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Planning Project 2: D-region Conductance & Multiple substorms

%However, our observations mostly discuss D-region contributions to total conductance to the order of $15-60$\%. Though this is within the acceptable variance, our results are still important to show that D-region contribution is comparable to the E-region contribution during substorms even though the total altitude range of the E-region is double that of the D-region.

%% Observations of a Single Event For the 26 March 2008 substorm discussed in chapters \ref{chapter4} and \ref{chapter5}, we applied the methodology described in the previous section, to develop 3-D conductivity data structures that vary as a function of time. Figure \ref{fig: ch6 hall conductivity map} a, shows small-scale maps of hall conductivity, with a coverage of 50 km and spatial resolution of 5 km. In this example, we see steep conductivity gradients at 82 km and 11:08 UT, when the energetic electron arc (i.e., the outer radiation belt boundary) moves equatorward through PFISR's field of view, during the substorm growth phase (figure \ref{fig: ch6 hall conductivity map} b). We do not see such a steep gradient at 120 km at 11:08 UT. This suggests that the physical mechanisms scattering lower energy electrons $1-10$ keV (which ionizes high altitudes) are different from current-sheet scattering that has a stronger effect on precipitating high energy electrons due to their higher gyro-radius (See section \ref{section: current sheet scattering}). If there is sufficient electric field in the D-region, equation \ref{eq: ch6 field-aligned currents} shows that energetic precipitation that causes high conductivity gradients can result in an increased field-aligned current flowing into this boundary \citep{Kosch2001b}. The Poynting flux form the magnetosphere communicates the electric field along the magnetic field down to the ionosphere. The electric field attenuates as it penetrates to lower altitudes, as the energy is lost to accelerating free electrons and ions and joule heating. However, $90$\% of DC electric fields perpendicular to the magnetic field can penetrate down to 70 km \citep{Vanhamaki2015}, which is at the altitudes of the conductivity gradient described here.

\begin{equation} \label{eq: ch6 field-aligned currents} J_{\parallel} = \sigma_P \nabla \cdot \boldsymbol{E} + \nabla \sigma_P \cdot \boldsymbol{E} + \nabla \sigma_H \cdot \boldsymbol{\hat{b} \times E} \end{equation}

In equation \ref{eq: ch6 field-aligned currents}, $J_{\parallel}$ is the current density along the magnetic field line, where $\hat{b}$ is the magnetic field-line direction.

\begin{figure} \centering \includegraphics[width=\textwidth]{figures/chapter6/conductivity_maps.pdf} \caption[Hall conductivity maps derived from PFISR]{Hall conductivity maps derived from PFSIR, induced by energetic electron precipitation from the outer radiation belt boundary moving equatorward during a substorm growth phase. Panel a) Small-scale maps of conductivity with each sub-panel at increasing height along the vertical axis and increasing time along the horizontal axis. Sub-panel (4,2) shows a steep latitudinal conductivity gradient as the energetic electron arc passes through PIFSR's field of view. Panel b) shows the optical emissions associated with the outer radiation belt boundary at 11:19 UT, and overlayed on it is the PFISR energy flux map of 100 keV electrons from the outer radiation belt boundary.} \label{fig: ch6 hall conductivity map} \end{figure}

\begin{figure} \centering \includegraphics[width=\textwidth]{figures/chapter6/Figure2.pdf} \caption[Magnetic conjugacy of PFISR, THEMIS-D, and THEMIS-E and their estimates of loss-cone flux]{a) differential energy flux of loss-cone electrons measured by THEMIS-D at the equatorial plane, b) differential energy flux of loss-cone electrons measured by THEMIS-E at the equatorial plane, c) differential energy flux of precipitating electrons estimated by PFISR at the ionosphere, d) magnetic footpoints of the satellite trajectory and PFISR location, e) the radial distance of the magnetically conjugate point in the magnetic equator of the satellites and ISR, calculated using T96 model.} \label{fig: ch6 magnetically conjugate loss cone} \end{figure}

The difference in the sources of low-energy and high energy electron precipitation during this growth phase can be visualized more clearly by comparing measurements of differential energy spectra from PFISR with that of near magnetically-conjugate THEMIS-D and -E satellites. Figure \ref{fig: ch6 magnetically conjugate loss cone}d) shows the northern magnetic footpoint of THEMIS spacecraft and their relative position to the PFISR radar system. Figure \ref{fig: ch6 magnetically conjugate loss cone}e) shows the equatorial distance of the magnetically conjugate point of the instruments on the magnetic equatorial plane. We see that the closest magnetic conjunction achieved by the radar with the satellites is between 11:03 - 11:10 UT. During this short period, figure \ref{fig: ch6 magnetically conjugate loss cone}c) shows the differential electron energy flux estimated by PFISR. Marked by a white-circle, we can observe an increase in 100-300 keV electrons, which indicate the electron isotropic boundary that marks the outer radiation belt boundary. Figures \ref{fig: ch6 magnetically conjugate loss cone}a-b) shows the differential electron flux estimated within the loss-cone of particle detectors onboard THEMIS. It was near the equatorial plane and magnetically conjugate with Poker Flat at the time. However, the equatorial magnetic region associated with THEMIS-D and -E from 9:00 UT to 11:10 UT is similar to the region associated with PFISR between 11:03 UT to 11:10 UT. We show this in figure \ref{fig: ch6 magnetically conjugate loss cone}e) using the gray shaded box. As a result, differential energy flux of electrons $\sim30-300$ keV seen in figure \ref{fig: ch6 magnetically conjugate loss cone}a-b) is likely associated with current sheet scattering. The flux values and time evolution between the satellite and PFISR measurements are remarkably similar once corrected for the magnetic conjunction.

The 9:00 -- 11:10 UT of loss-cone particle measurements made by THEMIS-D and -E satellites is the same plasma population as PFISR measurements from 11:03-11:10 UT. Keeping this in mind, we now turn to the conductivity estimates from precipitating electrons observed by THEMIS satellites, and PFISR. Figure \ref{fig: ch6 hall conductivity} shows the variation of hall conductivity with time. Figure \ref{fig: ch6 hall conductivity}a-b) shows hall conductivity calculated by estimating the ionization caused by THEMIS measurements of loss-cone electrons at the magnetic equatorial plane and using the conductivity formula described in section \ref{section: ch6 methodology}, \ref{section: conductance}. Figure \ref{fig: ch6 hall conductivity}c) shows the conductivity profile estimated using PFISR measurements of electron density along the magnetic field-aligned beam. The primary feature to notice here is that there seems to be a separate layer of conductivity in the D-region, distinct from the E-region, as seen in figure \ref{fig: ch6 hall conductivity map}. The source for this separation of the layer at about 90--95 km seems to be the separation of sources of energetic electrons at about 30--40 keV as seen figure \ref{fig: ch6 magnetically conjugate loss cone}. Apart from this feature, notice that the Hall conductivity in the D-region is also comparable to the Hall conductivity in the E-region during the growth phase. During the substorm onset and expansion, the D-region hall conductivity seems higher than in the E-region.

\begin{figure} \centering \includegraphics[width=\textwidth]{figures/chapter6/Hall_conductivity.pdf} \caption[Hall conductivity estimates by THEMIS-D, -E and PFISR]{Hall conductivity estimated from loss-cone particles measured by THEMIS-D and -E, agrees with measurements made by PFISR. The conductivity between 9:00 -- 11:10 UT of panel a-b) is magnetically conjugate with panel c) from 11:03-11:10 UT, according to the T96 model.} \label{fig: ch6 hall conductivity} \end{figure}

\begin{figure} \centering \includegraphics[width = \textwidth]{figures/chapter6/pedersen_conductivity.pdf} \caption[Pedersen conductivty estimate by THEMIS-D, -E and PFISR]{Pedersen conductivity estimated from loss-cone particles measured by THEMIS-D and -E, agrees with measurements made by PFISR. The conductivity between 9:00 -- 11:10 UT of panel a-b) is magnetically conjugate with panel c) from 11:03-11:10 UT, according to the T96 model. A net mobility minimum induces the minimum in Pedersen conductivity at 97 km. Below this ion-neutral collision constrains the ions to the neutrals. An increase in electron-neutral collisions steers the electrons from purely the Hall direction and more along the electric field direction.} \label{fig: ch6 pedersen conductivity} \end{figure}

A different reason causes the separation between the additional Pedersen conductivity layer induced by energetic precipitation in the D-region and the Pedersen conductivity in the E-region. Figure \ref{fig: ch6 pedersen conductivity} shows a characteristic altitude at around 97 km above which ions dominate Pedersen conductivity, and below that by electrons. At about 125 km altitude, the ions are only partially coupled to neutrals, and as a result, they move in the direction of the electric field $\boldsymbol{E}$ and carry the ion Pedersen current. However, electrons are unaffected by collisions and therefore drift in the $\boldsymbol{E} \times \boldsymbol{B}$ direction. Below $\sim$97 km, the ions are completely dominated by collisions with the neutrals, and they follow the neutral wind. The electrons start to become partially coupled to the neutrals through collisions and hence start drifting in the $\boldsymbol{E}$ direction causing an electron Pedersen current. The obvious minimum at $\sim 97$ km is perhaps also enhanced by a minimum in the precipitating electrons at $\sim30-40$ keV, which is a result of the two distinct source mechanisms driving the low and high energy precipitation. \begin{figure} \centering \includegraphics[width=\textwidth]{figures/chapter6/conductance_ratio.pdf} \caption[Ionospheric conductance and altitude profile of conductivity during the growth phase of 26 March 2008 substorm]{ Panel a) the First row shows integrated Hall conductivity across the range of the radar (60--140 km), i.e., Hall conductance. The second row shows the Pedersen conductance, and the third row shows the ratio of the Hall and Pedersen conductance. Each column is a time instant. Panel b) shows the altitude profile of the Hall and Pedersen conductivity at 11:08 UT during the growth phase. The profile is averaged across 2 minutes.} \label{fig: ch6 conductance ratio} \end{figure}

Figure \ref{fig: ch6 conductance ratio} a) shows the Hall and Pedersen \textit{conductance} (height integrated conductivity), and their ratio. The Hall conductance value shows a moderate conductance gradient at 11:08 UT. Let us recall that in figure \ref{fig: ch6 hall conductivity map}, the Hall conductivity was uniform in the E-region ($\sim$ 120 km) but had a steep gradient in the D-region ($\sim$ 82 km) at 11:08 UT. Therefore, a moderate conductance gradient suggests that D-region Hall conductivity, during energetic precipitation from the outer radiation belt boundary, contributes significantly to the total ionospheric conductance. The third row in figure \ref{fig: ch6 conductance ratio} shows the Hall to Pedersen conductance ratio, which peaks at around 11:20 UT. Hall to Pedersen conductance ratio is high when there are more energetic particles precipitating \citep{Robinson1987}. This is because the Hall conductance is affected by higher-energy electrons that ionize lower altitudes ($<$100 km), as compared to lower-energy electrons that ionize high altitudes ($>$100 km).

Figure \ref{fig: ch6 conductance ratio} b) shows an altitude profile of Hall and Pedersen conductivity at 11:08 UT, averaged over 2 minutes of ISR measurement along the magnetic field-aligned beam. The primary peak of the Pedersen conductivity is as expected to be -- about 120 km. The Hall conductivity peak is slightly lower at around 115 km. However, there is a second, additional, smaller peak around 80 and 82 km. This is a clear sign of the additional D-region conductivity enhancements, though the conductivity is one order of magnitude lower than the E-region maximum.

\begin{figure} \centering \includegraphics[width=\textwidth]{figures/chapter6/conductance_contributions.pdf} \caption{Hall and Pedersen conductance from the D-region, the E-region, and the total ionosphere.} \label{fig: ch6 quantifying conductance} \end{figure}

Finally, we can view the figure \ref{fig: ch6 quantifying conductance} as quantifying the contribution of D-region towards total ionospheric conductance. In both panels, about 10:30 UT is the quietest time in terms of precipitation. As a result, the conductance values we see during that time is very close to the quiet background. Total Hall and Pedersen conductance have a value of 8 S and 3.5 S, respectively. During the growth phase, when the outer radiation belt boundary passes through the PFISR field of view, the Hall conductance reaches 40 S and the Pedersen conductance 15 S. It is an almost five-fold increase. D-region contributes about 10 S of the Hall conductance and 0.7 S of the Pedersen conductance. This is about a 25\% and a 5\% increase. During the substorm onset, the Hall conductance rises to 100 S, and the Pedersen conductance to 30 S. This is more than a ten times increase from the quiet period. And here, the D-region Hall conductance contribution increases to 60\% (60 S) and the Pedersen conductance contribution to 15\% (5 S) of the total conductance. This enhanced D-region contribution is a result of energetic precipitation. The D-region Pedersen conductance contribution is likely higher than the above estimate if we incorporate the non-linear increase in Pedersen conductivity with large electric fields \citep{Buchert2008}. It is also important to note that the small-scale Hall conductance observed over the outer radiation belt boundary is 40\% of that seen during substorm onset.