Energy Distribution Of Protons Research Articles

Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy.

The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.

Dependence of single event upsets sensitivity of low energy proton on test factors in 65 nm SRAM**Project supported by the Major Program of the National Natural Science Foundation of China (Grant Nos. 11690040 and 11690043).

In order to accurately predict the single event upsets (SEU) rate of on-orbit proton, the influence of the proton energy distribution, incident angle, supply voltage, and test pattern on the height, width, and position of SEU peak of low energy protons (LEP) in 65 nm static random access memory (SRAM) are quantitatively evaluated and analyzed based on LEP testing data and Monte Carlo simulation. The results show that different initial proton energies used to degrade the beam energy will bring about the difference in the energy distribution of average proton energy at the surface and sensitive region of the device under test (DUT), which further leads to significant differences including the height of SEU peak and the threshold energy of SEU. Using the lowest initial proton energy is extremely important for SEU testing with low energy protons. The proton energy corresponding to the SEU peak shifts to higher average proton energies with the increase of the tilt angle, and the SEU peaks also increase significantly. The reduction of supply voltage lowers the critical charge of SEU, leading to the increase of LEP SEU cross section. For standard 6-transitor SRAM with bit-interleaving technology, SEU peak does not show clear dependence on three test patterns of logical checkerboard 55H, all “1”, and all “0”. It should be noted that all the SEUs in 65 nm SRAM are single cell upset in LEP testing due to proton’s low linear energy transfer (LET) value.

A system for online beam emittance measurements and proton beam characterization

A system for online measurement of the transverse beam emittance was developed. It is named 4PrOBεaM (4-Profiler Online Beam Emittance Measurement) and was conceived to measure the emittance in a fast and efficient way using the multiple beam profiler method. The core of the system is constituted by four consecutive UniBEaM profilers, which are based on silica fibers passing across the beam. The 4PrOBεaM system was deployed for characterization studies of the 18 MeV proton beam produced by the IBA Cyclone 18 MeV cyclotron at Bern University Hospital (Inselspital). The machine serves daily radioisotope production and multi-disciplinary research, which is carried out with a specifically conceived Beam Transport Line (BTL). The transverse RMS beam emittance of the cyclotron was measured as a function of several machine parameters, such as the magnetic field, RF peak voltage, and azimuthal angle of the stripper. The beam emittance was also measured using the method based on the quadrupole strength variation. The results obtained with both techniques were compared and a good agreement was found. In order to characterize the longitudinal dynamics, the proton energy distribution was measured. For this purpose, a method was developed based on aluminum absorbers of different thicknesses, a UniBEaM detector, and a Faraday cup. The results were an input for a simulation of the BTL developed in the MAD-X software. This tool allows machine parameters to be tuned online and the beam characteristics to be optimized for specific applications.

Considerations on employing a PMQ-doublet for narrow and broad proton energy distributions

Abstract We simulated a doublet of permanent magnet quadrupoles (PMQs) to estimate the sensitivity on positioning precision and its impact on the spectral properties of transported protons. The study guided the construction and testing of a focusing setup for laser-accelerated proton bunches with energies between 6 and 10 MeV. Our results shed light on possible applications that may arise from broad input particle spectra.

Laser radiation pressure proton acceleration in gaseous target

An analytical model for hole boring proton acceleration by a circularly-polarized CO2 laser pulse in a gas jet is developed. The plasma density profile near the density peak is taken to be rectangular, with inner region thickness l around a laser wavelength and density 10% above the critical, while the outside density is 10% below the critical. On the rear side, plasma density falls off rapidly to a small value. The laser suffers strong reflection from the central region and, at normalized amplitude a0≥1, creates a double layer. The space charge field of the double layer, moving with velocity vfzˆ, reflects up-stream protons to 2vf velocity, incurring momentum loss at a rate comparable to radiation pressure. Reflection occurs for vf≤ωpzflm/mp, where m and mp are the electron and proton masses, zf is the distance traveled by the compressed electron layer and ωp is the plasma frequency. For Gaussian temporal profile of the laser and parabolic density profile of the upstream plasma, the proton energy distribution is narrowly peaked.

Anomalous Distributions of Primary Cosmic Rays as Evidence for Time-dependent Particle Acceleration in Supernova Remnants

Abstract Recent precise measurements of cosmic-ray (CR) spectra show that the energy distribution of protons is softer than those of heavier nuclei, and there are spectral hardenings for all nuclear compositions above ∼200 GV. Models proposed for these anomalies generally assume steady-state solutions of the particle acceleration process. We show that if the diffusion coefficient has a weak dependence on the particle rigidity near shock fronts of supernova remnants (SNRs), time-dependent solutions of the linear diffusive shock acceleration at two stages of SNR evolution can naturally account for these anomalies. The high-energy component of CRs is dominated by acceleration in the free expansion and adiabatic phases with enriched heavy elements and a high shock speed. The low-energy component may be attributed to acceleration by slow shocks propagating in dense molecular clouds with low metallicity in the radiative phase. Instead of a single power-law distribution, the spectra of time-dependent solutions soften gradually with the increase of energy, which may be responsible for the “knee” of CRs.

Validating internal electron and proton energy configurations via a theoretical derivation of the mass ratio mp/me

<p><strong>Background:</strong> There are no particle models giving theoretical rest mass energy values for the electron or proton, and their internal energy configurations are unknown. Consequently there is no theoretical basis for the proton/electron rest mass ratio m<sub>p/</sub>m<sub>e</sub>. Previous articles established both electrons and protons consist of quantum loops of the same 6.8MeV base quantum energy, albeit in different relativistic states.</p><p><strong>Methods:</strong> Prior work is extended by considering internal particle energy cross coupling factors to derive detailed theoretical expressions for the internal energy distributions of electrons and protons. These expressions consist of the base quantum energy modified by terms containing only relativistic factors of the fine structure constant, α ~ 1/137. For m<sub>p</sub>/m<sub>e</sub> the base quantum energy cancels and the derived mass ratio is given by the particle’s internal quantum loop relativistic states. The derived mass ratio is compared to the empirical value. Newton’s gravitational constant, G, is calculated from the electron internal energy configuration.</p><p><strong>Results:</strong> Derived particle energy configurations give proton mass and proton/electron mass ratio values fully consistent with empirical data. The common base quantum loop energy is obtained to 6ppm. Combining particle mass energy expressions gives m<sub>p</sub>/m<sub>e</sub> to ten digits and consistent with the 2014 CODATA value via an expression containing only the fine structure constant. A theoretical value for Newton’s gravitational constant is obtained to an uncertainty of 6ppb. The Hierarchy problem is resolved, and the Planck scale of matter is adjusted. </p><p><strong>Conclusions:</strong> The particle energy configurations are validated by providing particle mass energy values and a proton/electron mass ratio consistent with empirical data. Newton’s G is shown not a natural constant, and misunderstanding its nature gave rise to the Hierarchy problem and an erroneous value for the Planck scale of matter, both now resolved.</p>

Channeling of protons in radially compressed chiral carbon nanotubes

Channeling of 10MeV protons in various types of point and area radially compressed chiral carbon nanotubes (CNTs) is considered. Monte Carlo simulation program is used for the calculation of the trajectories, energy losses and angular distributions of protons in (6,4) and (11,9) CNTs of 2000nm length, where the potential in Doyle-Turner approximation is used to describe the interaction between a proton and a nanotube. Carbon nanotubes, which are considered, are radially compressed at two points (500nm and 1500nm each), at a middle area of various lengths, at three points (both ends and at the centre) and at both ends with a middle area remaining uncompressed. The results show that in a specific case of compressed nanotube a decreased angular distribution of the beam is observed, compared even with propagation in a straight uncompressed nanotube. Furthermore, the energy distribution of channeled protons depends on the type of compression.

Proton acceleration by irradiation of isolated spheres with an intense laser pulse.

We report on experiments irradiating isolated plastic spheres with a peak laser intensity of 2-3×10^{20}Wcm^{-2}. With a laser focal spot size of 10μm full width half maximum (FWHM) the sphere diameter was varied between 520 nm and 19.3μm. Maximum proton energies of ∼25 MeV are achieved for targets matching the focal spot size of 10μm in diameter or being slightly smaller. For smaller spheres the kinetic energy distributions of protons become nonmonotonic, indicating a change in the accelerating mechanism from ambipolar expansion towards a regime dominated by effects caused by Coulomb repulsion of ions. The energy conversion efficiency from laser energy to proton kinetic energy is optimized when the target diameter matches the laser focal spot size with efficiencies reaching the percent level. The change of proton acceleration efficiency with target size can be attributed to the reduced cross-sectional overlap of subfocus targets with the laser. Reported experimental observations are in line with 3D3V particle in cell simulations. They make use of well-defined targets and point out pathways for future applications and experiments.

Characteristics of Protons Exiting from a Polyethylene Converter Irradiated by Neutrons with Energies between 1 keV and 10 MeV

Monte Carlo method has been used to determine the efficiency for proton production and to study the energy and angular distributions of the generated protons. The ENDF library of cross sections is used to simulate the interactions between the neutrons and the atoms in a polyethylene (PE) layer, while the ranges of protons with different energies in PE are determined using the Stopping and Range of Ions in Matter (SRIM) computer code. The efficiency of proton production increases with the PE layer thickness. However the proton escaping from a certain polyethylene volume is highly dependent on the neutron energy and target thickness, except for a very thin PE layer. The energy and angular distributions of protons are also estimated in the present paper, showing that, for the range of energy and thickness considered, the proton flux escaping is dependent on the PE layer thickness, with the presence of an optimal thickness for a fixed primary neutron energy.

TU‐H‐CAMPUS‐TeP3‐03: Dose Enhancement by Gold Nanoparticles Around the Bragg Peak of Proton Beams

Purpose:To make clear the spatial distribution of dose enhancement around gold nanoparticles (GNPs) located near the proton Bragg peak, and to evaluate the potential of GNPs as a radio sensitizer.Methods:The dose enhancement by electrons emitted from GNPs under proton irradiation was estimated by Geant4 Monte Carlo simulation toolkit in two steps. In an initial macroscopic step, 100 and 195 MeV proton beams were incident on a water cube, 30 cm on a side. Energy distributions of protons were calculated at four depths, 50% and 75% proximal to the Bragg peak, 100% peak, and 75% distal to the peak (P50, P75, Peak, and D75, respectively). In a subsequent microscopic step, protons with the energy distribution calculated above were incident on a 20 nm diameter GNP in a nanometer‐size water box and the spatial distribution of dose around the GNP was determined for each energy distribution. The dose enhancement factor (DEF) was also deduced.Results:The dose enhancement effect was spread to several tens of nanometers in the both depth and radial directions. The enhancement area increased in the order of P50, P75, Peak, and D75 for both cases with 100 and 195 MeV protons. In every position around the Bragg peak, the 100 MeV beam resulted in a higher dose enhancement than the 195 MeV beam. At P75, the average and maximum DEF were 3.9 and 17.0 for 100 MeV, and 3.5 and 16.2 for 195 MeV, respectively. These results indicate that lower energy protons caused higher dose enhancement in this incident proton energy range.Conclusion:The dose enhancement around GNPs spread as the position in the Bragg peak region becomes deeper and depends on proton energy. It is expected that GNPs can be used as a radio sensitizer with consideration of the location and proton beam energy.

Енергетичні розподіли протонів у d(d,p) реакції

Енергетичні розподіли протонів у d(d,p) реакції

POES MEPED differential flux retrievals and electron channel contamination correction

AbstractA correction method to remove proton contamination from the electron channels of the Polar‐orbiting Operational Environmental Satellites Medium Energy Proton/Electron Detector (MEPED) is described. Proton contamination estimates are based on measurements in five of the MEPED proton spectral channels. A constrained inversion of the MEPED proton channel response function matrix is used to calculate proton differential flux spectra. In this inversion, the proton energy distribution is described by a weighted combination of exponential, power law, and Maxwellian distributions. Proton contamination in the MEPED electron spectral channels is derived by applying the electron channel proton sensitivities to the proton fluxes from the best fit proton spectra. Once the electron channel measurements are corrected for proton contamination, an inversion of the electron channel response function matrix is used to calculate electron differential flux spectra. A side benefit of the method is that it yields an estimate for the integrated electron flux in the energy range from 300 keV to 2.5 MeV with a center energy at ~800 keV. The final product is a differential spectrum of electron flux covering the energy range from about 10 keV to 2.5 MeV that is devoid of proton contamination except during large solar proton events. Comparisons of corrected MEPED differential fluxes to the Detection of Electromagnetic Emissions Transmitted from Earthquake Regions Instrument for Detecting Particles show that MEPED fluxes are greater than what is expected from altitude‐induced particle population changes; this is attributed at least partially to measurement differences in pitch angle range.

Multiple scattering of proton via stochastic differential equations

Multiple scattering of protons through a target is explained by a set of coupled stochastic differential equations. The motion of protons in matter is calculated by analytical random sampling from Moliere and Landau probability density functions (PDF). To satisfy the Vavilov theory, the moments for energy distribution of a 49.1MeV proton beam in aluminum target are obtained. The skewness for the PDF of energy demonstrates that the energy distribution of protons in thin thickness becomes a Landau function, whereas, by increasing the thickness of the target it does not follow a Gaussian function completely. Afterwards, the depth-dose distributions are calculated for a 60MeV proton beam traversing soft tissue and for a 160MeV proton beam travelling through water. The results prove that when elastic scattering is taken into account, the Bragg-peak position is decreased, while the dose deposited in the Bragg region is increased. The results obtained in this article are benchmarked by comparison of our results with the experimental data reported in the literature.

Measurement of the stochastic radial dose distribution for a 30-MeV proton beam using a wall-less tissue-equivalent proportional counter.

The frequency distribution of the lineal energy, y, of a 30-MeV proton beam was measured as a function of the radial distance from the beam path, and the dosed mean of y, y¯(D), was obtained to investigate the radial dependence of y¯(D). A wall-less tissue-equivalent proportional counter, in a cylindrical volume with simulated diameters of 0.36, 0.72 and 1.44 µm was used for the measurement of y distributions, yf(y). The measured values of yf(y) summed in the radial direction agreed fairly well with the corresponding data taken from the microdosimetric calculations using the PHITS code. The y¯(D) value of the 30-MeV proton beam presented its smallest value at r = 0.0 and gradually increased with radial distance, and the y¯(D) values of heavy ions such as iron showed rapid decrease with radial distance. This experimental result demonstrated that the stochastic deposited energy distribution of high-energy protons in the microscopic region is rather constant in the core as well as in the penumbra region of the track structure.

Microdosimetry of the full slowing down of protons using Monte Carlo track structure simulations.

The article investigates two approaches in microdosimetric calculations based on Monte Carlo track structure (MCTS) simulations of a 160-MeV proton beam. In the first approach, microdosimetric parameters of the proton beam were obtained using the weighted sum of proton energy distributions and microdosimetric parameters of proton track segments (TSMs). In the second approach, phase spaces of energy depositions obtained using MCTS simulations in the full slowing down (FSD) mode were used for the microdosimetric calculations. Targets of interest were water cylinders of 2.3-100 nm in diameters and heights. Frequency-averaged lineal energies ([Formula: see text]) obtained using both approaches agreed within the statistical uncertainties. Discrepancies beyond this level were observed for dose-averaged lineal energies ([Formula: see text]) towards the Bragg peak region due to the small number of proton energies used in the TSM approach and different energy deposition patterns in the TSM and FSD of protons.

Channeling of protons in various types of radially compressed carbon nanotubes

Channeling of 10MeV protons in various types of radially compressed chiral carbon nanotubes is considered. Monte Carlo simulation program is used for the calculation of the trajectories, energy losses and angular distributions of protons in nanotubes of various lengths, where the potential in Doyle–Turner approximation is used to describe the interaction between a proton and a nanotube. Carbon nanotubes, which are considered, are radially compressed at the centre or at both ends. The results show that in some cases a decreased angular distribution of the beam is observed, compared with propagation through a straight nanotube. Furthermore, the energy distribution of channeled protons in nanotubes present a series of small peaks besides a main one, the number of which depends on the nanotube length and the angle of incidence, which in some cases are significantly high.

Theory of two-step two-proton decays of nuclei

A general theory of many-body diagonal and nondiagonal one-proton decays of spherical and deformed nuclei is developed on the basis of an approach not employing R-matrix theory in describing deep-subbarrier alpha and one-proton decays of nuclei but relying on integral formulas for the widths with respect to these decays. With the aid of this theory and by means of a diagram technique, a formalism is developed for describing two-step two-proton decays of a (Z, A) parent nucleus, which proceed as two successive time-separated one-proton decays of the parent and intermediate [(Z − 1, A − 1)] nuclei, these decays being related by the Green’s function for the intermediate nucleus, G(Z − 1, A − 1). It is shown that, upon taking into account, in this Green’s function, intermediate-nucleus states that are on- and off-shell states for the decaying system, there arise, respectively, sequential and virtual two-proton decays of parent nuclei. Expressions for the widths with respect to sequential and virtual two-proton decays from the ground and excited states of spherical and deformed nuclei and for the angular and energy distributions of emitted protons are obtained.

Prediction of production of 22Na in a gas-cell target irradiated by protons using Monte Carlo tracking

The 22Ne(p,n)22Na is an optimal reaction for the cyclotron production of 22Na. This work tends to monitor the proton induced production of 22Na in a gas-cell target, containing natural and enriched neon gas, using Monte Carlo method. The excitation functions of reactions are calculated by both TALYS-1.6 and ALICE/ASH codes and then the optimum energy range of projectile for the high yield production is selected. A free gaseous environment of neon at a particular pressure and temperature is prearranged and the proton beam is transported within it using Monte Carlo codes MCNPX and SRIM. The beam monitoring performed by each of these codes indicates that the gas-cell has to be designed as conical frustum to reach desired interactions. The MCNPX is also employed to calculate the energy distribution of proton in the designed target and estimation of the residual nuclei during irradiation. The production yield of 22Na in 22Ne(p,n)22Na and natNe(p,x)22Na reactions are estimated and it shows a good agreement with the experimental results. The results demonstrate that Monte Carlo makes available a beneficial manner to design and optimize the gas targets as well as calibration of detectors, which can be used for the radionuclide production purposes.

Determination of proton energy range in thyroid gland therapy and calculation of energy distribution of protons and neutrons from the (p,n) reaction in this gland using MCNPX code

Determination of proton energy range in thyroid gland therapy and calculation of energy distribution of protons and neutrons from the (p,n) reaction in this gland using MCNPX code