Main

There is substantial ambiguity in the strength of the electrostatic field of Earth, its physical drivers, and its role in the escape of ions to space. At a minimum, this field is thought to be underpinned by an ambipolar electric field8,9. These fields are generated as ionospheric electrons attempt to escape to space under their own thermal pressure. As the electrons attempt to pull away from the heavier ions, an ambipolar field arises to maintain charge neutrality6,11. However, ambipolar fields have not been unambiguously measured in nature because of their weak strength. If the ambipolar field is the only mechanism driving the electrostatic field of Earth, then the resulting electric potential drop across the exobase transition region (200–780 km) could be as low as about 0.4 V (ref. 12). However, modelling studies have proposed that the ambipolar field of Earth may be enhanced to several volts by suprathermal (>1 eV) photoelectrons that are omnipresent above the sunlit hemisphere of Earth12. Furthermore, recent observations at Venus and Mars have shown that other physical processes can strongly enhance the electric potential of a terrestrial planet by as much as tens of volts6,13,14,15,16. The few previous attempts to measure the electrostatic field of Earth have been able to establish only an upper bound on the electric potential drop in the ionosphere of ≤2 V (refs. 17,18). If it is as strong as 2 V, then it would be directly responsible for around 20% of the escape of O+ ions to space. Even a small difference of ±0.2 V relative to a low-end case of a 0.4 V potential would make a substantial difference to the fraction of H+ directly escaping from Earth by this mechanism (approximately 50%, 0.2 V compared with 100%, 0.6 V) (ref. 19).

The NASA Endurance rocket mission19 (yard number 47.001) launched from Ny-Ålesund, Svalbard, on 11 May 2022 at 01:31:00 Greenwich Mean Time (GMT) (Fig. 1d) to an altitude of 768 km (Fig. 1a,c) to attempt to make the first successful measurement of the intrinsic electrostatic field of Earth. The high-latitude launch site (78.93° N) was selected to fly on open magnetic field lines above the polar caps (Fig. 1b) that provide a key pathway for ion outflow to the magnetosphere. The launch occurred during geomagnetically quiet conditions (Extended Data Fig. 7) to have as few perturbations in the environment as possible during the observations. The trajectory was designed so that one would not expect a measurable difference in the electrostatic field along the trajectory. Furthermore, we would not expect any temporal changes during the approximately 13-min duration of science collection.

Fig. 1: The flight of the NASA rocketship Endurance.
figure 1

a, Scale map of the parabolic trajectory of the spacecraft colour coded by mission phase, showing regions explored of the upper polar atmosphere and ionosphere. Circles mark 1-min intervals beginning at launch at 01:31 GMT. The region marked ‘Photoproduction layer’ refers to the peak of He-II photoelectron production. b, Map of ground track of the flight from launch to LOS with respect to the open and closed magnetic field line boundary of the magnetic dipole field of Earth and the location of the EISCAT Svalbard radar that made simultaneous measurements of the ionosphere. c, Photograph taken by the Panoramic Camera near apogee showing the sunlit geographic North Pole of Earth. Image credit: NASA. d, Photograph showing booster ignition and lift-off of the Endurance. Image credit: Leif Jonny Eilertsen/Andøya Space.

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The scientific instruments were successfully deployed (Fig. 1a, teal) near 150 km altitude on the upleg, just 9.5 s after jettison of the third-stage booster motor. Endurance was then de-spun and aligned within 1° of the ambient magnetic field using cold-gas Attitude Control System (ACS) thrusters. Science operations began at T + 125 s after the launch at an altitude of 248 km on the upleg. The mission alternated between 70 s of uncontaminated science collection at which the ACS was off (Fig. 1a, blue), followed by 10 s at which the ACS re-aligned the spacecraft with the ambient magnetic field (Fig. 1a, amber). Apogee (768.03 km) (Fig. 1c) was chosen to measure the electric potential across the exobase (around 500 km), above which ions stop being collisionally bound to the neutral atmosphere and are free to escape upwards. Endurance gathered continuous data until loss of signal (LOS) at T + 900.6 s at an altitude of 70.94 km during re-entry into the atmosphere. The wreckage impacted the Greenland Sea near 78°1′40.31″ N, 1°41′55.8″ W, coming to rest in approximately 2,900 m of water.

The total potential drop below the Endurance was measured from the shift in the energy of electrons outflowing from the ionosphere13,14,17,18. The intense He-II emission line of the Sun at 30.4 nm is a source of photoionization throughout our solar system (ref. 20). This mono-energetic radiation generates several discrete peaks (photopeaks) in the energy spectrum of electrons originating in the dayside ionosphere. Figure 2 shows the in situ measurements of these He-II photopeaks by the photoelectron spectrometer (PES), a technology developed for the mission21. The brightest He-II photopeak observed by PES was dominated by the N2 A2Πu atomic transition, which generates electrons at 24.09 eV (refs. 22,23). He-II photopeaks are generated only over a narrow altitude range (250–300 km during the flight). Above this photoproduction region, the PES observed a decrease in the energy of the photopeak with increasing altitude (Fig. 2c (red line) and Extended Data Fig. 2). This is consistent with the presence of a weak positive electrical potential across the exobase of Earth, which slows electrons as they attempt to escape to space (but will push the ions outwards). The farther the Endurance drifted from Earth, the greater the electric potential drop below, resulting in a progressively larger shift of the photopeak towards lower energies (Fig. 2c and Extended Data Fig. 3).

Fig. 2: Measurements of the energy spectra of electrons escaping from ionosphere of Earth by the PES.
figure 2

a, Colour-coded timeline (consistent with Fig. 1a) of the mission and altitude of the rocketship during the flight. Vertical dashed lines on all three panels denote science collection periods. b, Standard resolution (15% ΔE/E) time versus energy spectrogram of the differential energy flux of electrons outflowing from the ionosphere of Earth. c, High-resolution (0.5% ΔE/E) time versus energy spectrogram resolving the He-II photopeaks and their shift to lower energies with altitude resulting from the electrostatic field of Earth. The peak energy of the primary He-II photopeak is overplotted in red. These data have been corrected for the absolute spacecraft potential19 using measurements by the SLP instrument.

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Figure 3a,b shows the ionospheric electric potential drop of Earth measured from this photopeak energy shift. These data have been corrected for the electrical potential of the spacecraft13 from the Swept Langmuir Probe (SLP)19 (Extended Data Fig. 4e), with a supporting cross-check by the Electromagnetic Fields and Waves (FIELDS) instrument19 (Extended Data Fig. 5b). Both SLP and FIELDS instruments gave a consistent measurement of spacecraft potential over the flight, albeit with closer agreement on the upleg.

Fig. 3: The electrical potential drop of Earth across the exobase and its role in controlling the structure of the topside polar ionosphere.
figure 3

a,b, Upleg (a) and downleg (b) measurements of the electric potential drop of Earth. White diamonds show the relative shift in the He-II photopeaks when corrected for the spacecraft potential measured by the SLP instrument, with a linear fit in pink. Error bars are described in the Methods. The grey dots show a correction for spacecraft potential by the FIELDS instrument for cross-checking with SLP. The orange region shows the parallel potential drop that would be expected from a classical ambipolar field driven by the electron pressure gradient as measured by SLP. c,d, Upleg (c) and downleg (d) measurements of the structure of the topside polar ionosphere of Earth measured in situ by SLP (orange region) and remotely by EISCAT radar (green region). The black dotted lines show a prediction by the IRI empirical model. Dashed red lines show how the ionosphere of Earth should fall off according to a classical hydrostatic equilibrium in which gravity is the only controlling force. The dark blue lines show hydrostatic equilibrium at which the intrinsic planetary electric field measured near Earth by Endurance partially counters gravity.

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Endurance measured two near-vertical profiles of electric potential versus altitude, first on the upleg (250 km to apogee) and again on the downleg (apogee to LOS). A mean potential drop of 0.55 ± 0.09 V was measured across the exobase of Earth (250–768 km). By taking the average gradient of these near-simultaneous vertical measurements, we find that the ionosphere of Earth intrinsically generates an electrical field parallel to its magnetic field (E∥) of 1.09 ± 0.17 μV m−1.

Using SLP measurements of electron density (ne) and temperature (te), we can calculate the electron thermal pressure (Pe = nekbTe). By taking the vertical gradient of electron pressure (∇Pe), we can compare the parallel electric field (E∥) against what would be expected from a pure ambipolar field. The derivation of the ambipolar field has been presented in numerous previous publications (also in the Methods) and is found by solving for E∥ in the steady-state electron momentum equation11,24,25. To the first order, E∥ ≈ −∇Pe/qne (refs. 26,27,28). We find a close agreement between this prediction (Fig. 3a,b, orange region) and our observations (Fig. 3a,b, diamonds). Thus, we conclude the only source of electrical potential was a classical electron pressure-driven ambipolar field. Unlike at Venus13,15,16 and Mars14,29, we find no evidence for additional mechanisms contributing to the electrostatic field of Earth.

Using classical ambipolar diffusion theory30, we calculate two altitude profiles of predicted plasma density during the flight of Endurance. The first without the contribution of E∥ (Fig. 3c,d, red dashed line) and the second with the measured 1.09 μV m−1 field (Fig. 3c,d, solid blue line). The latter (Fig. 3c,d, solid blue line) matches closely with the density profile from (1) in situ measurement by the SLP instrument (orange region), (2) simultaneous remote sensing by EISCAT radar (green region) (Extended Data Fig. 6) and is in good agreement with (3) the prediction by the International Reference Ionosphere (IRI) model (black dotted line). This close agreement gives an additional cross-check on the interpretation of the photoelectron peak shift as resulting from an ambipolar electric field.

The measurement of the electrostatic field of Earth has important consequences for our understanding of the structure of the topside ionosphere of Earth and the supply of heavy O+ ions into the magnetosphere. No further physical mechanisms were required to explain the observations of plasma density versus altitude (Fig. 3c,d). This implies that the ambipolar field was the primary driver of the structure of the topside polar ionosphere during the quiet geomagnetic conditions chosen for the flight. This analysis is specific to the near-vertical magnetic field lines near the magnetic poles, and at lower latitudes additional transport processes should be accounted for30.

Comparing the two altitude profiles, with and without the effect of E∥, enables us to quantify the impact of the ambipolar field on the vertical transport of O+ ions in the polar cap. The field increases the scale height of the ionosphere by 271% (from H = 77.0 km to H = 208.9 km). This enhances plasma density near the boundary of the magnetosphere (that is, near apogee at 768 km) by more than 3,800%. This demonstrates experimentally that the ambipolar field provides the initial lift to higher altitudes for heavy ions in the polar caps at which other acceleration mechanisms such as wave–particle interactions can come into play to drive them to escape velocity4,7.

The measurements support the hypothesis that the ambipolar electric field is the primary driver of ionospheric H+ outflow, and of the supersonic polar wind of light ions escaping from the polar caps. The 1.09 μV m−1 field measured over the sunlit polar region is sufficient to provide an outward force on ionospheric H+ of 10.6 times that of gravity. This value is close to eight times the gravity expected from theoretical calculations assuming an isothermal O+-dominated ionosphere with an electric field driven purely by the electron pressure gradient30. The escape velocity at the apogee of Endurance (768 km) is 10.62 km s−1, corresponding to an escape energy for H+ of 0.58 eV. This escape energy is identical within the errors to the total potential drop measured between 250 km and 767 km of 0.55 ± 0.09 V. Therefore, H+ accelerated by this field will not fall back to the atmosphere. Moreover, this field accelerates plasmas without heating. Thus, we posit that the ambipolar field is the most likely outflow mechanism for the dense cold plasmas persistently observed throughout the magnetosphere1,2.

Methods

Endurance instrumentation used in this study

We shall now give a brief description of the three scientific instruments carried by the rocketship from which data are directly used in this study. For more detailed information, see ref. 19.

Photoelectron spectrometer

The primary instrument aboard the Endurance was the PES consisting of eight boom-mounted dual electrostatic analyser (DESA) sensors (Extended Data Fig. 1), synchronized by a central main electronics box. The apertures of the eight sensors were physically aligned to view within 5° of the ambient magnetic field (look directions in and out of the page in Extended Data Fig. 1). Each sensor had two simultaneous look directions (field-aligned and anti-aligned) with a fixed 11° azimuth by 5° elevation field of view. The combined geometric factor of the eight DESA sensors was 1.8 × 10−3 (cm2 sr eV eV−1)−1 for the aft-looking (A) sides, and 1.71 × 10−3 (cm2 sr eV eV−1)−1 for the bow-looking (B) sides. The PES was sensitive to a differential energy flux down to 104 (eV(cm2 sr eV)−1)). The PES made 78 complete scans during the flight, each taking 10 s. Each scan produced two data products: a standard-resolution (15% ΔE/E) measurement between 8.4 eV and 991.6 eV in logarithmic steps (Fig. 2b); and a high-resolution (0.5% ΔE/E) scan between 20.30 eV and 25.85 eV in 0.15 eV steps (Fig. 2c).

For more information on the operational principle of the optics of the DESA sensor, see ref. 31. For a cross-section of the DESA sensor and a description of its test flight, see ref. 21.

Swept Langmuir Probe

SLP operates in plasma densities between 1 × 103 cm−3 and 1 × 109 cm−3. SLP was a traditional Langmuir probe consisting of a gold-plated needle probe mounted at the tip of the Fo’c’sle of Endurance (Extended Data Fig. 1). Once every 5 s, a sweeping bias voltage (±5 V) was applied to the needle probe, and the resulting collected current was measured. Before flight, measured current (I) versus applied voltage (VSLP) of SLP was calibrated in a thermal vacuum chamber from −30 °C to +50 °C. This resulted in less than 1% error in the in-flight measurement of I versus VSLP. As is standard practice for a Langmuir probe, the total plasma density (ne), electron temperature (te) and absolute spacecraft potential (ϕSC) are derived from fitting to the I–V curves measured during flight. For a time series of SLP measurements of ne, te and ϕSC, showing 1σ errors, see Extended Data Fig. 4. The close agreement between independent measurements of ne and te by SLP and EISCAT (Extended Data Fig. 6) and independent measurement of ϕSC by SLP and FIELDS (Fig. 3) give good confidence in SLP calibration and data analysis.

Electromagnetic Fields and Waves package

FIELDS (Extended Data Fig. 1) consisted of a pair of orthogonal 3.2-m (tip-to-tip) double probes in the plane perpendicular to the rocket axis (and therefore the magnetic field of Earth). Four spherical sensors with embedded pre-amps captured electrostatic and electromagnetic modes at frequencies between 5 Hz and 5 MHz.

Correction of electron measurements for spacecraft potential

Photoelectrons reaching the PES instrument fell through an additional potential drop arising from the electrical charging of the spacecraft (ϕSC). All exposed surfaces of the spacecraft were checked for electrical continuity before launch to ensure the chassis would provide a common electrical ground to all instruments and thus evenly distribute ϕSC. All measurements presented in this paper have been corrected for ϕSC, which was one of three plasma parameters measured directly by the SLP instrument (as described above; Extended Data Fig. 4). These spectra were then corrected for this potential using Liouville’s theorem (converting through phase space density). For a full description of this technique, see, for example, Supporting Information S1 of ref. 13.

An additional independent cross-check of ϕSC was supplied by the mean potential of each FIELDS sensor (Fig. 3). FIELDS mean sphere potentials floated during the flight according to ϕSC (Extended Data Fig. 5). These data were split before and after apogee, giving a relative change in potential (ΔϕSC) on upleg and downleg. The absolute spacecraft potential could be directly measured by PES for periods when Endurance was in the photoelectron production layer (250–300 km) by comparing the measured energy of the N2 A2Πu photopeak to its known energy of generation (24.09 eV). Using this calibration point, an estimate of absolute ϕSC was estimated for the upleg and downleg. This supporting measurement (Fig. 3a,b, grey dots) agreed within the errors to the primary measurement from SLP (Fig. 3a,b, black dots), giving good confidence in our determination of absolute ϕSC.

Method of calculation of potential drop from He-II photopeak measurements

Extended Data Fig. 2 shows two examples of PES scans illustrating the method for measuring the potential below the Endurance. Extended Data Fig. 2a,b shows PES scan 72, taken in the photoproduction region. Extended Data Fig. 2c,d shows PES scan 38, taken just after apogee in the exosphere. Extended Data Fig. 2b,d shows the high-resolution scans around the He-II photopeaks that resolved the peak dominated by N2 A2Πu photoemission. For each scan, the energy of this peak was measured by fitting a six-term Gaussian (Extended Data Fig. 2b,d, blue line).

Extended Data Fig. 3a,d shows the peak energy of the N2 A2Πu photopeak as measured throughout the flight by PES (Extended Data Fig. 3a, upleg, and Extended Data Fig. 3d, downleg). Measurements during ACS firings have been removed as this substantially perturbed the spacecraft potential and ambient plasma environment.

Horizontal error bars come from four sources: (1) the inherent 0.5% ΔE/E energy resolution of the sensor; (2) the estimated error in the measurement of spacecraft potential from SLP (and FIELDS for the supporting cross-check measurement); (3) the errors in the peak fitting resulting largely from Poisson noise in the data. This error source was most prevalent above 700 km as the N2 A2Πu-dominated main photopeak became increasingly degraded through Coulomb collisions on their journey up from the photoproduction region (Fig. 3d); and (4) the error arising from the weak electrical current induced within the structure of the conductive spacecraft from its motion through the magnetic field of Earth (Emotional = −VEndurance × B). These induced currents will result in a very small potential difference between the common electrical ground of the PES sensors, and hence an error in their measurement of the energy of the photopeaks. However, when measurements of VEndurance from the on-board GPS receiver were combined with the on-board magnetometer19, this final error was found to be very small (<0.05 V in a 0.55 V potential drop), but it is nonetheless included in our error analysis.

Extended Data Fig. 3b,e shows the peak energy of the N2 A2Πu-dominated main photopeak after correction for the time-varying spacecraft potential (ϕSC) by SLP (Extended Data Fig. 3b, upleg, and Extended Data Fig. 3e, downleg). After correction, measurements of the N2 A2Πu photopeak in the photoproduction region (250–300 km) were within the errors of its known atomic value of 24.09 eV, giving strong confidence in the accuracy of our measurement of ϕSC throughout the flight. To calculate the potential drop below the spacecraft, this corrected photopeak energy is subtracted from its known production energy of 24.09 eV. The result is shown in Extended Data Fig. 3c (upleg) and Extended Data Fig. 3f (downleg) and also in Fig. 3a,b.

The total potential drop on the upleg was 0.56 ± 0.09 V, corresponding to a 1.10 μV m−1 electric field parallel to the magnetic field. The total potential drop on the downleg was 0.54 ± 0.09 V, corresponding to a 1.07 μV m−1 parallel electric field.

Theory of the generation of ionospheric ambipolar electric fields

In this section, we derive the ambipolar electric field from the first principles, including why it is generally assumed to be dominated by the electron pressure gradient (∇Pe). The existence of such planetary-scale electric energy fields has long been predicted by theoretical studies11,24,25. Although these studies approach the problem slightly differently, all involve solving the time-varying plasma momentum equation (equation (1)) for parallel electric field (E∥). All arrive with the same fundamental prediction that the outward pressure on the topside ionospheric of Earth should generate a global-scale parallel electric field.

$$\mathop{\underbrace{\frac{\partial }{\partial t}(A{\rho }_{{\rm{e}}}{u}_{{\rm{e}}}^{2})}}\limits_{1}+\mathop{\underbrace{\frac{\partial }{\partial r}(A{\rho }_{{\rm{e}}}{u}_{{\rm{e}}}^{2})}}\limits_{2}+\mathop{\underbrace{A\frac{\partial {P}_{\parallel }}{\partial r}-A\frac{({P}_{\parallel }-{P}_{\perp })}{B}\frac{\partial B}{\partial r}}}\limits_{3}=A{n}_{{\rm{e}}}(\,\mathop{\underbrace{-q{E}_{\parallel }}}\limits_{4}-\mathop{\underbrace{{m}_{{\rm{e}}}\,g}}\limits_{5})+\mathop{\underbrace{A\frac{\delta {m}_{{\rm{e}}}}{\delta t}}}\limits_{6}+\mathop{\underbrace{A{u}_{{\rm{e}}}{S}_{{\rm{e}}}{m}_{{\rm{e}}}}}\limits_{7}$$
(1)

Equation (1) describes the generalized balance of electron momentum (ρe = meq) in a magnetic flux tube of area A, which expands with distance r from the centre of Earth (and ue is bulk electron velocity). Term 1 describes momentum density, which is the momentum inherent at a given distance from Earth (r) along the flux tube. Term 2 is the net flux of momentum being transported into this region of the flux tube. Note that in this derivation we are working in the observer frame (sometimes called the laboratory frame), and thus terms 1 and 2 must be separated. (When equation (1) is solved in the frame of a fluid parcel, terms 1 and 2 can be combined into a single term called the convective derivative). The final term on the left-hand side (term 3) is the gradient of electron pressure, which provides a net force and hence an impulse to the electrons, changing their momentum. Equation (3) separates the contributions from electron pressure parallel (P∥) and perpendicular (P⟂) to the magnetic field.

The right-hand side of equation (1) describes the four fundamental sources of electron momentum at a given distance from Earth (r). The first and foremost is the net force on the electrons with charge −q from the electric field E∥ (term 4). Next is the downward force of gravity (meg and term 5). Term 6 is the collisional term, broadly describing any momentum exchange arising from collisions of electrons with ions or neutral atoms (for example, Coulomb collisions and inelastic scattering). Term 7 is the production term, describing the increase in electron momentum arising from the creation of new electrons (at a rate Se particles per second) at a given distance along the flux tube (r).

Before we solve equation (1), we will make three common assumptions when describing ionospheric electrons. First, as electrons move very quickly and respond almost instantaneously to changes in the system, we will assume that the bulk population of ionospheric electrons is in a steady state (∂/∂t = 0). This is consistent with the EISCAT radar observations of the ionosphere throughout the Endurance mission, the structure of which was stable and constant during the flight (for example, consistent with this steady-state assumption). Thus, we may ignore term 1 of equation (1).

For our next assumption, we will consider that the electron mass is so small that to the first order we can ignore any term containing me (refs. 6,11,24,25). For more thorough derivations of E∥ in which the terms including me are carried all the way through, see refs. 11,24,25. However, here for brevity, we will simplify the electron momentum equation as follows:

$$A\frac{\partial {P}_{\parallel }}{\partial r}-A\frac{\left({P}_{\parallel }-\,{P}_{\perp }\right)}{B}\frac{\partial B}{\partial r}=-A{n}_{{\rm{e}}}q{E}_{\parallel }$$
(2)

Finally, as per most ionospheric models, we will assume that the bulk population of ionospheric electrons are isotropic (P∥ = P⟂ = PE). In reality, satellite measurements at the altitudes and latitudes explored by Endurance have shown a small degree of anisotropy in ionospheric electrons; however, this is of the order of only about 10–20% (ref. 32), and thus to the first order the assumption of isotropy is quite reasonable. Note that although the second term of equation (2) has a negative sign in front of it, the magnetic field (B) gets weaker with distance (r) (that is, ∂B/∂r points downwards), and thus overall this term is a net positive to the momentum equation. Assuming electron isotropy removes this additional term, and thus results in a more conservative approximation of E∥. With all these approximations made, we thus arrive at the final form of the steady-state momentum equation for ionospheric electrons:

$$A\frac{\partial {P}_{E}}{\partial r}=-A{n}_{{\rm{e}}}q{E}_{\parallel }$$
(3)

We may now re-arrange and solve for the predicted parallel electric field:

$${E}_{\parallel }=\frac{1}{{n}_{e}q}\frac{\partial {P}_{E}}{\partial r}=-\frac{\nabla {P}_{E}}{{n}_{e}q}$$
(4)

To test this prediction, we measured the gradient of electron pressure throughout the flight by the SLP instrument (Extended Data Fig. 4). Taking the gradient and then integrating with distance along the field line (∫−∇PE/neq dr) gives a prediction of the total accumulated vertical potential drop from equation (4). For the first time, we are thus able to compare directly with observations (Fig. 3a,b), finding a close agreement between this theory and observations (as described in the main text of this paper).

Ambipolar diffusion theory and calculation of altitude plasma density profiles

According to ambipolar diffusion theory, we consider the ionosphere as an isothermal hydrostatic ion atmosphere with a simple density profile given by

$$n\left(s\right)={n}_{0}\,\exp \left(-\frac{s-{s}_{0}}{H}\right)$$
(5)

where n is the density of plasma at altitude s above a reference altitude s0. H is defined as the scale height of the ionosphere and is given by

$$H=\frac{{k}_{{\rm{b}}}{T}_{{\rm{i}}}}{({m}_{{\rm{i}}}\,g)-(q\,{E}_{\parallel })}$$
(6)

where kb is the Boltzmann’s constant, Ti is the ion temperature, mi is the ion mass, g is the gravitational acceleration and q is the ion charge. Simply put, this theory implies that the electric field (E∥) effectively counters gravity, increasing the scale height of the ionosphere. As H shows up in the exponent of equation (5), this theory predicts that the presence of E∥ has an amplified effect on the plasma density at high altitudes.

Endurance measurements of n(s), Ti and, for the first time, E∥ can be combined with equations (5) and (6) to provide an additional cross-check on the interpretation of the photoelectron peak shift as resulting from an ambipolar electric field. We take the base density (no = 1.9 × 1011 cm−3) as measured by SLP at the top of the F-region of the ionosphere (so = 300 km). EISCAT radar measured a quasi-isothermal ion temperature profile during the flight with mean temperature (Ti) of 1,453 ± 376 K on the upleg and 1,614 ± 648 K on the downleg. We assume a mean ion atomic mass (mi) of 15.9 dalton as per the International Reference Ionosphere empirical model. These equations are used to calculate the altitude versus density profiles in Fig. 1.