the amJ cultural abdus salam orjan'»tion international centre for

SMR 1331/6

AUTUIVIN COLLEGE ON PHYSICS

8 October - 2 November 2001

Kinetic Physics of the Solar Corona and - III

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-PIanck-lnstitutfiir Aeronomie

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

• Structures and fluctuations in the solar wind • Alfven waves from the corona • Magnetosonic waves and density fluctuations • Coronal and interplanetary origin of fluctuations • Radial and latitudinal evolution of MHD turbulence • Spectral indices and cascading • Transport of waves and turbulence • Dissipation through wave-particle interactions • Kinetic wave-heating of the corona Spatial and temporal scales

Phenomenon Frequency Period Speed (s-1) (day) (km/s)

Solar rotation: 4.6 10"7 25

Solar wind expansion: 5 - 2 10~6 2-6 800 - 250

Alfven waves: 3 10"4 1/24 50C1AU)

Ion-cyclotron waves: 1-0.1 Ks) (VA) 50

Turbulent cascade: generation + transport -» inertial range -> kinetic range + dissipation Plasma waves and frequencies

b'LKCTHON PLASMA OSCILLATIONS Frequency/Hz SOLAR RADIO EMISSION

ION-ACOUSTIC MODE CUTOFF Non-uniformity ION-ACOUSTIC leads to strong WAVE TURBULENCE radial variations WHISTLERL,MOO£. ACOUSTIC WAVE RESONANCE AND SHOCK WHI$TLER-MODg . of the plasma TURBULENCE HEATING OF THE parameters! SOLAR CORONA

ION-CYCLOTRON AU-VEN WAVES MODH JUfSONANC

10 100 Gurnett, Solar distance /R< 1978 Power spectrum of fluctuations

(a) Alfven waves (b) Slow and fast magnetosonic (c) Ion-cyclotron (d) Whistler mode (e) Ion acoustic, Langmuir waves

MangeneyetaL, Log( frequency 1991 /Hz) Ion acoustic and Langmuir waves

ELECTRON PLASMA

w X C o

O

u

Gurnett , 1991

U.T. (HR UH] ODCX) 0200 0400 0600 0800 R CA.Ui 0.450 0A4B 0.447

HELIOS 2, DAY 92, APRIL I.-1976 Alfvenic fluctuations

b,

[Y]St*

• 5

Sb:

•5

600 ufkmi v| *-£" i 5 Bly! £00 o 0;00 6:00 9;00 200 R = 0.9? AU TIME (HOURS)

Neubaiier et cil., 1977 Sector boundary Alfven waves and solar E CL wind streams

Day 97^ 99 101 05 109 113 115 • High wave flux in fast 8 0,33AU«fcms-' 0,32AU379kms-] 0,30 AU 607 km r] 0.29 AU 733 km s'1 0.31 AU 659 km; streams 10 w 7: • Developed 10 turbulence CM : in slow 105 streams 1...04 1

® 10° - IO-I-I i

10

High-Speed Wind

Reduced wave number K* = k/2n (1/kmJ

Mcirsch und Tu, Kolmogorov-type JdJi59!i5 8^.11, 1990 Solar wind turbulence

Parameter Coronal Hole Current sheet (open) (closed)

Alfven waves: yes no Density fluctuations: weak (<3%) intense (> 10%) Magnetic/kinetic = 1 >1 turbulent energy:

Spectral slope: flat(-i) steep (-5/3)

Wind speed: high low

Tp tte): high (low) low (high) Wave heating: strong weak

10 Small magnetic flux tubes and photospheric granulation

ii' (I

:• '- 111 1 1 1 i t *, :4pi • • ,\\;V.! ii I///// 1 Whiter Fluxtubos '\5.y5'!.'i';'// "'••.

I' "M

3b Mm x 40 Mrn Maijnotif; regions (soon in (i band noar430 rim) botw(?on granules

.Scharmer, . • • i i* • 1993 Solar wind outflow from magnetic network lanes and junctions

10 km/s

Line-of- NeVllI770A sight (630 000 K) Doppler September, velocity 1996 images +10 krn/s

North and Raster scan midlatitude 540"x 300" polar region Network In Sill 1553 A Mcisslor ot (10 000 K) ill., Science, 283, Kin 12 iynamic network and magnetic furnace by reconnection

Static field Waves out Gabriel (1976) Microflares

New flux feel in at sides by convection (t ~ 20 minutes) Axford and McKenzie, 1992, and 7 Space Science Reviews, 87, 25, 1999 FE= 10 erg 13 EUV jets and reconnection in the magnetic network

Evolution of a jet in Si IV T 1393 A visible as blue and red shifts in SUMER spectra • E-Wstep size 1",At =

RED 40"

Jet head moves 1" in 60s 3 BLUE scan position

Innos at ol., Nuturo, 386, 811, 1997 14 Height profile of wave amplitude

Heliocentrlc distance / 1,20 1,25 1,30 1,35 100 SUMER Si Mil: 1997 May 28/29, 2215 ~ 0035 UT 1445 & D - - Interval vi Doppler 4- 1440 A m Silicon VII! f velocity

m U1440,1445 c

3p North polar a. coronal hole o 5 1 1 DC

At 1.33 Rs:

[50 200 250 300 350 7 Tsi*10 K Height above limb/ » 70 km s1 arcsec 6 3 ne« 10 cm™ Wilhelm et al., ApJ., 500, 1023, 1998 15 Stream interaction region

Dynamic Magnetic sector boundary, some 30°jDff_ processes stream in inner— planetary space • Wave amplitude steepening (n~ r2) • Compression and rarefaction • Velocity shear • Nonlinearity by advection (V*V)V

Sector boundary new within • Shock formation at; stream (co-rotating) "Interface* 16 Spectral indices and spatial evolution of turbulence

107J

N N ^ ioe w e

m *« 104

m3 *\ 8 4 3 io~ IO"5 io~ io Frequency (Hz) Frequency (Hz}

N x • Spectra e i 0.69 AU 1 420 km s1 steepen! i 95% + Mursch and • e » e~, Alfven I u, JGR, 9!i, 8Z11, 1990 slow <-> fast wind waves dominate! 17 Spectral evolution of Alfvenic fluctuations

m 18 „ • Steepening by

o cascading • Ion heating by wave sweeping o • Dissipation by wave absorption

at

io

High-frequency Frequency {Hz} Tu and Marsch, J. waves in the Geophys. Res., 100, 12323.1995 18 turbulence dissipation through absorption of dispersive kinetic waves

• Viscous and Ohmic dissipation in collisionless plasma (coronal holes and fast solar wind) is hardly important • Waves become dispersive (at high frequencies beyond MHD) in the multi-fluid or kinetic regime • Turbulence dissipation involves absorption (or emission by instability) of kinetic plasma waves! • Cascading and spectral transfer of wave and turbulence energy is not well understood in the dispersive dissipation domain!

19 Quasi-linear pitch-angle iffusion

Diffusion O +OO equation M i

X V v, ,t) Vida ± da "

Pitch- d V\ angle da dVv gradient in wave

Konnol and tlngolrruinn, 1966 20 Ingredients in the quasi-linear iffusion equation

Normalised ( M ) wave amplitude T=j £ (Fourier)

»«;vii 2 Ml) Wave-particle sCMz relaxation rate x + x 2^ M

_ Resonant speed v- / HU\ssol function Miirsch, N011I. Proc. Goophys., in prc\ss, 2001 21 Plateau formation by wave particle diffusion

Wave-frame coordinates ; u r2 Transformed velocity U\\ = U cos a; Ux = U sin a; /-- = fAU, a) distribution function UAk)

Miirsch s l Plateay in .= 0 UIKJ TU, da JGK, in pitch-angle press, 22 Pitch-angle diffusion of

Vt (kmfe) VDF contours are segments of circles centered - V,, (km/s) 120 160 120 160 in the wave frame (< VA)

Velocity-space resonant diffysion V, (fcm/s} caused by the cyclotron-wave

V,» field! 120 180 d 80 120

Marsch and Tu, JGR, in press, 2001

23 Quasilinear diffusion model of solar wind protons 0,2 0.2

z=4z0

0.1 0.

0.0 0.0 •0.2 0.0 0.2 -0.2 0.0 0.2 Qytward waves only!

0,1

0.0 -0.2 0 Galinsky and Shevchenko, Phys. Rev. Pitch angle diffusion! I -85.90.2000 24 Oxygen and hydrogen velocities in coronal holes Outflow velocities 700 ."(•"""I T""t T"~T"~ Preferential acceleration 600 of oxygen!

Jj 400 0 300 4 200

100 , mass flux conservation 0 1.5 2.0 2.5 3,0 3.5 4.0 r / IU

Cranmeretai., Ap. • Magnetic mirror in polar coronal J., 511,481, 1998 hole 25 as* if % # j*"^ I Absorption of cyclotron waves

•*• (••—••< Oxygen ion damping rate

Frequency sweeping

Self-consistent 200 210 220

power spectrym 0.1000 E

Height/km 0 ^ X 0010° \\ \\ \V 5000 \ \ \ \ \ \ / 10000 JZ 0.0010 15000 a.

0.0001 190 200 210 220 Tu and Miirsch, JGR, 106, 8233, Frequency (Hz} 2001 26 Resonant heating and acceleration of ions by cyclotron waves 600 600 Strong proton £ 400 .^400 0+5 heatin x g o S o 200

•3 O

2.4 2.8 3.2 3.6 2.4 2.8 3.2 3.6 2.4 2.8 3.2 3.6

r(Rs) r

P(t): =300 nTVM/ at 100 Hz at 2.6 Bs luandMarsch, +5 JGR, 106,8233, Good agreement,, but wrong 0 amisotropy 2001 27 Evolution of wave power spectrum

2-0

1.S

1.0

3.8 Rs Distance 0.01 atQ,

Variable wave spectral density P(f) [nP/Hz], f = 100-180 Hz

Tu and Marsrh, A&A, 368, 1071 2001 28 Reduced velocity distributions

oo W\ Number of fo particles

oo Perpendicular thermal speed

f x \ roo 0 Moments f „„ /1 i KW\\ J \ Normalisation

•2

•CO Marsch, Nonlinear Proc. Geophys., 5, 111, 1998 29 Model ion velocity distribution in coronal hole

+5 Oxygen 0 ion VDF at 1.44 Rs Waves+collisions+mirror force

D-

J5 *i t i t I I it I I 11 I t » 11 1 I Pj t 1 1 11 t i 11 11 t tit* 11 .frl 11 I t/l t I E I t *i I II it 2 0 •"i *;-n(ti/||) wj 2W ) 2wW^1(w|j) liMO

Vocks and Marsch, ApJ, in press, 2001 30 Semi-kinetic model of wave-ion interaction in the corona

dF\II dF\ dF\ dA(s) v z T I r dt as \m 8v\ 2A(s) ds SF, SF> Parallel VDF CouL St

8F± q \ 8F± 8A(s) E 9W ) -s h dt \ 2A(s) ds

.2 SF± t SF± Perpendicular 4 CouL VDF IT

Vocks and Marsch, GRL, 28, 1917, 2001 31 Reduced diffusion equations

a Number of J ****** n particles dui\ 3

w w dw\\ ^ i ll ill l

Perpendicular Tit 1 ^~"~^ 9 a D W F thermal speed St j j±d'

3 Aj{w\

— a 2 F-1 (11 ,AJ(W|I:

Marsch, Nonlinear Proc. Geophys., 5, 111. 1998 32 Diffusive transport coefficients

Diffusion roo \^ X Acceleration 3 M (2TT) */ ""UU Heating \

DO sCL X k OO fc \

Wave particle relaxation Mcirsch, Nonlincdr rote and resonance condition Proc. Goophys., in oress. 2001 33 Reduced velocity distributions and anisotropy in coronal hole

10! II I i I II -rrrrTTT rrri i i » i t r » ' rn-rrn I i > > i nn n 10' H+ I R E 10D He++ 10 i i i i i i i i i JL-1JL1...JUI-J-II I I Ml II t-JLJ-l.JLj..JlJ-1-J-i-l till ,JJLJLljLlJ--LJL-LJLJLJL 0+5

I I I I I I I I. I I. i.I 111! .I..I....1...1..1 L.Lt-J-1 1, I, I I, I. t.l I...I I ,IJ,,,,I,,I,,,,I t

Strong anisotropy -H

I, I I I II III I I I I I J^LJLJL.J_J_i. J-

(v,, v,} / V Vocks and Marsch, GRL, 28,1917,2001 Height = 0.43 R, 34 Plateau at marginal stability

5.0x10 :i nrTTTTTTT~ri rt t r m | i i i f t rrrryi r rt rt n i j i n TTTTTI [ t i i i > tin

•5.0x10

•1,0x10

•1.5x10

•2,0x10 I I I I I I t I I i I I .I...I I I i I 1 I I I I I I I Kl t I I t I I I I...I...J...J 11 t I...JULJLJ I I M I I I I t t I..I •2 1 2 3 .Vi v,, Resonance T\n rri • Vanishing 0+5 clamping rate for ion-cyclotron waves • Large temperature

3 -2 -I D 1 2. 5 APJ, .44 R 2002 35 Gyrotropic velocity distribution of oxygen Ions In corona

• Mirror force • Waves particle interactions • Coulomb collisions

leat flux cind unisotropy at «73

Vocks and Marsch, ApJ, 36 Obervations and semi-kinetic models of solar corona and wind

• Coronal imaging and spectroscopy indicate strong deviations of the plasma from thermal equilibrium

• Semi-kinetic particle models with with self-consistent wave spectra provide valuable physical insights

• Such models describe some essential features of the observations of the solar corona and solar wind

• But the thermodynamics of the solar corona and solar wind requires a fully-kinetic approach

• Turbulence transport as well as cascading and dissipation in the kinetic domain are not understood

37