Ionization cluster size (ICS) distributions resulting from the mixed radiation field behind the PMMA absorbers were measured using an ion-counting nanodosimeter. Two different measurements were carried out: (i) variation of the PMMA absorber thickness with constant carbon ion beam energy and (ii) combined variation of PMMA absorber thickness and carbon ion beam energy such that the kinetic energy of the carbon ions in the target volume is constant. The data analysis revealed unexpectedly high mean ICS values compared to stopping power calculations and the data measured at lower energies in earlier work. This suggests that in the measurements the carbon ion kinetic energies behind the PMMA absorber may have deviated considerably from the expected values obtained by the calculations. In addition, the results indicate the presence of a marked contribution of nuclear fragments to the measured ICS distributions, especially if the carbon ion does not cross the target volume.

Temperature and structure measurements of heavy-ion-heated diamond using in situ X-ray diagnostics

We present in situ measurements of spectrally resolved X-ray scattering and X-ray diffraction from monocrystalline diamond samples heated with an intense pulse of heavy ions. In this way, we determine the samples’ heating dynamics and their microscopic and macroscopic structural integrity over a timespan of several microseconds. Connecting the ratio of elastic to inelastic scattering with state-of-the-art density functional theory molecular dynamics simulations allows the inference of average temperatures around 1300 K, in agreement with predictions from stopping power calculations. The simultaneous diffraction measurements show no hints of any volumetric graphitization of the material, but do indicate the onset of fracture in the diamond sample. Our experiments pave the way for future studies at the Facility for Antiproton and Ion Research, where a substantially increased intensity of the heavy ion beam will be available.

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.

Quantum computation of stopping power for inertial fusion target design

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it-one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quant. 2, 040332 (2021)], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with an implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.

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.

Calculations of mass stopping power and range of protons in organic compounds (CH3OH, CH2O, and CO2) at energy range of 0.01–1,000 MeV

Calculations of mass stopping power and range of protons in organic compounds (CH₃OH, CH₂O, and CO₂) at energy range of 0.01–1,000 MeV

Ion beam-induced Surface Modification of PVC: A simulation Study

Ion beam-induced Surface Modification of PVC: A simulation Study

Validation of the single-event method for low-energy electron transport via stopping power calculations with MCNP

Monte Carlo simulations of low-energy (<50 keV) electron transport in matter are essential for a broad range of application fields. Several Monte Carlo codes have developed specialized treatments for this case, but a comprehensive validation of low-energy electron transport for general-purpose simulations remains lacking in the literature. One approach to accomplish this validation is calculation of stopping power using low-energy electron transport physics, as stopping power is a fundamental radiation transport quantity which must be simulated accurately for nearly any application. In this work, we use the Monte Carlo N-Particle (MCNP) radiation transport code with the single-event method for electron transport to calculate stopping powers of low-energy electrons (50 eV to 30 keV) in 41 elemental solids, 14 compound solids, and five rare gas solids, comparing simulation results to published semi-empirical stopping power calculations from optical measurements. In general, the simulations give good agreement (typically within ±10%) with semi-empirical stopping power values at higher energies: 300 eV and above for most elemental solids, 1 keV and above for compound solids, and 400 eV and above for rare gas solids. Agreement between MCNP and semi-empirical values is worse below these energies. The most significant source of error is the EPRDATA14 cross section data, which does not account for changes in electronic structure due to solid-state bonding, particularly in compound materials. The simplistic model of atomic excitation used to generate the EPRDATA14 cross sections is another key source of error. Additionally, the breakdown of the continuous slowing-down approximation introduces significant uncertainty at low energies, although this is a limitation of the calculation method and not of the simulation procedure. Accounting for these and other uncertainty sources, the single event method in MCNP is robust and able to give good accuracy for a variety of low-energy electron transport problems through diverse kinds of materials.

Trajectory sampling and finite-size effects in first-principles stopping power calculations

Real-time time-dependent density functional theory (TDDFT) is presently the most accurate available method for computing electronic stopping powers from first principles. However, obtaining application-relevant results often involves either costly averages over multiple calculations or ad hoc selection of a representative ion trajectory. We consider a broadly applicable, quantitative metric for evaluating and optimizing trajectories in this context. This methodology enables rigorous analysis of the failure modes of various common trajectory choices in crystalline materials. Although randomly selecting trajectories is common practice in stopping power calculations in solids, we show that nearly 30% of random trajectories in an FCC aluminum crystal will not representatively sample the material over the time and length scales feasibly simulated with TDDFT, and unrepresentative choices incur errors of up to 60%. We also show that finite-size effects depend on ion trajectory via “ouroboros” effects beyond the prevailing plasmon-based interpretation, and we propose a cost-reducing scheme to obtain converged results even when expensive core-electron contributions preclude large supercells. This work helps to mitigate poorly controlled approximations in first-principles stopping power calculations, allowing 1–2 order of magnitude cost reductions for obtaining representatively averaged and converged results.

Calculation of the electron stopping power of some components of human body tissues

The stopping power of the target material is an essential variable for evaluating the effects of radiation. In this study, the stopping power for an electron that interacts with some components of human body tissues (H, C, N, O, Na, P, S, Cl, K, Ca, Fe, I) was calculated using two methods: The Beth formula and the ESTAR code, in the energy range 0.01–1000 ​MeV. The total stopping power of these elements was calculated by adding their collisional stopping power to their radiative stopping power. The results from both methods were in good agreement. A semi-empirical formula was found to compute the total electron stopping power of electrons of these targets for a given electron energy. Our stopping power values show good agreement with ICRU 37 (1984).

Calculation of Electron Stopping Power in Some Material Targets Using New Mass-Energy Concept

Calculation of Electron Stopping Power in Some Material Targets Using New Mass-Energy Concept

Stopping Power Calculation of Protons and α–Particles for C2H4 and C6H6 in Energy Range 0.01-1000 MeV

In this research, a theoretical study was conducted to calculate the total stopping power of some relativistic heavy ions (protons and alpha particles) during their passage through some media (ethylene and benzene) in the energy range (0.01-1000 MeV). The equations were programmed using MATLAB2021, the curve fitting tool was used, and the calculated results were compared with the experimental data of the P- Star and A-Star programs for the same missiles in those organic compounds.

Energy deposition and formation of nanostructures in the interaction of highly charged xenon ions with gold nanolayers

The effect of the deposition of kinetic energy and neutralization energy of slow highly charged xenon ions on the process of the nanostructures creation at the surface of gold nanolayers is investigated. The nanolayers of thickness of 100 nm were prepared by e-beam evaporation of gold on crystalline silicon Si(100) substrate. The samples were irradiated at the Kielce EBIS facility of the Jan Kochanowski University (Kielce, Poland), under high vacuum conditions. The irradiations were performed for constant kinetic energy 280 keV and different ions charge states (Xeq+, q = 25, 30, 35, 36 and 40) and for constant charge state Xe35+ and different kinetic energies: 280 keV, 360 keV, 420 keV and 480 keV. The fluence of the ions was on the level of 1010 ions/cm2. Before and after irradiation the nanolayer surfaces were investigated using the atomic force microscope.As the result, well pronounced modifications of the nanolayer surfaces in the form of craters have been observed. A systematic analysis of the crater sizes (diameter on the surface and depth) allowed us to determine the influence of the deposited kinetic and the neutralization energy on the size of the obtained nanostructures. The results are theoretically interpreted within the micro-staircase model based on the quantum two-state vector model of the ionic Rydberg states population. The charge dependent ion–atom interaction potential inside the solid is used for the calculation of the nuclear stopping power. According to the model the formation of the nanostructures is governed by the processes of the ionic neutralization in front of the surface and the kinetic energy loss inside the solid. The interplay of these two types of processes in the surface structure creation is described by the critical velocity. Using the proposed theoretical model, the neutralization energy, deposited kinetic energy and critical velocities were calculated and compared qualitatively with the experimental results. The results are consistent (after normalization) with previous experimental data and molecular dynamics simulations for single ionized Xe and crystalline gold surface.

Precise measurement of the Bragg curve for 800 MeV/u 238U ions stopping in polyethylene and its implications for calculation of heavy ion ranges

Stopping power predictions in radiation transport codes are based on the Bethe-Bloch formula and different corrections. For very heavy ions at relativistic energies the available experimental data are scarce and therefore verification of stopping power predictions is only possible to a limited extent.In this work, a full experimental Bragg curve for 800 MeV/u 238U ions stopping in polyethylene is presented. The measurements were conducted at the experimental area Cave A at GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany. The 800 MeV/u 238U beam was provided by the SIS18 heavy ion synchrotron. The Bragg curve was measured with a setup consisting of a binary range shifter and two large area parallel plate ionization chambers. Complementary Monte Carlo simulations using the FLUKA code were performed and compared with the experimental Bragg curve. The mean ionization potential of polyethylene was fine-tuned to match the measured primary ion range with FLUKA simulations. The impact of the Bloch and Mott corrections to the stopping power calculation were studied by switching them off intentionally in separate simulations. A detailed description of the implementation of the stopping power formulae and the Mott correction in FLUKA is provided.Supplementary data for this article is available online.

Ab initio electronic stationary states for nuclear projectiles in solids

The process by which a nuclear projectile is decelerated by the electrons of the condensed matter it traverses is currently being studied by following the explicit dynamics of projectile and electrons from first principles in a simulation box with a sample of the host matter in periodic boundary conditions. The approach has been quite successful for diverse systems even in the strong-coupling regime of maximal dissipation. This technique is here revisited for periodic solids in light of the Floquet theory of stopping, a time-periodic scattering framework characterizing the stationary dynamical solutions for a constant velocity projectile in an infinite solid. The effect of proton projectiles in diamond is studied under that light, using time-dependent density-functional theory in real time. The Floquet quasienergy-conserving stationary scattering regime, characterized by time-periodic properties such as particle density and the time derivative of energy, is obtained for a converged system size of 1000 atoms. The validity of the customary calculation of electronic stopping power from the average slope of the density-functional total energy is discussed. Quasienergy conservation, as well as the implied fundamental approximations, are critically reviewed.

Nonadiabatic energy transfer in single wall carbon nanotube upon H+ irradiation from time-dependent density-functional theory

Accurate calculations of electronic stopping power (ESP) are critical to understanding ion–solid interactions for charged particle slowing down in materials. Basing on the nonadiabatic results from the time-dependent density-functional theory (TDDFT) for H ion intruding through single wall carbon nanotubes, we analyze and quantify the strength of the ion–solid interaction by tracking the momentum of the target atom. The slow-moving H is subjected to a friction force when the ion–solid interaction is weak. When the interaction is strong, the electrons in tube are excited and the coulomb repulsion between H ion and target atoms gradually dominates. A piecewise fitting physical model for ESP as a function of the impact parameter is built to show the dependency of ESP on impact parameters. These results explain energy loss of charged particles in matter at high-speed or large off-channel condition and provide a basis for understanding ion–solid interactions in more complex systems.

Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.

Calculations on the stopping power of the warm dense matter at the Bragg peak

This work aims to be useful for future experiments providing hydrodynamic and stopping power calculations to warm dense matter (WDM) analysis. For this purpose, the hydrodynamic simulations have been carried out using MULTI-fs code. Key plasma parameters - e.g., electron temperature, mass density, ionization, etc- have been studied at different expansion times to show the WDM behavior. Thanks to these data from the hydrodynamic simulations, precise stopping power calculations can be performed. A comparison is made between our present stopping power model with other models in the literature at the Bragg peak. Specifically, proton energy loss is estimated in carbon at a WDM state described by the hydrodynamic simulations. As the Bragg peak is the energy range where most differences arise between theoretical stopping power models, an experiment of the characteristics here described could be useful to differentiate between these models and to test their validity in the WDM regime.

Software for standard-based analysis of thick target PIGE data

Software, “SyrPIGE”, has been developed to perform particle induced γ-ray emission (PIGE) data analysis of thick targets relying on a standard-based method. It allows self-consistent and direct analysis of PIGE data considering easy calibration of PIGE spectra, on-screen identification of every γ-ray line, manual input or evaluation of E12 values for every element at established γ-ray energies, direct generation of stopping power data based on built-in electronic stopping power calculations for protons, ability to compare results with standards and batch mode analysis capability. The software was tested on standards and showed reliable and consistent results, with PIGE data analysis performed in a very short time compared with time-consuming traditional analysis.

Study of Stopping Power of Electron in Human Tissues

Charged particles lose energy by nuclear interactions during their passing in material are very significant and useful especially in nuclear therapy. We used Bethe-Bloch equation programmed with Matlab and compared the results with E-star program. There are calculated total stopping power (collisional and radiative stopping power) for electron in tissues (Brain and Lung) by considering that each tissue consists of several elements; the total stopping power was measured for those elements within the energy range from 0.01-1000 MeV, taking into account the density correction used in the stopping power calculation. Results are presented and compared with the latest published data.