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Polar cap patches are traditionally defined by plasma density enhancement and thus typically observed by LEO satellite or remotely sensed by ground‐based radars, but they can also be observed using optical instruments, such as 630 nm red line all‐sky imagers. The classical nighttime source for generating O(¹D) is through dissociative recombination:

(4.1)

This process is negligible in the sunlit atmosphere. The volume emission rate due to dissociative recombination in the absence of precipitating particles based on Link and Cogger (1988) is

(4.2)

The β₁ is the metastable yield of nightglow production reaction described by equation (4.2), and k₁, k₃, k₄, k₅ are the rate coefficients. The k₁ and k₅ depend on ion and electron temperature, respectively, while k₃ and k₄ depend on neutral temperature. β₁ is either 1.1 (Link et al., 1981) or 1.3 (Sobral et al., 1993). A_1D is the transition coefficient for A_630nm and A_636.4nm and equals 7.45x10^‐3 (Hays et al., 1978).

As one can see from the equations above, the patch luminosity depends on the altitude distribution of the electron density and also the neutral atmosphere property. It emits redline as it recombines. Therefore, its luminosity variation provides clues to some extent for the internal plasma dynamic processes. Hosokawa et al. (2011) used all‐sky imager at Resolute Bay to study patches, and found that the patch emission height should be around 295 km and not the 235 km obtained from the MSIS‐E90 and IRI‐2007 models, which highlight the deficiencies of these models in the polar region. They found that the e‐folding time of the patch decay can change from 1 hour to 4 hours for altitudes of 250 km and 290 km, respectively, due to charge exchange and recombination with molecular species. Therefore, characteristics of the polar cap patches, such as altitude profiles of electron density, are critical for the understanding of the ion‐neutral interactions within the patch, but they are often unknown because of a lack of continuous measurements deep in the polar cap. In fact, the ambiguity of the emission height introduced to the luminosity calculation has been realized before. Sojka et al. (1997) quantitatively estimated the effect of various density distribution vertically, and found that the patch emission can change as much as 400 R, when the F‐region peak height reduces from 360 km to 300 km.

Recently, Perry et al. (2013) also found that the luminosity could change up to a factor of 2 or more, when enhanced ExB convection leads to descending motion of the F‐region ionosphere, and the timescales for the emission variations are on the order of 10 to 20 min. Figure 4.8 displays a chart from the Perry et al. (2013) study showing the time (in seconds) needed for a patch's luminosity to decrease to 60% of its initial value and the ratio of the maximum luminosity versus its initial value as a function of vertical drift speed and of the neutral density at 250 km altitude (expressed as ratio). They further suggested the possibility of using changes in patches intensity to monitor the vertical motions of patches and possibly even their vertical position.

Figure 4.8 Chart of the time, in s, taken to go down to 60% of the initial luminosity (blue contours) and of the ratio of the maximum luminosity to the starting luminosity (red contours) as a function of vertical drift (horizontal axis) and of the ratio of the starting density to the density (vertical axis)

(from Perry et al., 2013; Reproduced with permission of John Wiley and Sons).

Besides the classical recombination‐induced red line emission, soft particle precipitation has also been suggested to be able to cause patch luminosity increase. Zou Y. et al. (2017) studied non‐storm‐time polar cap patches observed by the 630 nm all‐sky imager at Resolute Bay and particle precipitation measured by Fast Auroral Snapshot‐imager (FAST), and found that localized precipitation of soft electrons collocated with the patch luminosity increases. In another study, Sakai et al. (2014) compared the patch emissions calculated using EISCAT incoherent scatter radar with that measured by an 630 nm red line all‐sky imager. They found that the patch emission due to recombination can contribute up to 50% of measured luminosity with the coexistence of soft electron precipitation. When the electron temperature is relatively low, the observed and the calculated 630 nm emissions due to recombination agree with each other better. This also confirms that enhanced electron temperature is a good indicator of the existence of local soft electron precipitation.

On the other hand, when the electron gas is significantly heated, 630 nm emission can also be excited through thermal emission (Schunk & Nagy, 2018). This occurs when there are sufficient electrons with energy higher than 1.96 eV and they can excite the atomic oxygen ground state O(³P) to excited O(¹D) state. When the excited O(¹D) relaxes back to the ground state, a photon at 630 nm is emitted, such as seen in the stable aurora red (SAR arc) arc case (Kozyra et al., 1990). Kwagala et al. (2018) studied the occurrence rate of thermally excited 630 nm emission in the polar ionosphere and found that the emission has average intensity of 1–5 KR, higher than the typical recombination induced redline emission, and occurs more often when the electron temperature is higher than 3000 K. However, in high‐density regions ( >5 x 10¹¹ m^‐3), the electron temperature needs to be only ~2300 K to have a sufficient number of energetic electrons. This study suggests that in the case of particle precipitation, besides direct impact excitation, the luminosity increase in patches may also be partially attributed to thermal excitation. Because the classical patches have colder electron temperature than the surrounding region, the thermal emission may not be important, while this type of emission would be more significant in the hot patch case. Results from the above studies emphasize that variations in the patch emission could be attributed to multiple factors, and one needs to be very careful when interpreting those variations.

As shown in equations (4.1) and (4.2), the decay of patch and its emission rate not only depends on the electron density distribution, but also on the neutral atmosphere properties. However, many of the above studies have used the empirical MSIS model for the neutral atmosphere, and it has not been quantitatively evaluated before to what extent the neutral atmosphere properties can affect the patch emission and under what conditions. Future studies are required to understand the ion‐neutral coupling processes inside patch using fully coupled ionosphere‐thermosphere models.