What laboratory experiments reveal about the dynamics of arched plasma structures

163 Pages·2012·51.34 MB·English

Fields, forces, and flows: What laboratory experiments reveal
about the dynamics of arched plasma structures
Thesisby
EveStenson
InPartialFulfillmentoftheRequirements
fortheDegreeof
DoctorofPhilosophy
CaliforniaInstituteofTechnology
Pasadena,California
2012
(Defended15May2012)
ii
⃝c 2012
EveStenson
Exceptwhereotherwisenoted,thisworkislicensedundertheCreativeCommons
Attribution-ShareAlike3.0UnportedLicense. Toviewacopyofthislicense,visit
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iii
Defiantlydedicatedtomyparents,Dr. andDr. Stenson,whoreallyshouldhavebeenpushierif
they’dtrulywantedtopreventmefrombecominga“failedmathematician”.
iv
Acknowledgements
Mr. Spock: “Under impulse power she expends fuel like any other vessel. We call it
‘plasma.’ ButwhatevertheKlingondesignation,isitismerelyionizedgas.”
Lt. Uhura: “Well what about all that equipment we’re carrying to catalog gaseous
anomalies? Wellthething’sgottohaveatailpipe.”
—Stardate9523.8,figuringouthowtodetectacloakedbirdofprey
(StarTrekVI:TheUndiscoveredCountry)
Iusedtothinkplasmaswere“merelyionizedgas”(thoughIlackedMr. Spock’sexpertisewith
plasma propulsion). I had learned back in third grade that there were three states of matter, and
whenmysixthgradeteachersuddenlyaddedanother,Iwasskeptical. Whyshouldsomewayward
electrons make a gas worthy of being designated a whole separate state? I managed to maintain
thatskepticismallthewaythroughjuniorhigh,highschool,andevencollege. Then,whenIwasa
firstyeargradstudentatCaltech,IattendedaseminargivenbyanAppliedPhysicsprofessorbythe
nameofPaulBellan,whoopenedmyeyestohowfascinatingplasmascanbe.
In the years since, thanks to Paul’s expert tutelage and his years of patience, I have become
quite the fan of the fourth state of matter, joining the ranks of “scientists who have to explain to
friendsandacquaintancesthattheyarenotstudyingblood”1 [1]. Ithasbeenmygreatprivilegeand
pleasure to be a part of this research group — to be involved with plasmas and the community of
peoplewhostudythem,bothatCaltechandaroundtheworld.
FromamongtheranksofBellanPlasmaGroup,ImustthankinparticularSettYouandGunsu
Yun for being wonderful mentors as well as great officemates. My luck in officemates continued
with Bao Ha and Mark Kendall; I have very much enjoyed all of our conversations over the years,
1Itishighlygratifyingtoreportthatatthetimeofthiswriting,thetopresultofaGooglesearchfortheword“plasma”,
displayedjustbelowanadforan“LGFullHDPlasmaTV”,istheWikipediapageentitled“Plasma(physics)”. “Blood
plasma”comesinsecond.
v
both on science and other topics. Other group members with whom I’ve had the honor of work-
ingincludeShreekrishnaTripathi,DeepakKumar,StevePracko,RobMoeller,RoryPerkins,Auna
Moser,VernonChaplin(whomIowemanythanks,aswellasmanycookies,forallofthecomments
and corrections he suggested to this dissertation), Zach Tobin, Xiang Zhai — and, more recently,
Taiichi Shikama and K.B. Chai. Dave Felt has been an invaluable colleague, above and beyond
hisbuilding/repairingtheelectronicssystemsuponwhichmyresearchhasrelied,ashaveEleonora
Vorobieff,ConnieRodriguez,andChristyJenstad. Iamalsoindebtedtopreviousgroupalumni—
such as Carlos Romero-Talamas, Freddie Hansen, Scott Hsu, and Mike Brown — who at confer-
ences and meetings have been generous with their time and insights, even though their tenures in
thegroupfinishedbeforeminebegan.
Mytimeingraduateschoolhasbeenverymuchenrichedbymycurrentandformerroommates
(includingJessieRosenberg,NeilHalelamien,MatthewKelley,Tobiko,PlatoandSocrates,Xerion,
andespeciallymypartnerinlife,adventures,andsomuchmore,BrianStandley). Ihavealsobeen
lucky to enjoy the companionship of many other amazing people, be it via boba runs with Adam
Griffith, board games with Scott Tesmer and Photon, dinners (and more) with the potluck group,
divingwithPCHScubaandAAU,Frisbeegames,dancing,ortheCaltechY,AlpineClub,CCD,et
al. Meanwhile,fromthreetimezonesaway,mysisterKateandthemembersof“In/Out”havebeen
anongoingsourceofsupportandfriendship.
IwouldliketothanktheCaltechfacultywhoservedonmycandidacyand/ordefensecommit-
tees — Ed Stone, Joe Shepherd, Sunil Golwala, and Keith Schwab — for their feedback on my
researchand/orencouragement. IwouldalsoliketothankthosefacultyfromwhomItookexcellent
andvaluablecourses,aswellasotherswhoweresimplywillingtomaketimefordiscussions.
That I was in a position to attend Paul’s seminar at Caltech to begin with, I owe in part to the
countlesspeoplewhohelped,taught,andinspiredmeovertheyears. Ilearnedcalculus,forexample,
from Jim Voytas, whose intense enthusiasm for the subject, superhuman vigor, and attention to
importantsubtletiesarethestuffoflegend. Iwasluckytodomyundergraduatethesisresearchwith
Ben Crooker, whose amazing fluency in both the laboratory and classroom I will always strive to
match. The physics faculty at Fordham University provided not only an educational environment,
butalsoawelcomingone;yearslater,FreemanHallstillconnotestomeasenseof“home”. Though
there is neither time nor space to enumerate them all, to all of the teachers and administrators,
classmates and colleagues, friends and family members who have helped me in my personal and
professionaljourneythusfar,Iwillalwaysbegrateful.
vi
Abstract
Magnetic flux tubes and, more generally, magnetic field structures that link a plasma volume to
its boundary are prominent features in plasma systems of significant interest, such as the solar
atmosphereandtheinteriorsofmagneticfusiondevices.
Inordertostudythefundamentalphysicsofthesesystems,experimentswereconductedinthe
laboratory using a magnetized plasma gun to produce individual arched, plasma-filled magnetic
flux tubes. More complex plasma topologies were also explored. The absence of confining walls
allowed plasmas to evolve freely — which they did, very dynamically, over the course of several
microseconds. The experiment setup featured excellent reproducibility, extensive diagnostic ac-
cessibility, and several tunable parameters. In particular, a plasma “color coding” technique and
magneticmeasurementsprovidednewandinterestingresults.
Thesinglearchesor“loops”ofplasmaexhibitedsustainedaxialcollimation,evenduringadra-
maticevolutionfromasmall,semicirculararchintoakinkedstructureuptoseventimeslarger. The
loops’magneticstructurewasverifiedasconsistentwiththatofafluxtube,andtheirevolutionwas
foundtobeinquantitativeagreementwithtwointerrelatedmagnetohydrodynamic(MHD)theories:
a simplified hoop force model for the axis expansion and a recently proposed MHD flow model
for the collimation. More complex plasma structures were found to be similarly dominated by the
effectsofthemagneticfield,exhibitingbehaviorthatwashighlyrepeatablebutvariedsignificantly
fromonemagneticstructuretothenext.
ThesefindingssuggestthatMHD-drivenflowsareanimportantmechanismforthetransportof
plasma in arched flux tubes and other magnetic plasma structures. Because MHD has no inherent
length scale, the forces driving the evolution of these experiments are expected to similarly affect
othersystemswithlowplasmabetaandahighLundquistnumber.
vii
Contents
Acknowledgements iv
Abstract vi
ListofFigures xi
ListofTables xiv
1 Introduction 1
1.1 Thebigpicture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introductiontoplasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Plasmaregimes,especiallymagnetohydrodynamics . . . . . . . . . . . . . . . . . 5
1.3.1 Magneticfluxtubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Helicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Theuseoflaboratoryexperimentstoelucidatefundamentalplasmaphysicsrelevant
tosolarandastrophysicalphenomena . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Overviewofthisdissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Experimentdetails 11
2.1 Vacuumsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Magnetizedplasmagun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Historyandoverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Vacuummagneticfieldsystem . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Gasdelivery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Mainpowersystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Systemoverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
viii
2.3.2 Currentandvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Magneticprobearray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.5 Dual-gasplasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Calculationsofmagneticfieldlines . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 Loop-tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 Imageprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 PlasmaflowsinarchedmagneticfluxtubesduetoMHDforces 33
3.1 Model1: Simplifiedhoopforcemodel . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 Derivationforaperfectlyconductingcircularhoop . . . . . . . . . . . . . 34
3.1.2 The“contradiction”oftimederivatives . . . . . . . . . . . . . . . . . . . 36
3.1.3 Forcecalculationwithoutconstantfluxassumption . . . . . . . . . . . . . 37
3.1.4 Effectofhoopshapeoninductance . . . . . . . . . . . . . . . . . . . . . 39
3.1.5 R(t)predictedbyasimplifiedhoopforcemodel . . . . . . . . . . . . . . 40
3.2 Model2: Thegobbleeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Keyconcepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Predictedflowvelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Experimentswithsingleplasmaloops . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.1 Creatingarched,plasma-filledfluxtubes. . . . . . . . . . . . . . . . . . . 46
3.3.2 Visualizingflowswithdual-speciesloops . . . . . . . . . . . . . . . . . . 49
3.3.3 Gettingmorequantitativewithsingle-speciesloops . . . . . . . . . . . . . 51
3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.1 Hoop-force-drivenexpansion. . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.2 Gobble-drivenflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.3 Complementaryforceswithcomparablescaling . . . . . . . . . . . . . . . 59
3.4.4 Implicationsforothersystems . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Magneticmeasurementsofindividualfluxtubes 61
4.1 Measuringthethree-dimensionalmagneticfield . . . . . . . . . . . . . . . . . . . 61
4.2 Comparisontoaforce-freecylinder . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3 Calculationofcurrentchannelwidthfrommagneticdata . . . . . . . . . . . . . . 73
ix
4.4 Non-force-freecurrentprofiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 Beyondtheindividualarchedfluxtube,moreandless 77
5.1 Singleloopswithunusualvacuumfieldconfigurations . . . . . . . . . . . . . . . 77
5.2 Three-footpointstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3 Pairsofloops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6 Conclusionsandfuturework 85
6.1 Summaryofcontributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Ashotillustratingthesignificanceofthemagneticfieldtopology . . . . . . . . . . 86
6.3 Futurework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
A Measurementsofthevacuummagneticfield 90
A.1 Magneticfluxattheelectrodesurface . . . . . . . . . . . . . . . . . . . . . . . . 90
A.2 Vacuumfieldmeasurementswiththemagneticprobearray . . . . . . . . . . . . . 94
A.3 Calculationofthemagneticfieldduetoapairofsolenoids . . . . . . . . . . . . . 97
A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
B Detailsoffastgasvalveoperations 99
B.1 Species-dependentvariationintotalgasreleased. . . . . . . . . . . . . . . . . . . 99
B.2 Operatingregimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
B.3 Fastiongaugemeasurementsofrisetimeandpressureresponse . . . . . . . . . . 104
B.4 Summaryandsuggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
C Estimateford(cid:8)=dtandothercircuitparameters 109
D Analysesofuncertainty,variation,anderrorinlooptraces 113
D.1 Methodreproducibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
D.2 Shot-to-shotvariation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
D.3 Left-handedversusright-handedlooptraces . . . . . . . . . . . . . . . . . . . . . 117
D.4 Boundaryidentificationindual-gaslooptraces . . . . . . . . . . . . . . . . . . . 120
D.5 Negligibilityofviewingangleuncertainty . . . . . . . . . . . . . . . . . . . . . . 122
D.6 Systematicerrorof2Dprojection. . . . . . . . . . . . . . . . . . . . . . . . . . . 122
x
D.7 Summaryanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
E Speciesvariationinsingle-gasloops 126
E.1 Inimages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
E.2 InIVdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
E.3 Inmagneticdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
E.4 Regardingneonloops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
F Furtheradventuresinnumericalintegration 131
F.1 Keyissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
F.2 Theoptionsconsidered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
G Alfvenspeedcontoursforplasmaparameterrangesofinterest 135
H Timingsurveyforsingle-loopplasmas 138
H.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
H.2 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
H.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Bibliography 144