The aurora is a dynamical high-latitude phenomenon caused by magnetospheric electrons and protons with energies in the range of keV precipitating into the ionosphere. Precipitation leads to rapidly varying ionization, excitation and heating over a large range of spatial scales, with higher primary electron energy causing more ionization at lower heights. Precipitation also impacts the E-region substantially by inducing compositional changes and increasing conductivities. Spatial and temporal changes in ionospheric conductivities affect currents and field-aligned potentials. Precipitation can dominate power deposition at small spatial and temporal scales e.g.,, and, for all these reasons, plays an important role in magnetosphere-ionosphere (MI) coupling. The energy spectrum of primary electrons and its time variation make it possible to investigate the acceleration process in the magnetosphere causing aurora. Understanding the dynamics of MI coupling and the ionospheric response to rapid variation of precipitation are active research topics.

Ground-based measurements complement in-situ observations of electron precipitation. Satellites and rockets can measure the electron energy distribution directly, but their high velocities do not allow for extended measurements at a single location. Disentangling spatial from temporal variations can be challenging, and, for satellites, the resulting spatial resolution may be limited. Incoherent Scatter Radars (ISR) can follow the temporal evolution of auroral precipitation above the radar's field of view for extended time periods. On the other hand, ISR measurements for this purpose are restricted to the magnetic zenith direction, and at high time resolutions one needs to adapt to high noise levels. Optical observations can complement ISR in the horizontal direction e.g.,.

The electron energy spectrum can be estimated from the time-variation of E-region electron density profiles measured with ISR. The inversion starts from the electron continuity equation: 1dnedt+∇⋅(neve)=qe-α‾ne2 where qe is the ionization rate, α‾ the effective recombination rate and ve is the electron drift velocity. Transport of energetic electrons along the magnetic field and ionization are governed by a set of coupled linear differential equations e.g.,. The superposition principle applies for direct ionospheric responses such as ionization. Therefore it is possible to calculate the ionization profile as a matrix product with a discretized representation of the differential electron flux ϕ(E) at the top of the ionosphere: 2qe(z)=A⋅ϕ(E) where A is the ionization-profile matrix with the ionization rates at discrete energies E and altitudes z e.g.,. Quantifying the ionization rate profile qe(z) makes it possible to solve for the energy spectrum ϕ(E). For small-scale aurora, the convection of plasma in and out of the radar beam can be significant. However, since no full-profile multi-static velocity measurements have been available, the convective term ∇⋅(neve) is usually neglected.

The first methods to perform this inversion estimated qe(z) from Eq. () assuming steady-state, i.e., that ion production and recombination are in balance at all times, e.g., UNTANGLE by and CARD by . first considered non-steady-state conditions in the SPECTRUM algorithm, enabling reasonable estimates even when the electron precipitation varies on time-scales shorter than the recombination time, i.e., during auroral precipitation. first formulated this as a general inverse problem and used the maximum entropy method to regularize the solution. However, these direct methods run into two problems: The amplification of measurement noise when dne/dt and ne2 in Eq. () are taken directly from the measurements, and the ill-conditioned nature of the inverse problem from ionization profile to energy spectrum. Those are addressed with the ELSPEC method by , where the electron density is modeled by integrating the continuity equation, using Eq. () for the production term. Thereby the explicit calculation of dne/dt is avoided. The inversion is recast into a non-linear minimization problem, selecting for the best energy spectrum that minimizes differences between measured and modeled electron density.

In this work we present a refined ELSPEC version, where a dynamic ionospheric composition model, IonChem, is added. IonChem integrates the continuity equation for 15 ionospheric species, capturing the full dynamics in composition even during rapidly varying auroral precipitation. This enables us to study the effects of variation in ionospheric composition and, in consequence, the effective recombination rate on the estimation of primary electron spectra from ISR data. The method we present here aims to improve the electron energy spectra estimates and to study the effects of ionospheric variation.

This section begins with a description of ELSPEC, the method used to estimate electron energy spectra from electron density profiles. The following section describes the ion chemistry model. In Sect.  the coupling of IonChem into ELSPEC is explained. Next, the robustness of the technique under uncertain initial compositions is analyzed. In the last section a steady-state ion chemistry model, FlipChem, is introduced, which will be used for comparison.

To test this method and analyze the impact of ion composition variations on the electron energy spectra, we look at an event with rapid electron density variations in the E-region. Figure  shows enhanced electron densities when several auroral arcs passed over the radar at about 50 and 125s. The data was recorded on the 12 December 2006, 19:30–19:35 UT with the EISCAT UHF radar in Tromsø . GUISDAP is used to evaluate EISCAT lag profile data. A time resolution of 0.44s in electron density is achieved, with the ISR operating in the arc1 experiment mode. At this time resolution the raw back-scattered power is used as a measure for electron density, under the assumption that electron and ion temperature are equal. The reaction rates are calculated using ion and electron temperatures estimated from the ion line spectra, integrated for 4s to achieve an acceptable noise level. They are interpolated to match the time resolution of the electron density.

The measured electron density as well as the ELSPEC electron density models based on IRI and on IonChem composition are shown in Fig. , along with the relative variation (ne,IRI-ne,IC)/ne,IC. ELSPEC produces very similar electron densities with both composition models, modeling the measurements well in both cases.

The differential energy flux IE=Eϕ(E) produced using the IRI and IonChem models is shown in Fig. , along with the difference ΔIE=IE,IRI-IE,IC between the two. For three different slices in time, the results are also shown as a line plot, with the time marked in dashed lines in panel (c). The absolute difference (c) shows systematic negative values at the high energy tail, around 10keV. The differences are substantial as can be seen in the line plots, with a relative correction of about 50 %. Therefore, using IonChem composition, ELSPEC produces a lower flux at high energies for all time intervals. This systematic difference is explained by the ratio r=nO2+/nNO+, shown in Fig. . The IonChem composition has a higher ratio than IRI, especially towards the lower E-region. This is expected, since IRI does not take auroral precipitation into account and therefore represents quiet conditions where NO+ is more abundant. During auroral precipitation, however, the direct production of O2+ makes it the dominant species at lower altitudes. Due to the lower recombination rate of O2+, a lower flux of primary electrons is sufficient to produce the same electron density. Using the IRI composition, representing the ionosphere at a quiet state, therefore leads to a systematic bias in the energy distribution, overestimating the energy flux at higher energies.

Another comparison is made with FlipChem. Being a steady-state model, it adapts to auroral precipitation, as illustrated in Fig.  showing the O2+ density for both models. FlipChem predicts a large O2+ fraction, overestimating it above 120 km. Furthermore, it does not capture the short-timescale variation correctly. This can be seen during times of strong and rapidly varying precipitation, e.g. at 125s in Fig. . When IonChem models a reduction in O2+ fraction, FlipChem sees an increase. Lastly, noise in the temperature measurements affects reaction rates, leading to different steady-state densities. The noise in temperature is thereby propagated into the FlipChem densities. The noise in temperature is not affecting IonChem densities as much, as IonChem integrates the continuity equation dynamically. With the high time resolution (in this case 4s for temperature), IonChem tends towards, but does not reach, steady-state in that interval, dampening the effect of noise in temperature. Furthermore, the noise in subsequent time bins has an equalizing effect.

The differential energy fluxes produced using FlipChem and IonChem are compared in Fig. . Again, a systematic shift of the flux at 10–20 keV to slightly lower energies can be seen at all time-steps, due to the higher O2+ fraction at heights below 100km in the IonChem model (see Fig. ). Furthermore, between 30–70 s into the event, the flux at intermediate energies of 3–9 keV increases, due to the decreased O2+ fraction.

The difference in O2+ fraction between the two models during strong precipitation has been investigated further, as the decrease seen in IonChem during intense precipitation might seem counterintuitive at first. Since O2+ is produced directly by impact ionization, one might also expect its mixing ratio to increase. Instead, we find the O2+ fraction temporarily decreasing, while NO+ and O+ fractions are increasing, as shown in Fig. .

To study why the NO+ fraction increases, while O2+ decreases, a simulation with constant, strong precipitation is run. IonChem is initialized with the densities found just before 125s in Fig. , and the precipitation is set to what we find at 125s. Both O2+ and NO+ densities rise, as shown in Fig. . NO+ has a faster initial growth rate, which lowers the O2+ / NO+ ratio, before it recovers. Having a higher recombination rate, NO+ tends to the steady-state quicker than O2+. Furthermore, as atomic oxygen becomes more abundant with height, N2+ predominantly reacts with atomic oxygen producing NO+ . The large reaction rate enables the NO+ fraction to increase rapidly. This causes NO+ to become more abundant at high altitudes. After a period of high steady ionization a steady-state with an increased O2+ / NO+ mixing ratio is approached again.

Lastly, we find a significant O+ fraction down to 120km during strong precipitation, impacting the mean ion mass (Fig. ). This has consequences in fitting the electron and ion temperatures in ISR measurements, as they depend on the mean ion mass. Fitting the temperatures and mean ion mass simultaneously is difficult e.g.,, therefore, a model for the ion mass is commonly used. Even though the surges are short-lived, they may affect, for example, high-resolution analysis as in .

A new method to improve the inversion of electron density profiles to primary electron spectra is presented, that couples the fully dynamic ionospheric chemistry model IonChem with the time-dependent inversion algorithm ELSPEC. The iterative approach to simultaneously obtain electron energy spectra and ion compositions used here shows good results. It converges over a few iterations and is robust against uncertain initial conditions. The importance of using a dynamic model is shown with an example of transient effects in the O2+ / NO+ ratio and the O+ fraction.

ELSPEC presents an improvement compared to steady-state inversion procedures , as it integrates the electron continuity equation numerically without assuming balanced ionization and recombination rate at all times. Time-dependent inversion algorithms have been used, but assumed time-constant recombination rates . ELSPEC integrates the electron continuity equation instead of using it to explicitly calculate ionization profiles, similar to . This reduces the impact of measurement noise. Here, ELSPEC and IonChem adjust the ion composition iteratively, while used the Southampton ion-chemistry model to calculate the ion densities once, corresponding to one iteration. A similar method is used by , where the Sodankylä Ion-Neutral Chemistry model (SIC) is employed. The best-fitting ionization profile is found iteratively by integrating the coupled continuity equations of electrons and ions. The energy spectrum is then calculated using the CARD method, assuming steady-state conditions.

The method presented here is a tool that can help to improve studies of auroral precipitation, such as , and will be of interest for research with EISCAT_3D radar . ELSPEC can be used to provide additional insight in conjunction with other observations, complementing the field-aligned ISR measurements, for example, with optical measurements in the horizontal direction or satellite conjunctions .

Further improvements to the IonChem model could be made by taking production of excited states and spontaneous emissions into account; photoionization can be added to make it compatible with daylight conditions. With EISCAT_3Ds capability for volumetric measurements of both electron densities and plasma drifts, it should be possible to account for convection. Diffusion of neutral and ion species can be taken into account, in particular to account for transport of NO . Plasmaline measurements already allow for more precise determination of electron density profiles today, see . They should become routinely available with the higher sensitivity of EISCAT_3D.

Improved estimates of electron energy spectra from electron density profiles can be made by combining a dynamical ion chemistry model (IonChem) with the ELSPEC algorithm. The improvement of the dynamical chemistry is that it captures the variation of the ion composition during periods of rapidly changing precipitation. We find a systematic reduction of the electron fluxes at higher energies, in our test case at around 10keV, resulting from a dynamical variation of the ion composition. The cause of this reduction is due to the variability of the O2+ to NO+ mixing ratio. We have also made a comparison between our dynamical chemistry and a steady-state chemistry, FlipChem. The results show that variations in ion composition during rapid variations of ionization captured by the dynamical chemistry are not captured by a steady-state model. A rapid increase of ionization rate leads to a faster transient response of NO+ compared to O2+ density. Also here, a systematic reduction of the high energy tail is found when using a dynamic model, albeit to a lesser extend. Overall, modeling the ionospheric composition improves the quality of the inversion from electron density profiles to energy spectra.