Monte Carlo calculations of energy deposition distributions of electrons below 20 keV in protein

The distributions of energy depositions of electrons in semi-infinite bulk protein and the radial dose distributions of point-isotropic mono-energetic electron sources [i.e., the so-called dose point kernel (DPK)] in protein have been systematically calculated in the energy range below 20 keV, based on Monte Carlo methods. The ranges of electrons have been evaluated by extrapolating two calculated distributions, respectively, and the evaluated ranges of electrons are compared with the electron mean path length in protein which has been calculated by using electron inelastic cross sections described in this work in the continuous-slowing-down approximation. It has been found that for a given energy, the electron mean path length is smaller than the electron range evaluated from DPK, but it is large compared to the electron range obtained from the energy deposition distributions of electrons in semi-infinite bulk protein. The energy dependences of the extrapolated electron ranges based on the two investigated distributions are given, respectively, in a power-law form. In addition, the DPK in protein has also been compared with that in liquid water. An evident difference between the two DPKs is observed. The calculations presented in this work may be useful in studies of radiation effects on proteins.     

Microwave and Optical Gas Discharges in Superstrong Pulsed Fields

A review is given of theoretical papers on gas breakdown in high-power pulsed microwave and optical fields under conditions such that the electron oscillatory energy in the wave field is much higher than the ionization energy of gas atoms. In microwave fields, which are much weaker than the atomic field, the ionization mechanism for gas atoms is governed by electron-impact avalanche ionization. In high-power optical fields that are comparable in strength to the atomic field, the gas atoms are ionized via the tunneling of the bound electrons. It is shown that, in both cases, the electrons obey similar, highly anisotropic distributions, thereby strongly affecting the stability of the discharge plasma.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Nonisothermal theory of the positive column of an electric discharge in the axial magnetic field

A nonisothermal model of the positive column allowing for electron energy balance is analyzed. The influence of the axial magnetic field on the characteristics of the cylindrical positive column of a low-pressure discharge is investigated in the hydrodynamic approximation. It is shown that the magnetic field affects the plasma density distribution, plasma velocity, and electron energies. The radial dependences of the plasma density, electron energy, and plasma velocity, as well as the azimuthal velocities of electrons and ions, are calculated for helium at different values of the magnetic field strength. It is established that inertia should be taken into account in the equations for the azimuthal motion of electrons and ions. The results obtained in the hydrodynamic approximation differ significantly from those obtained in the framework of the common diffusion model of the positive column in the axial magnetic field. It is shown that the distributions of the plasma density and radial plasma velocity in the greater part of the positive column tend to those obtained in the diffusion approximation at higher values of the axial magnetic field and gas density, although substantial differences remain in the near-wall region.     

Monte Carlo simulation of the spatial distribution of energy deposition for an electron microbeam

Dosimetry calculations characterizing the spatial variation of the energy deposited by the slowing and stopping of energetic electrons are reported and compared with experimental measurements from an electron microbeam facility. The computations involve event-by-event, detailed-histories Monte Carlo simulations of low-energy electrons interacting in water vapor. Simulations of electron tracks with starting energies from 30 to 80 keV are used to determine energy deposition distributions in thin cylindrical rings as a function of penetration and radial distance from a beam source. Experimental measurements of the spatial distribution of an electron microbeam in air show general agreement with the density-scaled simulation results for water vapor at these energies, yielding increased confidence in the predictions of Monte Carlo track-structure simulations for applications of the microbeam as a single-cell irradiator.     

On pathlength and energy straggling of megavoltage electrons slowing down

Purposeto elucidate the effects of multiple scattering and energy-loss straggling on electron beams slowing down in materials.MethodsEGSnrc Monte Carlo simulations are done using a purpose-written user-code.ResultsPlots are presented of the primary electron’s energy as a function of pathlength for 20 MeV electrons incident on water and tantalum as are plots of the overall distribution of pathlengths as the 20 MeV electrons slow down under various Monte Carlo scenarios in water and tantalum. The distributions range from 1 % to 135 % of the CSDA range in water and from 1 % to 186 % in tantalum. The effects of energy-loss straggling on energy spectra at depth and electron fluence at depth are also presented.ConclusionsThe role of energy-loss straggling and multiple scattering are shown to play a significant role in the range straggling which determines the dose fall-off region in electron beam dose vs depth curves and a significant role in the energy distributions as a function of depth.     

Calculation of the proximity function of electrons

A new semianalytical method to calculate the proximity function for electrons is proposed. An integral equation for the proximity function that can be solved by using information on the spatial dose distributions is obtained. The proximity function for electrons in the energy range from 10 eV to 10 keV is calculated by solving the equation numerically, using a set of electron collision cross sections for water vapor. The results are in good agreement with those obtained using the Monte Carlo method. The proposed method can be used for electrons of high energies much more efficiently than the Monte Carlo method.     

Nonequilibrium electron distribution functions in a semiconductor plasma irradiated with fast ions

A kinetic equation for the electrons scattered by acoustic phonons in a solid is derived, and relationships between power-law asymptotic solutions and the particle and energy fluxes in phase space are established. The dependence of the nonextensivity parameter on the intensity of the particle flow in phase space is determined for a nonequilibrium solid-state plasma with sources and sinks. The formation of a steady-state nonequilibrium electron distribution function in a semiconductor with a source and a sink in phase space is numerically simulated using the Landau and Fokker-Planck collision integrals. The nonequilibrium electron distributions formed in the solid-state plasmas of semiconductors and of a Sb/Cs cathode are studied experimentally. It is shown that, within the electron energy range of 5–100 eV, the electron distribution functions decrease with energy according to a power law.     

Microdosimetry of electron microbeams

Track structures of 25, 50 and 80 keV primary electrons, simulated by the detailed-history Monte Carlo method, were analyzed for the frequency distributions of energy deposited in spheres with a diameter of 1 microm, placed in a cylindrically symmetrical array around the projected initial direction of the primary electron. The frequency mean of specific energy, the dose mean of lineal energy, and the parameters of lognormal functions fit to the dose distributions were calculated as a function of beam penetration and radial distance from the projected beam axis. Given these data, the stochastics of dose and radiation quality for micrometer-scale sites targeted by a medium-energy electron microbeam can be predicted as a function of the site's location relative to the beam entry point.     

One-dimensional semiempirical model of plasma in an accelerator with closed electron drifts

The plasma structure in an accelerator with closed electron drifts is investigated experimentally and numerically based on the measured data on the angular and energy ion distribution in a plasma jet. The mathematical model is constructed in a one-dimensional steady-state approximation and is aimed at calculating spatial distributions of the electric potential and plasma density in the region of the most intense ionization of neutral atoms. A comparison of the numerically calculated model potential distributions with the results from direct probe measurements shows that the proposed approach provides an online analysis of the plasma structure in the ionization-acceleration zone.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.     

Calculations of heavy-ion track structure

A Monte Carlo model is presented to study details of the energy deposition inside tracks of heavy charged particles in water vapor. The input data for most of the calculations based on the binary encounter approximation are double-differential cross sections for electron emission after heavy-ion impact. The paths of the liberated electrons are simulated, taking into account elastic scattering, ionization, and excitation. Each basic interaction of an electron or heavy ion is treated individually. Radial dose distributions and specific energy deposition are calculated for projectiles from protons to uranium in the energy range from one to several hundred megaelectron volts per unified atomic mass unit. Good agreement with measurements in tissue-equivalent gas and propane is obtained for light and medium-heavy projectiles, whereas for heavy projectiles such as uranium, deviations around a factor of 2–3 are observed.     

Contributions to quantum biology. I. Mobile electronic characteristics of riboflavin radicals

Quantum biology is the quantum mechanical study of electrons in molecules of biological interest. This requires the solution of problems involving many electrons. Approximation methods are therefore necessary and are discussed. The present study, concerned with the mobile electrons in riboflavin (FMN) and its radicals (FMN⁻, FMNH and FMNH₂ ⁺), is based on the approximation method, developed by B. Pullman and A. Pullman. The solution of the eigenvalue problems so obtained gives the energy levels of the mobile electron systems involved. The corresponding eigenvectors yield the mobile electronic charges of the atoms of riboflavin radicals which have contributed mobile electrons. Important differences of the net charge distributions of these radicals are emphasized. The longest wave length of light absorption is calculated from the obtained energy levels and agrees, within the accuracy of the method, with corresponding experimental results. From the appropriate calculated results, electronic assignments are obtained for the experimental transitions involved.     

Theoretical investigation of the bistability effect in non-self-sustained discharges in Kr and Ar

The electron energy distribution function and the related plasma parameters in non-self-sustained discharges in Kr and Ar are studied theoretically. The investigations are carried out by numerically solving the corresponding Boltzmann equation for the electron energy distribution function with allowance for electron-electron collisions. The electron energy distribution and electron density are calculated self-consistently as functions of the intensity q of the source of secondary electrons and the magnitude of the reduced electric field E/N. The main goal of the investigations was to determine the conditions under which the plasma exhibits bistable parameters. Calculations show that, for discharges in Kr, there is a certain range of q and E/N values in which the Boltzmann equation has two different stable solutions. For an Ar plasma, such a bistability effect was not found: over the parameter range under consideration, the Boltzmann equation has a unique solution. Various plasma parameters (such as the effective electron temperature, electron drift velocity, and electron current density) are calculated for different discharge conditions, including those corresponding to the bistability effect.     

The critical electric field in heated SF<Subscript>6</Subscript>

The critical electric field at which the ionization rate is equal to the rate of electron attachment to neutral particles in heated sulfur hexafluoride (SF₆) is calculated by numerically solving the Boltzmann equation for electrons. It is shown that the main causes of a decrease in the critical field with increasing gas temperature are the change in the electron energy distribution due to gas dissociation and the reduction in the rate of electron attachment to neutral particles. The calculated results are in qualitative agreement with the available experimental data.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Theory of proton hyperfine interactions in bacterial photosynthetic systems. Bacteriopheophytin cation and anion.

The electronic structures of the cation and anion of bacteriopheophytin alpha monomer are investigated by the self-consistent charge extended Hückel procedure including both pi and sigma electrons in the molecule. The calculated electron distributions are tested by comparison of the predicted hyperfine fields at proton sites with experimental data in both the ions and most important, by their ability to explain the observed trend in the hyperfine fields in going from the cation bacteriopheophytin+ alpha to the anion, a trend that is similar in many respects to the corresponding observed trend for the bacteriochlorophyll alpha cation and anion. Good agreement is obtained with experiment both for the absolute values of the observed proton hyperfine fields in both bacteriopheophytin a cation and anion as well as the ratio of the corresponding fields for the two systems. In particular, our calculated electron distributions in the two molecules lead, for the cation, to substantially different proton hyperfine fields for the two methyl groups attached to rings I and III, while for the anion, the corresponding fields are much closer to each other, a trend in good agreement with recent data. Also explained are the features of larger methine hyperfine constants in the anion as compared to the cation and the reverse trend for the protons in rings II and IV. Other features of the calculated electron distributions in the cation and anion are discussed and compared with each other. Possible additional measurements in the two systems that could provide further tests of the theoretically obtained electron distribution will be pointed out.     

Phosphorylation of the p68 subunit of Pol δ acts as a molecular switch to regulate its interaction with PCNA

DNA polymerase delta (Pol δ) is a central enzyme for eukaryotic DNA replication and repair. Pol δ is a complex of four subunits p125, p68, p50, and p12. The functional properties of Pol δ are largely determined by its interaction with its DNA sliding clamp PCNA (proliferating cellular nuclear antigen). The regulatory mechanisms that govern the association of Pol δ with PCNA are largely unknown. In this study, we identified S458, located in the PCNA-interacting protein (PIP-Box) motif of p68, as a phosphorylation site for PKA. Phosphomimetic mutation of S458 resulted in a decrease in p68 affinity for PCNA as well as the processivity of Pol δ. Our results suggest a role of phosphorylation of the PIP-motif of p68 as a molecular switch that dynamically regulates the functional properties of Pol δ.     

Theory of proton hyperfine interactions in bacterial photosynthetic systems.: Bacteriopheophytin cation and anion

The electronic structures of the cation and anion of bacteriopheophytin a monomer are investigated by the self-consistent charge extended Hückel procedure including both π and σ electrons in the molecule. The calculated electron distributions are tested by comparison of the predicted hyperfine fields at proton sites with experimental data in both the ions and most important, by their ability to explain the observed trend in the hyperfine fields in going from the cation bacteriopheophytin⁺a to the anion, a trend that is similar in many respects to the corresponding observed trend for the bacteriochlorophyll a cation and anion. Good agreement is obtained with experiment both for the absolute values of the observed proton hyperfine fields in both bacteriopheophytin a cation and anion as well as the ratio of the corresponding fields for the two systems. In particular, our calculated electron distributions in the two molecules lead, for the cation, to substantially different proton hyperfine fields for the two methyl groups attached to rings I and III, while for the anion, the corresponding fields are much closer to each other, a trend in good agreement with recent data. Also explained are the features of larger methine hyperfine constants in the anion as compared to the cation and the reverse trend for the protons in rings II and IV. Other features of the calculated electron distributions in the cation and anion are discussed and compared with each other. Possible additional measurements in the two systems that could provide further tests of the theoretically obtained electron distribution will be pointed out.