A study of the dynamics of a discrete auroral arc

High resolution electric field and particle data, obtained by the S23L1 rocket crossing over a discrete prebreakup arc in January 1979, are studied in coordination with ground observations (Scandinavian Magnetometer Array—SMA, TV and all-sky cameras) in order to clarify the electrodynamics of the arc and its surroundings. Height-integrated conductivities have been calculated from the particle data, including the ionization effects of precipitating protons and assuming a steady state balance between ion production and recombination losses. High resolution optical information of arc location relative to the rocket permitted a check of the validity of this assumption for each flux tube passed by the rocket. Another check was provided by a comparison between calculated (equilibrium values) and observed electron densities along the rocket trajectory. A way to compensate for the finite precipitation time when calculating the electron densities is outlined. The height-integrated HalI-Pedersen conductivity ratio is typically 1.4 within the arc and about 1 at the arc edges, indicative of a relatively softer energy spectrum there. The height-integrated conductivities combined with the DC electric field measurements permitted calculation of the horizontal ionospheric current vectors (J_⊥), Birkeland currents (from div J_⊥) and energy dissipation through Joule heating (Σ_pE²). An eastward current of typically 1 A m^?1 was found to be concentrated mainly to the arc region and equatorward of it. A comparison has been made with the equivalent current system deduced from ground based magnetometer data (SMA) showing a generally good agreement with the rocket results. An intense Pedersen current peak (1.2 A m^?1) was found at the southern arc edge. This edge constituted a division line between a very intense (> 10 μA m^?1) and localized (~ 6 km) downward current sheet to the south, probably carried by upward flowing cold ionospheric electrons and a more extended upward current sheet (> 10 μA m^?2) over the arc carried by measured precipitating electrons. Joule and particle heating across the arc were anticorrelated, consistent with the findings of Evans et al. (1977) with a total value of about 100mW m^?2.     

The influence of a turbulent region on the flux of auroral electrons

The influence of low-frequency electrostatic turbulence on the flux of precipitating magnetospheric electrons is analyzed in the framework of the quasilinear kinetic equation. It is shown that an electron population in a turbulent region, with an electric field parallel to the ambient magnetic field, can be separated into two parts by introducing a pitch angle dependent runaway velocity v_r(θ). Lower energy electrons with parallel velocity v_∥ < v_r are effectively scattered by plasma waves, so that they remain in the main population and are subjected to an anomalous transport equation. A distribution function f ∞ v^?4 (or the particle flux vs energy J ∞ E^?1) is established in this velocity range. Faster electrons with v_∥ ? v_r are freely accelerated by a parallel electric field, so that they contribute directly to hot electron fluxes which are observed at ionospheric altitudes. New expressions are derived for the magnetic-field aligned current and the electron energy flux implied by this model. These expressions agree well with empirical relations observed in auroral inverted-V structures.     

Electron plasma oscillations associated with type III radio emissions and solar electrons

An extensive study of the IMP-6 and IMP-8 plasma and radio wave data has been performed to try to find electron plasma oscillations associated with type III radio noise bursts and low-energy solar electrons. This study shows that electron plasma oscillations are seldom observed in association with solar electron events and type III radio bursts at 1.0 AU. In nearly four years of observations only one event was found in which electron plasma oscillations are clearly associated with solar electrons. For this event the plasma oscillations appeared coincident with the development of a secondary maximum in the electron velocity distribution functions due to solar electrons streaming outwards from the Sun. Numerous cases were found in which no electron plasma oscillations with field strengths greater than 1 μV m^?1 could be detected even though electrons from the solar flare were clearly detected at the spacecraft. For the one case in which electron plasma oscillations are definitely produced by the electrons ejected by the solar flare the electric field strength is relatively small, only about 100 μV m^?1. This field strength is about a factor of ten smaller than the amplitude of electron plasma oscillations generated by electrons streaming into the solar wind from the bow shock. Electromagnetic radiation, believed to be similar to the type III radio emission, is also observed coming from the region of the more intense electron plasma oscillations upstream of the bow shock. Quantitative calculations of the rate of conversion of the plasma oscillation energy to electromagnetic radiation are presented for plasma oscillations excited by both solar electrons and electrons from the bow shock. These calculations show that neither the type III radio emissions nor the radiation from upstream of the bow shock can be adequately explained by a current theory for the coupling of electron plasma oscillations to electromagnetic radiation. Possible ways of resolving these difficulties are discussed.     

Influence of the Variations of Current Sheet Parameters on the Acceleration of Electrons

By the test particle method, we have investigated the kinematic characteristics of the electrons in the reconnecting current sheet with a guiding magnetic field B_z after they are accelerated by the supper-Dreicer electric field E_z. Firstly, the influence of the guiding magnetic field B_z on the particle acceleration is discussed under the assumption that B_z is constant in magnitude but different in orientation with respect to the electric field. In this case, the variation of the B_z direction directly leads to the variation of electron trajectories and makes electrons leave the current sheet along different paths. If B_z is parallel to E_z, the pitch angles of the accelerated electrons are close to 180°. If B_z is anti-parallel to E_z, the pitch angles of the accelerated electrons are close to 0°. The orientation of the guiding magnetic field just makes the electric field accelerate selectively the electrons in different regions, but does not change the energy distribution of electrons, and the finally derived energy spectrum is the common power-law spectrum E^?γ. In typical coronal conditions, γ is about 2.9. The further study indicates that the magnitude of γ depends on the strengths of the guiding magnetic field and reconnecting electric field, as well as the scale of the current sheet. Then, the kinematic characteristics of the accelerated electrons in the current sheet with multiple X-points and O-points are also studied. The result indicates that the existences of the X-points and O-points have the particles constrained in the accelerating region to obtain the maximum acceleration, and the final energy spectrum has the characteristics of multi-power law spectra.     

Antarctic substorm events observed by sounding rockets,ionization of the D- and E-regions by auroral electrons

The ionization structure of the auroral arc was measured on a sounding rocket which penetrated into a bright auroral arc. The E-region electron density becomes large (2 ～ 5 × 10⁵ el/cm³ only in the moving auroral arc, whose N₂⁺ 4278 Å brightness is 1 ～ 2·5 kR. The electron density in the D-region beneath the lower boundary of the arc (75 ～ 98 km in altitude) is also considerably enhanced to 2 ～ 5 × 10⁴ el/cm³.The observed E-region electron density can be interpreted theoretically as due to the direct ionization by precipitating electrons, whose energy spectrum is approximately represented by an exponential type having the characteristic energy of 2 keV. The correlation between the electron density and the N₂⁺ 4278 Å brightness can be reasonably explained by considering the simultaneous effects on the ionization and the optical excitation caused by the primary electrons having a flux of 9 × 10⁹ el/cm²/sec per 1 kR of the 4278 Å emission.Further analyses using the electron density data from four other sounding rockets have shown that the D-region ionization has good correlations to the cosmic noise absorption (CNA) and the magnetic substorm activities observed simultaneously at the ground station, whereas it has poor correlation to the same quantity of the E-region measured in the same experiment. It is found that the observed D-region ionization is much larger than that predicted by the theory which takes into account the Bremsstrahlung X-ray ionization along with the direct impact ionization when it is applied to the precipitating electron flux spectrum consistent to the E-region ionization and optical excitation.After all the present experimental results suggest a dual nature of the electron precipitation spectrum in the substorm, i.e. the softer part which is localized in the auroral arc and the harder part which is spatially wide-spread over the substorm area.     

Characteristics of optical emissions and particle precipitation in polar cap arcs

Simultaneous optical and particle data from the ISIS-2 satellite are used to characterize polar cap arcs. Polar cap arcs are identified from two-dimensional geomagnetic transforms of the optical data along with precipitating electron data for the time at which the satellite is on the field line intersecting the arc. No precipitating protons were detected for any of the arc crossings. The pitch angle. distribution of the precipitating electrons is generally isotropic and the differential electron spectra show enhancements in the flux in the 300–750 eV energy range. The average energy of the precipitating electrons for the different arcs ranges from about 300 to 600 eV. A possible explanation of the observed precipitating particle characteristics is that parallel electric fields are accelerating polar rain type spectra at an altitude of several thousand km. For the arc crossings reported here the equivalent 4278 Å emission rate per unit energy deposition rate has a mean value of 162 R/(erg cm^?2 s^?1). Average 3914 Å intensities are about 0.8 kR while 6300 Å intensities range from 0.5 to 3 kR. Model calculations indicate that direct impact excitation is a minor source for the 5577 Å emission rate, but supplies approx. 40% of the 6300 Å emission.     

Jupiter's radiation belts

A model for the production and loss of energetic electrons in Jupiter's radiation belt is presented. It is postulated that the electrons originate in the solar wind and are diffused in toward the planet by perturbations which violate the particles' third adiabatic invariant. At large distances, magnetic perturbations, electric fields associated with magnotospheric convection, or interchange instabilities driven by thermal plasma gradients may drive the diffusion. Inside about 10 R_J the diffusion is probably driven by electric fields associated with the upper atmosphere dynamo which is driven by neutral winds in the ionosphere. The diurnal component of the dynamo wind fields produces a dawn-dusk asymmetry in the decimetric radiation from the electrons in the belts, and the lack of obvious measured asymmetries in the decimetric radiation measurements provides estimates of upper limits for these Jovian ionospheric neutral winds. The average diurnal winds are less than or comparable to those on earth, but only modest fluctuating winds are required to drive the energetic electron diffusion referred to above.The winds required to diffuse the energetic particles across the orbit of the satellite lo in a time equal to their drift period are also estimated. If Io is non-conducting, modest winds are required, but if Io is conducting, only small winds are needed. It is concluded that both protons and electrons are diffused in from the solar wind to small distances without serious losses occurring due to the particles being swept up by the satellites.Consideration of proton and electron diffusion in energy shows that once the electrons become relativistic, the ratio of proton to electron energy increases. Thus, if protons and electrons have the same energy in the solar wind, when the electrons reach nMeV, the protons will be nMeV if n ? 1 or n² MeV if n ? 1. If the proton-to-electron energy ratio is initially, e.g., 5, then these figures are 5n and 5n², respectively.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

A calculation of auroral hiss with improved models for geoplasma and magnetic field

Intensities of auroral hiss generated by the Cerenkov radiation process by electrons in the lower magnetosphere are calculated with respect to a realistic model of the Earth's magnetosphere. In this calculation, the magnetic field is expressed by the “Mead-Fairfield Model” (1975), and a static model of the iono-magnetospheric plasma distribution is constructed with data accumulated by recent satellites (Alouette-I, -II, ISIS-I, OGO-4, -6 and Explorer 22). The energy range of hiss producing electrons and the frequency range of the calculated VLF are 100–200 keV, and 2–200 kHz, respectively. Intensities with a maximum around 20 kHz, of the order of 10^?14 W/m²/Hz¹ at the ground seem to be ascribable to the incoherent Cerenkov emission from soft electrons with a differential energy spectrum E^?2 having an intensity of the order of 10⁸cm^?2/sec/sr/eV at 100 eV. It is shown that the frequency of the maximum hiss spectral density at geomagnetic latitudes 80° on the day-side and 70° on the night-side is around 20 kHz for the soft spectrum (～E^?2) electrons, which shifts toward lower frequency (～10 kHz) for a hard spectrum (～E^?1·2) electrons. The maximum hiss intensity produced by soft electrons is more than one order higher than that of hard electron produced hiss. The higher rate of hiss occurrence in the daytime side, particularly in the soft electron precipitation zone in the morning sector, and the lesser occurrence of auroral hiss in night-time sectors must be, therefore, due to the local time dependence of the energy spectra of precipiating electrons rather than the difference in the geomagnetic field and in the geoplasma distributions.     

Atmospheric expansion from Joule heating

An expression for the vertical velocity of the neutral atmosphere in the F-region is derived for Joule heating by the electric field that drives the auroral electrojet. When only vertical expansion is allowed, it is found that the vertical wind must always increase monotonically with altitude. The heating rate is proportional to the F-region ion density, so that appreciable heating, even during high electric fields, requires some production mechanism of ionization such as auroral secondary ionization or solar photoionization, in the lower F-region. Once started at night, when an ionizing source is present in the lower F-region, the expansion of the atmosphere transports ionization upward, thereby increasing the heating rate, and hence the expansion rate, i.e. positive feedback. Electric field strengths and F-region ion densities of 50 mV/m and 2 × 10¹¹e/m³, respectively, will produce vertal neutral wind speeds of several tens of m/sec in the 300–500 km altitude range. During periods of high magnetic activity, i.e. high electric field, Joule heating can produce large increases in the relative N₂ concentration in the upper F-region; computations made with a simple model suggest that tenfold increases can occur at 400 km altitude $\text{1}\text{2?1}\text{hr}$ after the onset of magnetic activity, a result in agreement with satellite observations. When the Joule heating theory is applied to incoherent scatter data taken during one period of high heating, the horizontal electric field in the F-region is found to decrease markedly, possibly approaching zero as the field penetrates a weak, discrete auroral arc; the decrease began 10–20 km from the arc.     

The effect of strong pitch angle scattering on the use of artificial auroral streaks for echo detection—Echo 5

During the Echo 5 experiment launched 13 November 1979 from the Poker Flat Research Range (Fairbanks, Alaska), a 0.75 A, 37 keV electron beam was injected both up and down the field line. The objective of the experiment was to test the use of optical and X-ray methods to detect the beam as it interacted with the atmosphere below the rocket for both the downward injections (markers) and the upward injected electrons which mirrored at the Southern Hemisphere and returned echoes. A ground-based TV system and rocket borne photometers and X-ray detectors viewed the interaction region. The artificial auroral streaks created by the markers were easily visible on the ground TV system but the large intensity of photons produced around the rocket masked any response to the markers by the on-board photometers and X-ray detectors. No echoes were detected with any of the detection systems although the power in some of the upward injections was 7.6 times the power in a detected downward injection thus setting an upper limit on the loss-cone echo flux. The magnitude of the bounce averaged pitch angle diffusion coefficient necessary to explain the lack of observable echoes was found to be 4 × 10⁻⁴ s⁻¹. Comparing with calculations done by Lyons (1974) for the pitch angle diffusion of electrons by electrostatic waves, it was found that an equatorial wave electric field of 11 mV m⁻¹ would account for the lack of echoes. Such fields should cause strong pitch angle scattering of up to 10 keV natural electrons and thus be consistent with the presence of diffuse aurora on the Echo 5 trajectory. Direct measurements have also revealed such fields in equatorial regions.     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

Observations of soft electron flux during SAR arc event

Attempts to test the validity of the soft electron flux hypothesis for the excitation of SAR arcs have heretofore met with no apparent success. However, observations of other emissions during the times of some SAR arcs repeatedly favour the presence of the soft electron flux in the topside ionosphere.Although no new cases of coincident measurements of SAR arc intensities and the corresponding soft electron flux values are available, an instance has been analyzed in which an SAR arc was examined shortly after an OGO 6 measurement of the soft electron flux. The SAR arc observations were then interrupted by the weather, but in view of the behaviour of the electron flux during the arc development it is believed that this event lends strong observational support to the hypothesis that soft electrons can be an excitation source for SAR arcs.In the case considered, the precipitation of soft electron flux peaks at about the same location and time of occurrence as the SAR arc. The peak value is found to be 5.2 × 10⁸ cm^?2 sec^?1, which is more than adequate to excite the observed arc.     

Localized ionization patches in the nighttime ionosphere of Mars and their electrodynamic consequences

Using an electron transport model, we calculate the electron density of the electron impact-produced nighttime ionosphere of Mars and its spatial structure. As input we use Mars Global Surveyor electron measurements, including an interval when accelerated electrons were observed. Our calculations show that regions of enhanced ionization are localized and occur near magnetic cusps. Horizontal gradients in the calculated ionospheric electron density on the night side of Mars can exceed 10⁴ cm⁻³ over a distance of a few tens of km; the largest gradients produced by the model are over 600 cm⁻³ km⁻¹. Such large gradients in the plasma density have several important consequences. These large pressure gradients will lead to localized plasma transport perpendicular to the ambient magnetic field which will generate horizontal currents and electric fields. We calculate the magnitude of these currents to be up to 10 nA/m². Additionally, transport of ionospheric plasma by neutral winds, which vary in strength and direction as a function of local time and season, can generate large (up to 1000 nA/m²) and spatially structured horizontal currents where the ions are collisionally coupled to the neutral atmosphere while electrons are not. These currents may contribute to localized Joule heating. In addition, closure of the horizontal currents and electric fields may require the presence of vertical, field-aligned currents and fields which may play a role in high altitude acceleration processes.     

Diffuse auroral precipitation in the jovian upper atmosphere and magnetospheric electron flux variability

The deposition of energetic electrons in Jupiter's upper atmosphere provides a means, via auroral observations, of monitoring electron and plasma wave activity within the magnetosphere. Not only does particle precipitation indicate a potential change in atmospheric chemistry, it allows for the study of episodic, pronounced flux enhancements in the energetic electron population. A study has been made of the effects of such electron injections into the jovian magnetosphere and of their ability to provide the source population for variations in diffuse auroral emissions. To identify the source region of precipitating auroral electrons, we have investigated the pitch-angle distributions of high-resolution Galileo Energetic Particle Detector (EPD) data that indicate strong flux levels near the loss cone. The equatorial source region of precipitating electrons has been determined from the locations of Galileo's in situ measurements by tracing magnetic field lines using the KK97 model. The primary source region for Jupiter's diffuse aurora appears to lie in the magnetic equator at 15-40 RJ, with the predominant contribution to precipitation flux (tens of ergs cm⁻² s⁻¹ sr⁻¹) stemming from <30 RJ. Variability of flux for energetic electrons in this region is also important to the irradiation of surfaces and atmospheres for the Galilean moons: Europa, Ganymede, and Callisto. The average diffuse auroral precipitation flux has been shown to vary by as much as a factor of six at a given radial location. This variability appears to be associated with electron injection events that have been identified in high-resolution Galileo EPD data. These electron flux enhancements are also associated with increased whistler-mode wave activity and magnetic field perturbations, as detected by the Galileo Plasma Wave Subsystem (PWS) and Magnetometer (MAG), respectively. Resonant interactions with the whistler-mode waves cause electron pitch-angle scattering and lead to pitch-angle isotropization and precipitation.     

Collisionless Magnetic Reconnection in the Presence of Initial Guide Field

By using the method of 2-dimensional, 3-component full particle simulation, collisionless magnetic reconnection in the presence of various initial guide fields and the Harris current sheet with 1-dimensional initial state are studied. The results show that strong guide fields with B_z0 > 0.5B₀ can evidently alter not only the trajectory of the particles, but also the structure of the electric and velocity fields in the vicinity of the reconnection region, thereby affecting the rate of reconnection and the acceleration of electrons. The generalized Ohm's law is employed to interpret the structural characteristics of the electric fields with various guide fields. Also, via the tracing of the electron beam near he diffusion region, it is revealed that in the 2-D model, for both strong and weak guide fields, the induced electric field perpendicular to the simulation plane at the center of the diffusion region plays the major role in the acceleration of electrons. The contribution of the planar electric field outside the diffusion region is very small.     

Acceleration of electrons and solar flares due to quasi-static electric field

The storage of flare energy, efficient acceleration of electrons and the trigger of the flares are suggested to be attributed to a quasi-static electric field caused by a gas motion near the photosphere without satisfying the frozen condition. The primary cause of the onset of flares would be the acceleration of electrons due to the electric field above a critical strength. The electrons excite plasma waves which make the conductivity lower by several orders in the lower corona, so that the electro-magnetic energy I ² L stored before the onset of the flare would be rapidly converted into the heat due to the ohmic loss in about 10 s.     

Particle precipitation in the south atlantic geomagnetic anomaly

A simple model of the motion of charged particles in the closed field line magnetic field for L ? 4·5 is used together with Injun 3 measurements of 40 keV precipitated electrons made in the northern hemisphere to estimate theoretically the extent of electron precipitation, the energy input and the 3914 Å airglow in the South Atlantic geomagnetic anomaly. Using average values of the northern hemisphere precipitated electron flux, two regions of significantly enhanced electron precipitation are found in the southern hemisphere. One occurs in the region 10–20°E and 40–50°S, with L ≈ 2, and the second near 30°E and 65°S, with L ≈ 4.5. Approximately 0.04 erg cm^?2 sec^?1 are deposited by 40 keV electrons for 50 per cent of the time in the first region and half that amount in the second. This increases to ～0·1 and 0·02 erg cm^?2 sec^?1 respectively for 15 per cent of the time for near sunspot minimum conditions. The results show a gradual increase in precipitation on the western side of the anomaly followed by a rapid increase and sudden cut-off in precipitation within a few degrees west of minimum B. The flux on L = 2 reaches a “spike” in the southern hemisphere ～f35 times greater than the average flux precipitated on L = 2 in the northern hemisphere. This increase in precipitation arises from the loss of “trapped” particles to the atmosphere where the mirror heights are lowest.     

Estimation of the escape of photoelectrons from Mars in 2004 liberated by the ionization of carbon dioxide and atomic oxygen

Photoelectron peaks in the atmosphere of Mars caused by the ionization of carbon dioxide and atomic oxygen by solar 30.4 nm photons have been observed by the Electron Spectrometer (ELS), a component of the Mars Express (MEx) Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) experiment. Ionization mostly occurs at the Mars exobase with the majority of the photoionized electron flux trapped in the remanent and induced magnetic field, with a portion of that flux escaping the planet down its tail. Since Mars is overall charge neutral, the number of electrons must be identical to the number of ion charges which escape the planet. An estimate of the fraction of the total number of escaping electrons is obtained for the year 2004, specifically those produced by the ionization of carbon dioxide and atomic oxygen by solar 30.4 nm photons. In achieving this process, an illustrative example pass is used to show how the electron spectrum is adjusted for the potential on the spacecraft; then the region of the electron spectrum which shows photoelectron peaks is integrated over energy, yielding a flux of 5.74 × 10⁶ electrons/(cm² s sr). This technique is then applied to a subset of 22 sample averaged spectra from the 2004 data (5 January 2004 through 25 January 2005), yielding an average result of 4.15 × 10⁶ electrons/(cm² s sr) for the 22 cases. The observation cone of 33.75° is used to integrate over solid angle (assuming the flux is constant), giving 4.39 × 10⁶ electrons/(cm² s). This average value was taken as representative of the full data interval. Frequency of occurrence statistics showing about a 6.2% occurrence rate for the 2004 data is applied to give an average escape flux from Mars of 2.72 × 10⁵ electrons/(cm² s) during 2004. By estimating the outflow area as 1.16 × 10¹⁸ cm² at X = −1.5 R_Mars the electron escape rate of 3.14 × 10²³ electrons/s is obtained. Thus about 9.92 × 10³⁰ electrons or 16.5 Mmole of electrons escaped Mars during 2004 due to the ionization of carbon dioxide and atomic oxygen by the He 30.4 nm line. Due to the caveats of the analysis, these derived escape rates should be considered lower limits on the total electron escape rate from Mars.