Initial Electron Energy Research Articles

Multipactor Analysis in Circular Waveguides Excited by TM01 Mode

A series of detailed numerical simulations are used to investigate the properties of multipactor breakdown in circular waveguides propagating the TM01 mode. A Monte Carlo model is constructed to track the motion of the electrons, study the multipactor scenarios, and predict the multipactor thresholds. The theoretical and numerical analyses indicate that the product of the frequency and the gap ( ${f}\cdot {D}$ ) affects both the intensity of the ponderomotive force and its spatial distribution, which results from the nonuniformity of the radio frequency (RF) field and significantly influences the electrons’ trajectories and multipactor trends. The decrease in ${f}\cdot {D}$ results in a remarkable enhancement in the magnitude of the ponderomotive force, while the maximal intensity gradually moves toward the half radius R/2 area. Low values of ${f}\cdot {D}$ correspond to high ponderomotive potential, which sustains the short-range electrons and triggers the single-sided multipactor. In contrast, high values of ${f}\cdot {D}$ correspond to low ponderomotive potential, contributing to long-range electrons and exciting the double-sided multipactor. Fitting to the susceptibility diagram produces the border line and a modified ${f}\cdot {D}$ threshold of ( ${f}\cdot {D}$ )th $\approx ~338.4$ GHz mm, which separates the susceptibility diagram into single-sided, double-sided, and mixed-sided zones. The initial electron energy influences their trajectories at high ${f}\cdot {D}$ and low RF power. This effect tends to dominate the multipactor behavior in the mixed-sided region.

Photon-Assisted Electron Transmission through a Quantum Point Contact

The theory of coherent photon-assisted electron transmission through a one-dimensional smooth barrier is successfully used to model the results of measuring the terahertz photoconductivity of a tunneling point contact in a two-dimensional electron gas. For this barrier in a deeper tunneling mode, photon steps in the curve of the transmission coefficient versus initial electron energy were found. Their position is determined by the terahertz photon energy.

PenNuc: Monte Carlo simulation of the decay of radionuclides

The Fortran subroutine package PenNuc that performs Monte Carlo simulation of the decay of radioactive nuclides is described. The adopted nuclear decay characteristics (possible disintegration modes and branching ratios, energies and half-lives of nuclear energy levels, types and energies of emitted particles) are from the nucleide evaluated database ( http://www.nucleide.org/DDEP_WG/DDEPdata.htm) in the specific format PenNuc. The initial energies of electrons and positrons emitted in beta disintegrations are sampled from their continuous spectra by means of the RITA (rational inverse transform with aliasing) algorithm, which is described in the Appendix. Electronic relaxation of the residual ion after electron capture and internal conversion is simulated by using the data and sampling methods of the penelope code system. At each call the subroutines deliver a list of state variables of the particles (photons, electrons, positrons and alphas) emitted in a random decay path of the considered radionuclide down to a metastable level or to the ground state of the daughter nucleus. The distribution package includes a main program that simulates the emission spectrum of a radionuclide and, optionally, produces a list of particles emitted in a prescribed number of decays. Program summaryProgram Title: PenNucProgram Files doi:http://dx.doi.org/10.17632/dy28h8xmkv.1Licensing provisions: CC by NC 3.0Programming language: Fortran 90/95Nature of problem:PenNuc simulates the emission of energetic particles in random decay pathways of radionuclides. The initial state of a particle is described by the following variables: type of particle (photon, electron, positron, or alpha), energy, direction, and emission time relative to the start of the decay. For each decay the program provides a list of initial states of the particles emitted with energies higher than the adopted cutoff ECNUC, which is set to 200 eV in the original source file.Solution method: The nuclear disintegration mode and the subsequent de-excitation of the daughter nucleus are simulated by using decay information from the nucleide evaluated databases. De-excitation of ions produced in electron capture and internal conversion is simulated by using atomic transition data and sampling methods from the Monte Carlo code system penelope [1]. The energy of beta particles is sampled using the RITA (rational inverse transform with aliasing) algorithm, which optimizes both simulation speed and accuracy.Additional comments: Although PenNuc can describe several radionuclides simultaneously, the selection of the active nuclide (appropriate to the characteristics of the radioactive source) must be done in the main program. The subroutines provide the complete set of particles emitted with energies higher than the cutoff ECNUC in each nuclear decay, including x rays and Auger electrons.[1] F. Salvat, penelope-2014: A code System for Monte Carlo Simulation of Electron and Photon Transport, OECD/NEA Data Bank, Issy-les-Moulineaux, France, 2015. Available from http://www.nea.fr/lists/penelope.html.

X-Ray Spectroscopy for Electrostatic Potential and Material Determination of Space Objects

Measuring the charge on a nearby space object during close proximity, servicing, and rendezvous and docking operations without requiring physical touch remains challenging despite decades worth of data on spacecraft charging and its risks. This paper proposes the means to identify the charge on a closely neighboring space object and its elemental composition by examining the X-ray spectrum generated by energetic electrons impacting the target. In particular, deconvolution of the bremsstrahlung X-ray continuum provides an estimate of the landing energy of the electrons. Knowing the initial electron energy, the potential difference between the source and the target is determined. Additionally, characteristic X-rays emitted during the process of energetic electron–matter impact allows the relative abundance of elements in the target to be determined. Spatial separations in the order of tens of meters are required between an electron gun and the corresponding detector to maximize the collection of the bremsstrahlung spectrum. This could be achieved with either the single-craft and deployable booms or through the use of two spacecraft. Electron beam energies of 40 kV are found to generate sufficient levels of X-rays for potential determination at over 10 m from the target and to determine the landing energy of the beam to within 0.14% using commercial X-ray detectors.

Spectral and amplitude-time characteristics of crystals excited by a runaway electron beam

The generation of runaway electrons (REs) is a significant problem in tokamak installations, causing energy loss, and melting and vaporization of the walls of the vacuum chamber. The wide deployment of Cherenkov-type detectors, in addition to other methods, is routinely used to detect high-energy electrons. This paper focuses on the cathodoluminescence and Cherenkov radiation excited in different crystals by REs. The spectral energy density of Cherenkov radiation in CaF2 (fluorite) and diamond at various initial electron energies is calculated, taking into account the ionization losses of electron energy, the dispersion of the refractive index of these substances, and the electron energy distribution of the beam.

Local photo-mechanical stiffness revealed in gold nanoparticles supracrystals by ultrafast small-angle electron diffraction.

We demonstrate that highly ordered two-dimensional crystals of ligand-capped gold nanoparticles display a local photo-mechanical stiffness as high as that of solids such as graphite. In out-of-equilibrium electron diffraction experiments, a strong temperature jump is induced in a thin film with a femtosecond laser pulse. The initial electronic excitation transfers energy to the underlying structural degrees of freedom, with a rate generally proportional to the stiffness of the material. Using femtosecond small-angle electron diffraction, we observe the temporal evolution of the diffraction feature associated with the nearest-neighbor nanoparticle distance. The Debye-Waller decay for the octanethiol-capped nanoparticle supracrystal, in particular, is found to be unexpectedly fast, almost as fast as the stiffest solid known and observed by the same technique, i.e., graphite. Our observations unravel that local stiffness in a dense supramolecular assembly can be created by van der Waals interactions up to a level comparable to crystalline systems characterized by covalent bonding.

Experimental characterisation of atmospheric pressure electron gun

In this work, we present the results of an experimental study focused on characterisation of an electron gun designed for atmospheric pressure ionisation - Atmospheric Pressure Electron Gun (APEG). The APEG generates electrons with energies of several keV and could be used as replacement for β-radiation-based ionization sources for Atmospheric Pressure Ionisation (API) in Ion Mobility Spectrometry (IMS) or Mass Spectrometry (MS). In present work we have used Si3N4 membranes with thicknesses of 100 and 150 nm as vacuum–atmosphere separators. For different initial electron energies we have measured electron currents, electron energy distribution functions, and electron energy after the transmission through the membrane. We have also tried to improve the electron transmittance characteristics of the APEG by modification of the membranes by deposition of thin gold films (2.5 to 10 nm), with only the 2.5 nm film achieving an improvement. Finally, we have investigated performance of APEG in air at atmospheric pressure achieving ion currents from 2.5 to 4 μA for 10 keV electrons and found similar thresholds for electron penetration in both the positive and the negative mode of 2.6 and 3.4 kV using the 100 and 150 nm membranes, respectively.

Investigating the effect of dental implant materials with different densities on radiotherapy dose distribution using Monte-Carlo simulation and pencil beam convolution algorithm.

The aim of this study was to investigate the effect of dental implant materials with different physical densities on dose distribution for head and neck cancer radiotherapy planning. Titanium (Ti), Titanium alloy (Ti-6Al-4V), Zirconia (Y-TZP), Zirconium oxide (ZrO2), Alumina (Al2O3) and polyetheretherketone (PEEK) dental implant materials were used for determination of implant material effect on dose distribution. Dental implant effect was investigated by using pencil beam convolution (PBC) algorithm of Eclipse treatment planning systems (TPS) and Monte Carlo (MC) simulation technique. 6 MV photon beam of the Varian 2300 C/D linear accelerator was simulated by EGSnrc-based BEAMnrc MC code system. Reasonable consistency was determined for percentage depth dose (PDD) curves between MC simulation and water phantom measurements at 6.4 MeV initial electron energy. The consistency between modelled linear accelerator PDD curve calculations and water-phantom PDD measurements were compatible within 1 % range. The dose increase in front of the dental implant calculated by MC simulation is in the range of 0.4-20.2%. We found by MC and PBC calculations that the differences in dose increase in front of the dental implant materials is in the range of 0.1-17.2% and is dependent on the physical density of the dental implant. Dose increase for Zirconia was noted to be maximum while PEEK implant dose increase was minimum among the whole dental implant materials studied. This study revealed that the Eclipse TPS PBC algorithm could not accurately estimate the backscatter radiation from dental implant materials.

Magnetic field assisted enhanced electron acceleration due to a chirped echelon phase modulated laser in vacuum

Electron acceleration employing chirped echelon phase modulated (EPM) linearly polarised (LP) laser pulse in vacuum under the influence of axial magnetic field has been explored. Echelon supported laser pulse with phase modulation sustains the trapping of pre-accelerated electron in the most favourable phase. Furthermore, the addition of linear frequency chirp enlarges the electron laser interaction duration. Here, application of axial magnetic field serves a critical role in boosting the electron acceleration upto larger distances in the laser propagation direction. So, few MeV electron can be expedited up to GeV energy and retains it upto longer distances due to the collective influence of the frequency chirp and phase modulation. Effect of laser initial intensity, pulse duration, beam waist and electron injection is taken into consideration and optimized for enhanced energy gain. It is observed that the electron of initial energy ˜0.5 MeV can achieve energy of ˜2.5 GeV with I∼1.38 × 1020 W/cm2 due to chirped LP EPM laser pulse in the existence of suitable axial magnetic field (˜41.7 MG) at most favourable values of electron injection angle and EPM gradient parameter.

Resonances in nonrelativistic free-free Gaunt factors with screened Coulomb interaction

The effect of Coulomb interaction screening on nonrelativistic free-free absorption is investigated by integrating the numerical continuum wave functions. The screened potential is taken to be in Debye-H\"uckel (Yukawa) form with a screening length $D$. It is found that the values of the free-free Gaunt factors for different Debye screening lengths $D$ for a given initial electron energy ${\ensuremath{\varepsilon}}_{i}$ and absorbing photon energy $\ensuremath{\omega}$ generally lie between those of the pure Coulomb field and field-free case. However, for initial electron energies below 0.1 Ry and fixed photon energy, the Gaunt factors show dramatic enhancements (broad and narrow resonances) in the vicinities of the critical screening lengths, ${D}_{nl}$, at which the energies of $nl$ bound states in the potential merge into the continuum. These enhancements of the Gaunt factors can be significantly higher than their values in the unscreened (Coulomb) case over a broad range of ${\ensuremath{\varepsilon}}_{i}$. The observed broad and narrow resonances in the Gaunt factors are related to the temporary formation of weakly bound (virtual) and resonant (quasibound) states of the low-energy initial electron on the Debye-H\"uckel potential when the screening length is in the vicinity of ${D}_{nl}$.

Effect of the electronic kinetics on graphitization of diamond irradiated with swift heavy ions and fs-laser pulses

Diamond preliminary damaged with neutrons was irradiated with swift heavy ions (SHI, 1030 MeV 209Bi) decelerated in the electronic stopping regime as well as with fs-laser pulses. The initial excess electronic energy densities appearing in the nanometric vicinity of the SHI trajectories and within the absorbing layers in laser spots were comparable (∼1024 eV cm−3).Graphitization of diamond in the central parts of the lased spots was observed above the threshold fluence of 15–30 J/cm−2. It was also found that the lower threshold fluence is required for initiating graphitization as well as destruction of the pre-damaged crystal by laser pulses in comparison to that for undamaged diamond. This indicates a noticeable effect of an existing defect ensemble on the kinetics of diamond transformations in laser spots.However, X-ray diffraction, atomic-force microscopy, and electron microscopy detected no graphitic domains within the SHI-irradiated pre-damaged crystal.The research demonstrated that the density of the initial excess electronic energy cannot be treated as the sole parameter governing subsequent structure transformations in diamond. Large differences between the spatial as well as temporal scales finally results in different pathways of the relaxation kinetics of this excess energy in laser spots and SHI tracks in diamond.

Investigation on Electron Absorbed Dose in a Mixture of Natural Rubber Latex and Cross-linking Agents

Natural rubber vulcanization using electron beam is one of interesting applications of electron accelerators with an energy in a range of a few hundred keV to a few MeV. At the Plasma and Beam Physics (PBP) Research Facility, Chiang Mai University, a 4-MeV radio-frequency (RF) linear accelerator is developed for utilizing in natural rubber vulcanization. To accelerate the vulcanization process, cross-linking agents are added in a natural rubber latex to increase the bonding probability between the chains of rubber molecules. This research used a Monte Carlo based program GEANT4 to simulate the electron absorbed dose in a mixture of natural rubber latex and cross-linking agents. The initial electron energy distributions were obtained from the beam dynamic simulation in the accelerator, which were done with program ASTRA. The initial electron beams have average energy in the range of 0.70 to 4.02 MeV at the position 6 cm prior the 50μm titanium vacuum window foil. The air gap between the vacuum window to the natural rubber latex was set at 18 cm. The electron beam transportation in the titanium foil, air gap and a mixture of natural rubber latex were simulated. The cross-linking agents that are added in the natural rubber latex are ethylene glycol dimethacrylate (EDMA) and 1,6-hexanediol-diacrylate (HDDA). Finally, electron absorbed dose distributions in both transverse direction and along the depth of the natural rubber latex mixed with each cross-linking agent were calculated and analyzed. The results from this work can be used for experimental planning of electron beam irradiation on the natural rubber latex with appropriate cross-linking agents and electron absorbed dose.

Evaluation of Monte Carlo tools for high-energy atmospheric physics II: relativistic runaway electron avalanches

Abstract. The emerging field of high-energy atmospheric physics studies how high-energy particles are produced in thunderstorms, in the form of terrestrial γ-ray flashes and γ-ray glows (also referred to as thunderstorm ground enhancements). Understanding these phenomena requires appropriate models of the interaction of electrons, positrons and photons with air molecules and electric fields. We investigated the results of three codes used in the community – Geant4, GRanada Relativistic Runaway simulator (GRRR) and Runaway Electron Avalanche Model (REAM) – to simulate relativistic runaway electron avalanches (RREAs). This work continues the study of Rutjes et al. (2016), now also including the effects of uniform electric fields, up to the classical breakdown field, which is about 3.0 MV m−1 at standard temperature and pressure. We first present our theoretical description of the RREA process, which is based on and incremented over previous published works. This analysis confirmed that the avalanche is mainly driven by electric fields and the ionisation and scattering processes determining the minimum energy of electrons that can run away, which was found to be above ≈10 keV for any fields up to the classical breakdown field. To investigate this point further, we then evaluated the probability to produce a RREA as a function of the initial electron energy and of the magnitude of the electric field. We found that the stepping methodology in the particle simulation has to be set up very carefully in Geant4. For example, a too-large step size can lead to an avalanche probability reduced by a factor of 10 or to a 40 % overestimation of the average electron energy. When properly set up, both Geant4 models show an overall good agreement (within ≈10 %) with REAM and GRRR. Furthermore, the probability that particles below 10 keV accelerate and participate in the high-energy radiation is found to be negligible for electric fields below the classical breakdown value. The added value of accurately tracking low-energy particles (<10 keV) is minor and mainly visible for fields above 2 MV m−1. In a second simulation set-up, we compared the physical characteristics of the avalanches produced by the four models: avalanche (time and length) scales, convergence time to a self-similar state and energy spectra of photons and electrons. The two Geant4 models and REAM showed good agreement on all parameters we tested. GRRR was also found to be consistent with the other codes, except for the electron energy spectra. That is probably because GRRR does not include straggling for the radiative and ionisation energy losses; hence, implementing these two processes is of primary importance to produce accurate RREA spectra. Including precise modelling of the interactions of particles below 10 keV (e.g. by taking into account molecular binding energy of secondary electrons for impact ionisation) also produced only small differences in the recorded spectra.

Fano cavity test for electron Monte Carlo transport algorithms in magnetic fields: comparison between EGSnrc, PENELOPE, MCNP6 and Geant4

A Fano cavity test was performed for four general-purpose Monte Carlo codes, EGSnrc, PENELOPE, MCNP6 and Geant4 to evaluate the accuracy of their electron transport algorithms in magnetic fields. In the simulations, a plane-parallel ionization chamber was modelled as a circular gas disk sandwiched between two circular solid wall disks. It was assumed that an isotropic and uniform line source per unit mass along the central axis of the gas and solid emits mono-energetic electrons with energies 0.01, 0.1, 1.0 and 3.0 MeV at different magnetic field strengths 0, 0.35, 1.0, 1.5 and 3.0 T in the electron transport mode (no Bremsstrahlung). The relative difference between the calculated dose to the gas region and the initial total energy of emitted electrons per unit mass was defined as the accuracy of Monte Carlo codes. In all results, EGSnrc with the enhanced electric and magnetic field (EEMF) macros was not considerably sensitive to the step size parameters and showed accuracy less than 0.18% ± 0.06% with a coverage factor k = 2. The other codes could not achieve competent accuracy with their default settings of step size parameters, compared to EGSnrc with the EEMF macros. With the step size parameters carefully selected, the accuracy of PENELOPE and MCNP6 was within 1.0% and 0.4%, respectively. However, Geant4 showed accuracy within 1.7% except in 3.0 T. EGSnrc with the EEMF macros achieved the best accuracy for the Fano test at the electron energies and the magnetic field strengths investigated in this study and thus, would be recommended to simulate dose responses of ionization chambers in the presence of magnetic fields.

Comparison of absorbed dose distribution 10 MV photon beam on water phantom using Monte Carlo method and Analytical Anisotropic Algorithm

Treatment planning is a process of radiation therapy performed by medical physicists in the hospital. This process can be understood as a simulation to determine parameters such as photon energy, field size, and the absorbable dose to be received by the patient. Simulation treatment planning is usually done using TPS ECLIPSE with AAA or Acuros XB method that has been integrated into it. In this research, the comparison of the distribution of absorbent dose of 10 MV photon at water phantom using Monte Carlo-EGSnrc and AAA-ECLIPSE method was used. Monte Carlo simulations were performed with 6x6 cm2, 10x10 cm2, and 20x20 cm2 field size variations and initial electron energy variations 10.1 MeV, 10.2 MeV, 10.3 MeV and 10.4 MeV. The design and simulation of Linac heads are done using BEAMnrc and the calculation of absorbent doses in this water phantom using DOSXYZnrc. The BEAMnrc simulated particle information was analyzed using BEAMDP. To obtain the depth dose distribution or PDD and PROFILE the dose is done using statdose code. Based on the data processing, the result shows that the mean deviation of PDD and Dmax from the three field sizes is 7.09% for 10.1 MeV, 2.71% for 10.2 MeV, 2.86% for 10.3 MeV and 7.39% for 10.4 MeV. These results indicate that the initial electron energy has the least deviation of 10.2 MeV. As for the dose profile in the field size 10x10 cm2 obtained deviation 6.65% to 10.2 MeV

Electron Energy Enhancement by Comparison of Linearly and Circularly Polarized Laser Pulse in Vacuum Using Different Values of Magnetic Fields

Energy enhancement by a comparison of circularly and linearly polarized laser pulse during acceleration of the electrons by a Gaussian laser pulses has been investigated. On comparison these two it is found that for the linearly polarized laser pulse the y-coordinate has a finite value and approximately zero for a circularly polarized laser pulse. It is noticed that there is a advantage of circularly polarized field. The comparison is done at high values of the magnetic field. The variation of electron energy with laser spot size, laser intensity, initial electron energy and initial phase has been studied. The maximum energy of the electrons gets enhanced for a circularly polarized in comparison to a linearly polarized laser pulse due to axial symmetry of the circularly polarized pulse. The ycomponent of the electric field of circularly polarized laser pulse contributes to the higher energy gained by the electrons.

Flaring of blazars from an analytical, time-dependent model for combined synchrotron and synchrotron self-Compton radiative losses of multiple ultrarelativistic electron populations

We present a fully analytical, time-dependent leptonic one-zone model that describes a simplified radiation process of multiple interacting ultrarelativistic electron populations and accounts for the flaring of GeV blazars. In this model, several mono-energetic, ultrarelativistic electron populations are successively and instantaneously injected into the emission region, that is, a magnetized plasmoid propagating along the blazar jet, and subjected to linear, time-independent synchrotron radiative losses, which are caused by a constant magnetic field, and nonlinear, time-dependent synchrotron self-Compton radiative losses in the Thomson limit. Considering a general (time-dependent) multiple-injection scenario is, from a physical point of view, more realistic than the usual (time-independent) single-injection scenario invoked in common blazar models, as blazar jets may extend over tens of kiloparsecs and thus most likely pick up several particle populations from intermediate clouds. We analytically compute the electron number density by solving a kinetic equation using Laplace transformations and the method of matched asymptotic expansions. Moreover, we explicitly calculate the optically thin synchrotron intensity, the synchrotron self-Compton intensity in the Thomson limit, as well as the associated total fluences. In order to mimic injections of finite duration times and radiative transport, we model flares by sequences of these instantaneous injections, suitably distributed over the entire emission region. Finally, we present a parameter study for the total synchrotron and synchrotron self-Compton fluence spectral energy distributions for a generic three-injection scenario, varying the magnetic field strength, the Doppler factor, and the initial electron energy of the first injection in realistic parameter domains, demonstrating that our model can reproduce the typical broadband behavior seen in observational data.

Self-Driving Energy-Recirculating Micromachined <inline-formula> <tex-math notation="LaTeX">${G}$ </tex-math> </inline-formula>-Band Folded-Waveguide Traveling-Wave Tube Oscillator

We propose a self-driving folded-waveguide traveling-wave tube (TWT) oscillator internally driven by a backward-wave oscillator (BWO). As a driving source, the initial beam energy obtained from the electrostatic field is converted to electromagnetic energy in the BWO. The TWT is designed to amplify the radio frequency signal from the spent electron beam condition as an energy-recirculating method. This paper presents a detailed design study and analysis of the individual circuits, as well as those of the combined circuit, which are conducted using the CST particle-in-cell commercial software and MAGIC code. A maximum average output power of 82.63 W at a frequency of 272 GHz is predicted under the lossless condition. Although the proposed self-driving circuit exhibits a relatively low output power, the key concept behind the novel circuit, which uses a spent electron beam as an amplification source, is validated via simulation. Furthermore, the tunable frequency of the proposed device is tested by changing the initial electron energy using CST Particle Studio, and the expected tunable frequency is 268–272GHz.

Electron Acceleration by a Relativistic Electron Plasma Wave in Inverse-Free-Electron Laser Mechanism

It has been revealed that a relativistic plasma wave, having an extremely large electric field, may be utilized for the acceleration of plasma particles. The large accelerating field gradient driven by a plasma wave is the basic motivation behind the acceleration mechanism. Such a plasma wave can be excited by a single laser in the form of wakefield in laser–plasma interactions. In this paper, we study the enhancement of electron acceleration by plasma wave in the presence of a wiggler magnetic field. Electrons trapped in the plasma wave are accelerated due to the additional resonance provided effectively by the wiggler field, which contributes in large energy gain of electrons during acceleration. The resonant enhancement of electron acceleration by the wiggler magnetic field has been validated by single particle simulations. The dependence of energy gain on plasma wave amplitude, initial electron energy, wiggler magnetic field strength has been investigated. Using the model, the involvement and importance of inverse free-electron laser mechanism in electron acceleration by the plasma wave was analyzed. A scaling law for electron energy optimization was proposed for future electron accelerator development.

Average stopping powers for electron and photon sources for radiobiological modeling and microdosimetric applications

This study concerns calculation of the average electronic stopping power for photon and electron sources. It addresses two problems that have not yet been fully resolved. The first is defining the electron spectrum used for averaging in a way that is most suitable for radiobiological modeling. We define it as the spectrum of electrons entering the sensitive to radiation volume (SV) within the cell nucleus, at the moment they enter the SV. For this spectrum we derive a formula that combines linearly the fluence spectrum and the source spectrum. The latter is the distribution of initial energies of electrons produced by a source. Previous studies used either the fluence or source spectra, but not both, thereby neglecting a part of the complete spectrum. Our derived formula reduces to these two prior methods in the case of high and low energy sources, respectively. The second problem is extending electron spectra to low energies. Previous studies used an energy cut-off on the order of 1 keV. However, as we show, even for high energy sources, such as 60Co, electrons with energies below 1 keV contribute about 30% to the dose. In this study all the spectra were calculated with Geant4-DNA code and a cut-off energy of only 11 eV.We present formulas for calculating frequency- and dose-average stopping powers, numerical results for several important electron and photon sources, and tables with all the data needed to use our formulas for arbitrary electron and photon sources producing electrons with initial energies up to ∼1 MeV.