Table Of Content1111992200__99778899881111222233774477__ttpp..iinndddd 11 77//1111//2200 88::5555 AAMM
b2530 International Strategic Relations and China’s National Security: World at the Crossroads
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Published by
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
KELVIN–HELMHOLTZ INSTABILITY IN SOLAR ATMOSPHERIC JETS
Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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system now known or to be invented, without written permission from the publisher.
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is not required from the publisher.
ISBN 978-981-122-374-7 (hardcover)
ISBN 978-981-122-375-4 (ebook for institutions)
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October27,202018:2 Kelvin–HelmholtzInstabilityinSolarAtmosphericJets-9inx6in b4047-fm pagev
Preface
ThestudyoftheSunprovidesusanopportunitytounderstandthephysicsofother
stars. One of the lively problems in solar physics is heating of the solar corona.
Currentlythereisacompetitionbetweentwomechanismsforitsheating,i.e.,dissi-
pationofenergybywavesandsmall-scalefrequentcoronalmagneticreconnection.
However, some studies indicate this may be a joint effect of these two possible
mechanisms. Kelvin–Helmholtzinstability(KHI)ofpropagatingmagnetohydro-
dynamicmodesinsolarflowingstructuresisconsideredtoplayanimportantrole
inthesolaratmosphere. Itcantriggertheonsetofwaveturbulenceleadingtoan
effective plasma heating and particle acceleration. Kelvin–Helmholtz instability
is a multifaceted phenomenon and the purpose of this book is to illuminate its
(instability)manifestationinvarioussolarjetslikespicules,darkmottles,surges,
macrospicules, Extreme Ultraviolet (EUV) and X-ray jets, as well as rotating,
tornado-like,jets,solarwind,andcoronalmassejections. ThemodelingofKHI
isperformedintheframeworkofidealmagnetohydrodynamics(andalsoinHall
magnetohydrodynamics for the solar wind). The book consists of 12 chapters
andisintendedprimarilyforadvancedundergraduateandpostgraduatestudents,
early carrier researchers. Our one-dimensional approach cannot compete, with
respecttocomprehensivenessofjets’topology,withthesophisticated2.5-and3D
numerical codes, but nonetheless yields reasonable instability characteristics in
goodagreementwithobservations. Moreover,ourapproachhasakeyadvantage:
everyplotinthisbookcanberecoveredbythereaderbecause,afterall,theproblem
comesdowntofindingthesolutionstothederivedinclosedformwavedispersion
relations in complex variables. That task, in general, is not easy one, but never-
thelesssolvable. WewouldliketoencouragethereadertomakemodelingofKHI
inanyjet-likeeruptionstudiedinthecurrentliterature,orbetter,totakeitsbasic
parameters directly from the data set of the Atmospheric Imaging Assembly on
v
October27,202018:2 Kelvin–HelmholtzInstabilityinSolarAtmosphericJets-9inx6in b4047-fm pagevi
vi Kelvin–HelmholtzInstabilityinSolarAtmosphericJets
boardSolarDynamicsObservatory(SDO)orfromtheInterfaceRegionImaging
Spectrograph(IRIS).
Acknowlegdments
We will be grateful to readers to notify us of typographical or other errors they
find: [email protected]fi[email protected].
We are indebted to Professors Teimuraz Zaqarashvili, Leon Ofman, and
AbhishekSrivastavafortheirconstructivecriticismandusefulcommentsduring
thepreparationofmanyarticlesonthissubject. WewishalsotothankNASAfor
using snapshots of various solar atmospheric events as illustrations in the book,
andDr.SnezhanaYordanovaforplottingacoupleoffigures.
I.Zhelyazkov,R.Chandra
October28,202013:44 Kelvin–HelmholtzInstabilityinSolarAtmosphericJets-9inx6in b4047-fm pagevii
Contents
Preface v
1. TheSun: GeneralIntroduction 1
1.1 Internalstructure. . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Core . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Radiativezone . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Convectivezone . . . . . . . . . . . . . . . . . . . . . 4
1.2 Externalstructure . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Photosphere . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Chromosphere . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Corona . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 QuietandactiveSun . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Prominences/filaments . . . . . . . . . . . . . . . . . . 8
1.3.2 Solarflares . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 Solarjets . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.4 Coronalmassejections. . . . . . . . . . . . . . . . . . 11
1.4 Solarcycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Solareruptionmechanisms . . . . . . . . . . . . . . . . . . . . 12
2. SolarJets: Origin,ClassificationandBasicPhysicalParameters 15
2.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Basicphysicalparameters . . . . . . . . . . . . . . . . . . . . . 21
3. MagnetohydrodynamicWavesandInstabilities 25
3.1 Magnetohydrodynamicsbasicequations . . . . . . . . . . . . . 25
3.2 Magnetohydrodynamicequilibrium . . . . . . . . . . . . . . . . 30
3.3 Magneticreconnection . . . . . . . . . . . . . . . . . . . . . . 31
vii
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viii Kelvin–HelmholtzInstabilityinSolarAtmosphericJets
3.4 Magnetohydrodynamicwaves . . . . . . . . . . . . . . . . . . . 36
3.4.1 MHDmodesinmagneticfluxtubes . . . . . . . . . . . 41
3.5 Magnetohydrodynamicinstabilities . . . . . . . . . . . . . . . . 44
3.5.1 Rayleigh–Taylorinstability . . . . . . . . . . . . . . . 44
3.5.2 Kelvin–Helmholtzinstability . . . . . . . . . . . . . . 45
3.5.3 Sausageandkinkinstabilities . . . . . . . . . . . . . . 48
4. NormalMagnetohydrodynamicModesinSolarJets 51
4.1 Jetgeometry,basicMHDequations,andwave
dispersionrelation . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.1 Derivationofwavedispersionrelationonusing
theoperatorcoefficienttechniques. . . . . . . . . . . . 57
4.2 Anexampleforfindingunstablesolutionstothewave
dispersionrelation . . . . . . . . . . . . . . . . . . . . . . . . . 60
5. Kelvin–HelmholtzInstabilityinSolarSpicules 65
5.1 Geometryandthewavedispersionrelations . . . . . . . . . . . 68
5.1.1 Dispersiondiagramsofkinkwaves . . . . . . . . . . . 71
5.1.2 Dispersiondiagramsofsausagewaves . . . . . . . . . 79
6. Kelvin–HelmholtzInstabilityinSolarPhotospheric
TwistedFluxTubes 83
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Geometry,thebasicMHDequations,andthewave
dispersionrelation . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3 Numericalsolutionsandwavedispersiondiagrams. . . . . . . . 89
7. Kelvin–HelmholtzInstabilityinSolarSurgesandDarkMottles 99
7.1 Kelvin–Helmholtzinstabilityinsolarsurges . . . . . . . . . . . 99
7.1.1 Surgemodels,basicparameters,andgoverning
equations . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.1.2 Wavedispersionrelations . . . . . . . . . . . . . . . . 104
7.1.3 Numericalcalculationsandresults. . . . . . . . . . . . 107
7.2 Kelvin–Helmholtzinstabilityindarkmottles . . . . . . . . . . . 114
7.2.1 Mottlesmodels,basicparameters,andgoverning
equations . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.2.2 Numericalcalculationsandresults. . . . . . . . . . . . 117
7.2.3 Discussionandconclusion . . . . . . . . . . . . . . . . 121
October27,202018:2 Kelvin–HelmholtzInstabilityinSolarAtmosphericJets-9inx6in b4047-fm pageix
Contents ix
8. Kelvin–HelmholtzInstabilityinEUVSolarJets 125
8.1 Observations,nature,andphysicalparametersofEUVjets . . . 125
8.2 Jetsgeometryandthegoverningmagnetohydrodynamic
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.3 Kelvin–HelmholtzinstabilityinanEUVjet
observedbyHinode . . . . . . . . . . . . . . . . . . . . . . . . 136
8.3.1 Kelvin–Helmholtzinstabilityofthekink
(m =1)mode . . . . . . . . . . . . . . . . . . . . . . 137
8.3.2 Kelvin–Helmholtzinstabilityofthem =2,3,
and4modes . . . . . . . . . . . . . . . . . . . . . . . 142
8.4 Kelvin–HelmholtzinstabilityinanEUVjetobserved
bySDO/AIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
9. Kelvin–HelmholtzInstabilityinX-raySolarJets 153
9.1 ObservationsandnatureoftheX-rayjets . . . . . . . . . . . . . 153
9.2 Magneticfieldtopology,physicalparameters,andMHDwave
dispersionrelations . . . . . . . . . . . . . . . . . . . . . . . . 157
9.2.1 Kelvin–HelmholtzinstabilityofMHDmodes
inuntwistedfluxtubes . . . . . . . . . . . . . . . . . . 159
9.2.2 Kelvin–HelmholtzinstabilityofMHDmodes
intwistedfluxtubes . . . . . . . . . . . . . . . . . . . 165
9.3 Concludingremarks . . . . . . . . . . . . . . . . . . . . . . . . 170
10. Kelvin–HelmholtzInstabilityinRotatingSolarJets 173
10.1 Observationsandnatureoftherotatingsolarjets . . . . . . . . . 173
10.2 Thegeometry,magneticfield,andphysicalparameters
inajetmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
10.3 Wavedispersionrelation. . . . . . . . . . . . . . . . . . . . . . 178
10.4 Numericalsolutions,wavedispersion,andgrowth
ratediagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.4.1 Kelvin–Helmholtzinstabilityinastandardpolar
coronalholejet . . . . . . . . . . . . . . . . . . . . . . 183
10.4.2 Kelvin–Helmholtzinstabilityinablowoutpolar
coronalholejet . . . . . . . . . . . . . . . . . . . . . . 186
10.4.3 Kelvin–Helmholtzinstabilityinajetemerging
fromafilamenteruption . . . . . . . . . . . . . . . . . 188
