Morphology of the pulsations

The morphology of the QP60 pulsations can provide clues about the acceleration mechanism and the source of the pulsed energetic electrons. Therefore the morphology of each individual pulse in the LEMMS electron data has been investigated individually.

The set of 720 quasi-periodic electron injections totals 3440 pulsations. One pulsation is counted if one peak is identified in at least one LEMMS E-channel. Most of the pulsa-tions do not appear at all energies of the LEMMS HET. Except for one particular event discussed in Section 7.2.2, no energy dispersion is observed in the electron injection. Con-sequently, when flux enhancements are present at different energies, they are concomitant in the different LEMMS channels.

In total, by considering the energy channels separately, 13 338 pulsations were identi-fied. Table 3.2 indicates the number of pulsations in each of the seven LEMMS channels considered. It appears that the number of pulses decreases with energy. Almost all pulsa-tions (∼96%) are present in the the energy range from 100 to 500 keV (E0-E1 channels).

At higher energies (E2-E4 channels), pulsations are less frequent. At these energies, flux enhancements preferentially occur in the center of the event time interval, as defined by the pulsations in the lowest energy channel E0, than at the start or the end of the interval.

This observation is illustrated in Figure 3.12 which gives, for each energy channel, the occurrence probability to observe thei^thflux pulse in an event made up ofnpulses (nand iare determined by the pulsations in the E0 channel). Only events with 3 to 7 pulses were

3.5 Morphological properties of the hourly electron pulsations Channel Energy passband Number of Percentage of

(keV) pulses sawtooth pulses

Table 3.2: Energy passbands for the different MIMI/LEMMS electron channels used in this study, total number of pulses and percentage of sawtooth pulses (rise rate shorter than 40% of the total duration of the pulse).

0 2 4 6 8

Figure 3.12: Normalized occurrence rate of each individual pulsation within a quasi-periodic pulsed event made up of 3 to 7 pulses, for the different LEMMS energy channels.

The number of pulsations is defined in the E0 channel.

considered in order to have good statistics. For the channels E2 to E4, this probability is the highest around the center of the electron injection event. Hence, the first pulse in the E3 and E4 channel generally corresponds to the second pulse in the E0 channel and the last one is the second last one in the lowest energy channel.

Additionally, the highest peak intensities are generally encountered in the middle of the event time interval. These findings suggest that the process producing the electron flux pulsations is progressive: it requires time to accelerate electrons up to the highest energies at a flux exceeding the background signal of the detector and it starts to fade out in the last third of the event.

Only few pulsations (3.2%) are present in the highest energy channels (E3 to E6) without concurrent pulses at the lowest energy (E0-E1 channels). A mixing of diff er-ent electron populations at lower energies may conceal the∼1-h pulsations. Finally, the higher is the peak pulse in one channel, the higher are the corresponding pulses in the other channels.

The rise time and the decay time of every pulse have been investigated, as well as the rise and decay rates (e.g. the slopes of the pulse) by means of a linear fit (in a linear scale) from the pulse start to the peak and from the peak to the pulse end. The histograms in Figure 3.13 represent the distribution of the ratio between the growth and the decay times of the pulses for the different LEMMS channels. The mean values of the rise-over-decay ratio, indicated in the upper right corner of each panel, are all lower than the unity, indicating that the growth time is generally shorter than the decay time. It is noteworthy that the rise-over-decay ratio decreases with energy. It is found that on average, the rise time diminishes with energy while the decay time increases.

Similarly, the ratio between the rise rate and the decay rate of the pulses follows a log-normal distribution centered on a positive value, meaning that the growth rate is usually higher than the decay rate (in absolute value). Again, this ratio increases with energy.

Hence, this statistical analysis of the morphology of the QP60 reveals that their most common shape is a fast growth followed by a slower decay. A rise time shorter than 40% of the full pulse duration or, similarly, a decay time longer than 60% of the pulse duration, characterize a “sawtooth” shape. The occurrence of sawtooth-shaped pulses increases with energy, from 52% in the E0 channel to 89% in the E6 channel, as listed in Table 3.2. The reverse shape (rise time longer than 60% of the pulse duration) is strictly speaking a sawtooth pattern too, but this designation will not be used hereafter for this morphology to avoid ambiguity. This morphology is encountered for 12% of the pulses in the E0 channel and this percentage decreases with energy to reach only 0.9% in the highest energy channel. The remaining pulses have a growth time comparable to the decay time (rise time between 40% and 60% of the pulse length).

No correlation has been found between the rise and decay rates of the electron flux enhancements and the interpulse period of an event nor the total number of pulses. How-ever, the growth duration and the decay duration are longer when the interpulse period is longer. The latitude and local time dependence of the rise and decay rates is shown in Figure 3.14 for the E0 and E3 channels (upper and middle panels). The rates are averaged over 1 h×20° latitude bins. The number of pulses included in each bin is indicated in white. The lower panel in Figure 3.14 gives the latitudinal average of the rates for every energy channel separately. The local time distribution of the growth and decay rates of the electron pulsations is practically uniform except in the sector 06-09 LT where they are higher at all energies. As shown by the upper panels, these increased averaged rates in the morning originate from the high rates encountered at high southern latitudes (ϕ < −30°) between 05 and 10 LT. In this magnetospheric region, most of the ∼1-h quasi-periodic electron events exhibit a foreground signal at energies above 1.6 MeV (see Figure 3.6).

Higher rates are also found at high northern latitude between 17 and 20 LT. However, only a few pulses are included in that region.

The analysis of the pulsation morphology reveals that the growth and decay slopes of the pulsations are steeper if the peak intensity of the pulse is higher, as shown for the E1 and E4 channels in Figure 3.15. Every pulse is represented by a black cross and the

3.5 Morphological properties of the hourly electron pulsations

Figure 3.13: Normalized histograms of the distribution of the ratio between the rise time and the decay time of each pulse for each considered LEMMS electron energy channel.

The average value of the ratio is indicated in the upper left corner. From Palmaerts et al.

(2016a).

scattered distribution is fitted by a linear fit in the log-log scale (red line). For all the LEMMS channels, the slope of the fit is higher for the rise than for the decay. The fit slope increases with energy up to the E3 channel and then lower at higher energies, as shown in the bottom panels of Figure 3.15. It should be noted that a low number of pulses are observed in the E6 channel, making the fit less reliable. The correlation coefficient between the pulse rates and peak intensity, indicated on the left corner of the panels in Figure 3.15, varies between 0.71 and 0.84, indicating a significant correlation.