MHDWaves
StephaneREGNIER
NorthumbriaUniversity
MSSLSOLARNETSchool
2016
1. Definitionofawave
2. ThethreeMHDwaves
a. LinearizedMHDequations
b. Dispersionrelation
c. Properties
3. MHDwavesindifferentgeometries
a. Rectangularslab
b. Cylinder
4. SolarobservationsofMHDwaves
1. Slowmodes
2. Fastmodes
3. Alfvénmodes
MSSLSOLARNETSchool
2016
Definitionofawave
MSSLSOLARNETSchool
2016
Thecaseofanelectromagneticwave:
- Theelectricfieldandmagneticfieldareperpendicular
- Thewaveispropagatingalongthedirectionperpendicularto
theelectricandmagneticfields
- Thepropagationspeed(phasespeed)isthespeedoflightc
Fig.1:basicdescriptionofanelectromagneticwave
MSSLSOLARNETSchool
2016
Awaveisdefinedby
- Thecomponentsoftheelectricfield(polarisation,Stokes
parameters)
- Thecomponentsofthemagneticfield
- Thedirectionofthepropagationorwavenumber
- Thedispersionrelation:relationbetweenthewavenumber
andtheangularfrequency(seedispersiondiagram)
- Thephaseandgroupspeeds
- Theperturbationofthethermodynamicquantities
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MHDwaves
MSSLSOLARNETSchool
2016
LinearizedMHDequations
TheMHDequationsare
MSSLSOLARNETSchool
2016
LinearizedMHDequations
MSSLSOLARNETSchool
2016
LinearizedMHDequations
MSSLSOLARNETSchool
2016
LinearizedMHDequations
MSSLSOLARNETSchool
2016
LinearizedMHDequations
MSSLSOLARNETSchool
2016
LinearizedMHDequations
MSSLSOLARNETSchool
2016
Dispersionrelations
MSSLSOLARNETSchool
2016
Dispersionrelations
MSSLSOLARNETSchool
2016
Dispersionrelations
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
SomeProperties
MSSLSOLARNETSchool
2016
SomeProperties
Magnetoacousticwaves
- Phasespeedvaryingwiththeangleofpropagation
- Groupspeedvaryingwiththeangleofpropagation
- Fastmodeefficienttotransportenergy
- FastmodemayhavephasespeedequaltoAlfvénspeed
MSSLSOLARNETSchool
2016
MHDwavesindifferentgeometry
MSSLSOLARNETSchool
2016
SlabandTubeGeometry
Waveinanon-uniformplasma
- Twomedia:internaland
external
- Jumpindensity,
temperature,magneticfield
- Discontinuityatthe
interface
- Totalpressurebalance
- SeeforinstancetheJoarder
andRobertsmodel
MSSLSOLARNETSchool
2016
TubeGeometry
Surfaceandbodymodes
- Generationofsurfacemodes
- Cylindricalcoordinates
- Besselfunctions
- Imposingboundaryconditions
tofullydeterminethewaves’
properties
MSSLSOLARNETSchool
2016
TubeGeometry
Representationofmagnetoacousticmodes:sausage,kinkandflute
MSSLSOLARNETSchool
2016
SomeProperties
Magnetoacousticwaveshavedifferentmodes:sausageandkink
MSSLSOLARNETSchool
2016
TubeGeometry
Dispersiondiagramforcoronalloop(coronalvalues)
MSSLSOLARNETSchool
2016
TubeGeometry
Dispersiondiagramforphotosphere/chromosphere
MSSLSOLARNETSchool
2016
Observationsofwaves
MSSLSOLARNETSchool
2016
Slowmodes
Slowmodesobservedincoronalloops
Fastkinkmodes
Examplesoffastmodesgeneratedbyexternalsources
suchasflares
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
MSSLSOLARNETSchool
2016
Alfvenicmodes
MSSLSOLARNETSchool
2016
Whytostudywaves?
- Ubiquitousinthesolaratmosphere
- Transportofenergy
- Coronalheating
- Chromosphericheating(reflectionandtransmissionofwaves)
- Magneticreconnection
- Flares
NotonlyMHDwavesbutalsoelectronicandionicplasmawaves
MSSLSOLARNETSchool
2016
Instabilities
StephaneREGNIER
NorthumbriaUniversity
MSSLSOLARNETSchool
2016
1. Perturbationtheory
2. Kinkinstability
3. Rayleigh-Taylorinstability
4. Kelvin-Helmholtzinstability
5. Thermalinstability
6. Interchangeinstability
PerturbationTheory
PerturbationTheory
PerturbationTheory
KinkInstability
Instabilityofatwistedfluxtubeexceedingathresholdoftwist
KinkInstability
Rayleigh-TaylorInstability
z
Twomediawithdifferent
thermodynamicandmagnetic
properties.Noflowalongx.
x
Twocases:
- Twoplasmaswithauniformmagneticfield
- Oneplasmasupportedbymagneticfield
Rayleigh-TaylorInstability
Rayleigh-TaylorInstability
Rayleigh-TaylorInstability
Kelvin-HelmholtzInstability
Hydrodynamicinstabilitywithtwomediawithdifferentflows
Kelvin-HelmholtzInstability
ThermalInstability
ThermalInstability