Kinetic Physics of the Solar Corona and Solar Wind - II

Transcription

1 JjjjjT «KK«S^ t\\q abdas salatn international centre for theoretical physics SMR 1331/5 AUTUMN COLLEGE ON PLASMA PHYSICS 8 October - 2 November 2001 Kinetic Physics of the Solar Corona and Solar Wind - II E. Marsch Max Planck Institute for Aeronomy Lindau, Germany These are preliminary lecture notes, intended only for distribution to participants.

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3 Kinetic Physics of the Solar Corona and Solar Wind Eckart Marsch Max-Planck-lnstitut fiir Aeronomie The Sun's corona and wind - structure, evolution and dynamics Ions and electrons - velocity distributions and kinetics Waves and turbulence - excitation, transport and dissipation

4 Ions and electrons - velocity distributions and kinetics Solar wind protons and alpha particles Heavy minor ions and elemental composition Solar wind electrons Coulomb collisions in coronal holes and solar wind Transport in a weakly collisional plasma Plasma waves in the solar wind Evidence for effects of waves on ion distributions Kinetic instabilities and pitch-angle scattering Coronal heating and ion-cyclotron resonance Kinetic modelling of ions in coronal holes and funnels Radial temperature profiles of ions and electrons Heating of coronal funnels and holes

5 Electron energy spectrum IMP spacecraf t Two solar wind electron populations: Core (96%) Halo (4%) Imp 7 electron spec!rum ti/15/72 I3:i6 UT.. Core: local, collisional, boyncl by electrostatic potential Halo: global, collisionless 5 free to escape (exopsheric) Feldman et al., JGR, 80, 41 81, Electron Velocity (xio^km/sed

6 Electron velocity distributions H&LO *7 / < CORE /FIT 'LEVEL '^"..^ \ "\ CORg "fv( 1 COUNT LEVEL -4-6 HALO / / ^ / > / t ' /' y 1 ' CORE V/ Frr \ 1 COUt. T LEVEL """' v -"!\ K. HCS' OWARDS HE SUN DIRECTION ALONG " high intermediate speed low Pilipp et: HL JGR, 92,1075,1987 Core (96%), halo (4%) electrons, and 99strahl"

7 Electron velocity istribution function Helios x- -X- x- -X- Sun Sonnen-- richtung 20 km s.-v e 10 cm" 3 = X- \/_ Non-Maxwellian Pilippetal.JGR, 92, 1 075,1 987 X- Heat flux tail

8 Electron heat conduction Heat carried by halo electrons! T H = 7 T c Interplanetar y potential: = ev 10. p (f) <M E io~ 3 o CO CD x LL cd CD X 0 " Median Q 5% Level - 95% Level Qoc R Heliocentric Distance [AU] 4.5 McComas et al., GRL, 19,

9 Proton velocity distributions C -.//// A 5*)) Temperature anisotropies Ion beams E Plasma instabilities G ivt ~""-vn--. g/^/- Interplanetary heating Plasma measurements made at 10s resolution (>0.29AU from the Sun) ^ \ ' s Helios Marsch et: al., JGR, 87, 52, 1982

10 Ion composition of the solar wind SOHO/CELIAS/CTOF raw counts - PHA, DAY Ion mass 10 "* $ 2 raw counts hackuyound Subtracted m Grunwaldl et al. (CELIAS on SOHO) 2 4 yass/charge 10

11 Elements (isotopes) in the solar wind el s: c; [, o isotopes: \\,t Mg AI Si )»S ClAr KOJ V1 s J> Si ( ''Ar Ca Ti Cr Mn»;c Crl-o Ni Ni o I Unfractionated sample of solar material! 100 -I Mass (arnu) SOHO CELIAS/MTOF lpavichetal. 3 GRL

12 Kinetic processes in the solar corona and solar wind I Plasma Is multi-component and nonuniform complexity Plasma is dilute -> deviations from local thermal equilibrium -» syprathermal particles (electron strahl) global boundaries are reflected locally Problem: Thermodynamics of the plasma, which is far from equilibrium... 10

13 Coulomb collisions winci e (cm 3 ) 1 Q10 : imz:mmim!x'\ 1 (J 10 T e (K) 1 CP o 5 A, (km) o 7 Since N < 1, Coulomb collisions require kinetic treatment! Yet 3 only a few collisions (N > 1) remove extreme anisotropies! Slow wind: N > 5 about 10% 3 N > 1 about 30-40% of the time.

14 Coulomb collisions in slow wind AU JOVAU V., /V, o 1.0 AU N = Heat flux by run-away protons v,, /v. i ( r r r Beam Marsch and Livi, JGR, 92, 7255,

15 Proton Coulomb collision statistics Fast protons are collisionlessl Slow protons show collision effects! Proton heat flux N = T ~ n V" T l exp v c "p* 'p Q k Livi et al., JGR, 91, 8045,

16 Proton and electron temperatures Electro nsare cool! P, s P! a h L(P slow wind fast wind 0.01 D-l R (AU) -. j i j i~.j- 1.0 HUIMJIKJ loil/s Protons are hot! Pf n0) fast wind i 1 U lcm/3 slow wind Morsch, K (AU)

17 Collisions and geometry Double adiabatic invariance, -> extreme anisotropy not observed! Spiral reduces anisotropy! Adiabatic collisiondominated -> isotropy g is not observed! t 10 e JD i : i r r in To" const _. Radial B No Collisions 1 1 I 1! 1, 1 1 T~ r~ Spiral B (V = 400 km/s) No Collisions T i r-r _ i / ' t t I r (-""TXT" TB/FJ : ; j f 1. I l l ' U 10 6 Philipps and Gosling, JGR, Collision-Dominated J_,,.I,,,,, I j 1, JUL Heliocentric Distance (AU)

18 Heating of protons by cyclotron and Landau resonance 0, ,1 Increasing magnetic moment Deccelerating proton/ion beams Evolving temperature anisotropy <ii» Tfe^ W\H JN J / / / O.fa4 0<)fi.- /'" )-i-'- B Velocity distribution functions ' /. 781 //> fast wind 618 kms! 717 Marsch et al., JGR, 87, 52-72,

19 Kinetic plasma instabilities Observed velocity distributions at margin of stability Selfconsistent quasi- or non-linear effects not well understood Wave-particle interactions are the key to understand ion kinetics in corona and solar wind! Marsch, 1991 ;Gary, Space Science Rev., 56, 373,

20 Wave-particle interactions Dispersion relation ysing measured or model distribution functions f(v), e.g. for electrostatic waves; = 0 -» co(k) = co r (k) + iy(k) Dielectric constant is functional of f(v) 5 which may when being non»maxwellian contain free energy for wave excitation. y(k) > 0 -^ micro-instability. Resonant particles: oo(k) - k-v = 0 oo(k) k-v = ± O (Landau resonance) (cyclotron resonance) -> Energy and momentym exchange between waves and particles. Quasi-linear or non-linear relaxation... 18

21 Proton temperature anisotropy Measured and modelled proton velocity distribution Growth of ioncyclotron waves! 0 30 Anisotropydriven instability by large «G.5QL i t.00 f *, 1 -i-i-t i t i»»-t r-rr-i-fi-ranisotro py jfq, y «0.05O P Marsch, 1991 X 0?. 19

22 Wave regulation of proton beam 1 Measured and modelled velocity distribution Growth of fast mode waves! Beam-driven instability 5 large drift \ r^.'to ^ 076 A: j 1.00, -, \ ro j (; beam co w 0.4Q p f/o, y «0.06fi p Marsch, 1991 o co; 0.1 : J-. >..i.,i i_. i..i! t i,,4 * Jooo

23 Electromagnetic ion beam instabilities Maximum growth rate Daughton and Gary, JGR, 1998 Proton beam drift speed 21

24 Whistler regulation of electron ^ * heat flux q B s * 8 ; ! 'L.i 2,05 >i * i i 4. i 2.1!< t R (AU) I 2.25 v » : \ 200 S Halo electrons carry heat flux Heat flux varies Day of Year (1991) Whistler instability regulates drift Simeetal., JGR,

25 Kinetic processes in the solar corona and solar wind 11 Plasma is multi-component and nonyniform -> multi-fluid or kinetic physics is required Plasma is dilute and turbulent -> free energy for micro-instabilities -> resonant wave-particle interactions -> collisions by Fokker-PIanck operator Problem: Transport properties of the plasma, which involves multiple 23

26 Length scales in the solar wind Mac restructure - fluid scales Heliocentric distance: Solar radius: r 150Gm (1AU) km (21 5 R s ) Alfven waves: X Mm Microstructyre -- kinetic scales Coulomb free path: Ion inertlal length: Ion gyroradius: Debye length: i V A /O p i\ x n ~ AU (CAD P ) ~ 100 km ~ 50 km ~ 10m Helios spacecraft: d ~ 3m Microscales vary with solar distance! 24

27 Theoretical description Boltzmann-Vlasov kinetic eqyations for protons, alpha-particles (4%), minor ions and electrons Distribution functions Kinetic equations + Coulomb collisions (Landau) + Wave-particle interactions + Micro-instabilities (Quasilinear) + Boundary conditions -> Particle velocity distributions and field Momen ts Multi-Fluid (MHD) equations + Collision terms + Wave (bulk) forces + Energy addition + Boundary conditions -> Single/multi fluid parameters 25

28 Solar electron exosphere and velocity filtration That suprathermal electrons drive solar wind through electric field is not compatible with coronal and in-situ observations! 24 sum of Maxwellians K e =4 o, 26 o Velocity (i0 e m/s) Maksi movie ot a I., A&A,

29 Fluid equations Mass flux: F M = pva p = n p p Magnetic flux: F B = BA Total momentum equation: V d/dr V = - 1 /p d/dr (p + p w ) - GM s /r 2 +a w Thermal pressure: p = n p k B T p + n e k B T e + n MHD wave pressure: p w = (8B) 2 /(8n) Kinetic wave acceleration: a w = (p p a p + Pia,)/p Stream/flux-tube cross section: A(r) 27

30 Energy equations Parallel thermal energy d 2 I dn dr 2g, w-p terms + sources + sinks Perpenclicyla rthermal energy dr M 1 A Heating functions: q 1,1 Wave energy absorption/emission by wave-particle interactions! Conductfon/coIIisional exchange of heat + radiative losses 28

31 Heating and acceleration of ions by cyclotron and Landau resonance f d d v 2 acceleration parallel heating perpendicular heating E OO f M k Marsch and Tu, JGR, 106, 227, 2001 Wave spectrum? Wave dispersion? Resonance function? 29

32 Fast solar wind speed profile Ulysses mass flux continuity Lyman Doppler" dimming Esser eta I., ApJ, 1997 iadial distance

33 Rapid acceleration of the high-speed solar wind Y' i i 10 8 F l > ^ 1000 v/km s ' Very hot protons T/K 10 L=0.50 R s Very fast acceleration L=0.25 R s Radial distance /R< Radial distance / 20 McKenzieetal., A&A, 303, L45,1995 Heating: Q = Q o exp(- (r - R s )/L); Sonic point: r «2 Re 31

34 Model ofthe fast solar wind N /cm" 3 Low density, n «10 8 cm- 3, consistent with coronagraph measurements hot protons, T max «5MK cold electrons small wave temperature, T, 10 3 Fast acceleration T/K 10 2 v 10 1 V <V A ) / km s 10 o 0 o McKenzieetal., Geophys. Res. Lett., 24, o Radial distance /IL 32

35 Four-fluid model for turbulence driven heating of coronal ions Four-fluid 1 -D corona/wind model Quasi-linear heating and acceleration by dispersive ioncyclotron waves Rigid powerlaw spectra with index: -2<y<-1 p r i i i rrr No wave absorption Turbulence spectra not selfconsistent Preferential heating of heavy ions by waves Hu 5 Esser & Habbal, JGR, 105,5093,2000 r (Solar Radii) 33

36 Multi-fluid equations Momentum equation 1 d 2 Mm ar 4 Wave acceleration? Parallel energy equation d dr Perpendicular Wave heating energy equation A Tu and Marsch, JGR, 106, 8233,

37 Wave heating/acceleration rates for wave-particle interactions f drr. \ m Wt v j d q JX wave acceleration parallel wave heating perpendicular heating M fcl 3 Wave spectrum and dispersion? Marsch and Tu, JGR, 106, 227, 2001 VDF and resonance function?

38 Resonant wave-absorption coefficient for bi-maxwellian ions Resonance function x 2 1 Number of resonant ions Pitch-angle gradient x Marsch and Tu,JGR,106, 227, 2001 Polarization vector efe(k) Current matrix element 36

39 Kinematics of ions in cyclotron resonance Frequency Damping rate Zero drift 0.0 0, ,0 0,0 r_a,_t_j,,...,,_, r r, 0,5 1, Finite drift Wave vector (kv A /O) Wave vector (kv A /Q) Tu et: al., Space Sci. Rev., 87, 331,1999 Cyclotron resonance condition; co = Q - k* 37

40 Ion differential streaming 200 T AV /kms" m a /m p 150 f 100 so "** "IMMST Fast Slow Vp ()«n/sl x C0-'i(J0 Alpha particles are faster than the protons! In fast streams the differential velocity is: VL< < 1A 1 Heavy ions travel at alpha particle speed I l I! I. 0,4 05 C KfAUl i i 0,9 IC Distance r/au Marsch et al., JGR, 87, 52,

41 r Wave heating and acceleration of protons and oxygen ions Machnumber Thermal speed squared _ LHW... ~ MQ= Mp RHW M M / AV 0^1.1V N A (plasma beta) TQL/TQII^O Preferential acceleration and heating of oxygen 0.4, /.-* - v A ) 2 Tpi/"ipii"«i.i Marsch, Nonlinear Proc. Geophys., 6,149, N, >---- """* ^i j i B Heliocentric Distance /R 0 39

42 Results from fluid and hybridkinetic models of corona and wind Multi-Fluid models with assumed heat sources reproduce well the bulk properties of the solar wind Thermodynamics of the solar corona and solar wind still requires a fully kinetic treatment Hybrid-kinetic models do not describe the detailed observations of the solar wind plasma adequately A semi-kinetic approach with with self-consistent spectra provides valuable first insights in the physics The problems of wave-energy transport as well as turbulent cascading and dissipation in the dispersive kinetic domain remain to be solved 40