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Planning Project 2: D-region Conductance & Multiple substorms

Steep conductance gradients emphasize the need to improve the spatial and temporal resolution of global conductance models.

Figure \ref{fig: ch6 conductance ratio} and \ref{fig: ch6 quantifying conductance} makes clear that there are steep conductance gradients in both space ($\sim 1$ S/km) and time ($\sim$2 S/min). Such gradients are completely smoothed out in global conductance models, where the spatial and temporal resolution are in the order of hundreds of kilometers or hundreds of minutes. Such small-scale and mesoscale descriptions of conductances are required to model field-aligned currents that electrically couple the ionosphere and magnetosphere.

Conductivity estimated from loss-cone measurements in the magnetosphere correlates well with measurements in the ionosphere.

Panels a), b), correlate well with panel c) in figures \ref{fig: ch6 hall conductivity} and \ref{fig: ch6 pedersen conductivity}, considering the magnetic conjugacy described in figure \ref{fig: ch6 magnetically conjugate loss cone}e) and associated text. It is a direct result of correlation in loss-cone particles and precipitating electrons in the magnetically conjugate period between THEMIS satellite and PFISR measurements (See figure \ref{fig: ch6 magnetically conjugate loss cone}a-c). Figure \ref{fig: ch6 validating magnetic conjugacy} shows the remarkable correlation between the loss-cone flux of electrons at the magnetic equatorial plane measured by THEMIS-D and flux of precipitating electrons in the ionosphere estimated by PFISR when both instruments are magnetically closest. Unlike the temporal correlation observed with time-series plots of conductivity (figures \ref{fig: ch6 hall conductivity},\ref{fig: ch6 pedersen conductivity}), this is a correlation of energy spectra of precipitating electrons. It is double-humped, with the first peak at around 3--5 keV corresponding to auroral electrons, which are probably cold plasma accelerated at the auroral acceleration region. The second hump is around 70-100 keV, which is a result of the current sheet scattering near the magnetic equatorial plane at about 9 R$_E $ in the plasma sheet.

![Validation of ISR estimate of precipitating electron spectrum using conjugate THEMIS-D measurement]{Precipitating electron energy flux estimated by magnetically conjugate measurements from the ionosphere and magnetosphere.](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/a30c3a27-b385-48b6-879a-9acecee74a2f/Untitled.png)

Validation of ISR estimate of precipitating electron spectrum using conjugate THEMIS-D measurement]{Precipitating electron energy flux estimated by magnetically conjugate measurements from the ionosphere and magnetosphere.

\label{fig: ch6 validating magnetic conjugacy}

\begin{table}[] \begin{tabular}{llcc} \hline \multicolumn{1}{c}{\textbf{\begin{tabular}[c]{@{}c@{}}Magnetospheric Source\\ of Precipitation\end{tabular}}} & \multicolumn{1}{c}{\textbf{Energy}} & \textbf{Altitude} & \textbf{\begin{tabular}[c]{@{}c@{}}Conductivity Increase\\ in the Ionosphere\end{tabular}} \\ \hline \begin{tabular}[c]{@{}l@{}}Scattering of cold plasma from \\ the plasma sheet\end{tabular} & \textless 3 keV & $>$120 km & mainly $\sigma_P$ \\ Auroral acceleration region & $\sim$ 10 keV & $>$100 km & mainly $\sigma_H$ \\ \begin{tabular}[c]{@{}l@{}}Outer radiation belt boundary\\ (current sheet scattering)\end{tabular} & $\sim$ 100 keV & $>$ 80 km & \begin{tabular}[c]{@{}c@{}}transient layer of high\\ electron mobility with \\ high $\sigma_H$ and\\ $\sigma_P$ in D-region\end{tabular} \\ \hline \end{tabular} \caption{The effect of precipitation from different magnetospheric sources on the conductivity of the ionosphere} \label{tab: ch6 magnetospheric sources of conductivity} \end{table}

% Magnetospheric sources of precipitation and its effect on conductivity increase in the ionosphere (Table)

Some magnetospheric sources of precipitation and its effect on ionospheric conductivity. Table \ref{tab: ch6 magnetospheric sources of conductivity} lists the magnetospheric source regions we have explored in the previous chapters and their approximate effect on ionospheric conductivity. Energetic precipitation, such as that from the outer radiation belt boundary, causes an additional, transient layer of conductivity below or the lower end of the ionospheric dynamo layer. However, most conductance contributions are by the lower, auroral energy electrons from the plasma sheet, accelerated by the AAR.

Joule heating due to energetic precipitation during the growth phase is relatively high. The conductance enhancement due to the outer radiation belt boundary can result in relatively high Joule heating rates. Joule heating, as a result of the collision of free electrons, accelerated due to an electric field into the surrounding plasma, can be expressed as $Q_J = \Sigma_P |E|^2$. We can estimate the electric field $E$ from the drift velocity of ions measured by PFISR in the F-region, which is about $25 mV/m^2$ with $V_D = 500 m/s$. Assuming the Electric field gets translated to the upper D-region without attenuation, the total $Q_P \approx 1$ GW. This is double the total power of the precipitating energetic electrons with energy $>10$ keV, which is $\sim$ 0.5 GW.