JjjjjT t\\Q «KK«S^ abdas salatn international centre for

SMR 1331/5

AUTUMN COLLEGE ON PHYSICS

8 October - 2 November 2001

Kinetic Physics of the Solar Corona and - II

E. Marsch

Max Planck Institute for Aeronomy Lindau, Germany

These are preliminary lecture notes, intended only for distribution to participants.

Kinetic Physics of the Solar Corona and Solar Wind

Eckart Marsch Max-Planck-lnstitut fiir Aeronomie

• The 's corona and wind - structure, evolution and dynamics • Ions and electrons - velocity distributions and kinetics • Waves and turbulence - excitation, transport and dissipation Ions and electrons - velocity distributions and kinetics

Solar wind 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 Electron energy spectrum

Imp 7 electron spec!rum ti/15/72 I3:i6 UT.. IMP Two solar wind electron spacecraf populations: t • Core (96%) • Halo (4%)

Core: local, collisional, boyncl by electrostatic potential Halo: global, collisionless5 free to escape (exopsheric)

Feldman et al., JGR, 10 80, 41 81,1975 Electron Velocity (xiO^km/sed Electron velocity distributions

H&LO CORE CORg /FIT "fV( CORE Frr 0 "\ / V/ < HALO / ^ / \ -2 > •4 -4 / ' ' y t / *7 / 1 ' -8 1 COUNT LEVEL -6 'LEVEL '^"••..^ \ 1 COUt. T LEVEL """'v-"!\ -8

-20 -12 -4 0 4 12 20 -20-12 -4 0 4 12 20 -20 -12 -4 0 4 12 20

5 10 K . HCS'

DIRECTION OWARDS HE SUN ALONG "£ high intermediate speed low Pilipp et: HL JGR, 92,1075,1987 Core (96%), halo (4%) electrons, and 99strahl" Electron velocity istribution function

-X- •x- •x-

-X-

Sonnen-- Sun richtung 20 .-v e km s 10 cm"3

= X- _\/ • Non-Maxwellian Pilippetal.JGR, 92, 1 075,1 987 •X- • Heat flux tail Electron heat conduction

Qoc R -2.36 Heat carried 10 . p by halo electrons! (f)

McComas et al., GRL, 19,1291 1992 velocity distributions

C - • Temperature .//// A anisotropies •5*)) • Ion beams

E • Plasma instabilities

iVt • Interplanetary heating g/^/- Plasma measurements

G made at 10s resolution (>0.29AU ~""-vN-- . from the Sun)

^ \ ' s

Helios Marsch et: al., JGR, 87, 52, 1982 Ion composition of the solar wind

SOHO/CELIAS/CTOF raw counts - PHA, DAY 96 150-199

20

Ion 10 mass

"*•$

2 raw counts hackuyound Subtracted m

9000

1 2 4 10

Grunwaldl et al. (CELIAS on SOHO) yass/charge Elements (isotopes) in the solar wind

el emails: c; [, o \\,t Mg AI Si )»S ClAr KOJ Ti Cr Mn»;c Ni V1 s ( isotopes: J> Si ''Ar Ca Crl-o Ni

10000 - Unfractionated sample of solar material! 1000 o I

100 -I

SOHO CELIAS/MTOF 10 14 18 22 26 30 34 38 42 46 50 54 58 62 Mass (arnu)

lpavichetal.3GRL51998 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 Coulomb collisions

winci

:iMZ:MMiM!x'\ 3 Q10 ••e (cm ) 1 1 (J 10 5 Te (K) 1CP 1-2 16 1o 7 A, (km) 10 1 000 1o

• Since N < 1, Coulomb collisions require kinetic treatment!

• Yet3 only a few collisions (N > 1) remove extreme anisotropies!

• Slow wind: N > 5 about 10%3 N > 1 about 30-40% of the time. Coulomb collisions in slow wind

100 0.2 AU

10-

1 -

-2 V., /V, o 100 JOVAU 1.0 AU N = 0.7

10-1

i ( r r—r 1 -•2 -1 0 1 2 1 2 v,, /v. Heat flux by Beam run-away protons Marsch and Livi, JGR, 92, 7255, 1987 12 Proton Coulomb collision statistics

• Fast protons are collisionlessl • Slow protons show collision effects!

Proton heat flux

Q k 1 N = T v ~ n V" T 111 lexpvc "p* 'p

Livi et al., JGR, 91, 8045, 1986 13 Proton and electron temperatures

P, slow wind Electro s

nsare P! a cool! h fast wind L(P -|. j i j i~.j- 0.01 D-l 1.0 R (AU)

HUIMJIKJ lOil/S Protons fast wind are hot! nPf 0) i 300-400 lcm/3 1 slow wind U

Morsch, 0.01 0.1 1.0 K (AU) 1991 14 i : i r r in t t I r—(-""TXT" To" const 6 Collisions and 10 _. _ i TB/FJ : ; 100

/' • geometry 104

• Radial B No Collisions 1 1 I 1 ! 1, 1 1 1 1 j f 1. Ill' Double adiabatic 3 T~ r~ invariance, -> extreme 03 10e anisotropy not observed! t JD Spiral reduces anisotropy! • Spiral B (V = 400 km/s) Adiabatic collision- No Collisions dominated -> isotropy g T i r-r is not observed! §

U 106

104 8 Collision-Dominated 10 •J_,, .I,,,,, I j 1, JUL Philipps and Gosling, JGR, 0.1 1.0 10. 1989 Heliocentric Distance (AU) 15 Heating of protons by cyclotron and Landau resonance

0,6 • Increasing magnetic 05 moment

0.3 • Deccelerating proton/ion beams

0,1 • Evolving temperature anisotropy

O.fa4 0<)fi .-• /'" Velocity )-i-'- B • 781 fast wind 618 kms ! 717 Marsch et al., JGR, 87, 52-72, 1982 16 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, 373,1991 17 Wave-particle interactions

Dispersion relation ysing measured or model distribution functions f(v), e.g. for electrostatic waves;

= 0 -» co(k) = cor(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 (Landau resonance) oo(k) ™ k-v = ± O| (cyclotron resonance) -> Energy and momentym exchange between waves and particles. Quasi-linear or non-linear

relaxation..... 18 Proton temperature anisotropy

• Measured and modelled proton velocity distribution • Growth of ion- cyclotron waves! 0 30

• Anisotropy- anisotro driven instability t.00f * , 1 -i-i-t i t i » »-t r-rr-i-fi-r- py by large «G.5QL i jfQ,

y « 0.05OP

X Marsch, 0 ?. 1991 19 Wave regulation of proton beam 1

.'to ^ • Measured and \ r^ modelled velocity distribution • Growth of fast \ ro j (;

mode waves! 076 A: j • Beam-driven beam instability5 1.00 , -, large drift

co w 0.4Qp f/O,

y « 0.06fip

o co; : J-. > ..i. ,i i_. i ..i ! t i , ,4 * Jooo 0.1 Marsch, 0 3 1991 20 Electromagnetic ion beam instabilities

Maximum growth rate

Daughton and Gary, JGR, Proton beam drift 1998 speed 21 8 ; 400

Whistler 7 350 300 6 » regulation 250 5 3 4 : \ 200 S of electron s * 150

100 heat flux !'L.i !< t I 50

. i 0 v • 0 8 2,05 2.1 2.15 2.2 2.25 •q R (AU) 7 B i 4 6 >i • Halo electrons * i carry heat flux ^—* 2.4 3 4 • Heat flux varies 3 1.6

2 0.8 • Whistler 1 instability 100 110 120 130 140 150 regulates drift Day of Year (1991) Simeetal., JGR, 1994 22 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 Length scales in the solar wind

Mac restructure - fluid scales • Heliocentric distance: r 150Gm (1AU)

• Solar radius: 696000 km (21 5 Rs) • Alfven waves: X 30 - 100 Mm Microstructyre -- kinetic scales • Coulomb free path: i ~ 0.1 -10AU

• Ion inertlal length: VA/Op (CADP) ~ 100 km

• Ion gyroradius: i\ ~ 50 km

• Debye length: xn ~ 10m Helios spacecraft: d ~ 3m Microscales vary with solar distance!

24 Theoretical description

Boltzmann-Vlasov kinetic eqyations for protons, alpha-particles (4%), minor ions and electrons

Distribution Momen functions ts Kinetic equations Multi-Fluid (MHD) + Coulomb collisions (Landau) equations + Wave-particle interactions + Collision terms + Micro-instabilities + Wave (bulk) forces (Quasilinear) + Energy addition + Boundary conditions + Boundary conditions -> Particle velocity -> Single/multi fluid distributions and field parameters 25 Solar electron exosphere and velocity filtration

That suprathermal electrons drive solar wind through electric field is not compatible with coronal and in-situ observations!

sum of Maxwellians •24 Ke=4 o,

26

28 o

32 Maksi movie -20 Velocity (i0em/s) ot a I., A&A, 1997 26 Fluid equations

• Mass flux: FM = pVA p = npp

• Magnetic flux: FB= BA • Total momentum equation: 2 V d/dr V = - 1 /p d/dr (p + pw) - GMs/r +aw

Thermal pressure: p = npkBTp + nekBTe + n 2 MHD wave pressure: pw = (8B) /(8n)

Kinetic wave acceleration: aw = (ppap + Pia,)/p Stream/flux-tube cross section: A(r)

27 Energy equations

2g, Parallel d 2 I dn thermal dr energy w-p terms + sources + sinks Perpenclicyla rthermal •M1 energy dr A

Heating functions: q Conductfon/coIIisional 1,1 exchange of heat + Wave energy absorption/emission by radiative losses wave-particle interactions!

28 Heating and acceleration of ions by cyclotron and Landau resonance

f acceleration d parallel heating d 2 v perpendicular heating

M f k E •OO

Wave spectrum ? Wave dispersion ? Marsch and Tu, JGR, 106, 227, 2001 Resonance function ? 29 Fast solar wind speed profile

Ulysses

mass flux continuity

Lyman Doppler" 100 dimming iadial distance Esser eta I., ApJ, 1997 30 Rapid acceleration of the high-speed solar wind

8 10000 Y' i—i 10 F l > ^ Very hot

1000 protons T/K v/km 10' s-1 100

10 L=0.50 Rs Very fast acceleration L=0.25 Rs

5 10 15 20 10 15 20 Radial distance / R< Radial distance /

McKenzieetal., Heating: Q = Q exp(- (r - R )/L); Sonic point: r « 2 A&A, 303, L45,1995 o s Re 31 Model ofthe fast solar wind

Low density, n « 108 cm-3, consistent with coronagraph measurements N /cm"3

• hot protons, Tmax «5MK • cold electrons • small wave temperature, T, Fast 3 acceleration 10 T/K 2 10 v 101 V

p—r i i i rrr • No wave • Four-fluid 1 -D absorption corona/wind model • • Quasi-linear Turbulence heating and spectra not acceleration by self- dispersive ion- consistent cyclotron waves • Rigid power- Preferential law spectra with heating of index: -2

Hu5 Esser & Habbal, JGR, 105,5093,2000 r (Solar Radii) 33 Multi-fluid equations

1 Momentum d 2 4 Mm® ar equation

Wave acceleration ?

Parallel energy d equation dr Wave Perpendicular heating energy equation A

Tu and Marsch, JGR, 106, 8233, 2001 34 Wave heating/acceleration rates for wave-particle interactions

f mdrr. \ wave acceleration parallel wave heating Wtvj d qJX perpendicular heating

M fcl

3

• Wave spectrum and dispersion ? Marsch and Tu, JGR, 106, 227, 2001 • VDF and resonance function ? Resonant wave-absorption coefficient for bi-Maxwellian ions

Resonance 2 1 function x Number of resonant ions Pitch-angle x gradient Marsch and Tu,JGR,106, 227, 2001

Polarization efe(k) vector

Current matrix element

36 Kinematics of ions in cyclotron resonance

Frequency

Damping rate

Zero Finite

drift r_A,_T_j|—,,...... ,—,_,— r r , drift 0.0 0,5 1.0 1.5 2,0 0,0 0,5 1,0 1.5 2.0

Wave vector (kVA/O) Wave vector (kVA/Q)

Tu et: al., Space Sci. Rev., 87, 331,1999 Cyclotron resonance condition; co = Q - k* 37 Ion differential streaming

200 T ™

• Alpha particles 150 f are faster than the protons! Fast • In fast streams AV /kms" 100 the differential velocity is: Vp ()«n/sl so + 700-800 VL<< 1A1 x 600-700 • Heavy ions

"** "IMMST 3C0-'i(J0 travel at alpha Slow particle speed ma/mp

•30 I l I ! I. i i 0.3 0,4 05 C.6 0.7 0.8 0,9 IC KfAUl

Distance r/AU Marsch et al., JGR, 87, 52, 1982 38 Wave heating and acceleration of protons and oxygen ions

_ LHW RHW Machnumber 1.0 ...... M M /AV0^1.1VA N Thermal speed squared 0.8 ~ MQ= Mp

(plasma beta) • TQL/TQII^O.9 0.6

2 vA) 0.4, Preferential acceleration Tpi/"ipii"«i.i 0.2 and heating of oxygen 0.025 / .-* -

r, >----••"""* 0.0N^i__j i 20 21 24 2B Marsch, Nonlinear Proc. Geophys., 6,149, Heliocentric Distance /R0 1999 39 Results from fluid and hybrid- kinetic 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