On the Radial and Longitudinal Variation of a Magnetic Cloud: ACE, Wind, ARTEMIS and Juno Observations
aa r X i v : . [ phy s i c s . s p ace - ph ] S e p On the Radial and Longitudinal Variation of a Magnetic Cloud:ACE, Wind, ARTEMIS and Juno Observations
E.E. Davies ∗ , R.J. Forsyth , S.W. Good , and E.K.J. Kilpua The Blackett Laboratory, Imperial College London, London, UK Department of Physics, University of Helsinki, Helsinki, Finland
Accepted for publication in
Solar Physics : 12 September 2020
Abstract
We present observations of the same magnetic cloud made near Earth by the Advance Composi-tion Explorer (ACE), Wind, and the Acceleration, Reconnection, Turbulence and Electrodynam-ics of the Moon’s Interaction with the Sun (ARTEMIS) mission comprising the Time Historyof Events and Macroscale Interactions during Substorms (THEMIS) B and THEMIS C space-craft, and later by Juno at a distance of 1.2 AU. The spacecraft were close to radial alignmentthroughout the event, with a longitudinal separation of 3 . ◦ between Juno and the spacecraftnear Earth. The magnetic cloud likely originated from a filament eruption on 22 October 2011at 00:05 UT, and caused a strong geomagnetic storm at Earth commencing on 24 October. Ob-servations of the magnetic cloud at each spacecraft have been analysed using Minimum VarianceAnalysis and two flux rope fitting models, Lundquist and Gold-Hoyle, to give the orientation ofthe flux rope axis. We explore the effect different trailing edge boundaries have on the results ofeach analysis method, and find a clear difference between the orientations of the flux rope axisat the near-Earth spacecraft and Juno, independent of the analysis method. The axial magneticfield strength and the radial width of the flux rope are calculated using both observations andfitting parameters and their relationship with heliocentric distance is investigated. Differencesin results between the near-Earth spacecraft and Juno are attributed not only to the radial sep-aration, but to the small longitudinal separation which resulted in a surprisingly large differencein the in situ observations between the spacecraft. This case study demonstrates the utility ofJuno cruise data as a new opportunity to study magnetic clouds beyond 1 AU, and the need forcaution in future radial alignment studies. Keywords:
Coronal Mass Ejections, Interplanetary; Magnetic Clouds; Multi-spacecraft Obser-vations; Radial Evolution; Longitudinal Variation; Juno.
Interplanetary coronal mass ejections (ICMEs: e.g. Kilpua, Koskinen, and Pulkkinen, 2017) arelarge scale structures of plasma and magnetic field that are driven from the solar atmosphere andpropagate through the heliosphere. These transient structures are distinguished from the ambientsolar wind in situ by features that may include an enhanced magnetic field, low plasma β , decliningvelocity profile and decreased proton and electron temperature amongst many other possible features(e.g. Zurbuchen and Richardson, 2006). ICMEs with a strong and sustained southward magneticfield component are known to be the main drivers of strong geomagnetic activity at Earth (Gonzalez ∗ Corresponding author email: [email protected] et al. , 2007;Eastwood, 2008; Kilpua et al. , 2017) and therefore their evolution is of great interest in spaceweather forecasting.Magnetic clouds are a subset of ICMEs which feature signatures including an enhanced magneticfield, smooth rotation of the magnetic field vector, low plasma β and a drop in proton temperature(Burlaga et al. , 1981). Magnetic clouds exhibit well structured magnetic fields consistent with force-free flux ropes (Goldstein, 1983) which comprise nested helical magnetic field lines wound arounda central axis. The proportion of ICMEs that can be identified as magnetic clouds is on average ≈
30% (Gosling, 1990), but this varies with the solar cycle: at solar minimum, 60% of ICMEs can beidentified as magnetic clouds, whereas at solar maximum, this falls to 15% (Cane and Richardson,2003).To understand the evolution of ICMEs as they move out in the solar wind, it is useful to tracksignatures of specific events over different heliocentric distances. There are unfortunately a verylimited amount of cases where multiple spacecraft that are at different heliospheric distances, butnear radially aligned, have encountered the same ICME. Studies that describe such encounters toanalyse ICME evolution include Burlaga et al. (1981), Cane, Richardson, and Wibberenz (1997),Bothmer and Schwenn (1997), Liu et al. (2008), M¨ostl et al. (2009a), M¨ostl et al. (2009b), Rouillard et al. (2010), Farrugia et al. (2011), Nakwacki et al. (2011), Kilpua et al. (2011), Nieves-Chinchilla et al. (2012), Ruffenach et al. (2012), Nieves-Chinchilla et al. (2013), Good et al. (2015)). Therehas been a number of case studies (Winslow et al. , 2016; Good et al. , 2018; Kilpua et al. , 2019;Lugaz, Winslow, and Farrugia, 2019) and statistical studies (Good et al. , 2019; Vrˇsnak et al. , 2019;Salman, Winslow, and Lugaz, 2020) that have greatly expanded the number of analysed events inrecent times.The studies mentioned above have primarily used spacecraft at or within 1 AU. Radial align-ment studies of ICMEs beyond Earth are particularly rare. One such study by Mulligan et al. (1999) compared four ICME events observed by the Near Earth Asteroid Rendezvous (NEAR) andWind spacecraft, with radial separations between 0.18 and 0.63 AU and longitudinal separationsbetween 1.2 and 33.4 ◦ . However, with the introduction of more spacecraft into the solar wind inrecent years, including planetary mission spacecraft during their cruise phase and/or outside oftheir respective planetary environments, there have been more opportunities for radial alignmentsbetween spacecraft and at larger heliospheric distances. The NASA Juno mission was launched inAugust 2011 with the science goals of exploring the origin and evolution of Jupiter (Bolton et al. ,2017). Juno cruise data, namely the magnetic field measured by the fluxgate magnetometer (MAG)between 2011 and 2016, provides a new opportunity to study ICME evolution beyond 1 AU, and isa key resource in understanding the chain of evolution of ICMEs through the heliosphere.We present observations and analysis of an ICME with a clear magnetic cloud structure regis-tered during 24 - 26 October 2011 by the Advance Composition Explorer (ACE), Wind, and theAcceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with theSun (ARTEMIS) mission in the near-Earth environment, and Juno at a heliocentric distance of 1.24AU shortly after commencing its cruise phase to Jupiter. The near-Earth spacecraft and Juno wereseparated longitudinally by a maximum angle of just 3.6 ◦ , with a maximum separation in latitudeof only 0.1 ◦ . This ICME is of particular interest as it caused the strongest geomagnetic storm atEarth in 2011, peaking at a Dst of -147 nT, driven by the southward magnetic fields preceding themagnetic cloud rather than the magnetic cloud itself where the magnetic fields were northward.In this study we use observations from the multiple near-Earth spacecraft to provide severalindependent fits indicating the degree of variability of the fits along different trajectories throughthe ICME, and also to determine the direction of propagation of structures such as the ICME shockusing the timing at each spacecraft, as discussed in Section 4. The performance of the force-free2n the Radial and Longitudinal Variation of a Magnetic Cloudfitting models is compared and explored for the different trailing edge boundaries chosen. Previousstudies investigating model performance and the importance of flux rope boundary selection includeRiley et al. (2004), Dasso et al. (2006), Al-Haddad et al. (2013, 2018), Janvier et al. (2015). The fluxrope orientations and other kinematic properties of the ICME resulting from the fitting techniquesin this study are compared between the near-Earth spacecraft and Juno to analyse the evolution ofthe ICME. In situ observations made by the ACE, Wind, ARTEMIS, and Juno spacecraft are presented. BothACE and Wind are NASA spacecraft that orbit the L1 Lagrangian point, upstream of the Earth.Wind was launched in November 1994, three years prior to ACE in August 1997. The ARTEMISspacecraft comprise the Time History of Events and Macroscale Interactions during Substorms(THEMIS) B and THEMIS C spacecraft, two of the five THEMIS spacecraft launched in February2007, and moved to a lunar orbit in 2010. The Juno mission was launched in August 2011 withthe purpose of studying the magnetosphere and atmosphere of Jupiter, and reached Jupiter in July2016. The five year cruise phase to 5 AU presents a new opportunity to study ICMEs beyond 1AU.The spacecraft positions of ACE, Wind, and ARTEMIS (denoted as ‘Near-Earth’), the SolarTerrestrial Relations Observatory (STEREO)-A, STEREO-B, and Juno on 25 October 2011 at00:00 UT are shown in Figure 1, using Heliocentric Aries Ecliptic (HAE) coordinates. Figure1 demonstrates that Juno and the near-Earth spacecraft were in near radial alignment, with amaximum longitudinal separation of just 3.6 ◦ . The near-Earth spacecraft configuration itself has amaximum radial separation of < .
01 AU and a maximum longitudinal separation of < . ◦ .To identify the ICME in situ near Earth, we use measurements of the magnetic field taken bythe magnetometers onboard ACE (Magnetic Field Experiment, MAG: Smith et al. , 1998), Wind(Magnetic Field Investigation, MFI: Lepping et al. , 1995), and the ARTEMIS mission (FluxgateMagnetometer, FGM: Auster et al. , 2008). Measurements of the solar wind plasma were usedat ACE (Solar Wind Electron Proton Alpha Monitor, SWEPAM: McComas et al. , 1998), Wind(Solar Wind Experiment, SWE: Ogilvie et al. , 1995) and ARTEMIS (Electrostatic Analyzer, ESA:McFadden et al. , 2008) to aid in the identification of the ICME in the near-Earth environment.To identify the ICME at Juno, only measurements of the magnetic field were used (MagneticField Experiment, MAG: Connerney et al. , 2017), as the plasma experiment onboard Juno was notturned on in October 2011 (it was first turned on during the final month of approach to Jupiter forcalibration).Figure 2 presents the magnetic field (1 minute resolution) and plasma (1 minute 38 secondresolution) signatures observed at Wind. These observations are very similar in the large-scaleto those at ACE and both ARTEMIS spacecraft (in situ signatures observed by these spacecraftcan be found in the electronic supplementary material: Figures 7, 8 and 9), and are thereforerepresentative of the near-Earth environment. The structure delineated by the dotted vertical linesdisplays features associated with an ICME such as the enhancement of the magnetic field (panel a),declining radial speed profile (panel e), and the decrease in both proton temperature (panel g) anddensity (panel h), which distinguish it from the ambient solar wind. A shock (vertical dashed line)driven by the ICME was observed at Wind at 17:40 UT on 24 October 2011. Table 1 lists the shockarrival time, t S , at each of the near-Earth spacecraft and the heliocentric distance, r H , at whichthe spacecraft were located, which are used in Section 4.1 to infer the propagation direction of theshock. Figure 2 also displays the magnetic field components in radial tangential normal (RTN)3.E. Davies et al. -1 -0.5 0 0.5 1 X [AU] -1-0.500.51 Y [ A U ] I C M E P r opaga t i on D i r e c t i on X [AU] Y [ A U ] Near-Earth
STEREO-B JunoNear-EarthSTEREO-A
WindACE THEMIS B THEMIS C
Figure 1:
Location of the near-Earth spacecraft (ACE, Wind, and ARTEMIS), Juno, STEREO-A andSTEREO-B on 25 October 2011 at 00:00 UT in Heliocentric Aries Ecliptic (HAE) coordinates. Imagersonboard the STEREO spacecraft can be used to estimate the initial propagation direction and extent of theICME, represented by the black arrow and dotted lines, respectively (for details, see Section 3). The near-Earth spacecraft are in near radial alignment with Juno, with a small maximum longitudinal separation of3.6 ◦ . The inset shows a close up of the configuration of the near-Earth spacecraft: ACE (red), Wind (blue),THEMIS B (green) and THEMIS C (magenta). The near-Earth spacecraft configuration has a maximumradial separation of < .
01 AU and a maximum longitudinal separation of < . ◦ . coordinates (panel b), the angle of the magnetic field vector to the R-T plane, θ (panel c), andthe angle of the magnetic field vector swept out anticlockwise from the Sun-Earth line, projectedonto the R-T plane, φ (panel d). The ICME meets the criteria detailed by Burlaga et al. (1981)to classify magnetic clouds: a strong enhancement of the magnetic field, smooth rotation of themagnetic field components, a low variance of the magnetic field, and low proton temperature anddensity.Identifying the leading and trailing edges of the magnetic cloud flux rope can often be subjectiveand features are not always coincident (e.g. see discussion in Richardson and Cane, 2010; Kilpua et al. , 2013). In the case of this event, we identify two possible trailing edges: the first coincides withthe earliest significant drop in magnetic field strength and a slight increase in proton temperatureand density, the second coincides with the end of both the smooth magnetic field rotation and thedeclining radial speed profile. The leading edge of the flux rope is easier to identify, marking thestart of the magnetic field enhancement, smooth rotation of the magnetic field, and the steadydecline in radial speed. There is also a short substructure featured by a dip in the magnetic fieldmagnitude (approximately 10 minutes in duration) at the leading edge of the ejecta observed ateach spacecraft. Such substructures are generally reported at the leading edges of magnetic cloudsand are thus a solid indicator of the boundary (Wei et al. , 2003). These substructures can resultfrom the interaction between the magnetic cloud and the preceding solar wind, or be relics of theCME release process at the Sun (Farrugia et al. , 2001; Kilpua et al. , 2013).We define the sheath of the ICME as the region between the shock front and the lead-ing edge of the flux rope. In Figure 2, the sheath region displays a variable and fluctu-ating magnetic field structure at Wind, followed by a region of low variance which begins4n the Radial and Longitudinal Variation of a Magnetic Cloudat approximately 22:00 UT. This region of low variance is also observed across each of thenear-Earth spacecraft and coincides with a change in electron pitch angle signature at ACE(not shown; available at ) where two oppositely directed strahls appear at both 0 ◦ and 180 ◦ pitchangles, meaning that counterstreaming electrons are present, a feature often indicative of closedmagnetic field lines associated with an ICME (Gosling, 1990). The onset of the counterstreamingelectron flows, which extend through the flux rope, indicates the true start of the ICME (but notthe flux rope itself), and is coincident with the fall of the proton temperature.The radial component of the proton velocity in Figure 2 displays a declining speed profile from527 kms − to 455 or 425 kms − , trailing edge boundary dependent, during this period indicatingthe expansion of the magnetic cloud. Following the flux rope, there is a steep increase in the radialcomponent of the velocity to 540 kms − , and clear velocity deflections in the transverse and normaldirections of -93 and 100 kms − , respectively. This feature is observed by each of the near-Earthspacecraft and is also reflected in the magnetic field data by a compressed region of magnetic fieldfollowing the later trailing edge boundary, preceding features consistent with a reverse shock. Itis possible that the compressed magnetic field region was the result of a weak ICME following theevent as the magnetic field has a low variance and temperature, or a consequence of a transientcoronal hole opened by the CME related to the magnetic cloud (Luhmann et al. , 1998). The dip inmagnetic field at the later trailing edge of the flux rope is in magnetic and thermal pressure balance(not shown), indicating that this is likely the true ICME boundary. Previous studies have alsodefined the trailing edge to be this later boundary (Lepping et al. , 2015; Wood et al. , 2017), whilstNieves-Chinchilla et al. (2019) define the ICME as a complex structure and extend the boundaryto the end of the region of increased radial velocity. It is probable that the cause of the ambiguityin trailing edge selection is due to the solar wind following the magnetic cloud having led to acompression and heating of the trailing part of the flux rope that moved the temperature increaseforward into the flux rope, affecting observed features until the earlier trailing edge defined.Figure 3 presents the magnetic field (1 minute resolution) signatures observed by Juno, inthe same format as Figure 2. The structure observed is very similar to that of Figure 2, withan enhanced magnetic field (delineated by the vertical dotted lines) and similar behaviour of themagnetic field components during this enhancement, which display a clear flux rope structure. Ashock front is registered by Juno at a heliocentric distance of 1.24 AU on 25 October at 14:23 UT,less than a day later than the shock at Wind. Assuming a constant velocity and radial propagation,the timing of the shock front between Wind and Juno gives an average velocity of 518 kms − ,in reasonable agreement with the observed shock velocity of 489 kms − at Wind. Much of thesheath magnetic field is lower in magnitude in the Juno observations except for an initial increasebehind the shock front in comparison to observations at Wind, and the low variance region isharder to distinguish. The duration of the sheath is longer at Juno than at Wind, suggestingthat it has expanded as the ICME has propagated, although the difference could also be due tospatial variation at different measurement locations (Kilpua, Koskinen, and Pulkkinen, 2017). Themean magnetic field enhancement within the flux rope is 19.7/18.9 nT (depending on trailing edgedefinition) at Juno in comparison to 22.4/21.5 nT at Wind. The format of ‘earlier/later trailingedge’ is used to present dependent values throughout. The mean magnetic field values at eachspacecraft are summarised in Table 1. The magnitude profiles, however, follow different trends: atWind the magnitude slowly increases between the leading and earlier trailing edge, whereas theprofile at Juno decreases slightly over the same boundaries. For faster ICMEs, the magnetic fieldprofiles are often asymmetric, with a larger magnetic field strength at the front of the flux ropethan the back (Janvier et al. , 2019), as we observe at Juno. This can be considered as an effect ofthe time difference in observations between the leading and trailing edges of the flux rope where,5.E. Davies et al. | B | , n T -30-1501530 B R T N , n T B R B T B N -90-4504590 WIND090180270360350400450500550 V R , k m s - -1000100 V T N , k m s - V T V N V T H E R M , k m s - Oct 24 Oct 25 Oct 26 Oct 27
Date P r o t on , c m - a)b)c)d)e)f)g)h) Figure 2:
In situ magnetic field (1 minute resolution) and plasma (1 minute 38 second resolution) signaturesobserved by Wind. The vertical dashed line indicates the shock and the vertical dotted lines indicate theboundaries of the flux rope, with two possible trailing edge locations. The respective panels display a) thetotal magnetic field, b) the components of the magnetic field in RTN coordinates (the radial component isshown in red, the transverse component in green, and the normal component in blue), c) the calculated θ ,and d) φ angles of the magnetic field, e) the radial proton speed, f) the transverse and normal componentsof the proton velocity, g) the thermal proton velocity, and h) proton density.
6n the Radial and Longitudinal Variation of a Magnetic Cloud | B | , n T -30-1501530 B R T N , n T B R B T B N -90-4504590 JUNOOct 25 Oct 26 Oct 27 Oct 28 Date
Figure 3:
In situ magnetic field (1 minute resolution) signatures observed by Juno displayed in the sameformat as Figure 2. et al. (2018) found in a study of 298ICMEs with well structured magnetic topologies that 22% of positively expanding structures hadcompression at the back of the flux rope, and suggested that this could be an effect of the curvatureof the passing structure. The observations at Wind show a declining radial speed profile, andtherefore a positive expansion of the flux rope. We suggest in this case that the increasing magneticfield profile at Wind is likely a product of magnetic field compression due to the increased radialspeed of the solar wind following the flux rope. However, this compression is not observed at Junoand therefore, a more typical magnetic field profile is observed. The difference in the magnetic fieldcomponents within the flux rope boundaries between Wind and Juno can be seen by comparingFigures 2 and 3: the normal component is similar in profile yet differs in value between the twoheliocentric distances changing from negative (south) to positive (north) at Juno but remainingnorth at Wind, while the radial component shows more significant dissimilarities. The transversecomponent is the only component to remain of a similar shape and magnitude between Wind andJuno. The field angles are also interesting, as although very similar in profile, we note that thediscontinuity in φ occurs later within the rope at Juno than at Wind relative to the trailing edgesof the flux rope. By studying the magnetic field components and how they evolve throughout theflux rope, we can obtain a sense of handedness. Using the classification system following Bothmerand Schwenn (1997) and Mulligan, Russell, and Luhmann (1998), the flux rope can be classified aseither SEN at Juno, or ENW at Wind. SEN means that at the leading edge of the flux rope thefield points to the south, then rotates to point east at the axis and finally rotates to north at thetrailing edge. Similarly for the ENW classification, the leading edge points to the east, rotates topoint north at the axis, and finally rotates to point west at the trailing edge. Both classifications areleft-handed. The consistency of the handedness is supporting evidence that the spacecraft observedthe same event, as the handedness of a flux rope remains the same as it propagates (Marubashi et al. , 2015). Following the flux rope, the clear drop in field magnitude observed by Wind is notpresent in the Juno observations, although there is a region of modestly enhanced but decliningmagnitude. This decrease is smoother at Juno implying expansion after the trailing edge, althoughthis may again be due to a difference in measurement location.The arrival times of the shock front, t S , and the flux rope leading, t L , and trailing edges, t T and t T , observed at each spacecraft are presented in rows 2–5 of Table 1. The difference betweenthe earlier/later trailing edge times and the leading edge time is consistent with the expansion ofthe flux rope as its duration is observed to be 12 hours and 14 minutes/13 hours and 53 minutesat Wind and 12 hours and 56 minutes/14 hours and 47 minutes when observed at Juno. However,the difference in duration may also occur due to the different spacecraft trajectories through theICME and the potentially different ICME propagation speeds at each spacecraft. The observedradial velocities at each boundary, v L and v T , are presented in rows 7 and 8 of Table 1, wherethere are two values for v T as the parameter is dependent on the trailing edge used. The leadingand trailing edge velocities are consistent for each of the near-Earth spacecraft. Row 9 of Table1 presents the expansion velocity, v E , calculated as half of the difference between the trailing andleading edge velocities. The mean expansion velocity, h v E i , is presented in row 11 of Table 1. Ittakes into account the timings and heliocentric distance between the leading and trailing edges ateach of the near-Earth spacecraft and Juno to give the mean propagation speed of the leading andtrailing edges. h v E i is calculated as half the difference between these speeds. The mean expansionvelocity between Wind and Juno was found to be 4.8/5.1 kms − ; much smaller than the observedexpansion velocity at Wind of 36/51 kms − . This indicates a slowing of the expansion velocity asthe ICME propagates. 8n the Radial and Longitudinal Variation of a Magnetic Cloud Wind ACE THEMIS B THEMIS C Juno r H [AU] 0.984 0.985 0.992 0.993 1.24 t S (2011) Oct 24 17:40 UT Oct 24 17:48 UT Oct 24 18:43 UT Oct 24 18:44 UT Oct 25 14:23 UT t L (2011) Oct 25 00:28 UT Oct 25 00:35 UT Oct 25 01:12 UT Oct 25 01:12 UT Oct 26 00:40 UT t T (2011) Oct 25 12:34 UT Oct 25 12:42 UT Oct 25 13:23 UT Oct 25 13:23 UT Oct 26 13:36 UT t T (2011) Oct 25 14:21 UT Oct 25 14:21 UT Oct 25 15:04 UT Oct 25 15:04 UT Oct 26 15:27 UT v S [kms − ] 487 475 486 484 - v L [kms − ] 527 494 485 496 - v T [kms − ] 455/425 442/426 440/414 451/415 - v E [kms − ] 36/51 26/34 22/36 43/41 - v c [kms − ] 472/468 462/458 449/442 443/440 - h v E i [kms − ] 4.8/5.1 4.7/6.1 4.1/5.2 4.1/5.1 - h v c i [kms − ] 490/476 468/460 463/449 473/455 - D [AU] 0.137/0.156 0.135/0.152 0.132/0.148 0.130/0.147 0.147/0.164 B max [nT] 26.7 25.0 26.9 25.4 21.0 h B i [nT] 22.4/21.5 22.7/21.8 23.0/22.1 22.8/22.0 19.7/18.9 Table 1:
Shock and flux rope parameters of the ICME observed at each spacecraft, including the heliocentricdistance of the spacecraft ( r H ) and the times at which the shock front, leading and trailing edges were observed( t S , t L , t T , t T , respectively). Shock front ( v S ), leading edge ( v L ), trailing ( v T ), expansion ( v E ), and cruisevelocities ( v c ) have been calculated for the near-Earth spacecraft where plasma data is available. The meanexpansion ( h v E i ) and cruise ( h v c i ) velocities have been calculated considering the propagation times betweenthe near-Earth spacecraft and Juno. The observed radial width of the flux rope ( D ), and the maximum andmean magnetic field magnitudes observed inside the flux rope are given ( h B i and B max , respectively). Twovalues separated by ‘/’ are presented where changing between trailing edge times, t T and t T , affects theparameters. The observed radial width, D , can be calculated considering the cruise velocity of the flux ropeand the time taken for a spacecraft to traverse the flux rope: D = v c ( t T − t L ). Here, the cruisevelocity for each individual spacecraft is taken to be the solar wind velocity at the mid-point ofthe flux rope (Owens et al. , 2005) and is used as an approximation of the average propagationspeed of the magnetic cloud. The cruise velocity, v c , is noted in Table 1 for each of the near-Earthspacecraft. As there is no plasma data for Juno during this period, the mean cruise speed, h v c i , hasbeen calculated between each of the near-Earth spacecraft and Juno using timing considerationsof both leading and trailing edges observed. The mean of these values, 473.5/460.0 kms − , hasbeen taken as the cruise velocity used to calculate the radial width of the flux rope at Juno. Thecalculated radial widths are also given in row 13 of Table 1. The radial width of the flux rope wascalculated to be 0.137/0.156 AU at Wind and 0.147/0.164 AU at Juno, with associated errors ofapproximately ± .
004 AU. The calculated widths are less than the average width of a flux ropeat 1 AU of approximately 0.2 AU (Bothmer and Schwenn, 1997; Liu, Richardson, and Belcher,2005; Gulisano et al. , 2010). Using the boundary times defined and expansion velocities given byTable 1, one would expect an expansion of 0.019/0.024 AU between Wind and Juno, trailing edgedependent. We actually observe an expansion of the flux rope of 0.010/0.008 AU between Windand Juno which is less than expected. The calculation of observed radial width does not take intoaccount the orientation of the flux rope and therefore, is in real terms the length of the spacecrafttrajectory through the rope. The mean cruise velocity of the ICME at each near-Earth spacecraftwas also used as an approximate cruise velocity at Juno, and therefore it is perhaps unsurprisingthat the expected expansion is not observed.The maximum magnetic field strength within the flux rope, B max , and the mean magnetic9.E. Davies et al.field strength within the flux rope, h B i , are given in rows 14 and 15 in Table 1, respectively. Themean magnetic field magnitudes decrease between the near-Earth spacecraft and Juno as h B i ∝ r − . ± . H for both trailing edge times defined, where r H is heliocentric distance. We also find that B max ∝ r − . ± . H . Previous studies that derived the relationship between magnetic field strengthand heliocentric distance beyond 1 AU include Ebert et al. (2009) who found B ∝ r − . ± . H and Richardson (2014) who found B ∝ r − . ± . H . Both studies used magnetic field data fromUlysses between 1 and 5.4 AU and calculated the relationships using the mean magnetic field of theICMEs studied. The B max relationship is most similar to these relationships, with a slight overlapin associated errors. The disagreement with the mean magnetic field relationship derived in thisstudy is likely due to the differences in the magnetic fields along the different paths taken by thenear-Earth spacecraft and Juno through the flux rope. These longitudinal effects dominate over theexpected small change in the field intensity due to the radial separation of 0.24 AU. To give context to the in situ observations, we try to locate the solar counterpart of the investigatedmagnetic cloud. Using the leading edge speed of the ICME at Wind and assuming a constantpropagation speed from the Sun to L1, we find an estimated eruption time on 21 October, at19:15 UT. Two potential candidate CMEs are listed in the Coordinated Data Analysis Workshop(CDAW) Solar and Heliospheric Observatory (SOHO) Large Angle and Spectrometric Coronagraph(LASCO) CME catalogue ( https://cdaw.gsfc.nasa.gov/CME list/ ) around this time. These were firstobserved in the LASCO C2 telescope field of view at 01:25 UT and 10:24 UT on 22 October,with 2 nd -order speeds at 20 R s of 663 and 1074 kms − , respectively. Both CMEs were also seenby the coronagraphs onboard STEREO-A and STEREO-B. Using the STEREO CME AnalysisTool (StereoCAT; https://ccmc.gsfc.nasa.gov/stereocat/ ) we find that the apex of the first CMEhad an initial propagation direction of 25 ◦ longitude west of the Earth-Sun line and 50 ◦ latitudenorth of the solar ecliptic (SE) plane with a half-width of 46 ◦ . The later CME had an initialpropagation direction of 90 ◦ longitude and 52 ◦ latitude with a half-width of 55 ◦ . Based on theseinitial propagation directions, it is therefore likely that the source of the transient observed in situat Earth and Juno is the first CME listed, in agreement with the Wood et al. (2017) STEREOsurvey of ICMEs observed in situ at Earth.The identified CME is associated with a filament eruption, studied in detail by Gosain et al. (2016). The magnetic configuration of filaments is observed to be that of a flux rope (Guo et al.2010). The filament was located in the solar northern hemisphere indicating that the flux rope shouldlikely be left-handed (Rust, 1994), which is consistent with the ENW/SEN flux rope classificationsobserved in situ. The propagation direction of the filament eruption stabilised at approximately 15 ◦ longitude and 45 ◦ latitude (Gosain et al. , 2016), consistent with the ICME propagation directionfound using the STEREO CME Analysis Tool.To further confirm the solar CME counterpart of the in situ magnetic cloud, we com-pare the observed ICME arrival times with those predicted by the Propagation Tool developedat the Institute of Research in Astrophysics and Planetology (IRAP) (Rouillard et al. (2017); http://propagationtool.cdpp.eu/ ). Inputting values to the Propagation Tool recorded by the CDAWSOHO LASCO CME catalogue with a background solar wind speed observed in situ at Wind of 320kms − and an approximate drag parameter of 0.2 × − km − resulted in predicted arrival timesof the flux rope leading edge of 25 October 2011 06:34 UT at Wind and 26 October 2011 04:58UT at Juno. The drag parameter used was derived using solar wind and magnetic cloud densitiesin combination with the observed radial width of the flux rope at Wind as in Cargill (2004). The10n the Radial and Longitudinal Variation of a Magnetic Cloudpredicted times compare well with the observed leading edge arrival times of 25 October 2011 00:28UT and 26 October 00:40 UT at Wind and Juno, respectively.The source of the sudden increase in radial speed following the flux rope observed insitu by each of the near-Earth spacecraft remains inconclusive. Inspection of Solar Dynam-ics Observatory data (Atmospheric Imaging Assembly, AIA: Lemen et al. , 2011) shows a smallcoronal hole already present prior to the eruption, at a similar latitude close to the fila-ment channel from which the source of the magnetic cloud originated. An ENLIL simula-tion at https://iswa.gsfc.nasa.gov/downloads/20111022 072000 anim.tim-vel.gif shows a slight narrowstream of higher speed solar wind around the time of the event at Earth, but care must be takenwhether to trust such small features. The in situ data at Wind in Figure 2 shows a region of lowtemperature following the flux rope which could be evidence of a weak ICME following the event.Although there are no suitable CMEs listed in the CDAW SOHO LASCO CME catalogue, manyICMEs observed at Earth do not have clearly identifiable associated solar counterparts (Richardsonand Cane, 2010; Kilpua et al. , 2014). We use five methods to analyse the ICME. These include using: (i) timing considerations betweenthe near-Earth spacecraft to determine a direction of propagation of the ICME shock, minimumvariance analysis to estimate (ii) the propagation direction of the sheath region of the ICME ateach spacecraft and (iii) the orientation of the flux rope, and the (iv) Lundquist and (v) Gold-Hoyleforce-free flux rope fitting methods to provide independent determinations of the flux rope axisorientation and other parameters such as the axial magnetic field strength, impact parameter, andradial width scale value. Table 2 summarises the results of each method, and Figure 6 presents avisualisation of the calculated directions/orientations in terms of θ and φ for each analysis methodand trailing edge definition. Assuming a constant propagation velocity, V s , and a planar shock front, we use timing considerationsof the shock front between the four near-Earth spacecraft to calculate the normal direction, n s , andspeed of the shock, ν : ( R x − R ) · n s = ν · ∆ t x , (1a) V s = ν · n s , (1b)where R x − R is the position of a spacecraft (where x = 2 , ,
4) relative to the spacecraft at R , and ∆ t x is the difference in shock arrival times (M¨ostl et al. , 2012). The calculated shockpropagation direction is listed in Table 2 as θ p = − . ◦ with respect to the solar ecliptic (SE)plane and φ p = 11 . ◦ with respect to the Sun-Earth line, and has a propagation velocity of 514kms − . This direction is visually presented in the first row of Figure 6 (shown in red). The observedshock velocity at each near-Earth spacecraft is given in Table 1, the mean of which was calculatedto be 483 kms − . The calculated propagation velocity is therefore in reasonable agreement withobservations. Minimum variance analysis (MVA) has been performed on both the sheath region and flux rope.The technique involves calculating the eigenvectors and eigenvalues of a covariance matrix of the11.E. Davies et al.magnetic field components. When applied to a planar magnetic structure (PMS; as in Nakagawa,Nishida, and Saito, 1989; Neugebauer, Clay, and Gosling, 1993) of the sheath region, the minimumvariance eigenvector corresponds to the normal direction of the PMS (Paschmann and Daly, 1998).The normal to the PMS has been found to be in good agreement with the shock normal in sheathregions where the PMS is found close to the shock front (Palmerio, Kilpua, and Savani, 2016).When MVA is applied to a flux rope, the intermediate eigenvector corresponds to the direction ofthe flux rope axis (Goldstein, 1983).Table 2 summarises the results of the MVA, performed on the PMS within the sheath regionthat immediately follows the shock front and the flux rope, where θ a is the elevation angle out ofthe SE plane and φ a is the angle from the Sun-Earth line anticlockwise in the SE plane. Figure 6presents the orientations calculated by MVA in black. The mean normal direction to the sheathregion at the near-Earth spacecraft was calculated to be θ = − . ◦ and φ = 7 . ◦ . Comparing thecalculated sheath normal with the direction of propagation of θ = − . ◦ and φ = 11 . ◦ calculatedin Section 4.1, we find these to be consistent between the near-Earth spacecraft, shown in the firstrow of Figure 6. The sheath normal at Juno was calculated to be θ = − . ◦ and φ = 21 . ◦ andtherefore there is a mean change in direction of θ = 10 . ◦ away from the SE plane and φ = 13 . ◦ anticlockwise in the SE plane between the near-Earth spacecraft and Juno.The flux rope orientations obtained are well defined considering that the ratios of the maxi-mum eigenvalue, λ , and minimum eigenvalue, λ to the intermediate eigenvalue, λ (both alsosummarised in Table 2) meet the criteria defined by Siscoe and Suey (1972) of λ λ > .
37 and λ λ < .
72. The resulting flux rope orientations, given in Table 2 and presented in the secondand third rows of Figure 6, are consistent within errors at the near-Earth spacecraft, with a meanorientation of θ = 52 . / . ◦ and φ = 220 . / . ◦ and a standard deviation from the mean of θ = 7 . / . ◦ and φ = 11 . / . ◦ , where the first result is calculated using the earlier trailing edgetime and the second uses the later trailing edge time. The flux rope orientation at Juno was cal-culated to be θ = 23 . / . ◦ and φ = 290 . / . ◦ . Between the near-Earth spacecraft and Juno,the flux rope orientations display a clear mean change of θ = 28 . / . ◦ towards the SE plane and φ = 69 . / . ◦ anticlockwise in the SE plane. Although the calculated flux rope orientations atthe near-Earth spacecraft are more moderately-inclined than highly-inclined, they support the fluxrope classification of ENW at the near-Earth spacecraft and a lower-inclination flux rope of SENat Juno. MVA was also used as a starting point for the first force-free flux rope model fit to the magneticfield components, based on the Lundquist solutions (Lundquist, 1950): B r = 0 , (2a) B φ = B J ( αr ) , (2b) B z = B J ( αr ) . (2c)These solutions assume a force-free magnetic field with a constant α in a cylindrical configuration,where J and J are the zeroth and first order Bessel functions, B is the magnetic field strengthalong the axis, and r is the radial distance from the rope axis. The magnetic field solutions were fittedto the data of ACE, Wind, THEMIS B, THEMIS C, and Juno using a least squares procedure similarto that developed by Lepping, Jones, and Burlaga (1990) where the calculated MVA orientation12n the Radial and Longitudinal Variation of a Magnetic Cloudinitialises the χ minimisation; details of this technique are given in Good et al. (2019) and Kilpua et al. (2019).The other flux rope fitting method used considers the magnetic field to have a uniform twistacross the rope cross-section: a ‘Gold-Hoyle’ tube (Gold and Hoyle, 1960). There has been recentinterest (e.g. Hu et al. , 2014; Hu, Qiu, and Krucker, 2015; Wang et al. , 2016) in using the Gold-Hoylemodel to fit flux ropes in situ. This has been motivated by evidence (Kahler, Krucker, and Szabo,2011) indicating that field line lengths, as estimated from strahl electron travel times from the Sun,are too short to be consistent with the highly twisted (and hence very long) field lines in the outerlayers of a Lundquist flux rope. In the Gold-Hoyle model, the azimuthal and axial field componentsare given as: B φ = B τ r τ r , (3a) B z = B τ r , (3b)where B is the axial field strength, r is the radial distance from the rope axis, and τ is the anglea field line rotates about the axis from the leading edge of the flux rope to the trailing edge. TheGold-Hoyle rope is therefore very different to the Lundquist rope, in which the field-line twist is ata minimum at the rope axis and infinite at the rope boundaries.Figures 4 and 5 present the Lundquist (dashed line) and Gold-Hoyle (solid line) fits to themagnetic field data of the flux rope using both the earlier trailing edge boundary (left-hand side)and the later trailing edge (right-hand side) at Wind and Juno, respectively. The fitting at ACE,THEMIS B and C is presented as electronic supplementary material (Figures 10, 11, and 12). Visualinspection of Figure 4 shows that both models fit the magnetic field data to a good approximation.The main difference between the two models can be seen to be in how they represent the weakestradial component. The goodness of fit of the Lundquist model fits at Wind is marginally better thanthe Gold-Hoyle model using the earlier trailing edge, but is more similar using the later trailing edge.At Juno, Figure 5 shows that the Lundquist and Gold-Hoyle model fits are of a comparatively similargoodness using the later trailing edge, similar to those at Wind. At Juno, the largest difference inthe fits arises when using the earlier trailing edge boundary - we find that the Gold-Hoyle model fitsmuch better to the magnetic field data than the Lundquist model using this boundary. Looking atthe large scale rope structure, inspection of the model fits shows that the two models follow similarpatterns across both spacecraft and both trailing edges. The exception to this pattern is seen inthe Lundquist fitting at Wind where the weakest radial component of the field is of opposite signfor the different trailing edge times.Both force-free fitting methods allow for estimates to be made of various global cloud propertiessuch as the axial field strength, B , its radial width, D ′ , the normalised closest approach distanceof the spacecraft to the flux rope axis known as the impact parameter, p , and the flux rope axisorientation.Table 2 also summarises the results of the force-free fitting. Both the Lundquist and Gold-Hoyle fitting methods show that the rope is consistently left-handed ( H = −
1) at the near-Earthspacecraft and Juno. Figure 6 presents the flux rope orientations calculated using the earlier trailingedge (second row) and the later trailing edge (third row). The Lundquist fitting gives a mean fluxrope orientation of θ = 27 . / . ◦ and φ = 214 . / . ◦ at the near-Earth spacecraft and anorientation of θ = 12 . / . ◦ and φ = 309 . / . ◦ at Juno. The Gold-Hoyle fitting gives a meanorientation of θ = 45 . / . ◦ and φ = 271 . / . ◦ at the near-Earth spacecraft and an orientationof θ = 18 . / . ◦ and φ = 278 . / . ◦ at Juno. The Lundquist and Gold-Hoyle fits at eachspacecraft meet the χ and δ error requirements for reasonably accurate fits (see Good et al. ,13.E. Davies et al. -30-1501530 B R T N , n T -30-1501530 B R B T B N -90-4504590 -90-4504590Oct 25, 00:00 Oct 25, 12:00 Date
Date
WIND | B | , n T t T1 t T2 LundquistGold-Hoyle
Figure 4:
Force-free flux rope models fitted to the in situ magnetic field signatures observed by Wind,displayed in a similar format as Figure 2. The Lundquist model (dashed line) and Gold-Hoyle model (solidline) fitting is shown using both the earlier trailing edge (left-hand side) and the later trailing edge (right-handside).
14n the Radial and Longitudinal Variation of a Magnetic Cloud -30-1501530 B R T N , n T -90-4504590Oct 26, 00:00 Oct 26, 12:00 Date | B | , n T t T1 t T2 LundquistGold-Hoyle -30-1501530 B R B T B N -90-4504590Oct 26, 00:00 Oct 26, 12:00 Date
JUNO
Figure 5:
Force-free flux rope models fitted to the in situ magnetic field signatures observed by Juno,displayed in the same format as Figure 4. -900 90
Near-Earth -900 90
Near-Earth -900 90
Juno -900 90
Juno Near-EarthNear-Earth F R O r i en t a t i on , t T S hea t h / S ho ck N o r m a l F R O r i en t a t i on , t T Juno
MVALundquistGold-Hoyle
Juno
MVALundquistGold-Hoyle -900 90
Near-Earth -900 90
Juno Near-Earth Juno
Multi-SCMVA ( ° ) ( ° ) Figure 6:
Calculated orientations presented in RTN coordinates, where θ is the angle to the R-T plane, and φ is the angle swept out anticlockwise from the Sun-Earth line, projected onto the R-T plane ( φ = 180 ◦ pointsSunwards). θ is presented for the near-Earth spacecraft and Juno in the first column, and φ is presented forthe near-Earth spacecraft and Juno in the second column. The normal directions to the sheath calculatedusing MVA (black) and the propagation direction of the shock calculated using timing considerations betweenthe near-Earth spacecraft (red) are presented in the first row. The flux rope orientations calculated by MVA(black), Lundquist (blue), and Gold-Hoyle fitting (orange) using the earlier trailing edge are presented in thesecond row, and in the third row using the later trailing edge. ≈ ◦ and ≈ ◦ in θ and φ , respectively. The χ values are listed in Table 2 and show comparable trends to those observed by visual inspection ofthe fitting: the Lundquist model fits at Juno are comparatively worse than at Wind using the latertrailing edge but are of similar goodness of fit using the earlier trailing edge, whereas the Gold-Hoylemodel fits at Juno are comparatively better than at Wind using the earlier trailing edge, but similarusing the later trailing edge. The force-free fitting orientations at the near-Earth spacecraft are alsoin reasonable agreement with those found in previous studies for the same ICME that used Winddata; Lepping et al. (2015) found that θ = 40 ◦ and φ = 291 ◦ and Wood et al. (2017) found that θ = 45 ◦ and φ = 286 ◦ . The flux rope orientations and left-handedness are supported by the fluxrope classifications observed in Section 2 (ENW at the near-Earth spacecraft and SEN at Juno).16 n t h e R a d i a l a nd L o n g i t ud i n a l V a r i a t i o n o f a M ag n e t i c C l o ud Table 2:
The results of the analysis performed at each spacecraft, organised by method. Multi-spacecraft timing considerations at the near-Earthspacecraft determine a propagation direction of the ICME shock front. MVA has been applied to both the sheath to determine the normal directionto the sheath, and the flux rope to determine the flux rope axis orientation. The flux rope axis orientation is also determined by the force-free fittingmethods (Lundquist and Gold-Hoyle). Both force-free flux rope fitting methods give estimates of the axial magnetic field strength, B , handedness, H , impact parameter, p , minimised chi-squared, χ , and modelled radial width, D ′ . AnalysisMethod Parameter Wind ACE THEMIS B THEMIS C JunoMulti-S/C Shock propagation direction θ p = -9.4 ◦ - φ p = 11.0 ◦ -MVA Sheath normal direction θ s = -11.4 ◦ θ s = -15.3 ◦ θ s = -10.2 ◦ θ s = -10.5 ◦ θ s = -22.4 ◦ φ s = 4.8 ◦ φ s = 1.1 ◦ φ s = 11.6 ◦ φ s = 12.0 ◦ φ s = 21.0 ◦ FR axis orientation θ a = 46.4 ◦ /70.1 ◦ θ a = 62.3 ◦ /75.4 ◦ θ a = 48.7 ◦ /66.7 ◦ θ a = 52.0 ◦ /67.6 ◦ θ a = 23.7 ◦ /49.9 ◦ φ a = 207.1 ◦ / 251.5 ◦ φ a = 232.8 ◦ /245.3 ◦ φ a = 216.1 ◦ /240.3 ◦ φ a = 224.9 ◦ /246.2 ◦ φ a = 290.1 ◦ /317.3 ◦ FR eigenvalue ratios, λ λ , λ λ θ a = 25.8 ◦ /38.9 ◦ θ a = 28.5 ◦ /43.0 ◦ θ a = 26.9 ◦ /37.5 ◦ θ a = 27.3 ◦ /38.5 ◦ θ a = 12.5 ◦ /16.2 ◦ φ a = 213.1 ◦ /322.3 ◦ φ a = 215.7 ◦ /324.0 ◦ φ a = 212.1 ◦ /323.5 ◦ φ a = 218.2 ◦ /319.4 ◦ φ a = 309.6 ◦ /307.1 ◦ Axial field strength, B [nT] 30.8/27.9 30.8/28.3 32.0/29.0 30.8/28.3 23.4/23.5Handedness, H -1/-1 -1/-1 -1/-1 -1/-1 -1/-1Impact parameter, p χ D ′ [AU] 0.102/0.131 0.107/0.131 0.100/0.121 0.104/0.125 0.115/0.136Gold-Hoyle FR axis orientation θ a = 44.1 ◦ /54.2 ◦ θ a = 50.9 ◦ /60.4 ◦ θ a = 44.6 ◦ /53.8 ◦ θ a = 44.1 ◦ /53.3 ◦ θ a = 18.2 ◦ /29.3 ◦ φ a = 270.9 ◦ /272.3 ◦ φ a = 270.5 ◦ /271.9 ◦ φ a = 271.5 ◦ /273.0 ◦ φ a = 271.5 ◦ /272.9 ◦ φ a = 278.6 ◦ /278.8 ◦ Axial field strength, B [nT] 25.3/26.3 25.8/26.8 26.2/27.2 25.8/26.8 21.6/23.0Handedness, H -1/-1 -1/-1 -1/-1 -1/-1 -1/-1Impact parameter, p χ D ′ [AU] 0.137/0.156 0.135/0.152 0.132/0.148 0.130/0.147 0.148/0.164 .E. Davies et al.Comparing the flux rope axis orientations for each of the force-free flux rope fitting methodsand those calculated using MVA, we find:i. MVA results in the highest inclination to the SE plane for both flux rope trailing edges, with amean θ = 52 . / . ◦ for the near-Earth spacecraft. This is in comparison to θ = 27 . / . ◦ forthe Lundquist model, and θ = 45 . / . ◦ for the Gold-Hoyle model. Comparing φ angles at thenear-Earth spacecraft, we find that the mean φ = 220 . / . ◦ for MVA, φ = 214 . / . ◦ for the Lundquist model, and φ = 271 . / . ◦ for the Gold-Hoyle model. Note that theLundquist model results in the highest and lowest mean value of φ given the different trailingedge times.ii. Comparing the results for each method at the near-Earth spacecraft to Juno, we find thatthe flux rope orientation differs by θ = 28 . / . ◦ , 14 . / . ◦ , and 27 . / . ◦ towards the SEplane, and φ = 69 . / . ◦ , 94 . / − . ◦ , 7 . / . ◦ anticlockwise in the SE plane, for MVA,Lundquist and Gold-Hoyle models, respectively. The overall trend in flux rope orientationbetween the near-Earth spacecraft and Juno is demonstrated clearly in Figure 6 by comparingthe subplots of each panel: the orientation is closer to the SE plane at Juno, and rotatesanticlockwise between the near-Earth spacecraft and Juno. The difference in θ exceeds the ≈ ◦ uncertainty found by Lepping, Berdichevsky, and Ferguson (2003) in the orientationfor all methods/trailing edges. However, this is not the case for each φ angle where just MVAand the earlier Lundquist value exceed the ≈ ◦ uncertainty. The difference in orientationtowards the SE plane is quite significant over a relatively small radial separation. As discussedin Section 3, the source of the faster solar wind following the event is unclear, but perhaps mayhave had an effect on the change in flux rope orientation between the near-Earth spacecraftand Juno. Different parts of an ICME can also evolve in a different manner in the structuredsolar wind which could lead to differences in flux rope properties, such as orientation, atspacecraft separated in longitude (e.g. Savani et al. , 2010; Owens, Lockwood, and Barnard,2017). However, over the small longitudinal and radial separation in this case, such differenceswould not be expected to be large.iii. Changing between the two trailing edge times (comparing the second and third rows of Figure6) produces the largest difference in θ with MVA - an average difference of 17.6 ◦ , compared to12.4 ◦ and 9.5 ◦ using the Lundquist and Gold-Hoyle models, respectively. However, the largestdifference in the φ angle is produced by the Lundquist model - 107.5 ◦ compared to 25.6 ◦ forMVA, and 1.4 ◦ for the Gold-Hoyle model. For these cases, the Gold-Hoyle model is leastaffected by the change in trailing edge time defined for the flux rope, whereas the Lundquistmodel is more sensitive to this, especially in the resulting fit to the radial component ofthe magnetic field. A previous study by D´emoulin, Dasso, and Janvier (2018) explores thesensitivity of flux rope orientation with changing flux rope boundaries for MVA and finds thatsimilarly, the boundaries defined strongly affect the resulting flux rope orientation.iv. Considering the uncertainty in the orientations at the near-Earth spacecraft, the Lundquistmodel is the least variant in results for θ , with a standard deviation of 1.1/2.4 ◦ in comparisonto 7.0/3.9 ◦ for MVA, and 3.3/3.3 ◦ for Gold-Hoyle. However, the Gold-Hoyle model is the leastvariant in results for φ , with a standard deviation of 0.5/0.5 ◦ , compared with 11.1/4.6 ◦ forMVA, and 2.7/2.1 ◦ for Lundquist. This is clearly demonstrated by the spread of orientationsin Figure 6. Overall, MVA produces the widest spread in results for the near-Earth spacecraft,with the force-free fitting models performing similarly.v. The difference between mean results at the near-Earth spacecraft across methods showsthat for θ , the Gold-Hoyle model results are most similar to MVA, with a mean difference18n the Radial and Longitudinal Variation of a Magnetic Cloudof 6 . / . ◦ . This is in comparison with Lundquist and MVA with a mean difference of25 . / . ◦ , and Lundquist and Gold-Hoyle with a mean difference of 18 . / . ◦ . The φ angleis more dependent on the trailing edge time, where the difference between MVA and Lundquistis 5 . / . ◦ , MVA and Gold-Hoyle is 50 . / . ◦ , and Lundquist and Gold-Hoyle is 56 . / . ◦ .The closer to the axis a spacecraft crosses the flux rope, the more reliable the estimated MVA axisorientation and calculated force-free fitting parameters have been found to be (Klein and Burlaga,1982; Bothmer and Schwenn, 1997; Farrugia et al. , 1999; Xiao et al. , 2004; Gulisano et al. , 2005,2007; Ruffenach et al. , 2012, 2015). Investigating the impact parameters at each spacecraft, wefind that the Lundquist model suggests that Juno passes through the flux rope closer to the centralaxis than any of the near-Earth spacecraft (at Juno, p = 0 . / . p = 0 . / . p = 0 . / .
139 at Juno and the mean p = 0 . / .
028 at the near-Earth spacecraft). Comparing fitting methods, the impact parametersare most similar for Juno, with more of a contrast between values for the near-Earth spacecraft.The two fitting methods give very different impact parameters due to the magnetic field geometry:the Lundquist p values are higher than the Gold-Hoyle values because an intermediate- p Lundquistflux rope encounter, in which the field is not observed to rotate by a full 180 ◦ between leading andtrailing edges, is similar to a low- p Gold-Hoyle rope encounter.If we consider the propagation of a perfectly cylindrical flux rope with a concentric sheathregion draped ahead of the flux rope, the sheath normal and the flux rope axis should ideallybe perpendicular to each other at each spacecraft. Comparing the flux rope axis orientations ofeach method/defined trailing edge to that of the normal direction to the sheath, we find the meanangle between these vectors for the near-Earth spacecraft as δ = 48 . / . ◦ , δ = 30 . / . ◦ , and δ = 77 . / . ◦ , with the MVA, Lundquist, and Gold-Hoyle methods, respectively. This angle canbe visualised by comparing the second and third rows of Figure 6 to the first. For the near-Earthspacecraft, we therefore find that the Gold-Hoyle model produced values closer to the ideal, andacross all methods, using the flux rope axis from fits with the later trailing edge produced resultsconsistently closer to the ideal than those using the earlier trailing edge. At Juno, δ = 80 . / . ◦ , δ = 78 . / . ◦ , and δ = 72 . / . ◦ for the MVA, Lundquist, and Gold-Hoyle methods, respectively.Overall, the values are closer to the ideal at Juno for each method/trailing edge time except for theGold-Hoyle model.The axial field strength estimated by the Lundquist model is consistently higher than thecorresponding value estimated by the Gold-Hoyle model: the Lundquist fitting gives the mean B = 31 . / . B = 23 . / . B = 25 . / . B = 21 . / . B ∝ r H − . ± . /r − . ± . H , and for the Gold-Hoyle results wefind B ∝ r − . ± . H /r − . ± . H . The earlier and later trailing edge Gold-Hoyle fit relationshipsand the later trailing edge Lundquist fit relationship are similar to the relationships derived usingin situ observations in Section 2. Interestingly, the relationship derived using the earlier trailingedge Lundquist fits is consistent with the previously mentioned relationships derived by Richard-son (2014) and Ebert et al. (2009) as the radial dependence may be quite different for B derivedfrom fits in comparison to the field parameters observed in situ. However, as previously discussed,disagreement between the relationships derived in this study with previous studies is likely due tothe small radial separation of 0.24 AU between spacecraft observations, and therefore the differencein longitude between observations and thus the different path taken by the spacecraft through the19.E. Davies et al.flux rope is likely to be the dominant effect.The observed radial width ( D ) does not take into account the orientation of the flux rope as itpasses the spacecraft, nor the impact parameter. To correct for this, a scale factor, estimated fromthe force-free fitting may be applied to the observed radial width to give an estimate of the true fluxrope width, D ′ . Hence D ′ = SD = Sv c ( t T − t L ), where S is the scale factor that can be less than,equal to, or greater than 1 and accounts for both the impact parameter and the rope orientation.The calculated modelled radial widths are listed in Table 2. For the Lundquist model, a scaling valueless than 1 is given to correct for the orientation of the flux rope at each spacecraft. The Lundquistfitting gives the mean D ′ = 0 . / .
127 AU at the near-Earth spacecraft, and D ′ = 0 . / . D ′ = 0 . / .
164 AU, in comparison to D = 0 . / . D ′ = D = 0 . / .
151 AU, likely due to the flux rope orientation lying close toperpendicular with the radial direction ( φ = 271.1/272.5 ◦ ) and the small impact parameter, andtherefore little adjustment is necessary for the spacecraft path length through the flux rope. Themodelled radial widths are similarly consistent between the near-Earth spacecraft, and show thatthere was very little expansion over the short distance between Earth and Juno for both modelsand trailing edges. The difference in modelled radial width between Wind and Juno is 0.013/0.005AU for the Lundquist model and 0.011/0.008 for Gold-Hoyle. These values are consistent with thedifference in observed radial width, and are less than the expected 0.019/0.024 AU calculated inSection 2. An ICME that caused a strong geomagnetic storm at Earth commencing on 24 October 2011 wasobserved in situ by ACE, Wind, ARTEMIS, and Juno. The geomagnetic storm was the strongestrecorded in 2011, with a minimum Dst of -147 nT at its peak. The ICME displayed a clear magneticflux rope structure which has been analysed using two fitting models, Lundquist and Gold-Hoyle,and MVA.Due to the positioning of the spacecraft in the near-Earth environment, ACE, Wind, and thetwo ARTEMIS spacecraft, THEMIS B and THEMIS C, have been used to perform multi-spacecraftanalysis in conjunction with Juno which had recently commenced its cruise phase to Jupiter andwas therefore close to radial alignment with the near-Earth spacecraft, longitudinally separated byonly 3.6 ◦ throughout the event. During this time, the radial separation between Juno and the near-Earth spacecraft was 0.24 AU. Cases where spacecraft are separated by such radial distances andlongitudinal separations are rare, and therefore these observations have allowed for an interestinganalysis of the evolution of a magnetic cloud and evaluation of whether radial or longitudinal effectsdominate.We find that the overall magnetic field magnitude profiles, as well as the behaviour of themagnetic field components, are similar between the investigated spacecraft. However, we have alsofound that observations made in situ between the near-Earth spacecraft and Juno display somesignificant differences, despite the small longitudinal separation between the spacecraft; e.g. weobserve a sudden increase in radial speed of the solar wind following the flux rope at the near-Earth spacecraft but not at Juno. These differences can arise from evolution in time and/or fromlongitudinal separation, although Juno and Earth are relatively close to each other both radiallyand longitudinally. Significant differences have previously also been reported in ICME flux rope20n the Radial and Longitudinal Variation of a Magnetic Cloudproperties over relatively small longitudinal separations of only a few degrees (Kilpua et al. , 2011;Winslow et al. , 2016). Lugaz et al. (2018) recently reported considerable differences in the magneticfield components for a magnetic cloud they observed near the Earth orbit where spacecraft were only0.01 AU apart. Studies based on more widely separated (several degrees in longitude) spacecrafthave reported highly different flux rope orientations, suggesting this to be a local rather than globalparameter (e.g. Savani et al. , 2010; Farrugia et al. , 2011; M¨ostl et al. , 2012).The flux rope orientation differs between the near-Earth spacecraft and Juno by θ = 28 . / . ◦ ,14 . / . ◦ , and 27 . / . ◦ (dependent on earlier/later trailing edge) towards the SE plane, and φ = 69 . / . ◦ , 94 . / − . ◦ , 7 . / . ◦ anticlockwise in the SE plane, for MVA, Lundquist and Gold-Hoyle models, respectively. The orientation of the flux rope axis has been shown to have a cleardifference in θ despite the relatively small spacecraft separations, irrespective of analysis methodor trailing edge defined. However, the difference in φ only exceeds uncertainties in orientation forthe MVA values and the earlier trailing edge value for the Lundquist method. We propose thatthe difference in flux rope orientation is not necessarily just due to the radial evolution of theICME, but more so due to the longitudinal separation of the spacecraft, despite this being small.This ambiguity, inherent to the localised nature of in situ measurements, has been a clear featureof previous alignment studies up to 1 AU; we note in agreement with a more limited number ofprevious studies (e.g. Mulligan et al. , 1999) that this ambiguity must also be taken into account whenanalysing ICMEs beyond 1 AU. Winslow et al. (2016) found that in situ observations of an ICMEbetween the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER)spacecraft and STEREO-A were significantly affected due to interactions between the ICME and aheliospheric plasma sheet/current sheet, despite a small longitudinal separation of just 3 ◦ . Similarly,in this study we note that differences between in situ observations may have arisen due to the suddenincrease in solar wind speed following the flux rope observed at the near-Earth spacecraft but notat Juno, the source of which remains unclear.Comparing the force-free fitting models, both the Lundquist and Gold-Hoyle methods givebroadly similar axis directions that are consistent with the ENW/SEN flux rope classifications.At the near-Earth spacecraft, there is a mean difference of θ = 18 . / . ◦ and φ = 56 . / . ◦ between the fitting methods. The Lundquist model is least variant in θ , with a standard deviationof 1 . / . ◦ in comparison to 3 . / . ◦ for Gold-Hoyle. However, the Gold-Hoyle model is the leastvariant in φ , with a standard deviation of 0 . / . ◦ , compared with 2 . / . ◦ for Lundquist. Despitethe difference in results, the similar standard deviations and visual inspection of the fitting at thenear-Earth spacecraft show that overall, both force-free fitting models performed similarly, and givecomparatively good fits to the data.As discussed in Sections 2 and 4, relationships found between the observed mean and maximumfield strengths and axial field strengths given by the force-free fitting with heliocentric distancewere mostly in disagreement with the relationships found in previous studies at distances greaterthan 1 AU (Ebert et al. , 2009; Richardson, 2014). The disagreement is likely the result of usingobservations/parameters calculated for five spacecraft over a relatively short radial separation of0.24 AU, whereas the previous studies used a large number of events observed between 1 and 5.4AU, thus differences in magnetic field due to the small longitudinal separation dominate.In conclusion, this case study demonstrates that Juno cruise data is a potentially valuableresource for studies, including multi-spacecraft studies, of the evolution of ICME magnetic fieldsbetween 1 and 5 AU, and further demonstrates that caution should be exercised in radial alignmentstudies. The presence of increased solar wind speed following the event at Wind but not at Junoshows that even small longitudinal separations of a few degrees between spacecraft can still resultin significantly different observations and event properties.21.E. Davies et al. Acknowledgements
We have benefited from the availability of ACE, Wind, ARTEMIS, Juno, SDO, andSTEREO data, and thus would like to thank the instrument teams and the PDS:PPI and SPDF CDAWeb dataarchives for their distribution of data. We are very grateful to the referee for the insightful and constructive com-ments that helped to improve the manuscript. E.D. would also like to thank Lucie Green and Mathew Owens for theuseful discussions regarding the solar sources and background solar wind, respectively. This research was supportedby funding from the STFC studentship ST/N504336/1 (E.D.). The work of E.K. and S.G. has received funding fromthe European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme(ERC-COG 724391). E.K. and S.G. acknowledges Academy of Finland project SMASH no. 310445. The results ofE.K. and S.G. presented here have been achieved under the framework of the Finnish Centre of Excellence in Research5 of Sustainable Space (FORESAIL; Academy of Finland grant numbers 312390), which we gratefully acknowledge.
Disclosure of Potential Conflicts of Interest
The authors declare that there are no conflicts of interest.
References
Al-Haddad, N., Nieves-Chinchilla, T., Savani, N.P., M¨ostl, C., Marubashi, K., Hidalgo, M.A., Roussev, I.I.,Poedts, S., Farrugia, C.J.: 2013, Magnetic field configuration models and reconstruction methods forinterplanetary coronal mass ejections.
Solar Phys. (1), 129.
DOI .Al-Haddad, N., Nieves-Chinchilla, T., Savani, N.P., Lugaz, N., Roussev, I.I.: 2018, Fitting and reconstructionof thirteen simple coronal mass ejections.
Solar Phys. (5), 73.
DOI .Auster, H.U., Glassmeier, K.H., Magnes, W., Aydogar, O., Baumjohann, W., Constantinescu, D., Fischer,D., Fornacon, K.H., Georgescu, E., Harvey, P., et al. : 2008, The THEMIS fluxgate magnetometer.
SpaceSci. Rev. (1-4), 235.
DOI .Bolton, S.J., Lunine, J., Stevenson, D., Connerney, J.E.P., Levin, S., Owen, T.C., Bagenal, F., Gautier,D., Ingersoll, A.P., Orton, G.S., Guillot, T., Hubbard, W., Bloxham, J., Coradini, A., Stephens, S.K.,Mokashi, P., Thorne, R., Thorpe, R.: 2017, The Juno Mission.
Space Sci. Rev. , 5.
DOI .Bothmer, V., Schwenn, R.: 1997, The structure and origin of magnetic clouds in the solar wind.
Ann.Geophys. (1), 1. DOI .Burlaga, L., Sittler, E., Mariani, F., Schwenn, R.: 1981, Magnetic loop behind an interplanetary shock:Voyager, Helios, and IMP 8 observations.
J. Geophys. Res. (A8), 6673. DOI .Cane, H.V., Richardson, I.G.: 2003, Interplanetary coronal mass ejections in the near-earth solar wind during1996–2002.
J. Geophys. Res. (A4).
DOI .Cane, H.V., Richardson, I.G., Wibberenz, G.: 1997, Helios 1 and 2 observations of particle decreases, ejecta,and magnetic clouds.
J. Geophys. Res. (A4), 7075.
DOI .Cargill, P.J.: 2004, On the aerodynamic drag force acting on interplanetary coronal mass ejections.
SolarPhys. (1), 135.
DOI .Connerney, J.E.P., Benn, M., Bjarno, J.B., Denver, T., Espley, J., Jorgensen, J.L., Jorgensen, P.S., Lawton,P., Malinnikova, A., Merayo, J.M., et al. : 2017, The Juno magnetic field investigation.
Space Sci. Rev. (1-4), 39.
DOI .Dasso, S., Mandrini, C.H., D´emoulin, P., Luoni, M.L.: 2006, A new model-independent method to computemagnetic helicity in magnetic clouds.
Astron. Astrophys. (1), 349.
DOI .D´emoulin, P., Dasso, S., Janvier, M.: 2018, Exploring the biases of a new method based on minimum variancefor interplanetary magnetic clouds.
Astron. Astrophys. , A139.
DOI .
22n the Radial and Longitudinal Variation of a Magnetic Cloud
Eastwood, J.P.: 2008, The science of space weather.
Phil. Trans. R. Soc. A. (1884), 4489.
DOI .Ebert, R.W., McComas, D.J., Elliott, H.A., Forsyth, R.J., Gosling, J.T.: 2009, Bulk properties of the slowand fast solar wind and interplanetary coronal mass ejections measured by Ulysses: Three polar orbits ofobservations.
J. Geophys. Res. (A1).
DOI .Echer, E., Gonzalez, W.D.: 2004, Geoeffectiveness of interplanetary shocks, magnetic clouds, sector boundarycrossings and their combined occurrence.
Geophys. Res. Lett. (9). DOI .Farrugia, C.J., Vasquez, B., Richardson, I.G., Torbert, R.B., Burlaga, L.F., Biernat, H.K., M¨uhlbachler, S.,Ogilvie, K.W., Lepping, R.P., Scudder, J.D., Berdichevsky, D.E., Semenov, V.S., Kubyshkin, I.V., Phan,T.-D., Lin, R.P.: 2001, A reconnection layer associated with a magnetic cloud.
Adv. Space Res. , 759. DOI .Farrugia, C.J., Berdichevsky, D.B., M¨ostl, C., Galvin, A.B., Leitner, M., Popecki, M.A., Simunac, K.D.C.,Opitz, A., Lavraud, B., Ogilvie, K.W., Veronig, A.M., Temmer, M., Luhmann, J.G., Sauvaud, J.A.: 2011,Multiple, distant (40 ◦ ) in situ observations of a magnetic cloud and a corotating interaction region complex. J. Atmos. Solar-Terr. Phys. , 1254. DOI .Farrugia, C.J., Janoo, L.A., Torbert, R.B., Quinn, J.M., Ogilvie, K.W., Lepping, R.P., Fitzenreiter, R.J.,Steinberg, J.T., Lazarus, A.J., Lin, R.P., et al. : 1999, A uniform-twist magnetic flux rope in the solarwind. In:
AIP Conference Proceedings , 745. AIP.
DOI .Gold, T., Hoyle, F.: 1960, On the origin of solar flares.
Mon. Not. R. Astron. Soc. (2), 89.
DOI .Goldstein, H.: 1983, On the field configuration in magnetic clouds.
Solar Wind Five, NASA
CP-2280 .Gonzalez, W.D., Tsurutani, B.T.: 1987, Criteria of interplanetary parameters causing intense magneticstorms (dst¡- 100 nt).
Planet. Space Sci. (9), 1101. DOI .Good, S.W., Forsyth, R.J., Raines, J.M., Gershman, D.J., Slavin, J.A., Zurbuchen, T.H.: 2015, Radialevolution of a magnetic cloud: MESSENGER, STEREO, and Venus Express observations.
Astrophys. J. (2), 177.
DOI .Good, S.W., Forsyth, R.J., Eastwood, J.P., M¨ostl, C.: 2018, Correlation of ICME magnetic fields at radiallyaligned spacecraft.
Solar Phys. (3), 52.
DOI .Good, S.W., Kilpua, E.K.J., LaMoury, A.T., Forsyth, R.J., Eastwood, J.P., M¨ostl, C.: 2019, Self-Similarityof ICME Flux Ropes: Observations by Radially Aligned Spacecraft in the Inner Heliosphere.
J. Geophys.Res. (7), 4960.
DOI .Gosain, S., Filippov, B., Maurya, R.A., Chandra, R.: 2016, Interrupted eruption of large quiescent filamentassociated with a halo CME.
Astrophys. J. (2), 85.
DOI .Gosling, J.T.: 1990, Coronal mass ejections and magnetic flux ropes in interplanetary space.
Physics ofmagnetic flux ropes , 343.
DOI .Gulisano, A.M., Dasso, S., Mandrini, C.H., D´emoulin, P.: 2005, Magnetic clouds: A statistical study ofmagnetic helicity.
J. Atmos. Solar-Terr. Phys. (17-18), 1761. DOI .Gulisano, A.M., Dasso, S., Mandrini, C.H., D´emoulin, P.: 2007, Estimation of the bias of the minimumvariance technique in the determination of magnetic clouds global quantities and orientation.
Adv. SpaceRes. (12), 1881. DOI .Gulisano, A.M., D´emoulin, P., Dasso, S., Ruiz, M.E., Marsch, E.: 2010, Global and local expansion ofmagnetic clouds in the inner heliosphere.
Astron. Astrophys. , A39.
DOI .Hu, Q., Qiu, J., Krucker, S.: 2015, Magnetic field line lengths inside interplanetary magnetic flux ropes.
J.Geophys. Res. (7), 5266.
DOI . Hu, Q., Qiu, J., Dasgupta, B., Khare, A., Webb, G.M.: 2014, Structures of interplanetary magnetic fluxropes and comparison with their solar sources.
Astrophys. J. (1), 53.
DOI .Janvier, M., Dasso, S., D´emoulin, P., Mas´ıas-Meza, J.J., Lugaz, N.: 2015, Comparing generic models forinterplanetary shocks and magnetic clouds axis configurations at 1 au.
J. Geophys. Res. (5), 3328.
DOI .Janvier, M., Winslow, R.M., Good, S.W., Bonhomme, E., D´emoulin, P., Dasso, S., M¨ostl, C., Lugaz, N.,Amerstorfer, T., Soubri´e, E., et al. : 2019, Generic magnetic field intensity profiles of interplanetary coronalmass ejections at Mercury, Venus, and Earth from superposed epoch analyses.
J. Geophys. Res. (2),812.
DOI .Kahler, S.W., Krucker, S., Szabo, A.: 2011, Solar energetic electron probes of magnetic cloud field linelengths.
J. Geophys. Res. (A1).
DOI .Kilpua, E.K.J., Koskinen, H.E.J., Pulkkinen, T.I.: 2017, Coronal mass ejections and their sheath regions ininterplanetary space.
Living Rev. Solar Phys. (1), 5. DOI .Kilpua, E.K.J., Isavnin, A., Vourlidas, A., Koskinen, H.E.J., Rodriguez, L.: 2013, On the relationship betweeninterplanetary coronal mass ejections and magnetic clouds.
Ann. Geophys. , 1251. DOI .Kilpua, E.K.J., Jian, L.K., Li, Y., Luhmann, J.G., Russell, C.T.: 2011, Multipoint ICME encounters: Pre-STEREO and STEREO observations.
J. Atmos. Solar-Terr. Phys. (10), 1228. DOI .Kilpua, E.K.J., Mierla, M., Zhukov, A.N., Rodriguez, L., Vourlidas, A., Wood, B.: 2014, Solar sources ofinterplanetary coronal mass ejections during the solar cycle 23/24 minimum.
Solar Phys. (10), 3773.
DOI .Kilpua, E.K.J., Balogh, A., von Steiger, R., Liu, Y.D.: 2017, Geoeffective Properties of Solar Transients andStream Interaction Regions.
Space Sci. Rev. , 1271.
DOI .Kilpua, E.K.J., Good, S.W., Palmerio, E., Asvestari, E., Lumme, E., Ala-Lahti, M., Kalliokoski, M.M.H.,Morosan, D.E., Pomoell, J., Price, D.J., Magdaleni´c, J., Poedts, S., Futaana, Y.: 2019, Multipoint Obser-vations of the June 2012 Interacting Interplanetary Flux Ropes.
Front. Astron. Space Sci. , 50. DOI .Klein, L.W., Burlaga, L.F.: 1982, Interplanetary magnetic clouds at 1 AU.
J. Geophys. Res. (A2), 613. DOI .Lemen, J., Title, A., Boerner, P., Chou, C., Drake, J., Duncan, D., Edwards, C., Friedlaender, F., Heyman,G., Hurlburt, N., Katz, N., Kushner, G., Levay, M., Lindgren, R., Mathur, D., McFeaters, E., Mitchell,S., Rehse, R., Waltham, N.: 2011, The Atmospheric Imaging Assembly (AIA) on the Solar DynamicsObservatory (SDO).
Solar Phys. , 17.
DOI .Lepping, R.P., Berdichevsky, D.B., Ferguson, T.J.: 2003, Estimated errors in magnetic cloud model fitparameters with force-free cylindrically symmetric assumptions.
J. Geophys. Res. (A10).
DOI .Lepping, R.P., Jones, J.A., Burlaga, L.F.: 1990, Magnetic field structure of interplanetary magnetic cloudsat 1 AU.
J. Geophys. Res. (A8), 11957. DOI .Lepping, R.P., Ac˜una, M.H., Burlaga, L.F., Farrell, W.M., Slavin, J.A., Schatten, K.H., Mariani, F., Ness,N.F., Neubauer, F.M., Whang, Y.C., et al. : 1995, The WIND magnetic field investigation.
Space Sci.Rev. (1-4), 207. DOI .Lepping, R.P., Wu, C.-C., Berdichevsky, D.B., Szabo, A.: 2015, Wind magnetic clouds for 2010–2012: Modelparameter fittings, associated shock waves, and comparisons to earlier periods.
Solar Phys. (8), 2265.
DOI .Liu, Y., Richardson, J.D., Belcher, J.W.: 2005, A statistical study of the properties of interplanetary coronalmass ejections from 0.3 to 5.4 AU.
Planet. Space Sci. (1-3), 3. DOI .
24n the Radial and Longitudinal Variation of a Magnetic Cloud
Liu, Y., Luhmann, J.G., Huttunen, K.E.J., Lin, R.P., Bale, S.D., Russell, C.T., Galvin, A.B.: 2008, Recon-struction of the 2007 May 22 magnetic cloud: How much can we trust the flux-rope geometry of CMEs?
Astrophys. J. Lett. (2), L133.
DOI .Lugaz, N., Winslow, R.M., Farrugia, C.J.: 2019, Evolution of a Long-Duration Coronal Mass Ejection andits Sheath Region Between Mercury and Earth on 2013 July 9-14.
J. Geophys. Res. (1), e27213.
DOI .Lugaz, N., Farrugia, C.J., Winslow, R.M., Al-Haddad, N., Galvin, A.B., Nieves-Chinchilla, T., Lee, C.O.,Janvier, M.: 2018, On the Spatial Coherence of Magnetic Ejecta: Measurements of Coronal Mass Ejectionsby Multiple Spacecraft Longitudinally Separated by 0.01 AU.
Astrophys. J. Lett. , L7.
DOI .Luhmann, J.G., Gosling, J.T., Hoeksema, J.T., Zhao, X.: 1998, The relationship between large-scale solarmagnetic field evolution and coronal mass ejections.
J. Geophys. Res. (A4), 6585.
DOI .Lundquist, S.: 1950, Magneto-hydrostatic fields.
Ark. Fys. , 361.Marubashi, K., Akiyama, S., Yashiro, S., Gopalswamy, N., Cho, K.-S., Park, Y.-D.: 2015, Geometricalrelationship between interplanetary flux ropes and their solar sources. Solar Phys. (5), 1371.
DOI .McComas, D.J., Bame, S.J., Barker, P., Feldman, W.C., Phillips, J.L., Riley, P., Griffee, J.W.: 1998, SolarWind Electron Proton Alpha Monitor (SWEPAM) for the Advanced Composition Explorer.
Space Sci.Rev. , 563. DOI .McFadden, J.P., Carlson, C.W., Larson, D., Ludlam, M., Abiad, R., Elliott, B., Turin, P., Marckwordt, M.,Angelopoulos, V.: 2008, The THEMIS ESA plasma instrument and in-flight calibration.
Space Sci. Rev. (1-4), 277.
DOI .M¨ostl, C., Farrugia, C.J., Temmer, M., Miklenic, C., Veronig, A.M., Galvin, A.B., Leitner, M., Biernat, H.K.:2009a, Linking remote imagery of a coronal mass ejection to its in situ signatures at 1 AU.
Astrophys. J.Lett. (2), L180.
DOI .M¨ostl, C., Farrugia, C.J., Biernat, H.K., Leitner, M., Kilpua, E.K.J., Galvin, A.B., Luhmann, J.G.: 2009b,Optimized Grad–Shafranov reconstruction of a magnetic cloud using STEREO-Wind observations.
SolarPhys. (1-2), 427.
DOI .M¨ostl, C., Farrugia, C.J., Kilpua, E.K.J., Jian, L.K., Liu, Y., Eastwood, J.P., Harrison, R.A., Webb, D.F.,Temmer, M., Odstrcil, D., et al. : 2012, Multi-point shock and flux rope analysis of multiple interplanetarycoronal mass ejections around 2010 August 1 in the inner heliosphere.
Astrophys. J. (1), 10.
DOI .Mulligan, T., Russell, C.T., Luhmann, J.G.: 1998, Solar cycle evolution of the structure of magnetic cloudsin the inner heliosphere.
Geophys. Res. Lett. (15), 2959. DOI .Mulligan, T., Russell, C.T., Anderson, B.J., Lohr, D.A., Rust, D., Toth, B.A., Zanetti, L.J., Acuna, M.H.,Lepping, R.P., Gosling, J.T.: 1999, Intercomparison of NEAR and Wind interplanetary coronal massejection observations.
J. Geophys. Res. (A12), 28217.
DOI .Nakagawa, T., Nishida, A., Saito, T.: 1989, Planar magnetic structures in the solar wind.
J. Geophys. Res. (A9), 11761. DOI .Nakwacki, M.S., Dasso, S., D´emoulin, P., Mandrini, C.H., Gulisano, A.M.: 2011, Dynamical evolution of amagnetic cloud from the sun to 5.4 AU.
Astron. Astrophys. , A52.
DOI .Neugebauer, M., Clay, D.R., Gosling, J.T.: 1993, The origins of planar magnetic structures in the solar wind.
J. Geophys. Res. (A6), 9383. DOI .Nieves-Chinchilla, T., Colaninno, R., Vourlidas, A., Szabo, A., Lepping, R.P., Boardsen, S.A., Anderson,B.J., Korth, H.: 2012, Remote and in situ observations of an unusual earth-directed coronal mass ejectionfrom multiple viewpoints.
J. Geophys. Res. (A6).
DOI . Nieves-Chinchilla, T., Vourlidas, A., Stenborg, G., Savani, N.P., Koval, A., Szabo, A., Jian, L.K.: 2013,Inner heliospheric evolution of a “Stealth” CME derived from multi-view imaging and multipoint in situobservations. i. propagation to 1 AU.
Astrophys. J. (1), 55.
DOI .Nieves-Chinchilla, T., Vourlidas, A., Raymond, J.C., Linton, M.G., Al-Haddad, N., Savani, N.P., Szabo, A.,Hidalgo, M.A.: 2018, Understanding the internal magnetic field configurations of ICMEs using more than20 years of Wind observations.
Solar Phys. (2), 25.
DOI .Nieves-Chinchilla, T., Jian, L.K., Balmaceda, L., Vourlidas, A., dos Santos, L.F.G., Szabo, A.: 2019, Unrav-eling the Internal Magnetic Field Structure of the Earth-directed Interplanetary Coronal Mass EjectionsDuring 1995–2015.
Solar Phys. (7), 89.
DOI .Ogilvie, K.W., Chornay, D.J., Fritzenreiter, R.J., Hunsaker, F., Keller, J., Lobell, J., Miller, G., Scudder,J.D., Sittler, E.C., Torbert, R.B., et al. : 1995, SWE, a comprehensive plasma instrument for the Windspacecraft.
Space Sci. Rev. (1-4), 55. DOI .Owens, M.J., Lockwood, M., Barnard, L.A.: 2017, Coronal mass ejections are not coherent magnetohydro-dynamic structures.
Sci. Rep. , 4152. DOI .Owens, M.J., Cargill, P.J., Pagel, C., Siscoe, G.L., Crooker, N.U.: 2005, Characteristic magnetic field andspeed properties of interplanetary coronal mass ejections and their sheath regions.
J. Geophys. Res. (A1).
DOI .Palmerio, E., Kilpua, E.K.J., Savani, N.P.: 2016, Planar magnetic structures in coronal mass ejection-drivensheath regions.
Ann. Geophys. (2), 313. DOI .Paschmann, G., Daly, P.W.: 1998,
Analysis methods for multi-spacecraft data , ESA Publication Division,The International Space Science Institute, 185.Richardson, I.G.: 2014, Identification of interplanetary coronal mass ejections at ulysses using multiple solarwind signatures.
Solar Phys. (10), 3843.
DOI .Richardson, I.G., Cane, H.V.: 2010, Near-Earth Interplanetary Coronal Mass Ejections During Solar Cycle23 (1996–2009): Catalog and Summary of Properties.
Solar Phys. , 189.
DOI .Riley, P., Linker, J.A., Lionello, R., Miki´c, Z., Odstrcil, D., Hidalgo, M.A., Cid, C., Hu, Q., Lepping, R.P.,Lynch, B.J., et al. : 2004, Fitting flux ropes to a global mhd solution: A comparison of techniques.
J.Atmos. Solar-Terr. Phys. (15-16), 1321. DOI .Rouillard, A.P., Lavraud, B., Sheeley, N.R., Davies, J.A., Burlaga, L.F., Savani, N.P., Jacquey, C., Forsyth,R.J.: 2010, White light and in situ comparison of a forming merged interaction region.
Astrophys. J. (2), 1385.
DOI .Rouillard, A.P., Lavraud, B., Genot, V., Bouchemit, M., Dufourg, N., Plotnikov, I., Pinto, R.F., Sanchez-Diaz, E., Lavarra, M., Penou, M., et al. : 2017, A propagation tool to connect remote-sensing observationswith in-situ measurements of heliospheric structures.
Planet. Space Sci. , 61.
DOI .Ruffenach, A., Lavraud, B., Owens, M.J., Sauvaud, J.-A., Savani, N.P., Rouillard, A.P., D´emoulin, P.,Foullon, C., Opitz, A., Fedorov, A., et al. : 2012, Multispacecraft observation of magnetic cloud erosion bymagnetic reconnection during propagation.
J. Geophys. Res. (A9).
DOI .Ruffenach, A., Lavraud, B., Farrugia, C.J., D´emoulin, P., Dasso, S., Owens, M.J., Sauvaud, J.-A., Rouillard,A.P., Lynnyk, A., Foullon, C., et al. : 2015, Statistical study of magnetic cloud erosion by magneticreconnection.
J. Geophys. Res. (1), 43.
DOI .Rust, D.M.: 1994, Spawning and shedding helical magnetic fields in the solar atmosphere.
Geophys. Res.Lett. (4), 241. DOI .
26n the Radial and Longitudinal Variation of a Magnetic Cloud
Salman, T.M., Winslow, R.M., Lugaz, N.: 2020, Radial evolution of coronal mass ejections between messen-ger, venus express, stereo, and l1: Catalog and analysis.
J. Geophys. Res. (1).
DOI .Savani, N.P., Owens, M.J., Rouillard, A.P., Forsyth, R.J., Davies, J.A.: 2010, Observational Evidence of aCoronal Mass Ejection Distortion Directly Attributable to a Structured Solar Wind.
Astrophys. J. Lett. , L128.
DOI .Siscoe, G.L., Suey, R.W.: 1972, Significance criteria for variance matrix applications.
J. Geophys. Res. (7),1321. DOI .Smith, C.W., L’Heureux, J., Ness, N.F., Acuna, M.H., Burlaga, L.F., Scheifele, J.: 1998, The ACE magneticfields experiment.
Space Sci. Rev. , 613. DOI .Tsurutani, B.T., Gonzalez, W.D.: 1997, The interplanetary causes of magnetic storms: A review.
Magneticstorms , 77. DOI .Vrˇsnak, B., Amerstorfer, T., Dumbovi´c, M., Leitner, M., Veronig, A.M., Temmer, M., M¨ostl, C., Amerstorfer,U.V., Farrugia, C.J., Galvin, A.B.: 2019, Heliospheric Evolution of Magnetic Clouds.
Astrophys. J. (2),77.
DOI .Wang, Y., Zhuang, B., Hu, Q., Liu, R., Shen, C., Chi, Y.: 2016, On the twists of interplanetary magneticflux ropes observed at 1 AU.
J. Geophys. Res. (10), 9316.
DOI .Wei, F., Liu, R., Fan, Q., Feng, X.: 2003, Identification of the magnetic cloud boundary layers.
J. Geophys.Res. , 1263.
DOI .Winslow, R.M., Lugaz, N., Schwadron, N.A., Farrugia, C.J., Yu, W., Raines, J.M., Mays, M.L., Galvin, A.B.,Zurbuchen, T.H.: 2016, Longitudinal conjunction between MESSENGER and STEREO A: Developmentof ICME complexity through stream interactions.
J. Geophys. Res. (7), 6092.
DOI .Wood, B.E., Wu, C.-C., Lepping, R.P., Nieves-Chinchilla, T., Howard, R.A., Linton, M.G., Socker, D.G.:2017, A STEREO survey of magnetic cloud coronal mass ejections observed at Earth in 2008–2012.
As-trophys. J. Suppl. S. (2), 29.
DOI .Xiao, C.J., Pu, Z.Y., Ma, Z.W., Fu, S.Y., Huang, Z.Y., Zong, Q.G.: 2004, Inferring of flux rope orientationwith the minimum variance analysis technique.
J. Geophys. Res. (A11).
DOI .Zhang, J., Richardson, I.G., Webb, D.F., Gopalswamy, N., Huttunen, K.E.J., Kasper, J.C., Nitta, N.V.,Poomvises, W., Thompson, B.J., Wu, C.-C., Yashiro, S., Zhukov, A.N.: 2007, Solar and interplanetarysources of major geomagnetic storms (Dst ≤
100 nT) during 1996–2005.
J. Geophys. Res. (A10).
DOI .Zurbuchen, T.H., Richardson, I.G.: 2006, In-situ solar wind and magnetic field signatures of interplanetarycoronal mass ejections.
Space Sci. Rev. , 31.
DOI . Electronic Supplementary Material | B | , n T -30-1501530 B R T N , n T B R B T B N -90-4504590090180270360350400450500 V R , k m s - -1000100 V T N , k m s - V T V N Oct 24 Oct 25 Oct 26 Oct 27
Date V T H E R M , k m s - ACEa)b)c)d)e)f)g)
Figure 7:
In situ magnetic field (1 minute resolution) signatures observed by ACE displayed in the sameformat as Figure 2.
28n the Radial and Longitudinal Variation of a Magnetic Cloud | B | , n T -30-1501530 B R T N , n T B R B T B N -90-4504590090180270360300400500 V R , k m s - -1000100 V T N , k m s - V T V N V T H E R M , k m s - Oct 24 Oct 25 Oct 26 Oct 27
Date P r o t on , c m - b)a)c)d)e)f)g)h) THEMIS B Figure 8:
In situ magnetic field (1 minute resolution) signatures observed by THEMIS B displayed in thesame format as Figure 2. | B | , n T -30-1501530 B R T N , n T B R B T B N -90-4504590090180270360300400500 V R , k m s - -100-50050 V T N , k m s - V T V N V T H E R M , k m s - Oct 24 Oct 25 Oct 26 Oct 27
Date P r o t on , c m - a)b)c)d)e)f)g)h) THEMIS C Figure 9:
In situ magnetic field (1 minute resolution) signatures observed by THEMIS C displayed in thesame format as Figure 2.
30n the Radial and Longitudinal Variation of a Magnetic Cloud | B | , n T LundquistGold-Hoyle -30-1501530 B R T N , n T -30-1501530 B R B T B N -90-4504590 -90-4504590Oct 25, 00:00 Oct 25, 12:00 Date
Date
ACEt T1 t T2 Figure 10:
Force-free flux rope models fitted to the in situ magnetic field signatures observed by ACE,displayed in the same format as Figure 4. | B | , n T LundquistGold-Hoyle -30-1501530 B R T N , n T -30-1501530 B R B T B N -90-4504590 -90-4504590Oct 25, 00:00 Oct 25, 12:00 Date
Date
THEMIS Bt T1 t T2 Figure 11:
Force-free flux rope models fitted to the in situ magnetic field signatures observed by THEMISB, displayed in the same format as Figure 4.
32n the Radial and Longitudinal Variation of a Magnetic Cloud | B | , n T LundquistGold-Hoyle -30-1501530 B R T N , n T -30-1501530 B R B T B N -90-4504590 -90-4504590Oct 25, 00:00 Oct 25, 12:00 Date
Date
THEMIS Ct T1 t T2 Figure 12: