Analytical Yield Spectrum Approach Research Articles

The dayside ionosphere of Mars: Comparing a one-dimensional photochemical model with MAVEN Deep Dip campaign observations

A one dimensional photochemical model for the dayside ionosphere of Mars has been developed for calculating the density profiles of ions and electrons under steady state photochemical equilibrium condition. The study focuses on the Deep Dip campaigns of the Mars Atmosphere and Volatile EvolutioN mission (MAVEN) and used the in-situ measurements of neutral density profiles, solar flux and electron temperatures from instruments onboard MAVEN as input to the model. An energy deposition model is employed for calculating the attenuated photon flux and photoelectron flux at different altitudes in the ionosphere. The Analytical Yield Spectrum approach is used for calculating the photoelectron fluxes. Volume production rates of major primary ions, CO2+, CO+, O+, C+, N2+, and N+, due to photon and photoelectron impact are calculated and used as input to the model in which ion-neutral chemistry in the dayside ionosphere is simulated. The modeled ion profiles are compared with the ion mode observations of Neutral Gas Ion Mass Spectrometer (NGIMS) and electron density estimates from Langmuir Probe and Waves (LPW). The model could reproduce the observed structure of the major ion profiles O2+, CO2+, and electron density reasonably well. However, when the magnitudes are compared, the modeled values are roughly a factor of 2 larger than observation. By reducing the neutral CO2 density, the model outputs and the observed ion profiles and electron density profile can become closer. The model also calculated the densities of 11 other ions, viz. N+, C+, O+, NO+, N2H+, HCO+, N2+, CO+, OCOH+, HNO+, and OH+. Profiles of each of these ions are compared with the NGIMS observations during the respective orbits and are discussed in detail. Such a comparison for the deep dip periods is reported for the first time, which showcases the level of the current understanding of the ion chemistry in the Martian ionosphere.

Dayside ionosphere of Titan: Impact on calculated plasma densities due to variations in the model parameters

A one dimensional photochemical model for the dayside ionosphere of Titan has been developed for calculating the density profiles of ions and electrons under steady state photochemical equilibrium condition. We concentrated on the T40 flyby of Cassini orbiter and used the in-situ measurements from instruments onboard Cassini as input to the model. An energy deposition model is employed for calculating the attenuated photon flux and photoelectron flux at different altitudes in Titan’s ionosphere. We used the Analytical Yield Spectrum approach for calculating the photoelectron fluxes. Volume production rates of major primary ions, like, N2+, N+, CH4+, CH3+, etc due to photon and photoelectron impact are calculated and used as input to the model. The modeled profiles are compared with the Cassini Ion Neutral Mass Spectrometer (INMS) and Langmuir Probe (LP) measurements. The calculated electron density is higher than the observation by a factor of 2 to 3 around the peak. We studied the impact of different model parameters, viz. photoelectron flux, ion production rates, electron temperature, dissociative recombination rate coefficients, neutral densities of minor species, and solar flux on the calculated electron density to understand the possible reasons for this discrepancy. Recent studies have shown that there is an overestimation in the modeled photoelectron flux and N2+ ion production rates which may contribute towards this disagreement. But decreasing the photoelectron flux (by a factor of 3) and N2+ ion production rate (by a factor of 2) decreases the electron density only by 10 to 20%. Reduction in the measured electron temperature by a factor of 5 provides a good agreement between the modeled and observed electron density. The change in HCN and NH3 densities affects the calculated densities of the major ions (HCNH+, C2H5+, and CH5+); however the overall impact on electron density is not appreciable ( < 20%). Even though increasing the dissociative recombination rate coefficients of the ions C2H5+ and CH5+ by a factor of 10 reduces the difference between modeled and observed densities of the major ions, the modeled electron density is still higher than the observation by ∼ 60% at the peak. We suggest that there might be some unidentified chemical reactions that may account for the additional loss of plasma in Titan’s ionosphere.

The generation of Ganymede's diffuse aurora through pitch angle scattering

Abstract. Diffuse auroral intensities of neutral atomic oxygen OI λ1356 Å emission on Ganymede due to whistler mode waves are estimated. Pitch angle diffusion of magnetospheric electrons into the loss cone due to resonant wave–particle interaction of whistler mode waves is considered, and the resulting electron precipitation flux is calculated. The analytical yield spectrum approach is used for determining the energy deposition of electrons precipitating into the atmosphere of Ganymede. It is found that the intensities (4–30 R) calculated from the precipitation of magnetospheric electrons observed near Ganymede are inadequate to account for the observational intensities (≤ 100 R). This is in agreement with the conclusions reached in previous works. Some acceleration mechanism is required to energize the magnetospheric electrons. In the present work we consider the heating and acceleration of magnetospheric electrons by electrostatic waves. Two particle distribution functions (Maxwellian and kappa distribution) are used to simulate heating and acceleration of electrons. Precipitation of a Maxwellian distribution of electrons can produce about 70 R intensities of OI λ1356 Å emission for electron temperature of 150 eV. A kappa distribution can also yield a diffuse auroral intensity of similar magnitude for a characteristic energy of about 100 eV. The maximum contribution to the estimated intensity results from the dissociative excitation of O2. Contributions from the direct excitation of atomic oxygen and cascading in atomic oxygen are estimated to be only about 1 and 2 % of the total calculated intensity, respectively. The findings of this work are relevant for the present JUNO and future JUICE missions to Jupiter. These missions will provide new data on electron densities, electron temperature and whistler mode wave amplitudes in the magnetosphere of Jupiter near Ganymede.

DIFFUSE AURORA ON GANYMEDE DRIVEN BY ELECTROSTATIC WAVES

ABSTRACT The role of electrostatic electron cyclotron harmonic (ECH) waves in producing diffuse auroral emission O i 1356 Å on Ganymede is investigated. Electron precipitation flux entering the atmosphere of Ganymede due to pitch-angle diffusion by ECH waves into the atmospheric loss-cone is calculated. The analytical yield spectrum approach for electron energy degradation in gases is used for calculating diffuse auroral intensities. It is found that calculated O i 1356 Å intensity resulting from the precipitation of magnetospheric electrons observed near Ganymede is insufficient to account for the observed diffuse auroral intensity. This is in agreement with estimates made in earlier works. Heating and acceleration of ambient electrons by ECH wave turbulence near the magnetic equator on the field line connecting Ganymede and Jupiter are considered. Two electron distribution functions are used to simulate the heating effect by ECH waves. Use of a Maxwellian distribution with temperature 100 eV can produce about 50–70 Rayleigh O i 1356 Å intensities, and the kappa distribution with characteristic energy 50 eV also gives rise to intensities with similar magnitude. Numerical experiments are performed to study the effect of ECH wave spectral intensity profile, ECH wave amplitude, and temperature/characteristic energy of electron distribution functions on the calculated diffuse auroral intensities. The proposed missions, joint NASA/ESA Jupiter Icy Moon Explorer and the present JUNO mission to Jupiter, would provide new data to constrain the ECH wave and other physical parameters near Ganymede. These should help confirm the findings of the present study.

Evidence of baroclinic waves in the upper atmosphere of Mars using the Mars Global Surveyor accelerometer data

Here we use accelerometer data of 115 orbits (#P0670–P0789) from 1–30 November 1998, between latitude ranges (50–70°N), and of 57 orbits (#P0588–P0648) from 30 September 1998 to 24 October 1998, between latitude ranges (50–70°N), both under spring equinox and medium solar activity conditions. The neutral densities of different gases are derived from their mixing ratio. From these neutral densities, the longitudinal distribution of total peak ionization rates of CO2+, N2+, O2+, O+, and CO+ are obtained for solar zenith angle 78° because of solar EUV and soft X‐ray (1–102.57 nm) radiation using Analytical Yield Spectrum approach. These calculations are made at different altitudes and longitudes starting from 115 to 220 km and from 0 to 360°E using intervals of 0.1 km and 5°, respectively. These conditions are appropriate for Mars Global Surveyor Phase 2 aerobraking period from which the accelerometer data is used. The Fourier analysis is carried out on the calculated total peak ionization rates for different gases both at midlatitude (17–42°N) and high‐latitude (50–70°N) range in the upper atmosphere of Mars. This analysis at high latitude indicates the presence of two dominant harmonic regions, in which the first is a class of long planetary‐scale waves, associated with the fixed topography of Martian surface, while the second is a class of rapidly moving transient disturbances associated with baroclinic instability processes. The similar analysis carried out at midlatitude (17–42°N) region indicates the absence of second peak at higher wave number, confirming that the baroclinic instability is almost absent at this latitude region.

Longitudinal distribution of thermospheric densities and ionization rates in the upper atmosphere of Mars at mid-latitude using MGS ACC data

The Accelerometer Experiment (ACC) onboard Mars Global Surveyor (MGS) measured 1600 density profiles in the upper atmosphere of Mars during aerobraking. These measurements reveal large-scale and small-scale structure in the thermosphere of Mars. Here, the measurements of mass density for 115 orbits (#P0670–P0789) from November 1 to 30, 1998, under spring equinox and medium solar activity conditions (average F 10.7 ∼ 137) during phase 2 of the aerobraking in the thermosphere of Mars at different altitudes and longitudes are presented for northern mid-latitude (17–42°N) in the dayside atmosphere using ACC onboard MGS. From these mass densities, the neutral densities of different gases are derived from their mixing ratios. Using these neutral densities, the longitudinal distribution of photoionization rates and photoelectron impact ionization rates are calculated at wavelength range 1–102.57 nm due to EUV and soft X-ray radiation under photochemical controlled region using Analytical Yield Spectrum approach (AYS). These conditions are appropriate for MGS Phase 2 aerobraking period from which the accelerometer data is used. Under the photochemical equilibrium condition, the electron density near the peak varies as the square root of the total peak ionization rate. Using this fact, an attempt is being made to estimate the mean primary and secondary peak electron density by averaging the longitudinal variations of total peak ionization rates in the northern mid-latitude (17–42°N) ionosphere of Mars, as there is no radio science measurement at this latitude region by MGS.

Zonal variations of peak ionization rates in upper atmosphere of Mars at high latitude using Mars Global Surveyor accelerometer data

The Accelerometer Experiment onboard Mars Global Surveyor (MGS) measured many density profiles in the upper atmosphere of Mars during aerobraking at many latitudes, longitudes, altitudes, local solar time (LST), and seasons. Here, in this paper, we use the accelerometer data of 57 orbits (P0588–P0648) from 30 September 1998 to 24 October 1998 between latitude ranges (50°–70°N) at LST 1600 hours, under spring equinox and medium solar activity conditions (average F10.7 ∼ 120). Using these densities, the neutral densities of different gases are derived from their mixing ratio. From these neutral densities the longitudinal distribution of peak photoionization rates, peak photoelectron impact ionization rates, and the total peak ionization rates of CO2+, N2+ and O+ are obtained for solar zenith angle 78° at wavelength range 10–1025.7 Å due to solar EUV radiation using analytical yield spectrum approach (AYS). These calculations are made at different altitudes and longitudes starting from 115 to 220 km and 0° to 360°E using intervals of 0.1 km and 5°, respectively. These conditions are appropriate for MGS phase 2 aerobraking period from which the accelerometer data are used. The Fourier analysis of the various peak ionization rates of CO2+, N2+, and O+ indicates the presence of two dominant harmonic regions at high latitude in the upper atmosphere of Mars. The first is a class of long planetary‐scale waves that may be associated with the fixed topography of Martian surface. The second is a class of rapidly moving transient disturbances that may be associated with baroclinic instability processes.

Radial distribution of production rates, loss rates and densities corresponding to ion masses ⩽40 amu in the inner coma of Comet Halley: Composition and chemistry

In this paper we have studied the chemistry of C, H, N, O, and S compounds corresponding to ions of masses ⩽40 amu in the inner coma of the Comet 1P/Halley. The production rates, loss rates, and ion mass densities are calculated using the Analytical Yield Spectrum approach and solving coupled continuity equation controlled by the steady state photochemical equilibrium condition. The primary ionization sources in the model are solar EUV photons, photoelectrons, and auroral electrons of the solar wind origin. The chemical model couples ion–neutral, electron–neutral, photon–neutral and electron–ion reactions among ions, neutrals, electrons, and photons through over 600 chemical reactions. Of the 46 ions considered in the model the chemistry of 24 important ions (viz., CH 3OH + 2, H 3CO +, NH + 4, H 3S +, H 2CN +, H 2O +, NH + 3, CO +, C 3H + 3, OH +, H 3O +, CH 3OH +, C 3H + 4, C 2H + 2, C 2H +, HCO +, S +, CH + 3, H 2S +, O +, C +, CH + 4, C + 2, and O + 2) are discussed in this paper. At radial distances <1000 km, the electron density is mainly controlled by 6 ions, viz., NH + 4, H 3O +, CH 3OH + 2, H 3S +, H 2CN +, and H 2O +, in the decreasing order of their relative contribution. However, at distances >1000 km, the 6 major ions are H 3O +, CH 3OH + 2, H 2O +, H 3CO +, C 2H + 2, and NH + 4; along with ions CO +, OH +, and HCO +, whose importance increases with further increase in the radial distance. It is found that at radial distances greater than ∼1000 km (±500 km) the major chemical processes that govern the production and loss of several of the important ions in the inner coma are different from those that dominate at distances below this value. The importance of photoelectron impact ionization, and the relative contributions of solar EUV, and auroral and photoelectron ionization sources in the inner coma are clearly revealed by the present study. The calculated ion mass densities are compared with the Giotto Ion Mass Spectrometer (IMS) and Neutral Mass Spectrometer (NMS) data at radial distances 1500, 3500, and 6000 km. There is a reasonable agreement between the model calculation and the Giotto measurements. The nine major peaks in the IMS spectra between masses 10 and 40 amu are reproduced fairly well by the model within a factor of two inside the ionopause. We have presented simple formulae for calculating densities of the nine major ions, which contribute to the nine major peaks in the IMS spectra, throughout the inner coma that will be useful in estimating their densities without running the complex chemical models.

Photoelectron flux and nightglow emissions of 5577 and 6300 Å due to solar wind electron precipitation in Martian atmosphere

The detailed model calculations of photoelectron flux and nightglow emissions of 5577 and 6300 Å lines are made using analytical yield spectrum approach based on Monte Carlo method. The calculated photoelectron spectra are compared with electron reflectometer (ER) measurements made by Mars Global Surveyor (MGS) at the energy range 10–1000 eV. This calculation suggests that X‐ray ionization is an important process in the dayside ionosphere of Mars at energy greater than 90 eV, and 10‐ to 90‐eV electron population is controlled by photoionization and photoelectron impact ionization. The secondary electron flux, excitation rates, emission rates, and limb intensities of 5577 and 6300 Å lines are calculated due to precipitation of solar wind electrons observed by ER experiment at the energy range 10–1000 eV in the nighttime ionosphere of Mars. In the vicinity of the peak altitudes, it is found that excitation/emission of atomic oxygen after the electron impact dissociation of CO2 is the main source of 5577 Å emissions, while dissociative recombination of molecular oxygen ion is the major source of 6300 Å emissions after the electron impact excitation of atomic oxygen. The calculated secondary electron spectra are also compared with ER experiment measurements between energies of 10 and 1000 eV. The nightglow limb intensities are compared with the upper limit set by Mars 5 spectroscopic observations.

An anomalous subauroral red arc on 4 August, 1972: comparison of ISIS-2 satellite data with numerical calculations

Abstract. This study compares the Isis II satellite measurements of the electron density and temperature, the integral airglow intensity and volume emission rate at 630 nm in the SAR arc region, observed at dusk on 4 August, 1972, in the Southern Hemisphere, during the main phase of the geomagnetic storm. The model results were obtained using the time dependent one-dimensional mathematical model of the Earth's ionosphere and plasmasphere (the IZMIRAN model). The major enhancement to the IZMIRAN model developed in this study to explain the two component 630 nm emission observed is the analytical yield spectrum approach to calculate the fluxes of precipitating electrons and the additional production rates of N+2, O+2, O+(4S), O+(2D), O–(2P), and O+(2P) ions, and O(1D) in the SAR arc regions in the Northern and Southern Hemispheres. In order to bring the measured and modelled electron temperatures into agreement, the additional heating electron rate of 1.05 eV cm–3 s–1 was added in the energy balance equation of electrons at altitudes above 5000 km during the main phase of the geomagnetic storm. This additional heating electron rate determines the thermally excited 630 nm emission observed. The IZMIRAN model calculates a 630 nm integral intensity above 350 km of 4.1 kR and a total 630 nm integral intensity of 8.1 kR, values which are slightly lower compared to the observed 4.7 kR and 10.6 kR. We conclude that the 630 nm emission observed can be explained considering both the soft energy electron excited component and the thermally excited component. It is found that the inclusion of N2(v &gt; 0) and O2(v &gt; 0) in the calculations of the O+(4S) loss rate improves the agreement between the calculated Ne and the data on 4 August, 1972. The N2(v &gt; 0) and O2(v &gt; 0) effects are enough to explain the electron density depression in the SAR arc F-region and above F2 peak altitude. Our calculations show that the increase in the O++N2 rate factor due to the vibrationally excited nitrogen produces the 5–19% reductions in the calculated quiet daytime peak density and the 16–24% decrease in NmF2 in the SAR arc region. The increase in the O++N2 loss rate due to vibrationally excited O2 produces the 7–26% decrease in the calculated quiet daytime peak density and the 12–26% decrease in NmF2 in the SAR arc region. We evaluated the role of the electron cooling rates by low-lying electronic excitation of O2(a1Δg) and O2(b1Σg+), and rotational excitation of O2, and found that the effect of these cooling rates on Te can be considered negligible during the quiet and geomagnetic storm period 3-4 August, 1972. The energy exchange between electron and ion gases, the cooling rate in collisions of O(3P) with thermal electrons with excitation of O(1D), and the electron cooling rates by vibrational excitation of O2 and N2 are the largest cooling rates above 200 km in the SAR arc region on 4 August, 1972. The enhanced IZMIRAN model calculates also number densities of N2(B3Πg+),N2(C3Πu), and N2(A3Σu+) at several vibrational levels, O(1S), and the volume emission rate and integral intensity at 557.7 nm in the region between 120 and 1000 km. We found from the model that the integral intensity at 557.7 nm is much less than the integral intensity at 630 nm.Key words. Atmospheric composition and structure (airglow and aurora; thermosphere – composition and chemistry) · Ionosphere (ionosphere – magnetosphere interactions)

An anomalous subauroral red arc on 4 August, 1972: comparison of ISIS-2 satellite data with numerical calculations

This study compares the Isis II satellite measurements of the electron density and temperature, the integral airglow intensity and volume emission rate at 630 nm in the SAR arc region, observed at dusk on 4 August, 1972, in the Southern Hemisphere, during the main phase of the geomagnetic storm. The model results were obtained using the time dependent one-dimensional mathematical model of the Earth's ionosphere and plasmasphere (the IZMIRAN model). The major enhancement to the IZMIRAN model developed in this study to explain the two component 630 nm emission observed is the analytical yield spectrum approach to calculate the fluxes of precipitating electrons and the additional production rates of N+2, O+2, O+(4S), O+(2D), O–(2P), and O+(2P) ions, and O(1D) in the SAR arc regions in the Northern and Southern Hemispheres. In order to bring the measured and modelled electron temperatures into agreement, the additional heating electron rate of 1.05 eV cm–3 s–1 was added in the energy balance equation of electrons at altitudes above 5000 km during the main phase of the geomagnetic storm. This additional heating electron rate determines the thermally excited 630 nm emission observed. The IZMIRAN model calculates a 630 nm integral intensity above 350 km of 4.1 kR and a total 630 nm integral intensity of 8.1 kR, values which are slightly lower compared to the observed 4.7 kR and 10.6 kR. We conclude that the 630 nm emission observed can be explained considering both the soft energy electron excited component and the thermally excited component. It is found that the inclusion of N2(v > 0) and O2(v > 0) in the calculations of the O+(4S) loss rate improves the agreement between the calculated Ne and the data on 4 August, 1972. The N2(v > 0) and O2(v > 0) effects are enough to explain the electron density depression in the SAR arc F-region and above F2 peak altitude. Our calculations show that the increase in the O++N2 rate factor due to the vibrationally excited nitrogen produces the 5–19% reductions in the calculated quiet daytime peak density and the 16–24% decrease in NmF2 in the SAR arc region. The increase in the O++N2 loss rate due to vibrationally excited O2 produces the 7–26% decrease in the calculated quiet daytime peak density and the 12–26% decrease in NmF2 in the SAR arc region. We evaluated the role of the electron cooling rates by low-lying electronic excitation of O2(a1Δg) and O2(b1Σg+), and rotational excitation of O2, and found that the effect of these cooling rates on Te can be considered negligible during the quiet and geomagnetic storm period 3-4 August, 1972. The energy exchange between electron and ion gases, the cooling rate in collisions of O(3P) with thermal electrons with excitation of O(1D), and the electron cooling rates by vibrational excitation of O2 and N2 are the largest cooling rates above 200 km in the SAR arc region on 4 August, 1972. The enhanced IZMIRAN model calculates also number densities of N2(B3Πg+),N2(C3Πu), and N2(A3Σu+) at several vibrational levels, O(1S), and the volume emission rate and integral intensity at 557.7 nm in the region between 120 and 1000 km. We found from the model that the integral intensity at 557.7 nm is much less than the integral intensity at 630 nm.Key words. Atmospheric composition and structure (airglow and aurora; thermosphere – composition and chemistry) · Ionosphere (ionosphere – magnetosphere interactions)

Chemistry of the ions ≤40 amu in the inner coma of comet Halley

The chemistry of ions corresponding to ≤40 amu inside the ionopause of comet Halley is studied using the Analytical Yield Spectrum approach and coupled continuity equations for the steady state condition. Six hundred reactions including the chemistry of carbon, hydrogen, nitrogen, oxygen and sulphur compounds are taken in this calculation. The ionization of these compounds due to the impact of solar extreme ultraviolet photon, photoelectron and auroral electron of solar wind origin have been studied. The effects of these ionization sources on the density of ions are discussed. The results are compared with the measurements made by High Intensity Spectrometer (HIS) onboard Giotto spacecraft.

Chemistry of the nightside ionosphere of Mars

The chemistry of seven ions, O2+, NO+, CO2+, O+, N2+, CO+, and H+, is studied in the nightside ionosphere of Mars using the analytical yield spectrum approach and coupled continuity equations for the steady state condition. The source and sink processes of these ions are discussed in detail. We have found that the nightside Martian ionosphere produced due to precipitation of magnetotail electrons agrees with the Viking observations rather than other sources of ionization such as the precipitation of plasma sheet electron or horizontal plasma transport from dayside ionosphere to the nightside similar to that operating on Venus, The precipitation of magnetotail electron produces major ion CO2+ which is quickly removed by the reactions (1) CO2+ + O → O2+ + CO, (2) CO2+ + O → O+ + CO2 and (3) O+ + CO2 → O2+ + CO leading to O2+ as a dominant ion in the nightside ionosphere of Mars. The reactions of O+ with N and NO are the major sources of NO+, which is lost entirely by dissociative recombination reaction. The second reaction is the major source of O+ below 190 km. Above this altitude the magnetotail electron impact ionization process is an important source of O+. This process is also important for the production of CO+ and N2+. The ion O+ is destroyed by the third reaction, while CO+ and N2+ are destroyed by charge transfer reaction with CO2. The ion H+ is produced due to charge exchange reaction between O+ and H which is lost by CO2.

Auroral and photoelectron fluxes in cometary ionospheres

Photoelectron and auroral electron fluxes in cometary ionospheres have been studied in detail using the analytical yield spectrum approach. The effects on photoelectron fluxes of cometocentric distance, solar zenith angle (using generalized Chapman function), and solar minimum and maximum conditions, on the assumption of local energy deposition, are determined. Energy loss to ambient electrons is accounted for. Auroral electron fluxes are calculated for monoenergetic and observed primary electron spectra. The results are compared with other theoretical works and good agreement is found. Auroral electrons make a larger contribution to the observed electron spectrum compared with the extreme ultraviolet-generated photoelectrons.

Analytical yield spectrum approach to photoelectron fluxes in the Earth’s atmosphere

The analytical yield spectrum approach has been applied to calculate the photoelectron fluxes in the earth’s atmosphere. The results have been compared with the experimental data of Lee et al. (1980a, b). Good agreement is obtained at low altitudes. At high altitudes our theoretical results are lower than the experimental data in the energy region 18–23 eV by a factor of 1.5 and in the 35–45 eV by a factor of 2. Comparison with theoretical calculations performed by other workers shows that if the same set of inelastic electron impact cross sections had been used, then the photoelectron models of Strickland and Anderson (1983) and Richards and Torr(1983) would be in good agreement with our work and the experimental data. However, the photoelectron fluxes calculated by the model of Victor et al. (1976) is not consistent with the other theoretical models or the experimental data.

Analytical yield spectrum approach to electron energy degradation in Earth's atmosphere

Analytical spatial yield spectrum approach has been applied to calculate the electron flux, volume excitation, and ionization rates for monoenergetic electrons incident on the earth's atmosphere. The results have been compared with the previous model calculations of Mantas and Walker (1976) and Banks et al. (1974).