Total Radiation Loss Research Articles

Experimental performance comparison and optical characteristics of aperture mechanisms for solar cavity receivers

Dynamic control of solar thermal processes is a critical bottleneck demanding to be addressed for the development of viable alternatives to traditional industrial processes that rely on high temperature process heat from fossil fuel combustion. Current technologies possess various concentrated solar power (CSP) control strategies to compensate for natural fluctuations of solar irradiation while some of the dynamic control problems are addressed by creative reactor design to capture solar energy more efficiently. In this paper, a solar receiver with two light entry controlling aperture mechanisms is proposed as a promising control method for manipulated radiation entry into the cavity. Design and motion characteristics of these aperture mechanisms govern the amount of flux intercepted by the receiver. Performance of these apertures in maintaining semi-constant temperature inside the receiver was tested numerically and experimentally for comprehensive explanation of the physics behind the results. An optical analysis was done by implementing two different Monte Carlo Ray Tracing (MCRT) approaches for comparison and verification of complex aperture designs. Total radiative losses were determined by considering the energy balance on the quartz window by taking the spectral-dependent optical properties of the window into account. A thermal analysis was done in conjunction with the optical analysis to demonstrate thermal-optic performance of both mechanisms. A 7 kW high flux Xenon bulb was optically modeled according to experimentally obtained radiation maps. The optical model was coupled as an input to a thermal computation with lumped parameter assumption. Numerical results were validated by comparison with experimental results for both steady and dynamic responses. Estimation of a high flux scenario at steady state as well as for a given DNI pattern were numerically predicted and comparisons with conventional control methods were made. Results demonstrated the potential of the variable aperture in terms of temperature control and receiver efficiency.

Exploration of hydrothermal alteration and monitoring of thermal activity using multi-source satellite images: A case study of the recently active Kirishima volcano complex on Kyushu Island, Japan

Three major successive plinian or subplinian eruptions, following a long dormant period, occurred in January 2011, September 2017, and March 2018 within the Kirishima volcano complex on Kyushu Island, Japan. Herein, we applied a Landsat 8 image to explore the most active hydrothermal altered area of the Kirishima volcano complex, and nine sets of nighttime ASTER thermal infrared data to explore changes of heat loss to the thermally active area of the Shinmoedake and Ohnamiike craters within this volcanic complex from 2009 to 2018. Color composite, band ratio, principal component analysis, and Crosta techniques were used to map hydrothermal alteration. Meanwhile, the normalized difference vegetation index threshold method for emissivity retrieval, the split-window algorithm for land surface temperature (LST), and the Stefan–Boltzmann equation were used to derive the radiative heat flux (RHF) for the study area. Total radiative heat loss (RHL) in megawatts was calculated by adding pixels positive RHF (W/m2) values after multiplying with the pixel area. Using these data, the spatial distribution of altered mineral zones was mapped for the Kirishima volcano complex. We estimated that the maximum LSTs above ambient values were about 24 °C, 12 °C, and 12 °C, immediately following the 2011, 2017 and 2018 eruptions. Highest pixel RHFs of 136 W/m2, 75 W/m2, and 61 W/m2 were also measured just after these eruptions, on 15 November 2011, 30 October 2017, and 8 April 2018, producing peaks in the total RHL of 233 MW, 198 MW and 101 MW, respectively. The Shinmoedake crater had more intense thermal activity than the Ohnamiike crater after both the 2011 and 2018 eruptions but had less intense activity after the 2017 eruption. The intensity of thermal unrest decreased during the study period from both craters. This study illustrates how Landsat TIRS/OLI data can be used for hydrothermal alteration as well as nighttime ASTER thermal infrared data to monitor effectively the thermal activity of active areas of the Kirishima volcano complex.

A numerical study on optical and thermodynamic characteristics of a spherical cavity receiver

In this paper, a 3D model is created to investigate optical and thermodynamic performance of the spherical cavity receiver. Spiral copper pipes placed in the cavity absorb radiation energy and achieve solar-thermal conversion. The reflected rays loss and optical efficiency is calculated by using Monte-Carlo ray-tracing method. The optical efficiency of spherical cavity receiver is 88.9%, slightly higher than other shape cavity receivers. When the spherical cavity receiver moves away from the focal plane either in positive location or negative location, the radiation flux distribution is more uniform. The reflected rays loss decreases with D/d increasing from 1.0 to 2.5, while optical efficiency maintains approximately 86.3%. The radiation flux resulted from Monte-Carlo method is used as boundary condition of the CFD model. On this basis, the temperature distribution and heat loss of the spherical cavity receiver are investigated. Convection heat loss of the receiver with different D/d is estimated by varying the inclination from 0° to 90°. For a certain D/d, the maximum convection heat loss is θ=0° and it decreases monotonously with inclination up to 90°. The temperature distribution with different D/d at θ=0° is investigated. The temperature differences between the heat transfer pipe and heat transfer fluid decreases with D/d increasing. An increase in the inlet temperature of heat transfer fluid leads to the radiation loss remaining unchanged, but convection loss and total heat loss increasing slightly. Three kinds of heat losses decrease as inlet velocity of heat transfer fluid increases, including total heat loss, radiation loss and convection loss. Based on the simulation results, solar thermal conversion efficiency of a concentrator-receiver system varies from 81.9% to 84.4%, and optimal aperture size is about 1.0–1.5.

Particulate matter air pollution may offset ozone damage to global crop production

Abstract. Ensuring global food security requires a comprehensive understanding of environmental pressures on food production, including the impacts of air quality. Surface ozone damages plants and decreases crop production; this effect has been extensively studied. In contrast, the presence of particulate matter (PM) in the atmosphere can be beneficial to crops given that enhanced light scattering leads to a more even and efficient distribution of photons which can outweigh total incoming radiation loss. This study quantifies the impacts of ozone and PM on the global production of maize, rice, and wheat in 2010 and 2050. We show that accounting for the growing season of these crops is an important factor in determining their air pollution exposure. We find that the effect of PM can offset much, if not all, of the reduction in yield associated with ozone damage. Assuming maximum sensitivity to PM, the current (2010) global net impact of air quality on crop production varies by crop (+5.6, −3.7, and +4.5 % for maize, wheat, and rice, respectively). Future emissions scenarios indicate that attempts to improve air quality can result in a net negative effect on crop production in areas dominated by the PM effect. However, we caution that the uncertainty in this assessment is large, due to the uncertainty associated with crop response to changes in diffuse radiation; this highlights that a more detailed physiological study of this response for common cultivars is crucial.

Total radiative heat loss and radiation distribution of liquid pool fire flames

The radiative characteristics of laboratory-scale pool fire flames have been studied in detail. Experiments were conducted in the ASTM E2058/ISO 12136 Fire Propagation Apparatus (FPA). Eleven liquid fuels with different sooting propensities, including alcohols and alkanes, burning in a 9.5cm diameter quartz dish were considered. Radiative power distribution (along the flame axis) and global radiant emission were measured for all the fuels by using slit and wide-view-angle radiometers, respectively. The effects of measurement location and fuel type on the measured data were investigated. Radiation distribution profiles for a given fuel, when adequately normalized, show little sensitivity to the horizontal separation distance of the slit radiometer. Fuels with similar chemical structures exhibit similar distributions, consistent with flame image analyses. The radiative power distributions along with the wide-view-angle radiometer data were used to derive radiant fractions for the pool fires studied by applying a multiple-point source (MPS) radiation model. To examine the sensitivity of the calculated radiant fractions to the measurement location, the position of the wide-view-angle radiometer was considerably varied both vertically and horizontally. The results show that the radiant fractions derived based on the measured radiative power distribution are independent of the location of the wide-view-angle radiometer and consistent with literature values. Therefore, the approach developed in this study presents a flexible methodology apt for the accurate determination of radiation properties of diffusion flames in a laboratory setting.

Using radiative energy losses to constrain the magnetization and magnetic reconnection rate at the base of black hole jets

We calculate the severe radiative energy losses which occur at the base of black hole jets using a relativistic fluid jet model, including in-situ acceleration of non-thermal leptons by magnetic reconnection. Our results demonstrate that including a self-consistent treatment of radiative energy losses is necessary to perform accurate MHD simulations of powerful jets and that jet spectra calculated via post-processing are liable to vastly overestimate the amount of non-thermal emission. If no more than 95% of the initial total jet power is radiated away by the plasma travels as it travels along the length of the jet, we can place a lower bound on the magnetisation of the jet plasma at the base of the jet. For typical powerful jets, we find that the plasma at the jet base is required to be highly magnetised, with at least 10,000 times more energy contained in magnetic fields than in non-thermal leptons. Using a simple power-law model of magnetic reconnection, motivated by simulations of collisionless reconnection, we determine the allowed range of the large-scale average reconnection rate along the jet, by restricting the total radiative energy losses incurred and the distance at which the jet first comes into equipartition. We calculate analytic expressions for the cumulative radiative energy losses due to synchrotron and inverse-Compton emission along jets, and derive analytic formulae for the constraint on the initial magnetisation.

Surface energy and water vapor fluxes observed on a megadune in the Badain Jaran Desert, China

The Badain Jaran Desert is the second-largest area of shifting sands in China. Our first measurements of the energy components and water vapor fluxes on a megadune using eddy covariance technology were taken from April 2012 to April 2013. The results indicate that the longwave and shortwave radiative fluxes exhibited large fluctuations and seasonal dynamics. The total radiative energy loss by longwave and shortwave radiation was greater on the megadune than from other underlying surfaces. The radiation partitioning was different in different seasons. The land-atmosphere interaction was primarily represented by the sensible heat flux. The average sensible heat flux (40.1 W/m2) was much larger than the average latent heat flux (14.5 W/m2). Soil heat flux played an important role in the energy balance. The mean actual evaporation was 0.41 mm/d, and the cumulative actual evaporation was approximately 150 mm/a. The water vapor would transport downwardly and appear as dew condensation water. The amount of precipitation determined the actual evaporation. The actual evaporation was supposed to be equal to the precipitation on the megadune and the precipitation was difficult to recharge the groundwater. Our study can provide a foundation for further research on land-atmosphere interactions in this area.

Universal statistical approach to radiative and collisional processes with multielectron ions in plasmas

The universal statistical approach for calculation of radiative and collisional processes with multielectron ions in plasmas is developed. It is based on the atomic structure representation similar to that used in a condensed medium. The distribution of local atomic electron density determines the set of elementary excitations with classical plasma frequency. The statistical method is tested by the calculations of the total electron impact single ionization cross-sections, ionization rates and radiative losses of various ions. In the coronal limit the radiative losses of heavy plasma impurities with any type of multielectron ions are determined by the excitation of collective atomic oscillations due to collisions with plasma electrons. It is shown that for low plasma densities the tungsten ions total radiative loss scatter within universal statistical approach does not exceed similar results of current complex numerical codes in the wide range of plasma temperatures. The general expression for the radiative losses in the case of the intermediate state between limiting cases of coronal and Boltzmann population distributions is derived as well. The total electron impact ionization cross-sections and ionization rates for ions of various charge stages for a wide range of elements from Ar to U are compared with experimental and conventional complex code data showing satisfactory agreement. As the universal statistical method operates in terms of collective excitations, it implicitly includes direct and indirect ionization processes.

Radiative properties of argon–helium–nitrogen–carbon–cobalt–nickel plasmas used in CNT synthesis

This work presents the radiative properties of argon–helium–nitrogen–carbon–nickel–cobalt thermal plasmas by the computation of net emission coefficients (NECs) under the assumption of a local thermodynamic equilibrium and at temperature range 1000–20 000 K. These mixtures were often used in the study of carbon nanotubes (CNTs) synthesis with arc plasma which becomes one of the most useful techniques in terms of flexibility of carbon nanostructures produced with fewer defects. The values of NEC allow estimation of total radiation losses in plasmas, by taking into account the emission radiation resulting from the atomic continuum, the molecular continuum, the atomic lines and some molecular bands. Free–free transitions (Bremsstrahlung) and free–bound (electron–ion recombination), have been considered for the calculation of atomic continuum. For bound–bound transitions, natural, resonance, Van der Waals, Stark and Doppler effects have been taken into account in the calculation of the lines broadenings while the self-absorption of the resonance lines has been treated using their escape factors. Molecular continuum has been only considered for N2, C2 and CN molecules whereas we have only taken into account diatomic systems N2, , CN and C2 for the emission of the molecular bands. The results obtained show that even for low concentrations of Ni and Co in the plasma, the NECs are modified and considerably increase only at a low temperature (T < 8000 K) and the major contribution in the total radiation arises from the lines emission. However, the effect of the thickness of the plasma on plasma radiation has been analysed based on the self absorption phenomenon of resonance lines.

The role of visible and resonance radiation in the energy balance of LTE plasma in argon

Energy losses due to radiation in an LTE arc plasma in argon are investigated in the temperature range from 5000 to 15 000 K. Calculations of the radiation transport require us to know the absorption spectra; for that purpose, free–free, bound–free and bound–bound transitions are taken into account. The energy losses due to resonance transitions with large absorption coefficients are analyzed. The transport of visible radiation with small absorption coefficients is calculated by accurate integration over a whole spectrum. The resonance radiation transport in LTE plasma is described by the Biberman–Holstein equation, which is usually used in non-equilibrium plasma. As the temperature grows, radiation processes become the main channel of energy losses. It is shown that, despite the resonance radiation being trapped, the energy losses due to resonance radiation escape can achieve 10% of the total radiation losses.

Thermal performance of lab-scale solar reactor designed for kinetics analysis at high radiation fluxes

The availability of lab-scale reactor designs with suitable control and monitoring of reaction parameters becomes essential when high flux/temperature conditions reproducing solar-driven thermochemical processes are needed. Since the chemical kinetics strongly depends on irradiance, temperature and fluid flow distribution around the reactant, a detailed thermal analysis supports the understanding of reactor response and kinetics assessment for specific solar reactor designs. This study describes a numerical model for analyzing the thermal performance of a laboratory-scale solar thermochemical reactor, which has been designed and built for analysis of reduction of metal oxides. Model validation is accomplished by comparing the simulation results with experimental measurements and previous published numerical results. Parametric simulations are performed to examine the influence of gas flow rate and sample position on the reactor's thermal performance. Thermo-fluid flow inside the reactor, the total energy absorption, radiation losses, absorption efficiency, and maximum temperature attained by the sample are predicted for different operating conditions.

Reducing radiation losses of one-dimensional photonic-crystal reflectors on a silica waveguide

Interferometric behaviours in radiation generation process of a one-dimensional photonic-crystal (PhC) reflector are investigated on a silica waveguide. An analytical model, which can calculate total radiation losses, is presented after analysing eigen-mode properties and radiation pattern characteristics. Our model takes into account the interference of component radiated waves generated at interfaces between different waveguide sections and is verified by comparing with numerical simulations of periodic and non-periodic one-dimensional PhC reflectors. Its capability to quickly find minimum-radiation tapering geometries helps circumvent time-consuming numerical simulations. Our model negates the conventional knowledge that a gradually tapered transition from uniform waveguide to PhC waveguide yields lower radiation loss. In one example, the gradually tapered transition produces 2.3dB more radiation than the optimum geometry.

THE THERMAL PROPERTIES OF SOLAR FLARES OVER THREE SOLAR CYCLES USING GOES X-RAY OBSERVATIONS

Solar flare X-ray emission results from rapidly increasing temperatures and emission measures in flaring active region loops. To date, observations from the X-Ray Sensor (XRS) onboard the Geostationary Operational Environmental Satellite (GOES) have been used to derive these properties, but have been limited by a number of factors, including the lack of a consistent background subtraction method capable of being automatically applied to large numbers of flares. In this paper, we describe an automated temperature and emission measure-based background subtraction method (TEBBS), which builds on the methods of Bornmann (1990). Our algorithm ensures that the derived temperature is always greater than the instrumental limit and the pre-flare background temperature, and that the temperature and emission measure are increasing during the flare rise phase. Additionally, TEBBS utilizes the improved estimates of GOES temperatures and emission measures from White et al. (2005). TEBBS was successfully applied to over 50,000 solar flares occurring over nearly three solar cycles (1980-2007), and used to create an extensive catalog of the solar flare thermal properties. We confirm that the peak emission measure and total radiative losses scale with background subtracted GOES X-ray flux as power-laws, while the peak temperature scales logarithmically. As expected, the peak emission measure shows an increasing trend with peak temperature, although the total radiative losses do not. While these results are comparable to previous studies, we find that flares of a given GOES class have lower peak temperatures and higher peak emission measures than previously reported. The resulting TEBBS database of thermal flare plasma properties is publicly available on Solar Monitor (www.solarmonitor.org/TEBBS/) and will be available on Heliophysics Integrated Observatory (www.helio-vo.eu).

Radiation Properties of Oxygen-Enhanced Normal and Inverse Diffusion Flames

Radiative heat transfer in oxygen-enhanced inverse flame configurations is an important area of study for fundamental combustion research and for terrestrial and spacecraft fire safety. Motivated by this, heat flux distributions, total radiative heat loss and spectral radiation intensities were investigated experimentally for oxygen-enhanced normal and inverse laminar ethane diffusion flames with increasing heat release rates. The oxygen mole fraction in the oxidizer was varied as 21%, 30%, 50%, and 100% with coflowing normal and inverse flame burners used to stabilize the flames. The inverse diffusion flames were essentially nonluminous while the normal diffusion flames with identical heat release rates were highly luminous. Oxygen enhancement led to reduced flame lengths, increased luminosities and increased total radiative heat loss and spectral radiation intensities for both normal and inverse diffusion flames. Using flame length as the characteristic length parameter, the normalized radiative heat flux distributions for flames approximately collapsed together, further establishing the effectiveness of the single point radiant output measurement technique. Radiative heat loss fractions of normal and inverse diffusion flames with varying oxygen concentrations in the oxidizer are compared. The radiation spectra of all flames included significant contributions from gas radiation from carbon dioxide and water vapor and the radiation spectra of the high oxygen concentration flames included contributions from soot radiation.

Dielectronic recombination and satellite line spectra of highly charged tungsten ions1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

We present our recent progress on theoretical studies that involve auto-ionizing states of highly charged tungsten ions. Such auto-ionizing states have two channels for decay, which requires that both radiative and auto-ionization atomic data be calculated and combined in a detailed study of the dielectronic recombination (DR). Three atomic codes are used to produce relativistic atomic data (energy levels, radiative transition probabilities, and auto-ionization rates). These are the relativistic many-body perturbation theory (RMBPT) code, the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (HULLAC), and the Hartree–Fock relativistic (Cowan) code. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and DR rate coefficients are determined for the excited states. The total DR rate coefficient is derived as a function of electron temperature, and it is shown that the contribution of the highly excited states is very important for the calculation of the total DR rates. Synthetic dielectronic satellite spectra are constructed, and the atomic properties specific to the relevant tungsten ions are highlighted. First, we will consider the results for Na-like tungsten (W63+) and Mg-like tungsten (W62+) using all three codes. Then, we move to even higher ionization states and present the results in Li-like W (W71+). For this we use the RMBPT code as well as the quasi-relativistic many-body perturbation theory (MZ) code. The inclusion of the DR process is essential for correct identification of the lines in impurity spectra and for understanding the main contributions to the total radiation losses.

Thermoregulation during Flight: Body Temperature and Sensible Heat Transfer in Free-Ranging Brazilian Free-Tailed Bats (Tadarida brasiliensis)

Bat wings are important for thermoregulation, but their role in heat balance during flight is largely unknown. More than 80% of the energy consumed during flight generates heat as a by-product, and thus it is expected that bat wings should dissipate large amounts of heat to prevent hyperthermia. We measured rectal (T(r)) and surface (T(s)) temperatures of Brazilian free-tailed bats (Tadarida brasiliensis) as they emerged from and returned to their daytime roosts and calculated sensible heat transfer for different body regions (head, body, wings, and tail membrane). Bats' T(r) decreased from 36.8°C during emergence flights to 34.4°C during returns, and T(s) scaled positively with ambient temperature (T(a)). Total radiative heat loss from bats was significantly greater for a radiative sink to the night sky than for a sink with temperature equal to T(a). We found that free-ranging Brazilian free-tailed bats, on average, do not dissipate heat from their wings by convection but instead dissipate radiative heat (L) to the cloudless night sky during flight ([Formula: see text] W). However, within the range of T(a) measured in this study, T. brasiliensis experienced net heat loss between evening emergence and return flights. Regional hypothermia reduces heat loss from wings that are exposed to potentially high convective fluxes. Additional research is needed to establish the role of wings in evaporative cooling during flight in bats.

Investigation on Total Bremsstrahlung Radiation in High-Density Operation of Large Helical Device Based on Visible Bremsstrahlung Profile Measurement

Visible bremsstrahlung emission profiles have been studied over a wide range of electron densities in H2 gas puff and solid-H2-pellet-fueled discharges of large helical device (LHD). Peaked profiles are observed in high-density discharges (ne≥1014 cm-3) with pellet injection, whereas hollow profiles appeared in the normal discharges (ne≤1014 cm-3) with gas puffing. The total bremsstrahlung radiation is analyzed from the visible bremsstrahlung profile by integrating the energy and plasma volume. It is found that the total bremsstrahlung radiation rapidly increases with the density in the pellet discharges, of which the increment is scaled by the square of density, while it is roughly constant against the density in the gas puff discharges. The total bremsstrahlung radiation becomes equal to the total radiation loss in the pellet discharges. The ratio of the total bremsstrahlung radiation to the total input power has only a range of 3–10% in the gas puff discharges. In contrast, the ratio increases with the density and reaches 30–40% in the pellet discharges. Flat Zeff profiles are observed not only in the gas puff discharges but also in the pellet discharges. This indicates that no impurity accumulation occurs in the high-density operation with H2 pellet injection.

Modeling of Plasma Parameters during High Pressure Gas Injection with a Three Temperature Model

AbstractA three temperature model is constructed to describe dynamics of plasma parameters during argon injection, which is aimed to mitigate disruption consequences. Model predicts fast decrease of electron and ion temperatures, distribution of ionization stages and average ion charge in time, the rate of total radiation losses and time dependent intensities of ArXVII lines, widely used in plasma diagnostics. It was found that rapid drop of electron temperature is not associated with radiation losses (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

G-BAND AND HARD X-RAY EMISSIONS OF THE 2006 DECEMBER 14 FLARE OBSERVED BYHINODE/SOT ANDRHESSI

We report on G-band emission observed by the Solar Optical Telescope onboard the Hinode satellite in association with the X1.5-class flare on 2006 December 14. The G-band enhancements originate from the footpoints of flaring coronal magnetic loops, coinciding with non-thermal hard X-ray bremsstrahlung sources observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager. At the available 2 minute cadence, the G-band and hard X-ray intensities are furthermore well correlated in time. Assuming that the G-band enhancements are continuum emission from a blackbody, we derived the total radiative losses of the white-light flare (white-light power). If the G-band enhancements additionally have a contribution from lines, the derived values are overestimates. We compare the white-light power with the power in hard X-ray producing electrons using the thick target assumption. Independent of the cutoff energy of the accelerated electron spectrum, the white-light power and the power of accelerated electrons are roughly proportional. Using the observed upper limit of ~30 keV for the cutoff energy, the hard X-ray producing electrons provide at least a factor of 2 more power than needed to produce the white-light emission. For electrons above 40 keV, the powers roughly match for all four of the time intervals available during the impulsive phase. Hence, the flare-accelerated electrons contain enough energy to produce the white-light flare emissions. The observed correlation in time, space, and power strongly suggests that electron acceleration and white-light production in solar flares are closely related. However, the results also call attention to the inconsistency in apparent source heights of the hard X-ray (chromosphere) and white-light (upper photosphere) sources.

Klein–Nishina steps in the energy spectrum of galactic cosmic-ray electrons

The full Klein–Nishina cross-section of the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared with the Thomson limit when the electron energy exceeds the critical Klein–Nishina energy EK=γKmec2=0.27m2ec4/(kBT), where T denotes the temperature of the photon graybody distribution. As a consequence, the total radiative energy loss rate of single electrons exhibits sudden drops in the overall -dependence when the electron energy reaches the critical Klein–Nishina energy. The strength of the drop is proportional to the energy density of the photon radiation field. The diffuse galactic optical photon fields from stars of spectral type B and G-K lead to critical Klein–Nishina energies of 40 and 161 GeV, respectively. Associated with the drop in the loss rate are sudden increases (Klein–Nishina steps) in the equilibrium spectrum of cosmic-ray electrons. Because the radiative loss rate of electrons is the main ingredient in any transport model of high-energy cosmic-ray electrons, Klein–Nishina steps will modify any calculated electron equilibrium spectrum irrespective of the electron sources and the spatial transport mode. To delineate most clearly the consequences of the Klein–Nishina decreases in the radiative loss rate, we chose as an illustrative example the simplest realistic model for cosmic-ray electron dynamics in the galaxy, consisting of the competition of radiative losses and secondary production by inelastic hadron–hadron collisions. We demonstrate that the spectral structure in the FERMI and HESS data is well described and even the excess measured by ATIC might be explained by Klein–Nishina steps.