Proton Core Behaviour Inside Magnetic Field Switchbacks
Thomas Woolley, Lorenzo Matteini, Timothy S. Horbury, Stuart D. Bale, Lloyd D. Woodham, Ronan Laker, Benjamin L. Alterman, John W. Bonnell, Anthony W. Case, Justin C. Kasper, Kristopher G. Klein, Mihailo M. Martinović, Michael Stevens
MMNRAS , 1–9 (2020) Preprint 22 July 2020 Compiled using MNRAS L A TEX style file v3.0
Proton Core Behaviour Inside Magnetic Field Switchbacks
Thomas Woolley, (cid:63) Lorenzo Matteini, Timothy S. Horbury, Stuart D. Bale, , , , Lloyd D. Woodham, Ronan Laker, Benjamin L. Alterman, John W. Bonnell, Anthony W. Case, Justin C. Kasper, , Kristopher G. Klein, Mihailo M. Martinović, , Michael Stevens Department of Physics, Imperial College London, London SW7 2AZ, UK Physics Department, University of California, Berkeley, CA 94720-7300, USA Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK Space Science and Engineering, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238, USA Smithsonian Astrophysical Observatory, Cambridge, MA 02138 USA Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA LESIA, Observatoire de Paris, Universite PSL, CNRS, Sorbonne Universite, Universite de Paris, 5 place Jules Janssen, 92195 Meudon, France
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
During Parker Solar Probe’s first two orbits there are widespread observations of rapid magnetic field reversals known asswitchbacks. These switchbacks are extensively found in the near-Sun solar wind, appear to occur in patches, and have possiblelinks to various phenomena such as magnetic reconnection near the solar surface. As switchbacks are associated with fasterplasma flows, we questioned whether they are hotter than the background plasma and whether the microphysics inside aswitchback is different to its surroundings. We have studied the reduced distribution functions from the Solar Probe Cupinstrument and considered time periods with markedly large angular deflections, to compare parallel temperatures inside andoutside switchbacks. We have shown that the reduced distribution functions inside switchbacks are consistent with a rigid phasespace rotation of the background plasma. As such, we conclude that the proton core parallel temperature is the same inside andoutside of switchbacks, implying that a T-V relationship does not hold for the proton core parallel temperature inside magneticfield switchbacks. We further conclude that switchbacks are consistent with Alfvénic pulses travelling along open magnetic fieldlines. The origin of these pulses, however, remains unknown. We also found that there is no obvious link between radial Poyntingflux and kinetic energy enhancements suggesting that the radial Poynting flux is not important for the dynamics of switchbacks.
Key words:
Sun: heliosphere - solar wind - magnetic fields
Despite the prediction (Parker 1958) and detection (Gringauz et al.1960; Neugebauer & Snyder 1962) of a supersonic wind from the Sunmore than 60 years ago, it is still unknown how the thermal energy ofthe million-Kelvin corona is converted into the bulk kinetic energyof the solar wind flow. In situ plasma observations throughout theheliosphere reveal ubiquitous non-thermal particle velocity distribu-tion functions (VDFs) in the plasma, suggesting that the heating andrelease of the solar wind close to the Sun, as well as its non-adiabaticexpansion in interplanetary space are related to kinetic processesthat regulate the energy exchanges between particles and fields (e.g.Marsch 2006; Verscharen et al. 2019).The solar wind is known to display a temperature-velocity (T-V)relationship on large scales over different streams (e.g. Burlaga &Ogilvie 1973; Lopez & Freeman 1986), but the exact drivers of thisrelationship remain unknown. Recent work suggests that the T-V re-lationship holds within a single stream (Horbury et al. 2018) and (cid:63)
E-mail: [email protected] evolves as a function of distance (Perrone et al. 2019). This leads toquestions about whether the T-V relationship also holds in individualsmall scale structures. To address this, it is important to considerVDFs in the solar wind which could carry fundamental informationabout the processes responsible for the heating and acceleration ofthe plasma close to the Sun. However, as solar wind expansion mod-ifies and reprocesses distributions, measuring more pristine plasmaconditions is fundamental to make a direct link between signaturesobserved in situ and processes at the Sun.To this aim, the Parker Solar Probe (PSP) mission (Fox et al.2016) was designed to measure the young solar wind. During its firstperihelion pass in November 2018 PSP reached a closest approachof 36.5 R S . Prior to this, the closest in-situ measurements to theSun were made by the Helios probes in the 1970s (62 R S ). Anunexpected result from PSPâĂŹs first orbit was the detection ofubiquitous magnetic field reversals (switchbacks) (Bale et al. 2019)in the young solar wind, associated with intense enhancements of theflow velocity, up to twice the local Alfvén speed (Kasper et al. 2019).These switchbacks are discrete, rapid and asymmetric magneticfield deflections away from the background field that can reverse the © 2020 The Authors a r X i v : . [ phy s i c s . s p ace - ph ] J u l T. Woolley et al. local magnetic field polarity. They have durations that last from afew seconds to tens of minutes, indicating that they are a multi-scalephenomenon (Dudok de Wit et al. 2020). They also seem to occur inpatches which are separated by regions of more quiet and stable radialmagnetic field (Bale et al. 2019; Horbury et al. 2020). Switchbacksare Alfvénic fluctuations with constant magnetic field intensity |B|,implying that the local plasma velocity inside a switchback is fasterthan the background flow (Matteini et al. 2014). As a consequence,they also carry significantly larger momentum and kinetic energythan the surrounding plasma (Horbury et al. 2018).Magnetic switchbacks have also been observed beyond 64 R S (Matteini et al. 2015; Horbury et al. 2018), although with differentproperties than in PSP data and mostly in the fast solar wind. Intrigu-ingly, during its first perihelion, PSP was embedded in Alfvénic slowwind coming from a small coronal hole (Bale et al. 2019; Kasperet al. 2019), similar to that previously discussed (D’Amicis & Bruno2015; Stansby et al. 2019; Perrone et al. 2020), revealing that thesestructures are more common than previously expected and suggestingthat they could play a fundamental role in different types of streamsand sources.Three questions about switchbacks then arise:(i) Since the switchbacks are faster are they also hotter than thebackground plasma? This would be expected if typical solar windT-V relationships are upheld inside these structures.(ii) Is the plasma inside a switchback distinctly different from thebackground plasma? If it is then this would imply that switchbacksare a transient-like event from a source region that is distinct fromthat which generates the background plasma. On the other hand, ifswitchback and background plasma are similar then it is possible thatswitchbacks are local perturbations of the background plasma (e.g.a propagating non-linear Alfvénic pulse Squire et al. 2020).(iii) Do switchbacks play a dynamical role in the generation ofthe solar wind? Mozer et al. (2020) showed that switchbacks carrysome significant radial Poynting flux that can eventually do work inaccelerating the plasma; are the fastest switchbacks characterised bythe largest Poynting flux?In this paper we address these questions by analysing magneticfield switchbacks which complete a full reversal in the radial com-ponent B R , corresponding to the largest acceleration of the bulkplasma. These switchbacks provide the only opportunity to comparethe parallel temperature inside and outside switchbacks using theSolar Probe Cup’s radial measurements. We discuss the behaviourof the full ion VDF during the magnetic field rotation and highlightthe thermodynamic properties of the proton core population. We alsomeasure the radial Poynting flux’s evolution within these structuresand verify whether it is directly related to the plasma kinetic energy. In this work we used data from the FIELDS (Bale et al. 2016) andSWEAP (Kasper et al. 2016) instrument suites in the Radial Tangen-tial Normal (
RT N ) coordinate system (Hapgood 1992). We definedthe magnetic field cone angle ( θ BR ) as the angle between the localmagnetic field vector and the R direction. It took a value between0 ◦ , when the magnetic field was exactly radial, and 180 ◦ , when themagnetic field was exactly anti-radial. . The SWEAP instrument suite (Kasper et al. 2016) consists of twoelectron electrostatic analysers (SPAN-E; Whittlesey et al. 2020), oneion electrostatic analyser (SPAN-I), and a Faraday cup (Solar ProbeCup; SPC; Case et al. 2020). SPC and SPAN-I have complimentaryfields of view. SPAN-I is situated on the ram side of the spacecraftbehind the heat shield and measures a three-dimensional distributionfunction. SPC is radially orientated towards the Sun and measuresa one-dimensional reduced ion distribution function, F ( v R ) , of theincoming solar wind that is blocked by the heat shield.The amount of solar wind measured by each instrument changeswith the plasma flow relative to the spacecraft. For radial flows SPCis more appropriate whereas flows with a large -T velocity compo-nent relative to the spacecraft favour the use of SPAN-I. During theearly phases of the mission, and at larger heliocentric distances, SPCis better suited for ion plasma measurements. As the spacecraft tan-gential velocity will increase for each subsequent perihelion pass,SPAN-I will capture more of the ion distribution in later encounters.Here we processed the level 2 SPC-measured F ( v R ) in accordancewith the procedure outlined by Case et al. (2020). During PSP’s firsttwo perihelia, SPC’s measurement cadence was typically between1.1 and 4.6 samples/sec. The FIELDS instrument suite (Bale et al. 2016) uses a variety ofinstruments to measure the magnetic and electric fields in the solarwind. These include two flux gate magnetometers (MAG), a searchcoil magnetometer (SCM), and five voltage probes. The magneticfield data used in this work was from the MAG instruments and wasdown sampled to the cadence of the SPC F ( v R ) .We used 2 dimensional DC electric field data from four voltageprobes approximately, but not exactly, in the T-N plane to calculatethe radial Poynting flux ( S R = µ ( E × B ) · (cid:98) R ). Using these twocomponents of E along with all three components of B allowed usto fully characterize the radial component of the Poynting flux. Forthe scales of interest, the planar electric field was dominated by themotional electric field ( E = − v × B ). We manually chose switchbacks from PSP’s first two perihelia thatwere some of the largest deflections with durations > F pc ( v R ) = n pc √ π w R · exp (cid:32) ( v R − v pc , R ) w R (cid:33) (1)with thermal speed: w R = k B T pc , R m p . (2)This was the proton core of the distribution function with a radialtemperature ( T pc , R ), number density ( n pc ), and mean radial velocity MNRAS , 1–9 (2020) roton Core Behaviour in Switchbacks Figure 1.
Fits of the proton core (red), proton beam (blue) and alpha(green) populations along with SPC’s reduced distribution function (blackdata points) within the background plasma (5th November 2018 01:22:45).Panel (a) shows the reduced distribution function and population fits. The redpoints indicate the data used to fit the core population and the orange lineshows the sum of the three population fits. Panel (b) shows the residuals inunits of percent (cid:16) × data − fitdata (cid:17) . ( v pc , R ). Quality checks were then used to ensure a consistent levelof fit.We constrained the fits so that the density did not exceed F ( v R ) ’stotal density. We only kept fits for which the residuals were less than0.05 cm − km − s. This filtered out cases which did not accuratelyrepresent the data points. Despite these filters, the core temperaturewas overestimated in some of the F ( v R ) with large proton beams(e.g. n beam / n pc ∼ F ( v R ) manually.Note that Verniero et al. (2020) has studied large proton beams inmore detail. We validated our fits by comparing the extracted physicalquantities to those in the level 3 SPC data files. As our fitting methodwas similar, we assign the same uncertainties on fitted parameters aspresented by Case et al. (2020). These are 9%, 3% and 19% for thedensity, radial velocity and temperature respectively.In the background plasma, it was occasionally possible to alsofit the beam and alpha populations using a similar procedure asthat applied to the core. Fig. 1 shows an example fit to the protoncore (red), proton beam (blue) and alpha (green) populations in thebackground plasma near to perihelion. Panel (a) shows the F ( v R ) as measured by SPC (black data points) and the fit populations.The sum of the distributions (orange line) closely follows the datapoints, suggesting that the extracted physical quantities represent themeasurements well. Panel (b) shows residuals in units of percent,confirming the fit quality. Note that the alpha particles’ velocity wasshifted by a factor of √ ∼
600 km s − ) in SPC because of thealpha’s energy-to-charge ratio. Accounting for this shift, the alphasare found to travel at approximately the local Alfvén speed and havea higher v R than the proton core.In the cases we selected, the proton beam and alphas were suffi-ciently well separated from the core that fitting them did not impactour proton core fits. We only mentioned them in this section forcompleteness. In order to make use of the SPC measurements, it was important tounderstand how different plasma species behaved inside and outsidemagnetic field switchbacks. Outside of switchbacks, the backgroundmagnetic field was approximately anti-radial close to perihelion (Baleet al. 2019; Kasper et al. 2019). As a result, SPC’s radial temperaturemeasurements corresponded to the component parallel to the localmagnetic field.When PSP observed an Alfvénic fluctuation with | B | constant, thehighly correlated velocity and magnetic field caused the ion VDF torotate in phase space around the velocity corresponding to the localwave speed in the plasma reference frame. As a result, SPC measuredthe VDF at different angles to the magnetic field. As protons haveanisotropic temperatures with respect to the local magnetic fieldin the solar wind, SPC measured a different radial temperature asa function of θ BR . This is why direct comparisons of SPC cutsand parallel temperatures inside and outside switchbacks were onlypossible for full reversals of the local magnetic field.Fig. 2 shows the magnetic field and proton core velocity duringAlfvénic fluctuations for a chosen interval. As these were constant | B | structures, the magnetic field vector was confined to move on thesurface of a sphere with constant radius equal to | B | centred at (0,0, 0) nT. When this motion was projected into a plane, it appearedas an arc as shown in panel (a). Similarly, the velocity vector wasconfined to the surface of a sphere in velocity space, the projection ofwhich is shown in panel (b). This shows that the velocity fluctuationswere also rotations (i.e. constant magnitude) in a reference framethat was close to the local wave speed, which is typically the Alfvénspeed (Matteini et al. 2015). As such, the velocity sphere’s radius was (cid:39) v phase . The centre of the velocity sphere was approximately thelocal de Hoffman Teller frame, i.e. the frame in which the motionalelectric field associated with the fluctuations vanished.A further consequence of the phase space rotation discussed abovewas that every particle above (below) the local wave speed travelledslower (faster) within a switchback, while the particles that streamedat exactly the local wave speed were neither accelerated nor deceler-ated during switchbacks (Matteini et al. 2015). In general, the localwave speed usually sits somewhere between the proton core velocityand the proton beam velocity. As such, the proton core accelerateswhile the proton beam decelerates during switchbacks (Neugebauer& Goldstein 2013). When the magnetic field is approximately per-pendicular to the radial direction, the proton core and beam havethe same radial velocity and hence the two populations overlap. Thismakes it difficult to distinguish the two populations in SPC data. Asthe alpha particles appear to stream at the local wave speed close tothe Sun (Fig. 1), they are expected to remain at a constant velocityduring switchbacks. We focused on a specific switchback that occurred on the 7th Novem-ber 2018 when PSP was approximately 37.6 R S from the Sun (seeFig. 3). This switchback lasted for approximately 25 minutes andpanel (a) shows that θ BR was close to 0 ◦ for most of this time. Themagnetic field magnitude in the switchback remained approximatelyconstant at a slightly greater value than the background field with oc-casional short-lived fluctuations. This magnitude increase was coun-teracted by a density decrease in the switchback plasma to maintain a MNRAS000
600 km s − ) in SPC because of thealpha’s energy-to-charge ratio. Accounting for this shift, the alphasare found to travel at approximately the local Alfvén speed and havea higher v R than the proton core.In the cases we selected, the proton beam and alphas were suffi-ciently well separated from the core that fitting them did not impactour proton core fits. We only mentioned them in this section forcompleteness. In order to make use of the SPC measurements, it was important tounderstand how different plasma species behaved inside and outsidemagnetic field switchbacks. Outside of switchbacks, the backgroundmagnetic field was approximately anti-radial close to perihelion (Baleet al. 2019; Kasper et al. 2019). As a result, SPC’s radial temperaturemeasurements corresponded to the component parallel to the localmagnetic field.When PSP observed an Alfvénic fluctuation with | B | constant, thehighly correlated velocity and magnetic field caused the ion VDF torotate in phase space around the velocity corresponding to the localwave speed in the plasma reference frame. As a result, SPC measuredthe VDF at different angles to the magnetic field. As protons haveanisotropic temperatures with respect to the local magnetic fieldin the solar wind, SPC measured a different radial temperature asa function of θ BR . This is why direct comparisons of SPC cutsand parallel temperatures inside and outside switchbacks were onlypossible for full reversals of the local magnetic field.Fig. 2 shows the magnetic field and proton core velocity duringAlfvénic fluctuations for a chosen interval. As these were constant | B | structures, the magnetic field vector was confined to move on thesurface of a sphere with constant radius equal to | B | centred at (0,0, 0) nT. When this motion was projected into a plane, it appearedas an arc as shown in panel (a). Similarly, the velocity vector wasconfined to the surface of a sphere in velocity space, the projection ofwhich is shown in panel (b). This shows that the velocity fluctuationswere also rotations (i.e. constant magnitude) in a reference framethat was close to the local wave speed, which is typically the Alfvénspeed (Matteini et al. 2015). As such, the velocity sphere’s radius was (cid:39) v phase . The centre of the velocity sphere was approximately thelocal de Hoffman Teller frame, i.e. the frame in which the motionalelectric field associated with the fluctuations vanished.A further consequence of the phase space rotation discussed abovewas that every particle above (below) the local wave speed travelledslower (faster) within a switchback, while the particles that streamedat exactly the local wave speed were neither accelerated nor deceler-ated during switchbacks (Matteini et al. 2015). In general, the localwave speed usually sits somewhere between the proton core velocityand the proton beam velocity. As such, the proton core accelerateswhile the proton beam decelerates during switchbacks (Neugebauer& Goldstein 2013). When the magnetic field is approximately per-pendicular to the radial direction, the proton core and beam havethe same radial velocity and hence the two populations overlap. Thismakes it difficult to distinguish the two populations in SPC data. Asthe alpha particles appear to stream at the local wave speed close tothe Sun (Fig. 1), they are expected to remain at a constant velocityduring switchbacks. We focused on a specific switchback that occurred on the 7th Novem-ber 2018 when PSP was approximately 37.6 R S from the Sun (seeFig. 3). This switchback lasted for approximately 25 minutes andpanel (a) shows that θ BR was close to 0 ◦ for most of this time. Themagnetic field magnitude in the switchback remained approximatelyconstant at a slightly greater value than the background field with oc-casional short-lived fluctuations. This magnitude increase was coun-teracted by a density decrease in the switchback plasma to maintain a MNRAS000 , 1–9 (2020)
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Figure 2.
Magnetic field and proton core velocity in the T-R plane froman ≈
25 minute interval (5th November 2018 06:55:05 - 07:19:30) closeto perihelion. Panel (a) shows the magnetic field (dark blue points) with acircle of radius 82 nT ( (cid:39) (cid:104)| B |(cid:105) ) centred on (0, 0) nT over plotted in orange.Similarly, panel (b) shows the velocity of the proton core (dark blue points)with a circle of radius 60 km s − ( (cid:39) v phase ) over plotted in orange. Thecentre of the velocity circle is (29, 342) km s − . similar total pressure to the background plasma (panel (b)). Panel (c)shows that this switchback started with a slow deflection away fromthe background field and ended with a sharp, rapid return to the back-ground orientation. In the middle of the switchback at approximately03:44 there was a small sharp feature which caused the magneticfield to almost return to the background orientation briefly. The ra-dial velocity profile (orange line) followed B R closely, as the plasmafluctuations were Alfvénic. Panel (d) highlights that the deflectionof the magnetic field occurred in the negative T direction with thefirst half of the deflection rotating towards the positive N direction.It also indicates that the plasma fluctuations were Alfvénic whenthe magnetic field components are compared to the plasma protoncore velocity components in panel (e). Finally, panel (f) shows boththe radial Poynting flux (calculated from µ E × B ) and the kineticenergy flux of the proton core population (Sect. 5.1.3). There was a ∼
20 minute interval without electric field or plasma data after theswitchback which can be seen as the gap in the data. All the velocitiesthat are plotted in Fig. 3 are for the proton core population and comefrom the fitting procedure outlined in Sect. 3.
The proton core radial temperature ( T pc , R ) for this case study isplotted in Fig. 4. Panel (a) shows its dependence on magnetic fieldcone angle and panel (b) shows how the cone angle changed through-out the interval. The data points are coloured based on time: purpleindicates the earliest times and yellow indicates the latest.Panel (a) shows that T pc , R generally follows a geometrical predic-tion (black line) for an anisotropic core plasma with T pc , (cid:107) = × K and T pc , ⊥ = × K (Kasper et al. 2002; Huang et al.2020): T pc , R = T pc , (cid:107) cos θ BR + T pc , ⊥ sin θ BR . (3)This is consistent with the same anisotropic ( T pc , ⊥ > T pc , (cid:107) ) VDFbeing seen from different angles as the magnetic field orientationchanges. This suggests that changes in T pc , R were due to changesin the geometrical cut through the VDF rather than variations in theunderlying distribution. Panel (a) also shows that the proton core’sparallel temperature was the same at 0 ◦ (within the switchback)and at 180 ◦ (in the background plasma). There are, however, somedeviations from the geometrical prediction, which could be related tosystematic errors in the SPC measurements. These will be addressedin future studies. Fig. 5 panels (a) through (c) present example F ( v R ) from the ap-proximately anti-parallel, perpendicular, and parallel cases. The redshaded region shows the core proton population. The green shadedregion shows the alpha particle population which we could onlyestimate for the perpendicular field case.Panel (b) shows a case where the proton core and beam overlappedfor θ BR around 90 ◦ . This was a consequence of both populationshaving the same radial speed and resulted in the core populationobscuring the beam as discussed in Sect. 4. The temperature ofthis core distribution is larger than the temperature of either of thedistributions in panels (a) and (c). It should be emphasised that thistemperature difference is a direct result of the anisotropy of theplasma and not because of the core-beam overlapping.Panels (a) and (c) show the anti-parallel (background) and parallel F ( v R ) respectively. As expected, the average velocity of the corepopulation in the parallel case was higher due to the motion of thepopulations under Alfvénic fluctuations (see Sect. 4). This motionnot only supported the idea that VDFs undergo a rigid phase spacerotation as presented previously but also allowed an independentestimate of the local phase speed ( v phase ). It is worth noting that v phase corresponds to the speed that fluctuations propagate in theplasma frame and hence, the frame in which the motional electricfield of the fluctuations vanishes (Matteini et al. 2015; Horbury et al.2020). v phase was estimated as 115 km s − by considering themotion of the core population in the two F ( v R ) . This was consistentwith the phase speed ( ∼
110 km s − ) obtained from the correlationbetween v pc , N and B N fluctuations before the switchback and wasin good agreement with the local Alfvén speed ( V A ∼
110 km s − ).Panel (d) compares the F ( v R ) from panel (a) rotated around avelocity v phase ahead of the core population (blue line) and the F ( v R ) from panel (c). The two distributions are very similar whichis again consistent with a phase space rotation of the same VDF.The average velocity of the alpha population was 412 km s − which, due to the energy-to-charge ratio of alpha particles, was shiftedby a factor √ ∼
583 km s − in SPC’s F ( v R ) (panel (b), Fig. 5). Thisaverage velocity was consistent with the alpha particles streaming MNRAS , 1–9 (2020) roton Core Behaviour in Switchbacks Figure 3.
A selected switchback showing: (a) the magnetic field cone angle θ BR , (b) the magnitude of the magnetic field | B | and the proton core density n pc ,(c) the radial components of the magnetic field B R and the proton core velocity v pc , R , (d) the tangential and normal components of the magnetic field B T and B N , (e) the tangential and normal components of the proton core velocity v pc , T and v pc , N , (f) the radial Poynting flux S R and the proton core kinetic energyflux. The grey shaded region highlights the magnetic field switchback and the thin vertical lines indicate the inner region with parallel magnetic field. faster than the proton core by v phase . As such, the alphas werelocated at the centre of the phase space rotation and hence remainedat the same velocity for all magnetic field angles. We conclude thatthe tail seen above 600 km s − in each F ( v R ) was alpha particles. Panel (f) in Fig. 3 shows the radial Poynting flux ( S R = µ ( E × B ) · (cid:98) R ) and the proton core kinetic energy flux through the period of study.The kinetic energy flux increased within the switchback because thecore velocity increased. As such, the kinetic energy flux’s profile(orange line) was very similar to the profile of the radial magneticfield and core velocity components.The radial Poynting flux was small in the background plasma before the switchback but as the field began to rotate from sunwardto anti-sunward polarity, this flux increased and reached a maximumat around θ BR = 90 ◦ . It then fell towards the background level as B R increased to its maximum value within the switchback. During theswitchback, when B was mainly radial, the Poynting flux was similarto the background level even though the velocity of the proton corewas much higher. At the end of the switchback, when the field beganto return to the background orientation, the Poynting flux once againincreased. It reached a maximum around θ BR = 90 ◦ before decreasingas the magnetic field returned to its pre-switchback orientation.The proton core kinetic energy flux was always significantly largerthan the radial Poynting flux (Fig. 3). The ratio of Poynting fluxto kinetic energy flux was ∼ θ BR = 90 ◦ when the radial MNRAS000
A selected switchback showing: (a) the magnetic field cone angle θ BR , (b) the magnitude of the magnetic field | B | and the proton core density n pc ,(c) the radial components of the magnetic field B R and the proton core velocity v pc , R , (d) the tangential and normal components of the magnetic field B T and B N , (e) the tangential and normal components of the proton core velocity v pc , T and v pc , N , (f) the radial Poynting flux S R and the proton core kinetic energyflux. The grey shaded region highlights the magnetic field switchback and the thin vertical lines indicate the inner region with parallel magnetic field. faster than the proton core by v phase . As such, the alphas werelocated at the centre of the phase space rotation and hence remainedat the same velocity for all magnetic field angles. We conclude thatthe tail seen above 600 km s − in each F ( v R ) was alpha particles. Panel (f) in Fig. 3 shows the radial Poynting flux ( S R = µ ( E × B ) · (cid:98) R ) and the proton core kinetic energy flux through the period of study.The kinetic energy flux increased within the switchback because thecore velocity increased. As such, the kinetic energy flux’s profile(orange line) was very similar to the profile of the radial magneticfield and core velocity components.The radial Poynting flux was small in the background plasma before the switchback but as the field began to rotate from sunwardto anti-sunward polarity, this flux increased and reached a maximumat around θ BR = 90 ◦ . It then fell towards the background level as B R increased to its maximum value within the switchback. During theswitchback, when B was mainly radial, the Poynting flux was similarto the background level even though the velocity of the proton corewas much higher. At the end of the switchback, when the field beganto return to the background orientation, the Poynting flux once againincreased. It reached a maximum around θ BR = 90 ◦ before decreasingas the magnetic field returned to its pre-switchback orientation.The proton core kinetic energy flux was always significantly largerthan the radial Poynting flux (Fig. 3). The ratio of Poynting fluxto kinetic energy flux was ∼ θ BR = 90 ◦ when the radial MNRAS000 , 1–9 (2020)
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Figure 4.
Proton core radial temperature within a single switchback on the 7thNovember 2018. Panel (a) shows the proton core radial temperature plottedagainst the magnetic field cone angle θ BR . The solid black line shows theexpected response of the temperature (Eq. 3). Panel (b) shows a timeseriesplot of θ BR . Both panels follow the same colour convention. The purple datapoints are the earliest and the yellow data points are the latest. Figure 5.
Reduced distribution functions measured by SPC for the 7th Novem-ber switchback. Panels (a) âĂŞ (c) show the SPC reduced distribution func-tions when θ BR was 167 ◦ (03:25:59), 90 ◦ (03:29:47) and 2 ◦ (03:52:58).As such, panels (a) and (c) were obtained when the magnetic field was al-most radial and anti-radial, whereas panel (b) was from a time during theswitchback when the field was almost perpendicular to the radial direction.The red shaded areas show the proton core and the red points show the dataused to fit the proton core. The green shaded area in panel (b) shows thefitted alpha particles. Panel (d) shows the distribution from panel (c) in blackwith the distribution from panel (a) rotated around v pc , R + V A and overplotted in orange. The blue vertical line indicates the velocity around whichthe distribution from panel (a) was rotated. Poynting flux was maximum, the ratio was also maximum ( ∼ ∼ v pc , R (cid:29) v pc , T , v pc , N and E (cid:39) − v pc × B for the study period (for brevity thesubscript pc has been dropped for terms in the following equations): Γ = S r KE f lux ∼ µ v R B ⊥ ρ v R ∼ v R B ⊥ µ ρ . (4)For spherically polarised fluctuations with approximately constant | B | (see Fig. 2), we expect Γ to be maximum at θ BR = 90 ◦ . This isbecause the increase of v R within the switchback is counteracted bythe decrease of B ⊥ for θ BR < 90 ◦ . As the maximum occurs when B R ∼ B ⊥ (cid:39) B , the maximum ratio can be written as: Γ max ∼ (cid:18) V A v R (cid:19) θ BR = ◦ . (5)This provides an approximate expression for the upper limit of theradial Poynting flux energy contribution for any switchback. Eq.5 predicts a maximum ratio of ∼ To validate our findings, we investigated other switchbacks fromPSP’s first and second near-sun encounters (see Appendix A fortimes of switchbacks). They showed properties similar to the examplepresented above. For example, the 5th November 2018 switchbackat 02:20 shown by Bale et al. (2019) displayed similar Poynting andkinetic energy flux behaviour.In order to obtain a meaningful sample, we relaxed our full mag-netic field reversal requirement. Instead of selecting switchbacks thatunder went a full reversal, any switchback that had > θ BR < ◦ were chosen. We fit the data for θ BR < ◦ and θ BR > ◦ separately using Eq. 3 to get estimates for T pc , (cid:107) insideand outside (background) of a switchback respectively. Even withthis relaxed condition, the number of switchbacks for which the in-side and outside fits were successful was only 5, as most events didnot rotate to θ BR < ◦ .Fig. 6 shows T pc , (cid:107) in a switchback ( T S , (cid:107) ) against T pc , (cid:107) in thebackground plasma ( T B , (cid:107) ) and the orange line indicates where the T S , (cid:107) to T B , (cid:107) ratio is 1. There are two data points for each switchbackwhich are indicated by the same colour and symbol. First, the pointswith error bars are the proton core parallel temperatures calculatedfrom the procedure outlined above. Since we use an analogous fit-ting procedure we use a temperature uncertainty of 19% as in Caseet al. (2020). Second, the points without error bars are estimates ofthe proton core parallel temperature inside each switchback, whichwe obtained by using the T-V relationship at 35 R S (Perrone et al.2019). The ratio of the switchback to background proton core paralleltemperature for each switchback deviates strongly from the T-V pre-diction and is instead remarkably close to 1. This is consistent with T S , (cid:107) being the same as T B , (cid:107) and unrelated to the plasma velocity. MNRAS , 1–9 (2020) roton Core Behaviour in Switchbacks Figure 6.
Proton core parallel temperatures inside ( T S , (cid:107) ) and outside ( T B , (cid:107) )of switchbacks. There are two data points for each switchback which are indi-cated with the same marker and colour. The data with error bars are the protoncore parallel temperatures obtained using the procedure in Sect. 5.2. The datawithout error bars are the proton core parallel temperature predictions thatarise by using the estimated T-V relationship at 35 R S . The 7th November2018 case study is shown with the red triangle. The orange line indicates T S , (cid:107) = T B , (cid:107) . The proton core parallel temperatures inside and outside of our casestudy (Fig. 4) and other switchbacks (Fig. 6) indicate that the plasmais not hotter within full or near-full switchbacks. This suggests that thetypical solar wind T-V relationship does not apply to the proton coreparallel temperature inside magnetic field switchbacks and answersquestion (i) from Sect. 1. The F ( v R ) measured before and duringthe 7th November 2018 switchback (Fig. 5) are consistent with arigid rotation in velocity space (Matteini et al. 2015), leading toa core-beam swap inside the switchback (Neugebauer & Goldstein2013). The centre of this velocity space rotation empirically agreeswith the local phase velocity of fluctuations. Our results suggest thatthe plasma inside a switchback is not distinctly different from thebackground plasma (question (ii) in Sect. 1).This seems to rule out that these structures are remnants of fasterand hotter plasma directly injected in the corona that propagatethrough a slower background. Our findings support the idea thatmagnetic field switchbacks are large amplitude non-linear Alfvénwaves propagating along open field lines such as those discussed byGosling et al. (2011). It is not obvious how such structures can remainstable for prolonged times (Landi et al. 2006) but it seems that a con-stant field magnitude is required (Tenerani et al. 2020). Alfvén pulsescould originate at the Sun through interchange reconnection eventsand propagate to large distances (Karpen et al. 2017; Roberts et al.2018; Sterling & Moore 2020). Alternatively, they could also orig-inate from the non-linear evolution of large amplitude fluctuationsduring expansion (Squire et al. 2020).The radial Poynting flux’s observed profile (Panel (f), Fig. 3) isconsistent with it being dominated by the electric field term ∼ v R B ⊥ .This term is largest when B is away from the radial, while it is smallfor radial or anti-radial field. Our observations are in agreement withthe functional form presented in Mozer et al. (2020) and suggestthat the intermediate velocity switchbacks carry the largest amountof wave energy radially outwards, while the very fastest (i.e. fullreversals) only carry small amounts (question (iii) in Sect. 1). The ratio of radial Poynting to kinetic energy flux is consistentwith negligible radial Poynting flux in the fastest switchbacks whichsuggests that the dynamics are not driven by the wave energy thatswitchbacks carry. We predict that the maximum ratio of radial Poynt-ing to kinetic energy flux inside any switchback is given by Eq. 5.The ratio in a switchback will tend to the upper limit given by Eq. 5as θ BR approaches 90 ◦ , but will be considerably less elsewhere. During the first perihelion pass of PSP ubiquitous local magneticfield reversals (switchbacks) were measured in the young solar wind(Bale et al. 2019; Kasper et al. 2019). These switchbacks, whichwere associated with large increases in the plasma flow velocity,were very different to the switchbacks observed previously in Heliosdata (Horbury et al. 2018) and were resolved in more detail with theimproved cadence of instruments on-board PSP. Here we have useda detailed analysis of ion distributions to address the microphysicsinside switchbacks.Our analysis suggests that the plasma inside switchbacks is notdistinctly different from the background plasma. We have also shownthat the proton core parallel temperature is not related to the enhancedvelocity of switchbacks. These results are consistent with a phasespace rotation of the plasma VDF, which could be a result of non-linear Alfvén pulses propagating through the background plasma.The origin and mechanisms that produce such Alfvénic pulses arestill unknown.We considered the behaviour of the radial Poynting flux and con-clude that the fastest switchbacks do not carry the largest radialPoynting flux. Instead it is the intermediate velocity switchbacksand field rotations, where B R ∼
0, that transport the most wave en-ergy radially outwards. This behaviour is what was expected frompurely geometrical considerations about the motional electric field E = − v × B . We conclude that there is no obvious link betweenkinetic energy enhancement and radial Poynting flux in the largestswitchbacks.As a word of caution, in order to exploit the capabilities of the SPCsensor we could only investigate the largest switchbacks. As such,we cannot make general assumptions about all switchbacks fromthe case studies addressed here. From our work, the proton paralleltemperature remains the same inside and outside of the largest switch-backs but previous work at 1 au (Woodham et al. 2020) suggests thatthe temperature anisotropy and parallel temperature of the protoncore depend on the magnetic field cone angle. Future work shouldaddress this using the SPAN instruments to determine whether theproton parallel temperature is the same inside intermediate velocityswitchbacks.Further work could also include a similar analysis for proton beamsand alphas, but instrument limitations may make this study diffi-cult. Instead, combining the data from the ion electrostatic anal-yser (SPAN) with that of SPC will allow a more comprehensive,3-dimensional distribution function to be constructed. With a 3-dimensional distribution, temperature anisotropies of each species,for example, could be investigated in-depth. Solar Orbiter’s recentlaunch presents the possibility of comparing measurements fromboth spacecraft. This will be especially helpful if the two spacecraftare connected to the same solar source region and may allow theradial and latitudinal evolution of the plasma to be studied in detail. MNRAS000
0, that transport the most wave en-ergy radially outwards. This behaviour is what was expected frompurely geometrical considerations about the motional electric field E = − v × B . We conclude that there is no obvious link betweenkinetic energy enhancement and radial Poynting flux in the largestswitchbacks.As a word of caution, in order to exploit the capabilities of the SPCsensor we could only investigate the largest switchbacks. As such,we cannot make general assumptions about all switchbacks fromthe case studies addressed here. From our work, the proton paralleltemperature remains the same inside and outside of the largest switch-backs but previous work at 1 au (Woodham et al. 2020) suggests thatthe temperature anisotropy and parallel temperature of the protoncore depend on the magnetic field cone angle. Future work shouldaddress this using the SPAN instruments to determine whether theproton parallel temperature is the same inside intermediate velocityswitchbacks.Further work could also include a similar analysis for proton beamsand alphas, but instrument limitations may make this study diffi-cult. Instead, combining the data from the ion electrostatic anal-yser (SPAN) with that of SPC will allow a more comprehensive,3-dimensional distribution function to be constructed. With a 3-dimensional distribution, temperature anisotropies of each species,for example, could be investigated in-depth. Solar Orbiter’s recentlaunch presents the possibility of comparing measurements fromboth spacecraft. This will be especially helpful if the two spacecraftare connected to the same solar source region and may allow theradial and latitudinal evolution of the plasma to be studied in detail. MNRAS000 , 1–9 (2020)
T. Woolley et al.
ACKNOWLEDGEMENTS
TW was supported by STFC grant ST/N504336/1, TSH by STFCST/S000364/1, RL by an Imperial College President’s scholarshipand LDW by ST/S000364/1. SDB acknowledges the support of theLeverhulme Trust Visiting Professor program. The SWEAP Teamacknowledges support from NASA contract NNN06AA01C. KGKwas supported by NASA grant 80NSSC19K0912.
DATA AVAILABILITY
The data used in this research is all publicly available at: https://cdaweb.gsfc.nasa.gov/index.html/
REFERENCES
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Switchback times for cases presented in Fig. 6.
APPENDIX A: SWITCHBACK TIMES
The times of the switchbacks in Sect. 5.2 are summarised below.
This paper has been typeset from a TEX/L A TEX file prepared by the author. MNRAS000