Incident Electron Kinetic Energy Research Articles

Classical theory of laser-assisted spontaneous bremsstrahlung

We study the process of laser-assisted spontaneous electron bremsstrahlung by running classical trajectories in a combined Coulomb and laser (ac) fields. Due to chaotic scattering in the combined Coulomb and ac fields, the radiation probability as a function of the impact parameter and the constant phase of the laser field exhibits fractal structures. However, these structures are smeared out when the cross section is integrated over the impact parameter and averaged over the phase. We analyze the role of different types of orbits, including the trapped orbits, and the dependence of the radiation probability on the impact parameter and the initial phase of the ac field. We show that, at low incident electron kinetic energy, the Coulomb focusing leads to a substantial extension of the range of impact parameters contributing to the bremsstrahlung cross section and results in a substantial increase (by one to two orders of magnitude) of the cross section as compared with the pure Coulomb case. As examples, we discuss the case of relatively high ponderomotive energy ${E}_{p}$ when we obtain an efficient production of photons with frequencies up to $2{E}_{p}$, and the case of low ${E}_{p}$ when only infrared photons are produced. Overall accuracy of the classical approach is estimated to be very good, although it does not describe resonant processes studied previously by quantum-mechanical methods.

C-I and C-F bond-breaking dynamics in the dissociative electron ionization of CF3I.

We present a comprehensive experimental study into the dissociative electron ionization dynamics of CF3I at energies ranging from 20 to 100 eV. A beam-gas instrument has been used to measure the absolute total ionization cross-section for the molecule over the energy range from 0 to 300 eV. Coupled with data from an electron-molecule crossed beam velocity-map imaging instrument, this allows absolute partial ionization cross-sections to be determined for formation of each ionic fragment. These reveal a number of fragmentation channels involving both C-I and C-F bond cleavage, in some cases followed by further fragmentation of the resulting molecular ion. Velocity-map images have been recorded for the I+ and CF3+ products of C-I bond cleavage and the CF2I+ products of C-F bond cleavage. Analysis of fragment kinetic energy distributions extracted from the images reveals that CF3+ product of C-I bond cleavage appears to be formed via a statistical mechanism occurring over long timescales, while the CF2I+ products of C-F cleavage are formed via a much faster, more direct dissociation mechanism involving one or more repulsive states of the parent molecular ion. The I+ fragments arising from C-I bond cleavage display behaviour intermediate between the two extremes. For all fragments, the images show little or no dependence on the energy of the incident electron, implying that the initially excited ion state or states undergo rapid relaxation to the dissociative state(s) in all cases. Only a very small fraction of the incident electron's kinetic energy is released into kinetic energy of the recoiling atomic and molecular fragments, implying that most of the available energy remains with the two departing electrons. The kinetic energy distributions obtained for the various fragments of dissociative electron ionization are compared with the corresponding distributions reported from photoionization studies in order to gain insight into the electronic states involved.

Vanadium fine-structure K-shell electron impact ionization cross sections for fast-electron diagnostic in laser–solid experiments

The K-shell electron impact ionization (EII) cross section, along with the K-shell fluorescence yield, is one of the key atomic parameters for fast-electron diagnostic in laser–solid experiments through the K-shell emission cross section. In addition, in a campaign dedicated to the modeling of the K lines of astrophysical interest (Palmeri et al. (2012)), the K-shell fluorescence yields for the K-vacancy fine-structure atomic levels of all the vanadium isonuclear ions have been calculated.In this study, the K-shell EII cross sections connecting the ground and the metastable levels of the parent vanadium ions to the daughter ions K-vacancy levels considered in Palmeri et al. (2012) have been determined. The relativistic distorted-wave (DW) approximation implemented in the FAC atomic code has been used for the incident electron kinetic energies up to 20 times the K-shell threshold energies. Moreover, the resulting DW cross sections have been extrapolated at higher energies using the asymptotic behavior of the modified relativistic binary encounter Bethe model (MRBEB) of Guerra et al. (2012) with the density-effect correction proposed by Davies et al. (2013).

Energy loss of charged particles traversing multilayer graphene

We derive a dielectric response model for dynamic polarization of freestanding multilayer graphene induced by an external charged particle moving at an arbitrary angle of incidence. Using a two-dimensional, two-fluid hydrodynamic model for the single-layer polarizability, we evaluate the probability density for energy loss and the total energy loss of fast electrons traversing graphene under normal incidence for a broad range of the incident electron kinetic energies. Numerical results are obtained in the cases of one, two, and three layers of graphene. When the incident electron kinetic energy T increases, both the probability density and the total energy loss strongly decrease. It is also found that when the kinetic energy T decreases, the π and σ+π plasmon peak positions move to higher energies ω. In addition, the total energy loss approximately scales with the number of graphene layers N for all observed incident electron kinetic energies.

Copper fine-structure K-shell electron impact ionization cross sections for fast-electron diagnostic in laser-solid experiments

The K-shell electron impact ionization (EII) cross section, along with the K-shell fluorescence yield, is one of the key atomic parameters for fast-electron diagnostic in laser-solid experiments through the K-shell emission cross section. In addition, copper is a material that has been often used in those experiments because it has a maximum total K-shell emission yield. Furthermore, in a campaign dedicated to the modeling of the K lines of astrophysical interest (Palmeri et al., 2012), the K-shell fluorescence yields for the K-vacancy fine-structure atomic levels of all the copper isonuclear ions have been calculated.In this study, the K-shell EII cross sections connecting the ground and the metastable levels of the parent copper ions to the daughter ions K-vacancy levels considered in Palmeri et al. (2012) have been determined. The relativistic distorted-wave (DW) approximation implemented in the FAC atomic code has been used for the incident electron kinetic energies up to 10 times the K-shell threshold energies. Moreover, the resulting DW cross sections have been extrapolated at higher energies using the asymptotic form proposed by Davies et al. (2013).

Interaction of electrons with light metal hydrides in the transmission electron microscope.

Transmission electron microscope (TEM) observation of light metal hydrides is complicated by the instability of these materials under electron irradiation. In this study, the electron kinetic energy dependences of the interactions of incident electrons with lithium, sodium and magnesium hydrides, as well as the constituting element effect on the interactions, were theoretically discussed, and electron irradiation damage to these hydrides was examined using in situ TEM. The results indicate that high incident electron kinetic energy helps alleviate the irradiation damage resulting from inelastic or elastic scattering of the incident electrons in the TEM. Therefore, observations and characterizations of these materials would benefit from increased, instead decreased, TEM operating voltage.

Polarization of the Lyman line emission following radiative recombination of bare ions: effects of relativity and radiation multipoles

We have calculated the degree of linear polarization of the Ly-α1 (2p3/2 → 1s1/2) and Ly-β1 (3p3/2 → 1s1/2) lines emitted after radiative recombination of spinless bare nuclei with unidirectional, unpolarized electrons. These calculations have been performed for various recombined H-like ions with atomic numbers in the range 10 ⩽ Z ⩽ 92. Several incident-electron kinetic energies ε0 ranging from 0.01 to 10 times the electron binding energy in the 1s1/2 ground state were considered and the radiative cascades following recombination into states with principal quantum number up to n = 6 were included. Three sets of cross sections for radiative recombination to individual magnetic sublevels of the excited levels of the recombined H-like ions were computed: the first two in the electric-dipole approximation with the nonrelativistic and relativistic electron wavefunctions and the third one in the exact relativistic method including all multipole orders of the radiation field. Results for the polarization calculated using these three sets of cross-section data were compared in order to stress the relative importance of relativistic and multipole effects as Z or ε0 increases.

An improved physics-based approach for unfolding megavoltage bremsstrahlung spectra using transmission analysis

To develop a physics-based approach to improve the accuracy and robustness of the ill-conditioned problem of unfolding megavoltage bremsstrahlung spectra from transmission data. Spectra are specified using a rigorously-benchmarked functional form. Since ion chambers are the typical detector used in transmission measurements, the energy response of a Farmer chamber is calculated using the EGSnrc Monte Carlo code, and the effect of approximating the energy response on the accuracy of the unfolded spectra is studied. A proposal is introduced to enhance spectral sensitivity by combining transmission data measured with multiple detectors of different energy response and by combining data from multiple attenuating materials. Monte Carlo methods are developed to correct for nonideal exponential attenuation (e.g., scatter effects and secondary attenuation). The performance of the proposed methods is evaluated for a diverse set of validated clinical spectra (3.5-25 MV) using analytical transmission data with simulated experimental noise. The approximations commonly used in previous studies for the ion-chamber energy response lead to significant errors in the unfolded spectra. Of the configurations studied, the one with best spectral sensitivity is to measure four full transmission curves using separate low-Z and high-Z attenuators in conjunction with two detectors of different energy response (the authors propose a Farmer-type ion chamber, once with a low-Z, and once with a high-Z buildup cap material), then to feed the data simultaneously to the unfolding algorithm. Deviations from ideal exponential attenuation are as much as 1.5% for the smallest transmission signals, and the proposed methods properly correct for those deviations. The transmission data with enhanced spectral sensitivity, combined with the accurate and flexible spectral functional form, lead to robust unfolding without requiring a priori knowledge of the spectrum. Compared with the commonly-used methods, the accuracy is improved for the unfolded spectra and for the unfolded mean incident electron kinetic energy by at least factors of three and four, respectively. With simulated experimental noise and a lowest transmission of 1%, the unfolded energy fluence spectra agree with the original spectra with a normalized root-mean-square deviation, %Δ(ψ), of 2.3%. The unfolded mean incident electron kinetic energies agree, on average, with the original values within 1.4%. A lowest transmission of only 10% still allows unfolding with %Δ(ψ) of 3.3%. In the presence of realistic experimental noise, the proposed approach significantly improves the accuracy and robustness of the spectral unfolding problem for all therapy and MV imaging beams of clinical interest.

Functional forms for photon spectra of clinical linacs

Specifying photon spectra of clinical linacs using a functional form is useful for many applications, including virtual source modelling and spectral unfolding from dosimetric measurements such as transmission data or depth-dose curves. In this study, 11 functional forms from the literature are compiled and quantitatively compared. A new function is proposed which offers improvements over existing ones. The proposed function is simple, physics-based and has four free parameters, one of which is the mean incident electron kinetic energy. A comprehensive benchmark set of validated, high-precision Monte Carlo spectra is generated and used to evaluate the strengths and limitations of different functions. The benchmark set has 65 spectra (3.5–30 MV) from Varian, Elekta, Siemens, Tomotherapy, Cyberknife and research linacs. The set includes spectra on- and off-axis from linacs with and without a flattening filter, and in treatment and imaging modes. The proposed function gives the lowest spectral deviations among all functions. It reproduces the energy fluence values in each bin for the benchmark set with a normalized root-mean-square deviation of 1.7%. The mean incident electron kinetic energy, maximum photon energy, most-probable energy and average energy are reproduced, on average, within 1.4%, 4.3%, 3.9% and 0.6% of their true values, respectively. The proposed function is well behaved when used for spectral unfolding from dosimetric data. The contribution of the 511 keV annihilation peak and the energy spread of the incident electron beam can be added as additional free parameters.

Low‐ target optimization for spatial resolution improvement in megavoltage imaging

Recently, several authors have shown contrast improvements in megavoltage portal imaging and cone-beam computed tomography using low atomic number (Z) targets. This work compliments previous studies by investigating the effects of varying different beam production parameters including target atomic number, target thickness, and incident electron energy on spatial resolution. Target materials of beryllium, aluminum, and tungsten were investigated over a range of thicknesses between 10% and 100% of the continuous slowing down approximation range of electrons. Incident electron kinetic energies of 4.5 and 7.0 MeV were used, in conjunction with custom targets installed above the carousel of a modern radiotherapy linear accelerator. Monte Carlo simulations of the accelerator were constructed and compared to the experimental results. The results showed that thinner targets, as well higher incident electron energies, generally produce more favorable modulation transfer function (MTF) curves. Due to an MTF dependence of the detector system on the photon energy, the experimental results showed that low-Z targets produced superior MTF curves. Simulations showed 14.5% and 21.5% increases in f50 for the 7.0 and 4.5 MeV targets (A1; 60% R% CSDA), respectively, when moved from the carousel to the location of the clinical target. f50 values for the custom targets were compared to the clinical 6 MV beam and were found to be between 10.4% lower (4.5 MeV/W) and 15.5% higher (7.0 MeV/Be). Integration of low-Z external targets into the treatment head of a medical linear was achieved with only minor modifications. It was shown that reasonably high resolution images on par or better than those acquired with the clinical 6 MV beam can be achieved using external low-Z targets.

Sci-Thurs AM: YIS-04: Low-Z Target Optimization for Spatial Resolution Improvement in Megavoltage Imaging

Recently, several authors have shown contrast improvements in megavoltage portal imaging and cone‐beam computed tomography(CBCT) using low atomic number (Z) targets. This work compliments previous studies by investigating the effects of varying different beam production parameters including target atomic number, target thickness and incident electron energy on spatial resolution. Target materials of beryllium,aluminum and tungsten were investigated over a range of thicknesses between 10% and 100% of the continuous slowing down approximation (CSDA) range of electrons. Incident electron kinetic energies of 4.5 MeV and 7.0 MeV were used in conjunction with custom targets installed above the carousel of a Varian 2100EX linear accelerator (Varian Medical, Inc.) to produce the experimental beams of interest. Monte Carlo simulated results were compared to measured data and it was shown that thinner targets, as well higher incident electron energies generally produce more favourable modulation transfer function(MTF) curves. Due to an MTF dependence of the detector system on photon energy, the experimental results showed that low‐Z targets produced superior MTF curves. Simulations showed a 14.5% and 21.5% increase in f 50 for the 7.0 MeV and 4.5 MeV targets (Al; 60% R % CSDA ) respectively when moved from the carousel to the location of the clinical target. f 50 values for the custom targets were compared to the clinical 6 MV beam and were found to be between 10.4% lower (4.5 MeV/W) and 15.5% higher (7.0 MeV/Be). This study has been partially funded by a Research Grant from Varian Medical Systems.

Calculation of x‐ray spectra emerging from an x‐ray tube. Part I. Electron penetration characteristics in x‐ray targets

The penetration characteristics of electron beams into x-ray targets are investigated for incident electron kinetic energies in the range 50-150 keV. The frequency densities of electrons penetrating to a depth x in a target, with a fraction of initial kinetic energy, u, are calculated using Monte Carlo methods for beam energies of 50, 80, 100, 120 and 150 keV in a tungsten target. The frequency densities for 100 keV electrons in Al, Mo and Re targets are also calculated. A mixture of simple modeling with equations and interpolation from data is used to generalize the calculations in tungsten. Where possible, parameters derived from the Monte Carlo data are compared to experimental measurements. Previous electron transport approximations in the semiempirical models of other authors are discussed and related to this work. In particular, the crudity of the use of the Thomson-Whiddington law to describe electron penetration and energy loss is highlighted. The results presented here may be used towards calculating the target self-attenuation correction for bremsstrahlung photons emitted within a tungsten target.

Mechanisms and dynamics of electron-stimulated desorption ofD−from deuterated diamond surfaces: Surface versus subsurface stimulated desorption

In this work we report on a study of low-energy electron-stimulated desorption (ESD) of ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ from in situ hot-filament-deuterated surfaces of diamond films. This deuteration procedure ensures that deuterium is predominantly adsorbed on the diamond surface and that no significant diffusion underneath the surface takes place. For incident electron energies in the 5--35-eV range, dissociative electron attachment (DEA) and dipolar dissociation (DD) processes occur. The cross section for ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ ESD obtains a maximum value at \ensuremath{\sim}8 eV, whereas the DD process displays a threshold at \ensuremath{\sim}14 eV. Ion kinetic-energy distribution (KED) measurements show that in the DEA regime desorption results in a narrow peak whose energy position increases with the incident electron energy to a value that corresponds, minus a multiphonon excitation factor, to the thermodynamic limit, in agreement with gas-phase considerations. In the DD regime the ion KED displays a peak at \ensuremath{\sim}2 eV which does not depend on the incident electron kinetic energy. To study the effect of inelastic interactions between the desorbing ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ ions and the surface, in the DEA regime, KED measurements were performed as a function of desorbing angle with respect to the surface normal. It was found that with an increasing angle from the surface normal the ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ KED broadens, and its lower-energy component increases in intensity. These results clearly show that inelastic interaction between the outgoing ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ and the solid surface takes place, and determines the KED of desorbing ions. The ESD results obtained for the in situ deuterated surface are compared with those previously obtained for deuterated diamond films that contain some subsurface deuterium for which broad KED's were measured. A difference in the ${\mathrm{D}}^{\mathrm{\ensuremath{-}}}$ KED in the DD regime is also measured. The indirect DEA process observed in the case of hydrogenated (deuterated) diamond films is strongly reduced in the present case of an on-top deuterated diamond surface. Our results show that ESD may be used to determine the presence of surface versus subsurface hydrogen (deuterium) adsorbed on diamond.

Effects of binding energy on exchange contributions in the stopping of electrons

We describe a theoretical treatment of the exchange contributions in Bethe's theory of the stopping of electrons. Starting with the first Born approximation, we obtain an expansion in powers of the ratio of the electronic energy of the target atom to the incident electron's kinetic energy. The binding of the electron within the atom is systematically taken into account, and the leading contribution recovers Bethe's results. The approach involves the use of sum rules that are generalizations of the Bethe sum rule, specifically dealing with the contributions from electron exchange. Though we restrict our discussion to the stopping power here, the method is quite general and may also be used to find the exchange contributions to other quantities related to cross sections of electron-atom scattering. Our results indicate that there may be significant corrections when one accounts for the binding energy.

Are predicted superluminal tunneling times an artifact of using the nonrelativistic Schrödinger equation?

AbstractFor many approaches to timing electrons scattering from an electrostatic potential barrier there are simple realistic situations, involving barrier heights and incident electron kinetic energies both many orders of magnitude less than the rest energy mc2, for which the calculated mean transmission times imply superluminal velocities. The question of whether or not this is an artifact of using the nonrelativistic Schrödinger equation is investigated for the Bohm trajectory and Salecker‐Wigner quantum clock approaches.

Electron-impact-excitation cross sections of hydrogenlike ions

Convergent close-coupling ~CCC! and Coulomb-Born with exchange and normalization ~CBE! methods are used to study electron-impact excitation of hydrogenlike ions. The nl!n8l8 cross sections demonstrate ~i! good agreement between the CCC and CBE results, ~ii! a scaling over ion nuclear charge z, ~iii! a domination of the dipole ( l85l61) contributions in total n!n8 cross sections, and ~iv! significant effect of electron exchange in the energy range x,3 ~here x is the ratio of the incident electron kinetic energy « to the transition energy En,n8 ). For ions with z.5 the n!n8 cross sections obtained in the CCC and CBE approximations agree with each other to better than 10% for any x. An accuracy of the cross sections scaling over z 4 depends on z: for z56 ‐18 the scaling is accurate to better than 10% ~quantitative analysis is done for n8,7), for ions with z,6 the cross sections deviate from the z 4 scaling more significantly~at x about unity!. The n!n8 cross sections are presented by a formula which fits our CCC and CBE results with an accuracy to better than 10% ~for transitions with n,n8,7 in ions with z.5). The new Gaunt factor G(x) suggested for the widely used Van Regemorter formula @Astrophys. J. 136, 906 ~1962!# makes this formula accurate to better than 50% in the x.3 range and to better than 20% in the x.100 range. It is shown that the semiempirical formula by Vainshtein, Sobelman, and Yukov @Electron-Impact Excitation Cross Sections of Atoms and Ions~Nauka, Moscow, 1973!# provides an accuracy to better than 50% for any incident electron energy. For x,2 this formula is accurate to better than 30%. These accuracy assessments are based on a comparison with our CCC and CBE results. @S1050-2947~97!00301-6#

High-resolution electron energy loss spectroscopy of thin crystalline highly oriented films of poly(tetrafluoroethylene)

High-resolution electron energy loss spectroscopy (HREELS) spectra of highly oriented films of poly(tetrafluoroethylene) (PTFE) are reported. With one exception, all peaks in the spectra correspond to IR active vibrations. They are well resolved, and with a remarkably high intensity, more than two orders of magnitude greater than we have observed on any other polymer in HREELS. The angular distributions of the elastic peak, and of the vibrational peaks are very narrow, which indicates both a well ordered system and a dipolar scattering behaviour. No evidence of amorphous regions in these films is found. A Raman active mode can be observed in off-specular geometry, using an incident electron beam coplanar with the PTFE fibers direction. This corresponds to resonance excitation of a transient negative ion state, with a maximum cross-section at an incident electron kinetic energy of about 4 eV.

Auger emission from Xe above and below the 4d ionization threshold

The Auger electron yield from xenon has been measured in the vicinity of the 4d inner-shell ionization threshold. Just above this ionization threshold the Auger line profile is modified by the post-collision interaction effect involving a slow photoelectron. The process is followed through threshold into a region where the photoelectron is recaptured and either shaken up/down or remains in its Rydberg orbital during the Auger decay. By measuring the electron yield as a function of both incident photon energy and electron kinetic energy a comprehensive study of these processes is made.

Circular polarization of the 3D state of atomic hydrogen excited by electrons

The theory of the circular polarization from the 32D state is analysed and angular correlation formulae are derived for the scattered n = 3 electron and the cascade Lyman-alpha radiation. The formulae include allowance for the polarization of the intermediate-state 2p electron from the LS coupling in the time evolution of the decay of the collisionally excited n = 32D states. The effect of a finite coincidence time window is also examined. The predictions of the model are compared with the model which assumes that the intermediate-state 2p electron is unpolarized. New experimental data at an incident electron kinetic energy of 54.4 eV are reported and indicate the circular polarization of the Lyman-alpha radiation has small negative values from 10 degrees to 120 degrees . The theoretical predictions of the correlation are illustrated in a six-state close-coupling model which gives a minimum at forward angles but does not agree quantitatively with the experimental data.

Average atom and detailed configuration accounting calculations of bremsstrahlung in aluminum plasmas

We have calculated sample bremsstrahlung spectra emitted from continuum electrons of specific kinetic energy in hot, dense aluminum plasmas, using three different theoretical approaches for modeling the scattering from ions in these environments. The models include the effects of neighboring ions solely through the potential seen by an electron in the vicinity of a given ion. We consider a Thomas-Fermi average atom approach (TFAA), a non-local thermodynamic equilibrium average atom approach (NLTEAA), and a detailed configuration accounting approach (DCA). The calculations were done for a plasma temperature of 500 eV and for plasma densities of 10 20 and 10 23 ions/cm 3. Results for isolated neutral atoms and nearly stripped isolated ions are presented for comparison. The isolated ions considered were ground-state ions with the same total bound electronic charge as in the plasma approaches. The calculations were performed for incident electron kinetic energies of 100 and 500 eV and 1 and 10 keV. In the low-density case, the TFAA approach gives somewhat different results from the DCA and NLTEAA approaches, reflecting corresponding differences in the potentials. In this case, comparisons of bremsstrahlung cross sections for nearly stripped isolated ions with corresponding plasma results showed better agreement than comparisons between the plasma approaches. In the high-density case, the two average-atom approaches show good agreement with each other and with the DCA approach, reflecting greater similarity among the potentials. However, in the high-density case, the bremsstrahlung process is not as well represented by an isolated ion as at low density. The neutral atom spectrum is quite different from the plasma spectra and from the ionic spectra in all cases.