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E A R T H ’ S M A G N E T O S P H E R E E A R T H ’ S M A G N E T O S P H E R E Formed by the Low-Latitude Boundary Layer Second Edition WAYNE KEITH WALTER HEIKKILA AcademicPressisanimprintofElsevier 125LondonWall,LondonEC2Y5AS,UnitedKingdom 525BStreet,Suite1650,SanDiego,CA92101,UnitedStates 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom ©2021ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearance CenterandtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN978-0-12-818160-7 ForinformationonallAcademicPresspublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Coverimagecourtesy:C.J.Kale Publisher:CandiceJanco AcquisitionsEditor:AmyShapiro EditorialProjectManager:AndreaDulberger ProductionProjectManager:KumarAnbazhagan CoverDesigner:MilesHitchen TypesetbySPiGlobal,India Dedication To my ever-supportive family. My wife Melinda, daughters Amy and Ella,and myparents,Donald and Lanita Keith. Wayne Keith To Jeanine, my wife, and sons Eric and Richard, and my father € Kustaa Heikkila: Fromhis lonelyperch he let his mind roam the cosmos. Walter Heikkila Preface to the first edition The magnetosphere is the vast region of space magnetically connectedtotheEarthandresponsibleforthatmagnificentspec- tacle,thenorthernlights,theauroraborealis(northerndawn).In northernOntario,alongtimeago,Iwasimpressedwiththeraysof lightofvariouscolorsdancingandprancingalongeast-westarcs (cid:1) (see the frontispiece drawn for me by Shere Chamness). My mothersaidominouslythatwarwouldcome.Iwouldspendmost of my working life trying to find an explanation for this strange and intriguing phenomenon. Earth with its magnetic field is embedded in a high-velocity stream of plasma of solar origin, the solar wind. This situation can be viewed in two ways. First, it constitutes a variable input of plasma, momentum, and energy to the magnetosphere; by observationaltechniquesnowfirmlyinplace,wecanseethecon- sequencesforthisintricatesystem.Second,thesolarwindisone result of processes that operate on the Sun, especially in the corona.ThesearesomewhatdifferentthanintheEarth’smagne- tosphere, partly because of scale,but it is generally thought that the two are essentially alike. For solar research, we have some additionalobservationaltechniquesthatwecanusetoouradvan- tage; for one, we can look from afar to witness radiation of all kinds,includingplasmoids,leavingthesystem.Solarflares,coronal mass ejections, heating of coronal plasma, changes in magnetic topology, collisionless shock waves, and solar energetic particles areobserved. The magnetosphere is readily accessible for direct observations,evenexperimentstotestwhatistheresultofaknowninput; as such, it is a giant laboratory for solar and astrophysical processes.Herewehavetheauroras,bothquiescentandactive.With thelatter,wehaverapidparticleenergization,likesolarflares.We haveburstybulkflows,plasmoidsandfluxropes,andmuchmore. Itwouldbeeasytooverloadouraccountwithobservationalfacts, for they exist in profusion. Yet, despite half a century of space research, there is still no definitive conclusion about the rapid particle energization, about substorms,oreven the obvious correlation between geomagnetic activity and the solar wind parameters, including the orientation oftheinterplanetarymagneticfield(IMF).Theoreticalarguments xiii xiv Prefacetothefirstedition are complicated for many reasons. Thus, forexample, Phan et al. (1996, p.7827) concluded that “crucial questions about the inter- play between the upstream magnetosheath conditions and the structure and dynamics of the magnetopause boundary [remain] unanswered.” Although Baker et al. (1999) “concluded that the global magnetospheric substorm problem has now largely been solved …” they nevertheless noted that “fundamental issues remain toberesolved…Why,forexample,isthemagnetosphere stable most of the time, and why do substorms occur just when theydo?Whatallowstheviolationofthefrozen-fluxconstraintnec- essaryforanefficientenergyreleasebyreconnectioninthecourse ofsubstorms?”Morerecently,Donovan(2006)stated,“AtthisICS, we somehow managed to avoid debates that are fundamentally unresolvable,butstillconsiderthedominantparadigms.” Perhapsthemainshortcomingofallprevioussubstormtheo- riesistheirdifficultyofexplainingtheinitiallocalizationinspace, therapidityoftheonsetoftheexpansionphaseofthesubstorm. “Explainingthesuddenonsetoftheexpansionphaseofmagneto- spheric substorms has proved to be one of the most intractable problemsinmagnetosphericphysicstodate”(Vasyliunas,1998). One semantic difficulty is that the language in general use in space plasma physics comes in large part from analogies with fluid theory. It is highly suggestive; unfortunately, it often gives theimpressionofprovidinganexplanationwhenitcanbepartly, oreventotally,wrong.Birkhoff(1960)hasnotedthat“itiseasyfor mathematicianstobecomeconvincedthatrationalhydrodynam- ics is, in principle, infallible.” He concluded that the failures of fluidtheorycouldgenerallybelaidupontheuseofvariousplau- sible hypotheses, sometimes made explicitly, sometimes implic- itly, that arenot fullyappropriate. Itis arguablethat,in ourcase,the plausible hypothesisis the useoftheB,Vparadigm;herethemagneticfieldBandtheplasma velocity V are regarded as the primary independent variables (Parker,1996).Theplasmaisdescribedbyafluidtheory,bymag- (cid:1) netohydrodynamics (MHD) invented by Hannes Alfven (1950), andtheso-called principleoffrozen-fieldconvection.According tothat,ifwefollowthefluidinitiallyonthesurfaceSasitmoves throughthesystem,thefluxthroughthesurfacewillremaincon- stantevenasthesurfacechangesitslocationandshape.Further- more, the frozen-flux condition implies that all particles initially on a flux tube will remain along a single tube as they convect throughspace(Kivelson,1995).“Thekeypointhereisthatthepar- ticleandfluidpicturesgiveusequivalentanswers”(Hughes,1995). However,thatstatementisonlypartlytrue;theuseoftheB,V paradigm requires an equation of state to get a complete set of Prefacetothefirstedition xv equations so that the problem is well posed; that can, and does, lead to difficulties (Heikkila, 1997). An equation of state is local, bydefinition,whileglobalforcesbytheprincipleofsuperposition (suchasduetotheelectricfield)areimportantinaplasma.Even (cid:1) Alfven (1986) was opposed to this extreme use of MHD, without considering its limitations. The use of a different paradigm, the E,J paradigm where the electric field E and current density J are regarded as primary, is sometimes a necessity. Energization of plasma particles is due to anelectricfield,withaforceF¼qEactingonparticleswithacharge q.Incontrast,theforceduetoamagneticfieldistransversetothe particlemotion,andso,byavectoridentity,qV(cid:2)(V(cid:3)B)¼0:thepar- ticlesmovewithoutenergization.Thetwoparadigmsarenotequiv- alent; this can be forced through an equation of state but it has limitations of its own. I believe that the E,J paradigm is the key tosolvingthe“intractableproblemsinmagnetosphericphysics.” Theequivalenceofthetwoparadigmshasbeenquestionedfor some time. On the energization of particles within the plasma sheet Hines said: Ithasbeenshownthatenergizationofparticlesinthepresenceofan electricfieldandaninhomogeneousmagneticfieldmaybedescribed equivalentlybymeansofahydromagnetic–thermodynamicapproachor …aparticle-driftapproach,insofarasdriftstransversetothemagnetic fieldareconcerned,andifattentionisconfinedtodifferentialvariations [emphasisadded].Ifcollisionsmaintainanequipartitionoftheenergy amongstthethreetranslationalmodes,thenthisconclusioncanbe extendedtointegratedvariationsandtheonlyimportantdriftsarethose transversetothemagneticfield.…Theequivalencemightberestoredfor integratedvariationsifsuitabledefinitionsofthe‘energization’are introducedandsuitablelimitingcasesareconsidered,butingeneralthere seemstobelittleadvantageinthefurtherpursuitofthehydromagnetic– thermodynamicapproachwhenaprecisedescriptionisrequired.The particleapproachisthennecessaryforatleastsomeaspectsoftheproblem, anditmightaswellbeadoptedforall. Hines(1963) Thishasbeenrepeatedmanytimes(e.g.,Kivelson,1995,p.41), regrettablyto no avail.Schmidtexpressed itas follows: Itisratherfortunate,therefore,tohavefoundthatthesefictitious quantitiesobeysomequasi-hydrodynamicequations:anequationof continuityandanequationofmotion.Thisisaboutasfarastheanalogy canbestretched.Unfortunatelytheseequationsdonotsufficetoprovide solutionsforthegreatnumberofunknownquantities. Schmidt(1979,p.57) xvi Prefacetothefirstedition IwillnotgosofarasdidColinHines(mythenboss!);thereis muchworkbasedonMHDtheorythatistrulyworthwhile.Rather, mytaskwillbetoseparatethegoodfromthebad.Examplesofthe goodarethesearchforthedeHoffman-TellerframebySonnerup et al. (2004) and the MHD Gumics theory of Laitinen (2007). An example of the bad is the model used for reconnection (in two dimensions?),forexample,in the summary byBirnet al.(2001). AsRichmond(1985)hasrecognized,“Thesolarandmagneto- sphericplasmasarerepresentedasohmicmediainwhichthecur- rent and electric field are linearly related by a conductivity parametereventhoughcollisionlessplasmacomesnowherenear to satisfying Ohm’s law [even the generalized version]. Unfortu- nately,inmanycasestheparametersthatareusedinthemodels [eventhemodels]tendtoconcealordistortsomeofthekeyphys- icalprocessesthatoccur,ahighpricetopayforsimplifiedanalyt- ical [orcomputer] solutions.” When David Winningham and I discovered the cusp (cleft) (Heikkila et al., 1970; Heikkila and Winningham, 1971) using ISIS-1 data, Ithought we had verified Dungey’s concept of mag- neticreconnection.ItwasIanMcDiarmidusingenergeticparticle data on ISIS-1 who convinced me otherwise: something was wrongwiththissimplisticinterpretation.Heshowedthattrapped particleswerepresentregularlyinthecleft,implyingclosedfield lines.Atthe AGUfall meeting in 1972, Bill Olson, Juan Roederer, and I shook hands to fight reconnection as presently conceived. For me, the case was proved in their paper by McDiarmid et al. (1976)“Particlepropertiesinthedaysidecleft.”AsIansaid,par- ticleswouldgoawayonopenfieldlineswithoutdoinganywork! My interest in the low-latitude boundary layer (LLBL) was a direct result, initially at the Royal Institute of Technology, where (cid:1) I had the privilege of using Hannes Alfven’s office. This research was published 10 years later (Heikkila, 1984), but hardly anyone noticed(but see Lundinand Evans, 1985; Lundin,1988). Another person who has influenced me greatly is Joseph Lemaire.Hisworkonthepatchinessofthesolarwindinthelate 1970s(LemaireandRoth,1978)openedmyeyetowhatmightbe happening.Henotedthatthesolarwindplasmamustbepatchy, andblobswithmoremomentumthantheadjacentplasmacould penetratethroughthemagnetopausecurrentsheetbyanimpul- sivepenetrationmechanism(IP).Schmidt(1960,1979)haddem- onstrated a mechanism that could be involved, a polarization currenttoformanelectrostaticfieldthatdrawsonelectricenergy. My ideas wereadvanced six years later, the same principle but a complementary idea of a plasma transfer event (PTE) drawing on magnetic energy. Prefacetothefirstedition xvii Chapter1ismorethanahistoricalintroduction.Itisorganized by material on spatial location starting with the solar wind, with Figure 1.1 showing the different regions of the magnetosphere, inthreedimensions,asaguide.Asecondarythemeistopresent ahistoricalapproachwhereverpossible,atthesametimecover- ingthe simple material ofthe earlyinvestigations.Athirdobjec- tive is to cover the assumptions made in each case, to test for applicabilityof the results,quite often in hindsight. Kineticstatisticaltheoryofplasmaproblemsmayprovidefora complete analysis, but it is difficult at best. Chapter 2 discusses variousapproximatemethods,suchascircuittheory,plasmafluid theory,andcomputersimulation.Eachhasitsownproblemsand benefits. Observations are excellent, leaving little doubt about what happens. Chapter 3 treats the electric field quite differently from the usual in plasma physics. The implications of Helmholtz’s theorem on any vector field Vare discussed first. The sources of any generalvectorfieldV,theinhomogeneoustermsintheequations of the governing differential equations, are the divergence and curl;divVandcurlVarenotsimplycharacteristicsofthevector V. The same holds true for the electric fieldEwherediv E is the charge density, the source for the electrostatic field, and curl E, source for the field due to induction to a perturbation current. Thepivotalconceptistodividetheelectricfieldintoparallel andtransversecomponentswithreferencetothemagneticfield. Since the electrostatic field has zero curl, it cannot modify the curl of the inductive component, nor the electromotive force; if the parallel component of the total electric field is reduced byfield-alignedchargeseparation(eventozero),thetransverse component will be increased to preserve the curl (Heikkila and Pellinen, 1977; Heikkila et al., 1979). This has many conse- quences, for example, solar wind plasma transfer across the magnetopause,currentthinningeventduringthegrowthphase, tailward-moving plasmoids, bursty bulk flows, omega band auroras, and prompt particle acceleration to high energies. Chapter4(Chapter5inthesecondedition)dissectsPoynting’s theorem at some length. Perhaps the main objection to the cur- rentpracticeinspaceplasmaphysics,includingtheoreticalanal- ysisofmagneticreconnection,isthatthetime-dependentvolume integral concerned with magnetic energy was not used. By this simple,yetfundamental,argumentitcanbeconcludedthatmag- netic reconnection, as presently understood and practiced, is flawed. There is no doubt that there can be changes in the state of interconnection between the geomagnetic and the IMFs, but the present theory for that is not appropriate. For that, we must