Physical Origin of Recurrent Magnetic Dipolarization Events in Saturn’s Equatorial Plasma Sheet

We consider the physical origin of reconnection‐related events in Saturn’s equatorial current sheet revealed by Cassini, specifically the dipolarization events discussed by Yao et al. (https://doi.org/10.1029/2018JA025837) that recur close to the ∼10.7 h planetary period oscillation (PPO) period. We argue that Yao et al.’s preferred recurrence explanation in terms of complete rotations of dipolarized field/current structures around the planet at close to the PPO period is highly implausible. All‐mission observations of ion flows at relevant radial ranges ∼20–30 Saturn radii are essentially invariably sub‐corotational, including reconnection‐related hot ion injections, thus requiring implausible structure propagation at significant speeds through the plasma. We further show their assertion that the nightside events occur at PPO phases unfavorable for reconnection is incorrect. These events instead occur under PPO conditions associated with outward radial plasma displacement and/or a thinning plasma sheet with falling colatitudinal field, shown previously to be optimal for modulated reconnection bursts leading to dipolarizations and plasmoids. We instead suggest these events are related to well‐documented Vasyliunas cycle disturbances, when two reconnection episodes happen to be triggered at similar favorable PPO phases on successive PPO cycles. Yao et al.’s dayside events do occur at phases unfavorable for recurrent reconnection, but may then simply be an effect of periodic field/plasma modulations during the regular PPO cycle combined with subcorotating small‐scale structures often present in the plasma sheet. Both dayside and nightside events can thus be understood within existing knowledge of PPO modulations of the structure and dynamics of Saturn’s equatorial current sheet.

. The increase in power and LFE are indicative of an enhancement in the strength of magnetosphere-ionosphere coupling currents during these intervals with an associated extension in the altitude of auroral electron acceleration, given that SKR is generated on auroral field lines at a frequency close to the local electron gyrofrequency proportional to the field strength (e.g., Lamy et al., 2010).
Overall, the features during these intervals are indicative of the excitation of Vasyliunas cycle mass loss of plasma originating from the moon Enceladus, a ∼100 kg s −1 source of water ion plasma orbiting at a radial distance of ∼4 R S within the inner magnetosphere (Bagenal & Delamere, 2011;Vasyliunas, 1983). Although in principle reconnection during these events could continue beyond plasmoid ejection to further involve the tail lobe field, study of the associated auroral emissions indicates that typically only small amounts of open flux are closed (Radioti et al., 2016). This feature strongly distinguishes these events from the less frequent but longer-lived solar wind compression events, during which large fractions of the polar open flux may become closed via Dungey cycle tail reconnection (e.g., Badman et al., 2005;Bradley et al., 2020;Bunce et al., 2005;Cowley et al., 2005;Jia, Hansen, et al., 2012;Meredith et al., 2014;Nichols et al., 2014).
The structure of the magnetospheric plasma regimes to which these processes give rise consists of an inner region dominated by cool (∼10-100 eV) dense outflowing Enceladus plasma, and an outer region of mass-reduced flux tubes that also contains hot plasma (∼1-100 keV) that has been energized in the tail and injected inwards (e.g., Cowley et al., 2004Cowley et al., , 2005Thomsen, 2013;Thomsen & Coates, 2019). Empirically, the boundary between these two regimes lies typically at an equatorial radius ∼10 R S , which is consequently the site of frequent centrifugally driven flux tube interchange events between the two regimes in which hot plasma fingers may be injected deep into the inner magnetosphere (e.g., Azari et al., 2019;Chen et al., 2010).
A key feature of the reconnection and injection events is that their occurrence is strongly influenced by the phase of the ubiquitous Saturn planetary period oscillations (PPOs), comprising rotating modulations in the magnetic field, plasma, auroras, and radio emissions that occur near the planetary rotation period (e.g., Andrews et al., 2019;Bader et al., 2019;Hunt et al., 2014Hunt et al., , 2015Lamy, 2017;Provan et al., 2018;Ramer et al., 2017). In fact, two such modulation systems are usually simultaneously present in the magnetosphere, one driven from the northern polar ionosphere and the other from the southern polar ionosphere, that generally rotate with slightly different seasonally dependent periods lying in the range ∼10.6-10.8 h (e.g., Andrews et al., 2010;Gurnett et al., 2009;Provan et al., 2016Provan et al., , 2019Ye et al., 2018). The first indication that these "short-lived LFE" events are influenced by the PPO modulations was noted by Jackman et al. (2009), who showed for a small set of observed nightside reconnection events and associated SKR LFEs that their time of onset strongly favored the rising phase of the regular PPO-related SKR modulation cycle. That is, if the maximum SKR power in the regular PPO cycle is defined to occur at a cycle phase of 0°/360°, the event onsets showed a strong preference to occur in the (then-dominant southern system) phase range 180° to 0°/360° via 270°, when the power is generally increasing with time. Subsequent work by Reed et al. (2018) using a much larger catalog of LFE onsets from the 2006 Cassini tail-orbit season confirmed this effect, also showing a preference for events to occur at times when the power of both PPO systems were simultaneously increasing. Examination of large data sets of reconnection-related disturbances in Saturn's nightside current sheet has similarly shown that the occurrence of plasmoid and dipolarization events are both strongly modulated by the PPO phases Jackman et al., 2016), specifically in these cases by the phase systems determined from magnetic field data, that are closely linked to the SKR phases (e.g., Provan et al., 2019).
Studies of the nightside equatorial plasma/current sheet have indeed shown that its properties are dual-modulated by the two PPO systems, not only oscillating north-south about its averaged position (e.g., Arridge et al., 2011;Szego et al., 2013), but also thickening and thinning with the cyclic PPO modulations (Agiwal et al., 2020;Morooka et al., 2009;Provan et al., 2012;Thomsen et al., 2017). In addition, magnetospheric plasma and field lines also undergo equatorial radial displacements during the PPO cycle, as observed directly in radial oscillations of the dayside magnetopause and bow shock (Clarke, Andrews, Arridge, et al., 2010;, and also in latitudinal oscillations of magnetosphere-ionosphere coupling currents (Hunt et al., 2014). Both modulation of the current sheet thickness as well as radial displacements of the field lines and plasma may influence the stability of the plasma/current sheet to magnetic reconnection, thus providing a physical explanation COWLEY AND PROVAN 10.1029/2021JA029444 2 of 27 of the PPO-related dependencies outlined above. As discussed further in Section 3.1, reconnection events occur preferentially at PPO phases when the current sheet is thin and the plasma displaced radially outward from the planet.
In a recent study, Yao et al. (2018) have proposed that in addition to the two types of Saturn disturbance outlined above, a third category of event is also revealed by Cassini data, which they term "recurrent magnetic dipolarizations." In these events, three proposed examples of which are discussed, related signatures of field dipolarization events are identified which are separated by an interval close to one planetary rotation period, by which we specifically mean close to one PPO period ∼10.7 h. The recurrent dipolarization signatures in these events thus occur at close to the same PPO phases in each pair of events, superposed on the regular field variations associated with the PPOs. By way of introduction, Figure 1 shows magnetic field data encompassing Yao et al.'s (2018)    phases of the northern (N, blue) and southern (S, red) PPO systems determined from analysis of magnetic field data by Andrews et al. (2012). Details of these phase systems will be discussed in Section 3.1, but for present purposes it is sufficient to note that the data in Figure 1 span approximately four ∼10.7 h PPO cycles as evident particularly from the near-antiphase modulations in the radial r B and colatitudinal B  field components. The recurrent field dipolarization events discussed by Yao et al. (2018) are the two ∼30 min disturbances marked by vertical arrows, that involve sudden sharp reductions in r B indicative of an expansion of the plasma/current layer across the spacecraft, together, at least in the first event, with a sharp positive peak in B  . Yao et al. (2018) also show that these events are accompanied by enhanced fluxes of electrons over a wide energy range ∼100 to ∼500 keV. It is evident that the two features identified occur under very similar PPO modulation conditions on successive cycles, that is, with a temporal displacement close to one planetary (PPO) rotation period ∼10.7 h. Specifically, comparing with the previous PPO cycle during which no comparable event was observed, the dipolarizations occurred when r B was rising from minimum toward maximum values in the cycle, while B  was falling from maximum toward minimum values.
Although their overall discussions are somewhat inconclusive, Yao et al. (2018) have proposed (e.g., their Section 2) that the recurrence of such events could be due to the presence of a persistent structure which near-corotates around the planet, with the absence of observed events having a third successive signature at the same PPO phase likely being due to the motion of the spacecraft out the finite spatial region occupied by the rotating structure. They also discuss the possibility (e.g., their Section 3.2) that the events could be directly associated with the PPOs through the triggering of reconnection in the equatorial current sheet, but argue against this possibility on the grounds that the events occur at PPO phases that are not conducive to reconnection and plasma mass loss down the tail, specifically when the field lines are displaced inward and the current sheet is thick.
Here, we consider Yao et al.'s (2018) discussions, focusing on two principal topics. In Section 2, we consider their proposal that the recurrent events correspond to long-lived magnetic field structures with associated magnetosphere-ionosphere currents that rotate fully around the planet at least once at close to the PPO period. Following examination of previous observations of plasma flows in Saturn's middle and outer magnetosphere, however, we argue that this proposition is highly implausible. In Section 3, we then investigate the possibility that event recurrence is instead associated with PPO-related periodic modulations of the plasma/ current sheet, as expected on the basis of the results of Jackman et al. (2016) and Bradley et al. (2018) discussed above. We show that Yao et al.'s (2018) rationale for discounting this possibility is based on an erroneous discussion of the prevailing PPO phases, and that their nightside events (but not the dayside events) do indeed occur at phases found previously to be conducive to the occurrence of reconnection, thus plausibly leading to the recurrent signatures observed.

Plasma Rotation Periods in Saturn's Magnetosphere
In this section, we thus consider Yao et al.'s (2018) proposition that recurrent dipolarization events such as that shown in Figure 1 could correspond to persisting magnetic field structures, confined in LT extent, that rotate fully around the planet potentially multiple times at close to the planetary (PPO) rotation period. This picture then requires either that the plasma population within the event rotates around the planet at close to the PPO period, or that the field structure itself propagates with this period through the otherwise rotating plasma. Here, we begin by examining previous studies of plasma flows within Saturn's magnetosphere, focusing particularly on the middle and outer magnetosphere where the recurrent events were reported.

Mean Plasma Rotation Periods in Saturn's Magnetosphere
Plasma flows within Saturn's magnetosphere have been determined using four distinct methodologies. Two involve direct in situ measurement of ion anisotropies, either of the bulk thermal population typically ∼100 eV-10 keV (Thomsen et al., 2010;Wilson et al., 2017), or of the higher-energy population typically ∼10-100 keV (Kane et al., 2020). Such data have provided information on flows throughout the dayside magnetosphere to typical subsolar magnetopause distances of ∼25 R S , and to distances of a few tens of R S downtail. Indirect determinations involve analysis of the energy dispersion signatures of energetic ions COWLEY AND PROVAN 10.1029/2021JA029444 4 of 27 and electrons injected into the inner magnetosphere at radial distances ∼5-10 R S as mentioned in Section 1 (Müller et al., 2010), and the azimuthal motions of hot ion clouds injected from the nightside observed over the radial range ∼5-20 R S in remotely sensed energetic neutral atom (ENA) emissions (e.g., Carbary & Mitchell, 2014;Palmaerts et al., 2020). The results of these studies all agree that the flow is principally azimuthal in the sense of planetary rotation within the region explored by Cassini, but with angular velocities that consistently and increasingly lag that of the planet with increasing radial distance.
Of the three data intervals discussed by Yao et al. (2018), one was observed in the dayside magnetosphere at ∼10 h LT at a radial range of ∼20 R S (their Event 2 discussed here in Section 3.4), while the other two (Events 1 and 3 discussed here in Sections 3.2 and 3.3, respectively) were observed post-dusk at ∼20 h LT at a radial distance of ∼30 R S (Event 1 is shown in Figure 1). Here we therefore first consider direct measurements of ion azimuthal velocities as mentioned above that span the radial distances of these events, and in Figure 2a provide an overview over the radial range to 35 R S . Specifically, we plot simple estimates of the plasma rotation period versus perpendicular radial distance from the planet's spin axis, simply assuming plasma rotation at a fixed perpendicular radius  at a fixed speed V  (period . We note, however, that from consideration of the overall flow pattern observed, Kane et al. (2020) suggest that streamlines on the nightside are unlikely to close around the dayside of the planet at distances much beyond ∼25 R S typical of the subsolar magnetopause (see their Figure 18). If correct, this would, of course, directly exclude the occurrence of rotationally recurrent events at larger nightside distances, such as nightside Events 1 and 3 discussed by Yao et al. (2018). For purposes of comparison, the blue horizontal bar between 10.6 and 10.8 h in Figure 2a shows the seasonal range of PPO rotation periods, as discussed in Section 1.
The periods shown by red symbols in Figure 2a were obtained from fits to thermal ion data (protons and oxygen ∼1-50 keV) within 10° of the planetary equator by Wilson et al. (2017), using carefully selected data to ensure adequate instrument field of view. These show median values in 2 R S radial bins together with upper and lower quartiles. Plasma rotation periods are already clearly subcorotational in the inner part of the system, with  ∼ 15 h at ∼7 R S (corresponding to a flow of ∼75% of rigid corotation), increasing to ∼22 h at ∼20 R S (∼50% of rigid corotation).
Here for definiteness we have taken "rigid corotation" to correspond to a rotation period of 10.7 h in the center of the PPO band. The periods shown by green symbols were obtained from fits to energetic oxygen flux data (68-231 keV) within 20° of the equator by Kane et al. (2020), again showing median values in 2 R S radial bins together with upper and lower quartiles. These two data sets generally agree well within their region of overlap, the rotation period increasing to ∼35 h at ∼30 R S (∼30% of rigid corotation). Figure 2a demonstrates the physically important point that the PPO modulations, driven from the two polar neutral atmospheres, propagate around the planet in the sense of planetary rotation through the subcorotating plasma throughout the middle and outer magnetosphere, increasingly so at increasing radial distances.
The results in Figure 2a show that at the ∼20-30 R S radial distances of Yao et al.'s (2018) recurrent dipolarization events, the plasma typically exhibits azimuthal flows of around half of rigid corotation or less, with consequent rotation periods (assuming that complete rotations are possible) of ∼20-30 h. Any structure rotating at such speeds would thus recurrently return to the same LT meridian at a modulo 360° PPO phase that is generally far removed from that of its previous pass. To quantify this point, in Figure 2b   . The red data were derived from velocities determined by Wilson et al. (2017) from thermal ion (∼1-50 keV) measurements, while the green data were derived from velocities determined by Kane et al. (2020) from energetic O + ion (68-231 keV) data (confined to fits for which the average deviation per pixel is less than 0.6). Median and quartile values are shown for both data sets. (b) PPO phase difference  experienced by a given element of the plasma relative to a corotating PPO modulation after one complete turn about the planet at the rotation periods shown in panel (a), given by Equation 1, with the PPO rotation period taken for definiteness to be 10.7 h.  Kane et al. (2020) plot of the change in PPO phase relative to a corotating PPO modulation experienced by a given volume of plasma after one complete turn about the planet at the median and quartile plasma periods  shown in 1 , where PPO  is the PPO rotation period taken to be 10.7 h. A volume element rotating with the same period as the PPO period yields 0   , meaning that the element arrives back at the initial LT meridian with the same modulo 360° PPO phase in the following PPO cycle, while, for example, 360    means that the element arrives back with the same modulo 360° PPO phase after skipping a cycle. It can be seen that even in the inner region covered by the data, where the plasma rotates at ∼75% of the PPO propagation speed, the phase difference is ∼130°, that is, a feature rotating with the plasma would recur later between quadrature and antiphase relative to the PPO modulations on successive rotations. The PPO phase difference per turn increases to antiphase at equatorial distances of ∼10 R S , corresponding to the inner edge of the hot plasma region at Saturn mapping to the equatorward edge of the auroral region in the ionosphere, and then increases beyond a full turn (360°) at equatorial distances beyond ∼15-20 R S . In contrast, as illustrated in Figure 1, the successive dipolarization events discussed by Yao et al. (2018) occur at PPO phases that clearly differ by only a small fraction of a PPO period, as these authors themselves demonstrate (their Figure 2).

Electron Differential Velocities
In their discussion of plasma particle motions, Yao et al. (2018) (their section 3.1) also mention possible differences between the rotation speeds of ions and electrons, with the electrons "most likely frozen onto magnetic fields." However, the local relative velocity between ions and electrons can be simply estimated from the electric current density flowing in the plasma (the sum of effects due to relative drift plus magnetization), determined from magnetic field data. Using the tail field model of Jackman and Arridge (2011), combined with the current sheet number density model of Arridge et al. (2011) and a typical sheet half-thickness of ∼2 R S as determined in the latter study, yields current densities at relevant radial distances ∼20-30 R S of ∼30-40 pA m −2 , particle number densities ∼0.02-0.04 cm −3 , and hence relative drifts of ∼5-10 km s −1 . Such relative velocities are thus at least an order of magnitude smaller than the ion bulk speeds ∼100 km s −1 at these distances determined in the studies leading to the rotation periods in Figure 2a, and are only a few percent of the azimuthal flows required for rigid rotation. In addition, of course, the electrons drift westward relative to the ions, resulting in (marginally) smaller overall azimuthal velocities with (marginally) longer rotation periods. Such considerations do not, therefore, contribute significantly to discussion of the rotation of plasma particles and field structures near to the planetary/PPO rotation period.

Rotation Periods of Injected Hot Plasma Clouds
While rotation with the overall azimuthal speeds indicated in Figure 2 clearly provides no explanation of these recurrent events, it remains possible that localized regions associated with dipolarization events might rotate with significantly faster speeds and hence with shorter periods, though the specific relevance of the planetary/PPO period to such a scenario does not seem obvious. Yao et al. (2018) (their section 3.1) suggest a connection with the particle events mentioned in Section 1, likely reconnection related, in which hot plasma is injected into the outer magnetosphere typically in the post-midnight sector which then rotates around the planet via dawn.
The most detailed examination of the azimuthal propagation of such hot ion injections has been provided by Carbary and Mitchell (2014), through keogram analysis at specific equatorial radial distances of several hundred individual rotating features observed in ENA images. Results derived for equatorial distances of 5, 10, 15, and 20 R S yield mean rotation periods of ∼12.2, 14.0, 15.3, and 15.9 h, again significantly longer than the planetary/PPO periods, with corresponding PPO phase differences per turn  of ∼50°, 110°, 155°, and 175°. These mean values are on the smaller side of those derived directly from in situ ion measurements shown in Figure Carbary and Mitchell (2014), they nevertheless go on to "speculate that the ENA emission enhancements associated with dipolarization process would have high rotating velocity and may even rigidly corotate with the planet." However, although the rotation rates derived by Carbary and Mitchell (2014) at a given radius do have a significantly broad distribution of values, at the larger radii comparable with the Yao et al. (2018) events the vast majority of their azimuthal speed determinations are distinctly smaller than for rigid corotation (see their Figure 5 particularly for 20 R S radial distance), with very few values comparable with or larger than rigid corotation.

Distribution of Ion Azimuthal Velocities at ∼30 R S
To take this point a little further we have examined the Kane et al. (2020) energetic ion velocity data obtained at ∼30 R S radial distances, near those of Yao et al.'s (2018) nightside events (e.g., Figure 1). In Figure 3, we show a histogram of 884 individual azimuthal velocity determinations within the 5 R S perpendicular radius range between 27.5 and 32.5 R S , each value being normalized to the local rigid corotation velocity for a fixed period of 10.7 h (given by   S 9.83 R V    km s −1 yielding values between ∼270 and ∼320 km s −1 over this radial range). Each value corresponds typically to a ∼30 min instrument integration over a full spacecraft spin. The median normalized value corresponds to ∼30% of rigid corotation, within an interquartile range between ∼18% and ∼39%, as shown by the arrows at the top of the plot, in line with the rotation periods indicated in Figure 2a. The additional point we stress here, however, is that out of 884 determinations this data set contains no values at all greater than ∼85% of rigid corotation (implying 65   ), this fractional value corresponding to ∼250 km s −1 at ∼30 R S . Indeed, there are very few determinations with values greater than ∼55% of rigid corotation (implying  super-corotational flow have all been found to result from poor fits to the data with large uncertainties, this including the apparent super-corotation flow interval reported by Masters et al. (2011) and cited by Yao et al. (2018) (see Wilson et al. (2017) Supporting Information Section 4.2). Overall, therefore, neither the direct determinations of ion velocities discussed here, nor the indirect determinations from ENA imaging discussed above, support the occurrence of significant intervals of near-rigid corotation flow in these regions of Saturn's magnetosphere. Yao et al.'s (2018) speculation noted in Section 2.3 above is not supported by these results.

Implications of Dipolarization Structure Propagation Through the Plasma
The results outlined above establish with some certainty that the recurrent dipolarization events discussed by Yao et al. (2018) are not due to long-lived field/current system structures that rotate around the planet to a first approximation "frozen in" to the plasma. This is the case whether we consider the overall plasma azimuthal flows observed in the relevant equatorial ∼20-30 R S region of Saturn's magnetosphere (Sections 2.1 and 2.4), or some significant differentially rotating particle component of the plasma (Section 2.2), or the intermittently injected hot plasma structures likely associated with tail reconnection bursts and dipolarization/plasmoid production that are commonly observed to rotate in the outer magnetosphere (Section 2.3). All these situations are found to be associated with persistently and significantly subcorotational plasma flow that would give rise to easily observable PPO phase shifts after one turn around the planet, at odds with the closely similar PPO phases that are observed for the recurrent dipolarization events seen, for example, in Figure 1.
To maintain the physical picture suggested by Yao et al. (2018) of a near-rigidly rotating field/current structure, therefore, we must consider instead that the dipolarized region propagates as a coherent structure eastward through the plasma around the planet, such that the relative propagation speed and the plasma speed combine to yield a total speed near to that for rigid corotation with the planet/PPO modulations. Noting the results on the plasma speed in Figures 2 and 3, the eastward propagation speed of the structure through the plasma must then be some significant fraction of the planetary/PPO corotation velocity, typically greater than half, corresponding to relative propagation velocities of ∼100-200 km s −1 at relevant radial distances. In fact, of course, the structures must propagate through the subcorotating plasma with nearly the same relative speed as do the PPO perturbations themselves, as mentioned in Section 2.1. However, while overall rotation near the planetary rotation period is clearly relevant for the PPO perturbations driven from the planetary polar upper atmospheres, as will be briefly discussed in Section 3.1 below (e.g., Hunt et al., 2014;, its relevance remains less than obvious for the rotation of a dipolarized region propagating through the subcorotational plasma. Considering in further detail the implications of the latter scenario, we then require to picture the eastward "leading" edge of the dipolarized region as forming an eastward-propagating dipolarization "front", across which tail-like field lines collapse toward the planet, compressing and heating the plasma as they do so. While this picture may not seem physically unreasonable, in order to retain a coherent propagating structure localized in azimuth as required, we must also envisage an opposite process occurring on the trailing edge of the dipolarized region, where the field and plasma return to near its previous tail-like state. That is, as this westward boundary propagates eastward across the dipolarized field lines subcorotating within the event, they must rapidly extend back into the tail, expanding and cooling the plasma as they do so. However, we know of no physical process that would explain such behavior, which we regard as highly unlikely. Taking these discussions together with those in previous Sections 2.1-2.4 above, it is thus our view that Yao et al.'s (2018) proposed recurrent dipolarization picture in which a coherent long-lived dipolarized region rotates around the planet through the subcorotating plasma at close to the planetary rotation period seems highly implausible.

PPO Modulation of Reconnection in Saturn's Equatorial Current Sheet
Given the conclusions of Section 2, we now consider the possibility that recurrent dipolarization events are instead generated through periodic PPO modulations of Saturn's plasma/current sheet. That is to say, following the prior results of Jackman et al. (2016)  recurrent reconnection bursts are excited at particular favorable PPO phases on successive PPO cycles, giving rise to recurrent dipolarization events (as well as recurrent plasmoids). Following each event, hot plasma is injected into the outer magnetosphere in the nightside sector as indicated in Sections 1 and 2, and subsequently sub-corotates around the planet in the outer magnetosphere at the measured velocities (Carbary & Mitchell, 2014), decaying in intensity due to charge-exchange and precipitation losses. As indicated by the discussion in Section 2 (e.g., Figure 2b), the PPO-induced hot plasma injection associated with any subsequent reconnection event occurring at a similar modulo 360° PPO phase would generally occur significantly prior to the completion of one full turn around the planet by the prior injection. Although investigation has shown that reconnection-related events can occur in Saturn's nightside current sheet at any PPO phase, this scenario nevertheless seems plausible given the significant modulation of event occurrence by PPO phase mentioned in Section 1, combined with an overall reconnection-related episode frequency (generally consisting of several individual dipolarizations/plasmoids over a few-hour interval) approaching one episode per ∼10.7 h PPO cycle Jackman et al., 2016). Yao et al. (2018) discount this possibility on the basis that the PPO phases during all three events they discuss were associated with field lines displaced radially in toward the planet and a thickened plasma sheet, quoting (without attribution) northern phases of ∼90° and southern phases of ∼300°, both effects being likely to suppress the occurrence of reconnection events. However, examination of Figure 1e for Event 1 shows that these phase values correspond to the global PPO phases , N S  that describe the orientation of the PPO systems relative to the Sun (see definitions below), rather than the local phases , N S   that describe the position of the observer (spacecraft) relative to the two PPO systems, which are the phase values that determine the locally modulated physical conditions. Furthermore, for the two (of three) Yao et al. (2018) intervals located in the nightside LT sector, including Event 1 in Figure 1, the global and local phases are approximately in antiphase (see discussion of Equation 3 below) as can be seen in Figure Figure 1e. In this case the local physical conditions in the current sheet are thus expected to be the opposite of those indicated by Yao et al. (2018), that is, field lines displaced radially outward and a thinned plasma sheet, both effects thus conducive to the modulated occurrence of reconnection. This is the case for the two nightside events discussed by Yao et al. (2018) (their Events 1 and 3), but not for dayside Event 2, for which the global and local phases are similar to a first approximation, such that the local current sheet conditions are indeed expected to be those indicated by Yao et al. (2018). In this section, we thus reexamine the magnetic field data for the three Yao et al. (2018) event intervals (Sections 3.2-3.4) to establish the extent to which the expected PPO modulation conditions are realized. However, we begin in Section 3.1 by outlining the theoretical background concerning the definitions of the PPO phases and the related modulations of the current sheet which underpin these discussions.

PPO Phases and Current Sheet Modulations
Appropriate background from previous studies is summarized in Figure 4. Figures 4a and 4b, taken from Figures 1a and 1b of Bradley et al. (2020), summarize the currents (green), perturbation magnetic fields (blue), and plasma flows (red) in views of the northern and southern polar ionospheres, respectively, looking down from the north ("through" the planet for the southern hemisphere). The sense of the perturbation fields within the magnetosphere can be obtained by mapping the perturbation fields to larger distance along the planetary field lines. Around the perimeter of the diagrams we show the local phases , N S  which give the azimuthal position with respect to these systems, defined such that the phases increase with time at a fixed position as each system rotates in the sense of planetary rotation (anticlockwise) at their corresponding PPO periods. The prime meridians of these phase systems,   , respectively, giving rise to a quasi-uniform near-equatorial perturbation field, while the colatitudinal perturbation fields vary as cos N    for the northern system and cos S    for the southern system, such that the perturbation field lines of the northern and southern systems close over the northern and southern poles, respectively. However, observations show that beyond the "core" region of the magnetosphere extending to radial distances ∼12 R S , within which the magnetic field is dominated by the planetary dipole, radial phase propagation away from the planet must be taken into account, at a rate of ∼3° per R S Provan et al., 2012). Beyond a radial distance of 12 R S we thus employ the retarded local PPO phases where radial phase gradient , and 12 r  is the radial distance in R S . These are the retarded local phases shown in Figure 1d, which are employed throughout these studies since equatorial reconnection-related events are confined to distances well beyond the core field region (e.g., Smith et al., 2016).
We also emphasize that when the amplitudes of the two PPO systems are comparable (as is the case during the intervals examined here), the modulations of the plasma/current sheet will be strongly dependent on the relative phase between the two PPO systems. For example, following the above discussion, when the two systems are in phase the field perturbations associated with the radial and azimuthal components combine constructively, while those associated with the colatitudinal component combine destructively. However, when the two systems are in antiphase the field perturbations associated with the radial and azimuthal components combine destructively, while those associated with the colatitudinal component combine constructively. The relative phase between the two systems, the "beat phase" , is simply given by which evidently is a global quantity that does not depend on the observer position. For Event 1, the beat phase is shown as a function of time by the purple dashed line in Figure 1d, indicating that the two systems were close to antiphase at that time.  . Diagrams summarizing the physical structure of the two planetary period oscillation (PPO) systems and the current sheet perturbations to which they give rise. (a) Currents and fields of the northern PPO system looking down onto the northern polar ionosphere. Electric currents are shown by the green symbols, with ionospheric currents being shown by green arrows, and field-aligned currents by circled dots and crosses showing currents directed out of and into the diagram respectively. Blue arrowed lines show corresponding magnetic field perturbations, while red arrowed lines show the ionospheric flow pattern. Around the perimeter of the diagram we show the northern local phase N  corresponding to these currents and field perturbations. (b) Currents and fields of the southern PPO system showing the southern polar ionosphere in a view looking "through" the planet from the north. Currents, fields, and flows are shown using the same format as panel (a). Around the perimeter of the diagram we show the southern local phase S  corresponding to these currents and field perturbations. (c and d) summarize the north-south oscillatory and thickening-thinning effects on the current sheet due to the northern and southern PPO systems, respectively, where in each case the effects in the  3 and related text) is plotted between −180° and +180° on the vertical axis together with related northern system effects, while the southern retarded local phase * S  is plotted between 0° and 360° on the horizontal axis together with related southern system effects. Dual phases where both systems act in concert to produce a given current sheet effect are indicated in circles on the phase grid, specifically displacements to the north or south, thickening or thinning, and inward or outward radial displacements. Colored circles and squares show the directional mean phases at which nightside dipolarization events preferentially occur as determined by Bradley et al. (2018) using the event catalog of Smith et al. (2016). Circles correspond to the set of isolated events (separated from others by more than 3 h) plus the initial events of clusters (separated from others by 3 h or less). Squares correspond to subsequent events within clusters. S    , opposite to the planetary field at the equator, the equatorial field is weakened and the plasma sheet thinned. Third, in addition to these effects, the PPO systems are also associated with radial displacements of the current sheet field lines and plasma. Considering the rotating flow pattern imposed on the magnetospheric plasma indicated in Figures 4a and 4b by the red streamlines (e.g., Hunt et al., 2014;, we see that the field lines move radially inward (equatorward in the ionosphere) for cos 0   is plotted between 0° and +360° on the horizontal axis. The effects due to each system are indicated along the vertical and horizontal axes. However, as indicated above, the overall effect on the equatorial plasma/current sheet clearly depends on the superposed action of the two systems, a particularly important consideration for the near-equinoctial intervals discussed by Yao et al. (2018) when the amplitude of the two systems was near-equal . The circled effects within the grid in Figure 4e show the combinations of northern and southern phases where the effects of the two systems act in concert to produce the effects indicated. When the two systems are close to antiphase along the central diagonal in the diagram (bottom left to top right where beat phase 180    modulo 360°), the north-south oscillations of the plasma/current sheet are suppressed for near-equal amplitudes, while the thickening-thinning and radial displacement effects are enhanced. Oppositely, when the two systems are close to in phase under these conditions (beat phase 0 / 360     modulo 360°), the thickening-thinning and radial displacement effects are suppressed for near-equal amplitudes, while the north-south oscillations are enhanced.
The colored symbols in Figure 4e then give the directional means of the northern and southern retarded local phases at which dipolarization events in the Smith et al. (2016) catalog preferentially occur . Circles correspond to both isolated events (separated from others by more than 3 h) and to the initial (primary) events of a cluster (separated from each other by less than 3 h). Squares correspond to the subsequent (secondary) events in a cluster. Black symbols correspond to the data set as a whole, while the colored symbols represent various data subsets divided by Cassini orbit interval (see figure caption). It can be seen that isolated and primary dipolarization events occur preferentially under near antiphase conditions when N   lies between 270° and 0°/360° while S   lies between 90° and 180°. In each case these are the phases at which the plasma is moving inward from its maximum outward radial displacement toward its mean and then minimum radial distance, while at the same time the current sheet is thinning between its mean configuration and conditions of minimum thickness. The secondary events then peak at slightly later phases as may be expected, near maximally thinned conditions. Both outward displacement and thinned conditions (minimum colatitudinal field threading across the current sheet) are likely to be conducive to reconnection and mass loss via Vasyliunas cycle reconnection, as noted in Section 1. Although Figure 4e shows results specifically for dipolarization events as discussed by Yao et al. (2018), we note that related results derived from more numerously observed plasmoid events in the Smith et al. (2016) catalog are essentially similar .

Simple Current Sheet Modulation Model
To gain further insight into the field modulations observed during these events (e.g., Figure 1), below we also show outputs from the simple mathematical current sheet modulation model introduced by , developed and applied to Cassini nightside magnetic data by  and Agiwal et al. (2020). The current sheet radial field is modeled by the sum of two hyperbolic tangent functions COWLEY AND PROVAN 10.1029/2021JA029444 12 of 27   , such that the normalized field approaches   , / 1 r ro B z t B   as z  . Field ro B is a normalization constant, effectively the field strength in the tail lobe at large distance from the current sheet center. The main current sheet is given by the first term (for a b  ), while the second, with 1 c  , provides a more gradual approach of the normalized field toward 1  at larger distances from the center. It was found by  that inclusion of the second term, associated with a broader weaker current layer surrounding a narrower more intense central current layer, improves the empirical fit between the model and Cassini tail field data. Both terms have a common center at where the undisturbed width N S d d d   , so that   D t does not become unphysically negative during the PPO cycle. We further assume for simplicity that the modulation effect of the two systems is in simple proportion to the relative north/south field amplitudes k of the two systems determined from the combined field oscillations observed near the equator within the core region. That is, we take As mentioned above, the results of Andrews et al. (2012) show that the two systems were of near-equal amplitude during the near-equinoctial interval examined here, such that we take 1 k  throughout.
We also use the following simple normalized form for the colatitudinal field 1 1 cos cos , where the first term represents the positive (southward) planetary colatitudinal field near the equator on which the PPO perturbations are superposed. We also arbitrarily fix 1 / 3 a   , such that normalized B  remains positive (for 1) k  throughout the PPO cycle, and varies in amplitude only via the relative phasing of the two systems. We emphasize that this expression is employed principally to examine the relative phasing of the expected modulations in the colatitudinal  and radial r field components. Here we do not consider the azimuthal field component, which in general is a complicated sum of effects due to the PPO systems, the sweepback associated with plasma subcorotation, and the magnetotail field.

Nightside Event 1
With this background we can examine the PPO phases for Event 1 in Figures 1d and 1e, and note again from Section 3.1.1 that the two PPO systems were near to antiphase during the interval, with a slowly increasing beat phase (for northern period ∼10.64 h shorter than southern period ∼10.76 h) which reached ∼150° at the time of the first dipolarization event (vertical arrow). The interval is thus one in which the thickening and thinning of the plasma/current sheet together with radial displacements of the plasma are expected to combine near-constructively for the two systems, both effects potentially significantly modulating reconnection in the current sheet. However, north-south oscillations of the current sheet due to the two systems are expected to combine near-destructively. Figure 4e shows that, as might be expected, statistically the most likely PPO phase conditions for observing reconnection signatures are those where the plasma is displaced radially outward and the plasma sheet is thinning with a weakening colatitudinal field threading through it, that is, with N   between 270° (radially out) and 0°/360° (thin), and S   between 90° (radially COWLEY AND PROVAN 10.1029/2021JA029444 13 of 27 out) and 180° (thin). In Figure 1, these intervals are marked by the vertical lines, where the dotted lines show the times of expected maximum outward radial displacement for the northern (blue) and southern (red) PPO systems, while the following dashed lines similarly show times of expected maximum thinning for the two systems. We note that each pair of dotted lines and each pair of dashed lines lie relatively close together in time, indicating that the expected effect of the two systems combine near-constructively, as would be exactly the case if the two PPO systems were exactly in antiphase, with the pairs of dotted lines and the pairs of dashed lines then being superposed.
Comparing the times of the dipolarization events (vertical arrows) with the vertical lines shows that the events occurred near expected times of maximum outward radial displacement of the field lines, as the plasma sheet was in process of thinning from maximum to minimum thickness. In terms of the observed field variations, in particular comparing with the field variations during the first PPO oscillation shown in Figure 1 when no event was evident, the dipolarizations occurred as r B increased from minimum toward maximum values, while B  began to decrease from maximum toward minimum values (or approximately plateaued in the case of the first dipolarization event). To gain insight into these field variations, in Figure 5    for the modulated north-south position of the current sheet center. While these model values, similar to those employed previously by , are considered to be indicative, we do not place stress on their detailed values. The two parameters that are specific to Event 1 are the spacecraft position S 6 R z  northward of the center of the undisturbed current sheet (see position coordinates in Figure 1 during this near-equinoctial interval), and the beat phase given by Equation 4 of 150 ,    such that as indicated above (Figure 1d) the two PPO systems lie within 30° of antiphase. Figures 5a and 5b show the variations of the current sheet thickness D and the current sheet center Z plotted over two and a half cycles of the northern PPO system phase N   . The value of the southern phase is taken to sufficient approximation to be simply given from Equation 4 by S N       , with  held constant at the above value of 150° (thus effectively assuming equal PPO system periods for this short interval). The blue and red dashed curves in Figure 5a show the effects on the current sheet thickness of the northern and southern systems acting alone, with the black curve being their sum (Equation 7), varying about the undisturbed value d of 2.5 R S shown by the horizontal dotted line. As in Figure 1, the vertical blue and red dashed lines show the phases 0 / 360 N      (modulo 360°) and 180 S     (modulo 360°), respectively, for which the separate effects of the two systems produce maximum current sheet thinning, with the minimum combined thickness occurring centrally between these two phase conditions. Overall, the model suggests that large variations in the current sheet thickness D take place during each PPO cycle. Also as in Figure 1, the vertical blue and red dotted lines show the phases 270 N     (modulo 360°) and 90 S     (modulo 360°), respectively, for which the separate effects of the two systems produce maximum outward radial displacement of the plasma and field lines. As for the current sheet thickness, the two systems are expected to act in approximate concert to produce larger radial motions under these near-antiphase conditions. By contrast, the effect of the two systems on the north-south position of the current sheet approximately cancel under these conditions to leave only weak oscillations in the position of the sheet center Z, as shown by the black curve in Figure 5b. It may be noted that the remaining oscillations are in approximate quadrature with the thickness variations, such that the current sheet is deflected to the south when the current sheet is thickening, while being deflected to the north when it is thinning. The purple dashed lines in Figure 5b on either side of Z indicate the position of the upper and lower boundaries of the main current sheet located at

The black lines in
where the normalized radial field has the value ∼±0.73 (for the above values of a, b, and c in Equation 5). The model position of the spacecraft at S 6 R z  is shown by the horizontal black dashed line. It can be seen that at this position, well northward of the current sheet center, the spacecraft is expected to approach the northern boundary of the current sheet b Z  once per PPO cycle, close to the time of maximum current sheet thickness, but also when the current sheet is moving slowly northward. Directly after this time the current sheet recedes from the spacecraft due to the thinning of the layer, while the current sheet center continues for an interval to move northward toward the spacecraft.
The normalized radial field component in Figure 5c correspondingly displays a single minimum in value every PPO cycle near to the time of its close encounter with the northern current sheet boundary b Z  , after which the value starts to rise again due to the thinning of the current sheet, despite the continued northward motion of the current sheet center toward the spacecraft. The maximum northward displacement of the current sheet center occurs near the time of maximum outward radial displacement of the field lines marked by the pairs of red and blue dotted lines, which corresponds to the times at which the two dipolarization events occur as seen in Figure 1. These times are also indicated by arrows in the panels of Figure 5. Figure 1a shows that the observed radial field indeed starts to rise from minimum values prior to these events, which according to the model is a direct signature of current sheet thinning while the sheet center continues to move slowly northward toward the spacecraft. Thus while the outward radial displacement of the plasma may be the principal physical factor associated with the occurrence of these events, the data also provide evidence for on-going thinning of the current sheet at these times. The events correspondingly relate to phases for which the colatitudinal field threading the current sheet is beginning to decline from maximum toward minimum values, or has plateaued in the case of the first dipolarization event, as seen COWLEY AND PROVAN 10.1029/2021JA029444 15 of 27 in Figures 1b and 5d. Given that these events thus occurred under conditions expected to be favorable for Vasyliunas cycle reconnection and downtail mass loss, near to the PPO phase conditions for peak event probability (Figure 4e), it seems perhaps unremarkable that two such events might on occasion be excited at similar PPO phases on successive PPO cycles separated by ∼10.7 h.

Nightside Event 3
We now turn to the second nightside interval discussed by Yao et al. (2018), their Event 3, observed at similar ∼30 R S radial distances in the dusk sector (∼19 h LT) on Rev 138 on 19 September (DoY 262) 2010. Magnetic field and PPO phase data for this interval are shown in Figure 6 in the same format as Figure 1. The main positional difference to Event 1, however, concerns the spacecraft latitude, in this case just south of the planetary equator rather than well to the north as for Event 1. Consequently, the PPO modulations of the field cause the current sheet to oscillate fully across the spacecraft between the northern and southern tail lobes, as can be seen in the radial field in Figure 6a, rather than simply dipping into the outer northern current sheet once per cycle as in Event 1 in Figure 1a. The two dipolarization events identified by Yao et al. (2018), associated with sudden increases in B  , the onsets of which are again marked by arrows at the top of the figure, are seen to occur at similar oscillation phases on successive PPO modulation cycles as the current sheet moved northward across the spacecraft, such that the dominant sign of the radial field reversed from positive to negative.
The other apparent major difference between the two nightside events, however, is that the Andrews et al. (2012) phases of the two PPO systems are close to in phase, with a beat phase 340   , rather than being close to antiphase as for Event 1. As discussed in Section 3.1 in relation to Figure (Figures 7a and 7d). Figures 7c and 7c with the observed fields in Figures 6a  and 6b, however, clearly reveals two areas of discrepancy. The first is that the PPO modulations of the colatitudinal field are expected to be much smaller than for Event 1 in Figure 1b, whereas they are observed to be of comparable magnitude (the variation of the near-normal field with colatitude is not expected to be large within the near-equatorial regimes observed). The second is that the oscillations in the model radial field in Figure 7c are closely symmetrical in the positive-to-negative and negative-to-positive transitions, whereas the observed oscillations exhibit a pronounced asymmetry, as noted previously by Thomsen et al. (2017) in their overall study of 2010 Cassini tail data. Specifically, it is clear that the negative-to-positive transitions occur much more slowly in time than do the positive-to-negative transitions, consistent with the current sheet being much thicker when moving southward than when moving northward. The occurrence of both significant thickness and related colatitudinal field modulations is not consistent with the near in phase conditions indicated by the Andrews et al. (2012) PPO phase model, but is instead characteristic of approximate quadrature conditions, specifically for beat phases in the vicinity of 270   , as demonstrated in previous related studies Thomsen et al., 2017). For 90    the sense of the radial field asymmetry is reversed compared with that observed in Figure 6, with positive-to-negative transitions occurring much more slowly in time than negative-to-positive transitions. We demonstrate this in the model output in Figure 8  Output of the simple theoretical model of current sheet planetary period oscillation (PPO) modulations described by Equations 5-9 applied to the data in Event 3, in the same format as Figure 5 for Event 1. The current sheet parameters are the same as for Event 1, except for a beat phase of 340    as indicated in Figures 6d and 6a spacecraft location S 1R z   just southward of the center of the undisturbed current sheet (data at the foot of Figure 6). S     modulo 360° (southern system maximum radial outward displacement), which coincide for this value of . The observed sense of the asymmetry in the radial field oscillations is clearly evident, as well as a much more significant modulation in the colatitudinal field in Figure 8d than in Figure 7d, peaking near to the times when the sense of the radial field switches from negative to positive, as observed. Relative to these model results, the dipolarization event onsets occur shortly after the times indicated by the purple vertical dashed lines, again marked by the arrows in the panels of Figure 8, associated with a near-maximally thinned plasma/current sheet threaded by a near minimum colatitudinal field, but still where the current sheet is moving significantly from south to north across the spacecraft, as observed. As indicated above, the corresponding event onset phases are 0 / 360 N      modulo 360°, ∼25° less than indicated in Figure 6d, and 90 S     modulo 360°, ∼45° more than indicated in Figure 6d.

Comparison of the model normalized fields in
Previous studies have shown that the PPO phase models derived from magnetometer data are generally accurate to within ∼10°-20° (e.g., Provan et al., 2011), such that comparisons of model profiles with nightside magnetic field data have not previously revealed significant beat phase mismatches such as that identified here (e.g., Agiwal et al., 2020;Thomsen et al., 2017). This issue is discussed further in Appendix A where we show that the interval during Event 3 was one of particular difficulty for PPO phase determination, being determined from near-equatorial combined northern and southern oscillations of similar amplitude during an interval with very closely spaced PPO periods, and hence a lengthy beat period, compounded by a one-Rev data gap. A model beat phase discrepancy of the magnitude indicated is thus plausible for this specific interval, though not in general. Irrespective of these detailed considerations, however, the main point we wish to stress is that the data itself in Figure 6a clearly and directly demonstrate that the thickness of the current sheet was strongly modulated by the PPO systems during Event 3, giving rise to the "sawtooth" variation in the main radial field component, and that the recurrent dipolarizations occur specifically at the points in the cycle when the current sheet was thin, as well as being radially extended away from the planet.  Figures 5 and 7) and 90 S     modulo 360° (red dotted lines in Figures 5 and 7), which coincide for this value of . The arrows in each panel indicate the corresponding approximate timing of the dipolarization event onsets in Figure 6.

Dayside Event 2
The third interval we discuss concerns Event 2 of Yao et al. (2018), which occurred pre-equinox on Rev 102 on 6 February (DoY 37) of 2009, and differs from Events 1 and 3 in a number of ways. The first is that the spacecraft orbit plane was highly inclined (by ∼70°) to the planetary equator rather than being approximately equatorial, with apoapsis lying close to the equator at ∼20 R S (near Titan's orbit). To a first approximation the spacecraft motion near apoapsis where the events were observed was thus from south to north through the equatorial region at a relatively fixed LT. The second difference is that, rather than being located in the nightside sector as for Events 1 and 3, apoapsis for Event 2 lay in the pre-noon dayside sector at ∼10 h LT. Data for Event 2 are shown in Figure 9 in a format similar to Figures 1 and 6, though extending over a slightly longer interval on the outbound pass in the southern hemisphere ending just prior to the crossing of the equator (and Titan T-50 encounter at 08:51 UT on DoY 38 of 2009). The interval encompasses ∼5 PPO oscillation cycles compared with ∼4 in Figures 1 and 6 Yao et al. (2018). Specifically in Figure 9d, we show a color-coded spectrogram of thermal electron fluxes obtained by the Electron Spectrometer of the Cassini Plasma Spectrometer instrument (CAPS/ELS), spanning energies 0.6 eV to 26 keV (Young et al., 2004), while Figures 9e and 9f show energetic ion and electron fluxes, respectively, obtained by the Low Energy Magnetospheric Measurement System instrument of the Magnetosphere Imaging Instrument package (MIMI/LEMMS), spanning energies 35-255 keV for ions and 27-300 keV for electrons (Krimigis et al., 2004). See the figure legend and caption for further details. The retarded local PPO phases are shown in Figure 9g, with the vertical dashed lines again indicating the times when the northern (blue) and southern (red) PPO systems are expected to produce a locally thinned current sheet with minimum colatitudinal field threading through it. Figure 9g also shows the PPO beat phase (purple dashed line), which increased from post-antiphase to near quadrature ( 270   ) over the interval. The red and blue pairs of vertical dashed lines are thus relatively closely spaced, indicating that the two systems act in approximate concert during the interval with regard to radial plasma motions and thickening/thinning of the plasma/current sheet, while acting to reduce the amplitude of north-south oscillations.
We note that these phase values are not subject to the same degree of uncertainty as those discussed in Section 3.3 for Event 3, not least because the northern and southern phases in this case were separately determined using high-latitude data from the northern and southern polar regions on these inclined orbits, rather than from the beat-modulated combined oscillations observed on more equatorial orbits within the "core" region . This also means, however, that there is no direct estimate available of the relative amplitude of the two systems as determined from near-equatorial data, but since the north/ south amplitude ratio was found to be 0.9 k  during an immediately prior interval (Revs 56-97 essentially spanning 2008), and to increase only slightly to 1.0 k  during an immediately following interval (Revs 106-146 spanning from vernal equinox in mid-2009 to early 2011), it seems reasonable to suppose that nearequal amplitudes 1 k  apply to this interval as well . The near-equatorial PPO oscillations observed on the pass may thus be taken to be due to northern and southern system contributions of approximately equal amplitude.
Examining the magnetic data in Figure 9 it can be seen that PPO-related modulations are indeed present throughout the interval, observed particularly clearly in Figure 9b in the colatitudinal component expected to be associated with plasma/current sheet thickness modulations, though there is little evidence in the radial component for significant north-south oscillations similar to those observed on the night side. The general pattern of modulations was disrupted in the first part of the interval, however, by a crossing into the magnetosheath between 15:33 and 19:04 UT on DoY 36 (see the catalog of Jackman et al., 2019), indicated by the sharp transitions in each field component toward smaller values, together with the appearance of enhanced fluxes of low-energy electrons in Figure 9d. It is interesting to note that this transition coincided approximately with PPO phases when the magnetospheric field lines are expected to be displaced in toward the planet during the PPO cycle, as previously observed by Clarke, Andrews, Arridge, et al. (2010). These phases ( 90 N     and 270 S    ) are shown in this vicinity (only) by the pair of blue and red dot-dashed lines for the northern and southern systems, respectively. No similar transitions were observed on the other orbits of closely similar geometry (Revs 98-102), such that it appears that Saturn's magnetosphere was unusually compressed by the solar wind during this interval, with the entry into the magnetosheath being modulated by the phases of the PPOs. We note that magnetospheric compressions occurring under PPO phase conditions within ∼±90° of antiphase are often associated with the occurrence of major magnetospheric storms with hot plasma injections from the nightside via dawn, due to enhanced nightside reconnection and open flux closure (Bradley et al., 2020).
The onset times of the sequential events discussed as recurrent dipolarization structures by Yao et al. (2018) are indicated by vertical arrows at the top of Figure 9, identified principally with maxima in the colatitudinal field component and associated entries into the plasma sheet indicated in the radial component. Because these events occurred on the dayside relatively close to noon where the local PPO phases and the global phases discussed by Yao et al. (2018) Figure 4e) that are unconducive to local periodic reconnection, or any reconnection event for that matter. However, as seen in Figure 9b, this also means that the events occurred near the times of expected colatitudinal field maxima in the regular PPO cycle, combined with associated periodic entries into the thickened plasma/current sheet as indicated in Figure 9a by the reductions in magnitude of the radial field component (negative in the southern hemisphere) and the onset of enhanced field fluctuations. It thus seems reasonable to suggest that the features identified as dipolarizations from peaks in the colatitudinal field and entries into the plasma sheet by Yao et al. (2018) may simply be associated with colatitudinal field and sheet thickness modulations due to the regular PPO cycle, combined with subcorotating small-scale structures and field fluctuations that were perhaps enhanced during the interval by the magnetospheric compression and possible ensuing storm interval.
In support of their discussion in terms of local reconnection dynamics, Yao et al. (2018) note the appearance during these events of energetic charged particles, such as the electrons and ions extending to energies well above ∼10 keV in Figures 9d-9f. However, examination of data from other similar Revs indicates that energetic particles are commonly observed within the central plasma sheet in this regime. Figure 10 shows data in the same format as Figure 9 over a corresponding segment of the previous orbit, that is, the outbound pass of Rev 101 also ending near the equator crossing. Similar PPO conditions apply on this Rev as on Rev 102 in Figure 9, except that the beat phase approached near antiphase from near quadrature, with the northern system leading the southern ( 90 )    in this case (Figure 10g). Similar PPO-related modulations are consequently observed in the field data (Figures 10a-10c  field that occur near centrally between the successive closely spaced pairs of red/blue vertical dashed lines as expected, indicative of thickenings of the current sheet. Focusing in particular on the colatitudinal field peak indicated by the arrow at the top of the plot, we note related fluctuating reductions in the radial field magnitude indicative of transient spacecraft entries within the southern border of an expanded plasma/ current sheet, where enhanced energetic ion and electron fluxes are also observed (Figures 10d-10f) that are comparable in magnitude with those occurring during the Yao et al. (2018) events in Figure 9. During the following PPO cycle, however, no such plasma sheet signatures were evident during the interval of the colatitudinal field peak, indicating a lesser thickening in this case (or otherwise displacement of the sheet). Subsequently, more continuous contact with the plasma sheet was maintained toward the end of the interval as the spacecraft near apoapsis moved northward through the equatorial plane, where comparably large energetic particle fluxes were again observed in the plasma sheet region of weakened radial field.

Summary and Conclusions
We have discussed the physical origin of dynamic events observed in Saturn's equatorial current sheet, specifically observations of field dipolarizations that recur close to the planetary rotation period, meaning close to the period of the PPO oscillations in the magnetic field. Yao et al. (2018) presented three such event intervals with two (possible) dipolarizations observed in each, and suggested that the recurrence could be due to the rotation around the planet of a coherent long-lived dipolarized field structure and related current system at close to the ∼10.7 h PPO period. They also discussed the possibility that such events are generated separately but recurrently at similar PPO phases due to modulation of the current sheet magnetic field in the PPO cycle, but did not favor this scenario on the basis that the events were related to PPO phases associated with radial inward displacements of the field lines and a thickened plasma/current sheet. Such conditions are expected to suppress rather than to promote current sheet reconnection and dipolarization/ plasmoid formation, such that recurrent events at similar PPO phases are not then expected to occur.
Here, we have examined these discussions in two respects, first the suggestion that recurrent events could be associated with the rotation of a dipolarized region around the planet at close to the PPO rotation period, and second that the PPO conditions during the events is not conducive to recurrent reconnection. Principal points are as follows.
1. Examination of whole-mission ion velocity data (Kane et al., 2020;Wilson et al., 2017) shows that the near-equatorial flow in Saturn's middle and outer magnetosphere is persistently and significantly subcorotational, such that any structure rotating with the flow would recurrently return to the same azimuth (LT) at a modulo 360° PPO phase significantly displaced from that of the previous pass, unlike the recurrent events observed. Specifically, median flows at radial distances ∼20 to ∼30 R S where the events were observed correspond to rotation periods ∼22 to ∼35 h (azimuthal speeds ∼100 km s −1 corresponding to ∼50% to ∼30% of rigid corotation), assuming that complete rotations are indeed possible at such distances. These periods correspond to PPO phase differences per rotation of ∼380° to ∼820°, meaning such structures would return ∼1.1 to ∼2.3 PPO cycles later than for a rigidly corotating structure at such distances. 2. Similar conclusions apply to the rotating hot ion clouds injected into the outer magnetosphere, likely following tail reconnection bursts associated with dipolarization/plasmoid formation, which have a mean period at ∼20 R S of ∼16 h corresponding to 65% of rigid corotation (Carbary & Mitchell, 2014). This period corresponds to a PPO phase difference per rotation of ∼175°, meaning that such a structure would return close to half a PPO cycle later than a rigidly corotating structure at this distance. Although empirical velocity determinations are quite broadly spread, there are no indications in any of these data sets, including direct determinations from ion anisotropies, for significant intervals of near-corotational azimuthal flow. Recurrent dipolarization events cannot therefore be due to field/current system structures that to a first approximation rotate around the planet "frozen" into the plasma. 3. An alternative possibility is that the recurrent events correspond to long-lived structures that propagate through the subcorotating plasma near the planetary/PPO rotation period. This implies propagation through the plasma at a significant fraction of rigid corotation, ∼100-200 km s −1 at ∼20-30 R S , the same speed as the PPO modulations themselves propagate through the subcorotating plasma. While an overall rotation period near the planetary period is clearly relevant to the PPOs driven from the two polar upper COWLEY AND PROVAN 10.1029/2021JA029444 22 of 27 atmospheres, its relevance is not obvious for a propagating dipolarization region. Further, while the eastward edge of such a structure might possibly represent a dipolarization front propagating eastward through the plasma at the above speed, across the similarly propagating westward edge of the structure the field and plasma must then return to near its previous tail-like state. We know of no physical process that would account for such behavior. Considering points (1)-(3) together, we conclude that the physical picture of recurrent dipolarization events suggested by Yao et al. (2018) in terms of a coherent structure rotating around the planet close to the planetary/PPO rotation period is highly implausible. 4. The alternative physical picture in which recurrent dipolarizations are generated by individual reconnection bursts occurring sequentially at similar favorable phases of the PPO modulation cycle provides an a priori reasonable scenario given the strong PPO modulation of reconnection events found in previous studies, combined with an overall occurrence rate approaching one reconnection-related episode per PPO cycle. Following the reconnection event, the injected heated plasma is taken to sub-corotate around the planet via dawn at the observed speeds . Reconnection occurs preferentially when the two PPO systems combine to extend plasma sheet field lines radially outward from the planet, and to thin the current sheet with minimum colatitudinal field threading through it. For northern and southern PPO system amplitudes that are near equal during the equinoctial conditions prevailing, such modulations are maximized under antiphase conditions between two PPO systems, specifically in the retarded local phase quadrants N   ∼270° to ∼0°/360° and S   ∼90° to ∼180° Jackman et al., 2016), and are not expected to occur during in phase conditions. 5. Yao et al.'s (2018) assertion that their events occur at PPO phases that are essentially the opposite of optimum conditions, with field lines displaced radially inward and with a thickened current sheet, appears to be based incorrectly on consideration of the global phases that describe the instantaneous orientation of each PPO system relative to the Sun, rather than the local phases that determine the local conditions within the plasma/current sheet. On the nightside of the planet near midnight the local phases are approximately in antiphase with the global phases, with expected PPO modulation conditions that are consequently the opposite of those indicated by Yao et al. (2018). On the dayside near noon, however, the local phases are approximately the same as the global phases, with expected PPO modulations conditions that are the same as those indicated by Yao et al. (2018). 6. For Yao et al.'s (2018) nightside Event 1 observed post-dusk at ∼30 R S , we consequently find that the recurrent dipolarizations occur under near-antiphase PPO conditions near to expected times of maximum outward radial extension of the plasma sheet field lines as the sheet thickness was declining from peak values, thus favorable for recurrent reconnection. Consideration of similarly located Event 3 is somewhat muddied by an apparent inaccuracy in the PPO phases reported by Andrews et al. (2012) for that specific interval, which indicate near in phase conditions at that time unfavorable for recurrent reconnection. As discussed in the Appendix, this was a uniquely difficult time for PPO phase determination from magnetic data. However, the field data themselves show unequivocally that the recurrent dipolarizations occurred sequentially at times when the current sheet was thin with near-minimum colatitudinal field. These findings suggest that the nightside recurrent dipolarization events, presented as a new phenomenon by Yao et al. (2018), are instead part of the well-documented Vasyliunas cycle-associated "short-lived LFE" phenomenon in which two reconnection episodes happen to be triggered at similar favorable PPO phases on successive PPO cycles. 7. Following point (5) above, as indicated by Yao et al. (2018), pre-noon dayside Event 2 occurred at PPO phases related to inward radial displacement of field lines and a thickened current sheet with maximum colatitudinal field threading through it, unfavorable for any reconnection event and certainly for recurrent reconnection at the same unfavorable phases. However, as just indicated, at these phases the PPO modulations themselves produce field/plasma variations which have the same senses as those occurring in dipolarization events (increases in colatitudinal field and expansion of the plasma sheet), though typically occurring on longer few-hour time scales. While it thus seems unlikely that these dayside events are due directly to reconnection-related dynamics similar to the nightside events, they may simply be due to the regularly occurring plasma and current sheet modulations associated with the PPO cycle, combined with subcorotating small-scale field structures that appear always to be present at some level within the plasma sheet. This discussion does not, of course, preclude the possibility more generally of reconnection-related events occurring on the dayside related to those observed on the nightside. These may similarly produce, for example, well-marked ∼10 min field and plasma signatures, expected to be COWLEY AND PROVAN 10.1029/2021JA029444 23 of 27 formed preferentially under favorable radially extended and thinned plasma/current sheet conditions opposite to those for Event 2 discussed above. However, clarification of these issues requires a more comprehensive study of the characteristics of Saturn's dayside current sheet, its PPO modulation and dynamical signatures, and their dependence on the state of expansion of the magnetosphere (e.g., Bunce et al., 2008), than has been carried out to date. 8. Overall, both dayside and nightside events discussed by Yao et al. (2018) can readily be understood in terms of existing knowledge of how the PPO systems modulate the structure and dynamics of Saturn's equatorial current sheet. They require the introduction of no new physics.

Appendix A: Discussion of PPO Phase Model Values During Event 3
The modeling of Event 3 in Section 3.3 shown in Figures 7 and 8 suggests a discrepancy in the value of the PPO beat phase during that interval having too large a value by ∼70°. Of this, the model results suggest that a modest amount ∼25° may be contributed by too large a value of N   in the Andrews et al. (2012) phase model, while a larger part appears to be contributed by too small a value of S   by ∼45°, both effects thus contributing to too large a beat phase by roughly the ∼70° indicated.
Examination of the source data from which the Andrews et al. (2012) phase models were derived shows that this specific interval corresponds to one of special difficulty for PPO phase determination. Due to the near-equatorial orbit of Cassini during the interval, the individual system phases were determined from near-equatorial core region observations of combined oscillations of near-equal amplitude, during an interval when the periods of the two systems were very closely spaced, hence with a very lengthy beat period. Simple analysis shows that when the two systems have equal amplitudes the phase of the combined oscillations varies only with the mean phase of the two systems   / 2 m N S      . (We do not indicate retarded phases here because the oscillations are observed within the "core" region.) Specifically, taking account of the near-equatorial component oscillatory behaviors indicated in Section 3.1.1, simple trigonometry gives for the radial (r), colatitudinal (θ), and azimuthal (φ)   is negative. In effect, these oscillations thus jump in phase by 180° across the times when the two systems reach in phase conditions, again when the combined oscillations pass through zero amplitude in effect reversing in sign.
In addition to determination of the mean phase m  , the phase difference between the two systems, the beat phase, can thus be followed through determination of these times. The overall Andrews et al. (2012)  138 as seen in Figure 6e, and passed through the in phase condition between the periapsides of Revs 138 and 139. However, the individual core region colatitudinal component phase measurements instead suggest that in phase conditions actually occurred somewhat later, between the periapsides of Rev 139 and 141 (see the analysis shown in Figure 1c of Cowley, Provan, & Andrews, 2015), the uncertainty in timing compounded by the lack of core phase measurements on Rev 140 due to a magnetic field data gap. These phase data further indicate that the beat period had lengthened to ∼190 days during this interval (indicating a difference in system periods of only ∼0.025 h, the northern period remaining shorter than southern), corresponding to ∼9 spacecraft Revs each spanning ∼20 days, with the beat phase thus increasing by ∼40° per Rev. A likely increase in the occurrence time of in phase conditions by ∼2 Revs could then readily correspond to the ∼70° phase difference envisaged between Figures 7 and 8.