Table Of ContentE 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.
ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher
(otherthanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour
understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecome
necessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusing
anyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethods
theyshouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhavea
professionalresponsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability
foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or
fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein.
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,coro-
nal mass ejections, heating of coronal plasma, changes in mag-
netic topology, collisionless shock waves, and solar energetic
particles areobserved.
The magnetosphere is readily accessible for direct observa-
tions,evenexperimentstotestwhatistheresultofaknowninput;
as such, it is a giant laboratory for solar and astrophysical pro-
cesses.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 theo-
rem 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
