Pitch angle distribution of the pulsations

In this section, the pitch angle dependence of the periodic electron flux enhancements is investigated. As a reminder, the pitch angle indicates the angle between the magnetic field lines and the direction of the particle hitting the LEMMS detector. The isotropy of the pulsed energetic electrons can be known only when all pitch angles are covered, providing then the pitch angle distribution (PAD). The PADs are available only when LEMMS orientation is changing, thus when Cassini is spinning.

Information about the pitch angle distribution is available for 161 pulses from 78 dif-ferent quasi-periodic∼1-h electron injections. Three of them are visible at the beginning of the event depicted in Figure 3.1. In Roussos et al. (2016), the pitch angle dependence of an event is analyzed in detail. In that particular event shown in the upper panel of

Fig-0 5 10 15 20

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Figure 3.14: Upper and middle panels: Latitude-local time diagrams of the rise (left) and decay (right) rates of the pulses (absolute value of the slope of a beginning-to-peak and peak-to-end linear fit of the pulses) in the E0 (110-365 keV) and E3 channels (600-4950 keV), averaged over 1 h LT × 20° latitude bins. The number of pulses included in each bin is indicated in white. Lower panels: Latitude average of the rise (left) and decay (right) rates binned on 1 h LT for each considered LEMMS electron channel. From Palmaerts et al. (2016a).

ure 3.16, periodic enhancements with a short periodicity are observed at lower energies (C0-E0 channels) in addition to clear∼1-h pulsations at energies above 790 keV (E4-E6 channels). These narrow peaks are in phase with the pitch angle variation (lower panel of Figure 3.16) caused by Cassini rolling. At intermediate energies (E2 channel), both periodic flux variations are mixed. The short-period flux peaks at low energy indicate the presence of a bidirectional electron beam along the field lines. The analysis by Roussos et al. (2016) revealed a quasi-isotropic PAD of the decay of the pulse.

The disentangling between the field-aligned electron and the∼1-h quasi-periodic elec-tron populations is highlighted in the pulsed event which occurred on day 027 of 2008.

This event is shown in the upper panel of Figure 3.17. In addition to the E-channels, a combination between the low energy electron channels C4, C5 and C7 is indicated. This combination, noted E0^?, is calculated using the formula

E0^? = 0.1×C4+0.5×C5−0.25×C7

This combination of C-channels gives a pseudo-channel with an energy passband similar

3.5 Morphological properties of the hourly electron pulsations

Figure 3.15: Upper and middle panels: Rise (left) and decay (right) rates for each pulse (in absolute value) in the E1 (220-485 keV) and E4 channels (790-4750 keV) as a function of the peak intensity of the pulse. A linear fit is plotted in red. The slope of the fit and the correlation coefficient are indicated in the upper left corner. Lower panels: Slope of the fit for each channel for the rise (left) and decay (right) rates. The vertical error bars are the 1-sigma uncertainty for the slope. From Palmaerts et al. (2016a).

as E0 but it measures electrons coming from the opposite direction and entering in the LEMMS LET telescope. Following the method described in Gurnett et al. (2010), the ratio between E0^? and E0 indicates if LEMMS is located on open or closed field lines.

On closed field lines, the flux of particles at a certain energy is the same in both directions because of the bouncing motion (Section 1.2.4.1), as illustrated in Figure 3.18. Hence, when the pointing of the two telescopes of LEMMS is aligned with the magnetic field lines (i.e. the pitch-angle is around 0° or 180°), the fluxes in E0 and in E0^?are equivalent if Cassini crosses closed field lines and are significantly different on open field lines. In the bottom panel of Figure 3.17, the local pitch angles in the LEMMS HET (thick line) and LET (thin line) are indicated with a color scale giving respectively the intensity in the E0 and E0^? channels. During the main part of the event, Cassini is rolling, providing a good pitch angle coverage.

During the event shown in Figure 3.17, three flux enhancements separated by around 60 min are detected between 0030 and 0300 UT. Three green rectangles are on top of these ∼1-h pulsations. After 0300 UT, narrow peaks, indicated by short red lines, are

Figure 3.16: Quasi-periodic pulsed event observed on day 048 of 2009 in different LEMMS electron channels (top panel) and pitch angle of the LEMMS HET (bottom panel). From Roussos et al. (2016).

observed simultaneously with a pitch angle close to 0°. This observation, made in the northern hemisphere, reveals the presence of upward field-aligned electron beams similar to the beams reported by Saur et al. (2006). Hence, when HET is pointing in the field-aligned direction toward Saturn, a short but intense flux enhancement is detected in the E-channels. The same peaks appear in the E0^?when the LET telescope is in the field-aligned direction toward the planet. Since the E0^?and E0 fluxes do not peak simultaneously, it is revealed that LEMMS is on open field lines after 0300 UT.

Five narrow flux peaks are also present earlier in the interval, superimposed to the first two 1-hour pulsations. At that time, the field-aligned electron beams are bidirectional since they are observed at pitch angle of∼0° and∼180°. Thus, Cassini resides on closed field lines between 0030 and 0215 UT. During the last 1-hour pulse at 0230 UT, LEMMS pointing is fixed and not in the field-aligned direction so that no narrow flux peak is detected. Like for the event presented in Figure 3.16, the field-aligned variations of the electron intensities are larger at low energies.

The event shown in Figure 3.17 and depicted in the previous paragraphs demonstrates the coexistence of two different electron populations: the hourly quasi-periodic relativistic electrons and the field-aligned electron beams. While the∼1-h pulsations (green rectan-gles) stop after 0300 UT, the narrow field-aligned flux peaks (red lines) persist. It should

3.5 Morphological properties of the hourly electron pulsations

Figure 3.17: Upper panel: Quasi-periodic pulsed event observed on day 027 of 2008 mixed with a field-aligned electron beam population. Time series of the differential inten-sities of LEMMS electron channel E0 to E4, E6 and E0^?(combination of C4, C5 and C7).

The quasi-periodic pulsations are indicated by the green rectangles. Red lines point at the electron beams. Lower panel: Pitch angle pointing of the LEMMS HET (thick line) and LET (thin line). The colors indicate the intensity of the E0 and E0^? channels. Adapted from Palmaerts et al. (2016a).

be also noted that Cassini is on closed field lines till 0300 UT and then is on open field lines, as indicated by the comparison between the E0^?and E0 channels.

Using the set of 161 pulses with an available pitch angle distribution, a statistical analysis of the PAD of the hourly quasi-periodic electron pulsations has been achieved.

Each pulse has been divided in three parts: the growth of the pulse, the peak (one single value per pulse) and the decay. The statistical PAD for each part in the E0 channel is shown in Figure 3.19. In order to conceal the flux level variations between different events, the intensity is normalized to the unity at the start of the pulse for the growth part and at the end of the pulse for the decay. The average distribution indicated by the black line is superimposed to the individual measurements (gray crosses). The growth and decay parts of the pulses exhibit a quasi-isotropic pitch angle distribution, in agreement with the single-case analysis for the decay performed by Roussos et al. (2016). For a few events, the PAD has a more field-aligned shape. Unlike the rise and decay phase, the PAD of the pulse peak intensity is mainly aligned with the magnetic field. This is explained by the mixing between the hourly pulsed electrons and the field-aligned electron beams which tends to increase the peak intensity of the∼1-h pulsations, especially at low

Figure 3.18: Illustration of the method described by Gurnett et al. (2010) to identify if Cassini is on open or closed field lines using Cassini/LEMMS instrument. On closed field lines, the flux of particles at a given energy is the same in both direction (blue arrows).

Hence, when LEMMS is pointing in the field-aligned direction, the flux measured by HET and LET are the same. On open field lines, the particle flux is not the same toward the planet (light blue arrows) and backward the planet (dark blue arrows). Therefore, the measurement of particles at a given energy is not identical in the two LEMMS telescopes.

energies. At higher energies, the statistical PADs for the three parts of the pulses are similar.

Based on the E0^?/E0 ratio and the method of Gurnett et al. (2010), it appears that all the duskside field-aligned pulses but one are associated with closed field lines. The only exception is a high-latitude event on day 297/2008 occurring while Cassini was crossing open flux tubes during a brief time. This result is only valid in the dusk flank of the magnetosphere since only two dawnside events provide a pitch angle distribution.