the amJ cultural abdus salam orjan'»tion international centre for theoretical physics SMR 1331/6 AUTUIVIN COLLEGE ON PLASMA PHYSICS 8 October - 2 November 2001 Kinetic Physics of the Solar Corona and Solar Wind - 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 Sun'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 <D 10-2 106 104 103 106 104103 106104 103106104 103106104 103 in c>i <ii., , 17,283, 1990 Frequency (HZ) Compressive fluctuations in the solar wind 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 protons Vt (kmfe) VDF contours are segments of circles centered - V,, (km/s) 120 160 120 160 in the wave frame (< VA) Velocity-space Helios 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 proton, 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<RS) Flow velocity Distance from Sun Thermal speed 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.