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Transferencia de energía y cantidad de movimiento en magnetósferas inducidas Romanelli, Norberto Julio 2015 12 04 Tesis Doctoral Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires www.digital.bl.fcen.uba.ar Contacto: digital@bl.fcen.uba.ar Este documento forma parte de la colección de tesis doctorales y de maestría de la Biblioteca Central Dr. Luis Federico Leloir. Su utilización debe ser acompañada por la cita bibliográfica con reconocimiento de la fuente. This document is part of the doctoral theses collection of the Central Library Dr. Luis Federico Leloir. It should be used accompanied by the corresponding citation acknowledging the source. Fuente / source: Biblioteca Digital de la Facultad de Ciencias Exactas y Naturales - Universidad de Buenos Aires

t s 1 t s 2 t r s rt t ís r s r r 2 t t tós r s s s s r s t r t r r tít t r rs s r s ár s ís s r r rt r t r s t s s r és r rt 2 r ó 3 s r st s r r ss r r st t t str í 2 ís s s r s r s r

s r s t t s s r t r tr r st s s s str ís s r s t s s r r s 2 tr r t s tós r s s s st s r ás s í t s rt tá s 2 t P 2 t 3 s r st s r st t s s s s s t t rr t s t ór s s st r s t s s s s 2 s r ó s st t s ó s tr s r r í 2 t t tr s t s 2 s q s r s í t s t r r s s s s r s s r í s rt 2 s r s s s rs r 2 r 2 s 1 r ss 2 s r ó st s r s ó s q r t r ó s s 1ós r s t s r t s t 3 r t ór r s r ó t r á q t t t é t s s t s rr t 2 tr s r s rt r t rí ét rt r s t ór s rt s q s s s r s r r t ér tr s t s ér s s t s s s rt r s s t é s str t r s tós r s s 2 s s r s r t t r s t s r t s s r s r í ét r st s r t r r r í ét s t é st t r t 2 st t r s r s r st s r s r t t r st s r s r s s t s s t s tr st s tós r s r s s r s r st s r s ss s s t r t é s r s s r ó rtí s r s r t s t ós r tá s st s str rt s r3 s t s ó ét st s t r s 2 s r t r r st s rtí s q r s té t sí t s s tr t st t s s s tr t r ó s t s t s ér s s s s r s t s t r s s t 3 s 2 r t tr tr s s s r st t s r s s tr s r r í 2 t t P r s s P s s str ís s tós r s s í ét s s tr r r s ó t s ér

r s r r 2 r t t s r s str t t r s t t s s s t tr t t t st 2 t str 2s s s t s rr s t r t t s r s s t s r s2st r s 2 t s rs t s 2 s t 2 s s r ts r 2 r t s ss s t t r t t r t t s st 2 t r rt s t s r ts t r r t s t r t tr s r r 2 r t t t s ts t s r t 2 t r r rt s t s s s r 2 t rs r 2 r s 1 r ss s r ts t s rr s rs s t r r t s t r s st t s t t r s s r s t t t r t t r 1 s r s t t s r t s s t t 2 r 2 s r t s r t r t r r t s t t t ts s s t rr t t r t ts r t r t s t t t s s r r t t ss tr t s r rt s t ts t 2 2 s t q t s t str t r t s ts r s s t r t s t s rr r r s ts r r t t s r t s t t r 2 t 2 t rt r t t r 2 s s st t s rr s 2 s t t st t 2 s s r ts r 2 t s r t s s t t r s r s t t s t t s t s t s t s r s s t s r ts r 2 t ss s r t s st t t r t r ss s r rt s r t t t s r t s st s s t rt t t t s r s t s r ts t r st t s t 1 rt s t t s r t s s r2 t r r r t s t s s s s t 1 t r t t t r s 2 t t s r ts t r r s t t 3 s r ts t r t s t r s t st 2 s t t r t r ss s tr s r r 2 r t 2 r s str 2s s s t s r s t t 2 tr r q 2 s s t s r r s

s r s

r t s r r r q r r r rs s r s 2 s st s tí s 2 é s rt r r 3 st t t str í 2 ís s r r r s st s 2 t s s r s r s rr st tr é q r r r és r r r rt tr r st t s s st s t át st t s s P r r s s r s tr P r s s s r r r s r r r t 1t 3 r s tr s r s r r s 2 r s ó r r ñ r t t t r r st r s t 2 á 3 r 2 s st tr r q r t r s r r s 2 r s r st r s r 2á P r t 2 á 2 3 q s s r 2 st r r r s r t ír r r t 3 r r r ñ r t r á t s r 2 q s r s t t s r s r

t r s s r t t q st s t s 2 r t s t s t 2 2 2 r tr tr t t s t st rs st t s 2 2 r

P t s r r r s rt ó 3 3 Pr t 2 tr s str r rs s r t s r rs r 2 r P t rt r 2 ó 3 3 3á 3 r r r t2 s t t r t 2 tr r q 2 str r rs t r rs st t 2 r 1 s r 2s s tt rt s r t r2 r t t 2 P t ó 3 rt t 2 st t t 2 r 2 r t 3 t s r str 2s r rt r rt P r t rt r tt t s rt2 t s r t t s t t t t s r s 2s s P 2s s s rr rt P r s r ss r r t s t s s r t 2s s tt rt r 3 str r t 2 tr s t s r s r 1 2s s P 2s s rt ó 3 3 t rt t s t t t r t r2 t r t s r t s r rs r 2 r 2s s P 2s s r ss

List of Abbreviations AB ASPERA AU BS CA CAPS DOY DRAP E/C ELS ER ESA EUV FGM FOV GCM GZ HT IC ICA ICE IM IMA IMB IMF IMS IN INMS Aerobraking Analyzer of Space Plasma and Energetic Atoms Astronomical Unit Bow Shock Closest Approach Cassini Plasma Spectrometer Day of Year Draping Energy-per-Charge Electron Spectrometer Sensor Electron Reflectometer Electrostatic Analyzer Extreme Ultra-violet Fluxgate Magnetometer Field of View Global Climate Model Giacobini-Zinner dehoffmann-teller Ion Cyclotron Ion Composition Analyzer International Cometary Explorer Induced Magnetosphere Ion Mass Analyzer Induced Magnetospheric Boundary Interplanetary Magnetic Field Ion Mass Spectrometer Inner Negative Ion and Neutral Mass Spectrometer

IP IPRL KSO LEF LH LMD LP MAG MAVEN MCP MEX MGS MHD MISCHA MOI MPB MPR MSH MSO MVA MVAB ON OP PCW PH PRL PSD PVO RH RHS Inner Positive Inverse Polarity Reversal Layer Kronocentric Solar Orbital Linear Electric Field Left Hand Laboratoire de Météorologie Dynamique Langmuir Probe Magnetometer Mars Atmospheric Volatile Evolution Microchannel Plate Mars Express Mars Global Surveyor Magnetohydrodynamics Magnetic field in Interplanetary Space during comet Halley s approach Mars Orbit Insertion Magnetic Pile-up Boundary Magnetic Pile-up Region Magnetosheath Mars Solar Orbital Minimum variance Analysis Minimum variance Analysis of Magnetic Field Vector Outer Negative Outer Positive Proton Cyclotron Waves Perihelion Polarity Reversal Layer Power Spectral Density Pionner Venus Orbiter Right Hand Right Hand Side

RPC RPWS SAE SC SD SEM SLT SNG SOHO SPO SSE SSS ST SW SWIA TIIS TOF UCT ULF UM VEX VHM VSO WH Rosetta Plasma Consortium Radio and Plasma Wave Spectrometer Southern Hemisphere Autumn Equinox Spacecraft Standard Deviation Solar Extreme Ultra-violet Monitor Saturn Local Time Singles Solar and Heliospheric Observatory Science Phase Orbit Southern Hemisphere Spring Equinox Southern Hemisphere Summer Solstice Straight-Through Solar Wind Solar Wind Ion Analyzer Titan Titan Ionospheric Interaction System Time of Flight Coordinated Universal Time Ultra Low Frequency Unstable mode Venus Express Vector Helium Magnetometer Venus Solar Orbital Whistler

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s 1 r ss t t r s str t P t s 2s s t s r ts r 2s s s r t r r r s r r ss rr t t s r t s s r r 2s s é st t t 2 t t s r s t t t r t t r t r ss t P 2t s r t t t r t r t t tr t r t t t r s st t2 ts t P t P r r 2 t t ss s r t r st s t t t rt t s t r t s r t s r t 2s s s t r t r s ts t t str t r BXDRAP IMF s ss s s Pr t 2 tr s str r rs s tr t s r t r ss s s str r rs t s 2s s 1 s s r t s 2 s tr rr t P r 3 t P r 3 t r r tr 1 t t t rt s r rr r r t2 P s str r rs t s r rs st t 2 r 1 s r s str r s 11 P s s

s ss s s t s s r t t 2 s r s r t r ss s t t r t 3 s s r s t s t t r s r t r ss s s r t s P s r t P s t r t t é t2 r Pr rt s r 2s s t é st r 2s s s ss s s r s é r t r t r s 2 s s rs s r s 11

P tr t s s q s tr s r tr rt s 1 ts t r st t s s s r s r t r 3 2 1tr 2 s t s t rt r s r s r s2st s t s r t t s s t s r s s s s sts st 1 s 2 r rt s r 1 t s t s r t t t t 2 3 t s 2 s r t s tr s t t s r ss t r t t ttr t t s r s t t r s r ss r r t t t s r r t t rst r s s t ts 1tr 2 s t2 t s 3 t t r t t rt t s 1 t tr t r s s s t rt s r 1tr 2 r r r st t r t r t t s rr s r t s t r r 10 8 s r s t ts t t2 t ts t s r t s r s t t s s t t r t r2 t r t s r s s r tr t t s s t r st r r r t t 2 t (L D ). t t rt s r t t 2 t t s t r r t t s ss t 3 t rr s t r t t t t s s s rs s r s t t rt s r t r

tr t t r s st s t s s s r 2 r r t t s s t t rt r t r t st s t t t s ts t ss t t r t2 s s r rs s s r t t r ts r t 2 t t r s r s st s t tr s t s s s t rt ts t tr s t s t s r s r t 2 t r t t t t s r s r s t t s r 3 s s rt r t str t 3 s t r r t r ss s s st r ts r t s r s t s r s2st t ts rs s t r s r st s t t t s t t ts ss t s s 2s t t ts s r ts r s r s2st s t s t t ts ts t t t tr s t s r t st r r rs t t 3 r < 10 18 ss t s < 10 21 ss t rs < 10 21 ñ t t < 10 20 t rt 10 25 t ts r t t2 s ts r s t t s r s2st t s s r ts s t s t s s r r 2 s r s ss s r t t s rs s t 2 s t s t r t t r t t t rs t r rt s t s s r 2 r t 1 r 2 t t t 1t r str t 3 s t rr s t s r t 3 st t r st 2 s t t r r s t s r s t s 3 str t t s t t s r t 3 st s rt r t str t 3 s s r 2 t s s st t t 2s r ss s r t r s r t s r rt 2 t r s t t r s s r s t t2 s r2 r t t t s t t s ts t 1t 1 s r s tr rt s s 3 t 1t r s r s t t ts r r s t t r2 r s t ss t 3 s t r ts t t s ts t s t t str t 3 s s r 2 t r s r t r t t s t s st t r P s s

tr t tr t st s r r r s ts rr ts t t s s r rr ts t r r t t 1t r str t t r r t t s t 1t r s s t t2 t s s r t t t s s t r s r t str 2 s t t r 2 s r t s rr s t s st s 1 s r tr t s 3 r 1 s r s r t s s s t s rs t s s r r t 2 t tr t s r 3 t t s s r r r s r r r t t t 1t r t s tt r t t r 2 t r t 1t r s s t t s s s t s s ss rt r r t r s 2 t 1t r t 3 s r s r s st t s s s t r 2s r rt s t t t s 1t r 1 s r s t r rt t r t st 2 t 1t r t r 1 s r r rt s r r t s t t s r t 3 t s t r tr t t t r s ts t s r t rt t s q s r ts t t t 2 t s rt t t str ss t t t r s s t t s t t s r t t t r s t t r t s r s t tr s r t r 2 t s s 1 t r t r s r t r s 2s s r t s rs t s r r r2 r t rt r r r t 2 r t r 2 t t str r 1t r r t t rt s t s 2 r t s tr s t s s 1 t r t t t t r t r2 t s t2 t s t2 t t s t s s t 2 s t rt 1 s r 1t s t t s st s r s r 2 r s 3 t s s r t r t s st t s t t r s t tr r q 2 s s s r s t 2 t s r 2 r ss r t t t r t s t s r r 1 t t tr ss t t t t t 1t r t rs s r s

tr t r s s t str r t 2 t t t r rt s t s r r r t r t s r s t st t s t t s t s s s t r2 t t s rs t t 3 s s s s s r t r r rt s t s rt t t t t s t s r t t t t ts t tr s t s r t r st t s s r t rs s t t R M r ts t r R M st s r r s rs 1R M = 3400 r t t r t r t t s r t s t t 2 s r r t t s t t R M r t t r rs t s t t r t t t t t s r r2 1t t t s 2 t s s rt s t 2 t s t r s r ss r t s r t r 3 2 str t t2 t str t r s s t r t t s r t s t2 r s s s r s t ss s s t t r2 P s r t s t r t 2 s r t t 2 t t r2 s t s r t r 3 2 s t s t t r 2 tr s tr t t str t r t t r r r t t r t ts s t s ts s s r t s t t R M r t t r rs r t t r t r s t t R M r t t r rs t s r t r t t P t s s s t r2 s t 2 t t r ss r s 2 t r s ss t t2 t t t s t r t t t 2 t s r r r t rt s r s s t t t t r s r ss r s t t s r t r 3 2 r r s t t r tr s t s s t t t r s s r t s t s t t 450 t t t 2s t r t t s r t t r t r s r t t s s r t r t r2 s t t r s ts r t t 3 t t r t s r tr s t rt t s t s r2 t s P s s

tr t t t t s t str r t P s t ts 1t s t t s t t r2 s s sts t t s s t t r t s rr t s s t s t r t t t r t rs s t t t s t r t t r2 s r P s r s r s t s r t s rr rs r t r t 2 t s rt t t t t t t t s 1 st t rs ss ss s r st t s r t t s t t s t t s r r t s t s r t s s r s ss t t t s r t rs s s r r t str t t st t t 3 s t s r t s r2 t t t s P t s s s t st 2 s r 2s rr t s rr s s s s s r ts r rs s r s

tr t 2 r s s ss s t r r t t s r r r t t r t s rt r s r 2s s r ts rs t s t t 2 s t s s s str t r s s t r r s t s r t r t s r t s s s t s r rr t s r ts t r t s t 2 r 2 s r t t s t r t r s t t 1 r s t q s t 2s s r q r t t r r t s r ts t 2 r t s r ts t t s t s t str ts r t s ss s r s s ss t r r ss s t t t 2 t s r rst 23 s r t r s t r s 2 2t 2 s t r r t 2 t t 3 s s r s r t 2 r s r r t t s t r t 2 s r 1 t2 t r t ss t tr t r st 2 st t s r t st t t t r 2 t r ts rs t P 2 s s r ts t 2 t t t rs r t rs r 2 r s r ts r s t 2 t r st 2 t r rt s t r t s s tr r q 2 tr t s s s r t 2 tr s r P s s r 2 s 1 r ss t str r s rs s r s t 2 P rt r 2 23 t r t tr r t t r r t r t t 23 r P s r t t s P r t r r s t t 3 s r t s rr t r s r st s t t t t r t r ss s s r s ts r t s rt r t s 23 t r 2 t ss P s tr t r P r tr s s t t t r t P s P r ss t t r r t t s r s t t r 2 t s t s t t 2 t r r s ts t s s t s t s s P s s

tr t s st t r r s t t s s t r s st r r s r s s ís s q t r s r r s 2 tr tós r s s r s r st s r st t s s s s s t r r t s r s rt r st t s s t ór s rt r s 3 str á s s tr t s rt t s 2 t 2 st t s s stá str t r s t r ít r s t s r s s r s t ór s s s s q s t 3 s r s r r st t s ó s q rr st s t r s tr tr s t s t rí t r á 2 stá t s st ít ít stá s rr r r s té s á s s t s s r s r t r r t r s r st s r st t s s s s s s t s 2 s s str t s r st s s s t é s s t s ít tr t s r t í ét tós r Pr r t 3 s st t s r t ríst s rr t ét r s ít t r q s t 3 r t t t r 2 r r s r t r r st t s r t s ét s r s 2 r t r s s s é tr s 2 ét s s s s r ó st r ás st s r í ét s t r s rt 2 t P 2 sá s s r st s r s tó tr s r s s s rs r 2 r 2 r s t t ít st s s r s 2 s s s r ó s tr ét s s tr r s s tró r tó s r s r 2 s 1 r ss s r s s rr rt 2 s r s t t rt r 3 s t s r st s r tó tr 2 r tó tr tr s r 2 2 3 r P s s 2 t s r ét s P r rs s r s

tr t ít stá tr t r s t 3 q r tá s té t ás r t r 2 s r s s r ó s s ér q t r tr s tós r P r st t r rt r 3 s t s r st s r s tró tr P s r tr s 2 r t s tó tr 2 str t s P s 2 P r ss t r r t s s s s r s r í ét s rí r s t t tá t ít r s t s s s s r s r s t t s s P s s

P P 2s s r t s s t r t s st t s s s r 1tr 2 t s s s 3 rt s r t r s t r s r s t t r r2 s t2 r t t t 1tr 2 r t r2 t r r r2 s t rs t r rt s t 2 2 r s t t r s r s t 2 t r t s r s t s t r s t r t s s rt s t ts r2 r t rt s r t t r rt s t s r 2 r s s t r r 2 t t t r t s t rt s r rt t r r s t t t r t s s r r r s t 3 s t t r t s s t st t s t r s t s s ss t st 2 s s s t r s t s r t t s t r r s t t t r t ts r t t rt t s r t s s s s s t t r r t s r t s s s q t t rs

P 2s s r t s s t r t s rt t s s tr 2 tr s r s 2 r rt s t r s tr t r s r t r rst t r s t s s t s r t 2 s r rt 1t r tr E t B s r 2 2 t r ts st t r s ts r t r r t s r t2 rt s t t t t s t t t t s s r t r t s t r t r s st t r s q t t r r t st rt r q t2 v s t t t s E B s ts m dv dt = q(e+ v c B) r t t s E = 0 B st t t r t3 r r s t q v c B t s r s r r t t t2 t r t r s r t r t rt t t t s v s t r s s B v s s st t s s t t v B s s t s t t r rt t r r t B t t r r s r r t r s r L = mc q B v : Larmor radius or Gyroradius s r r q 2 s Ω cq = q B mc : Cyclotron frequency or Gyrofrequency r s t tr t r2 s 1 st t t r t s t r r r s t 2r r q 2 s t s s t rt 2r t 2 s t r r 1 t s t t s t2 t t t s rr t rt s r t s r r t s t2 r r r s 2 tr r q 2 t r s 1. P s s

P 2s s r t s s t r t s tr r r t tr s t 3 r t rt tr t r2 s t r s t t r s s t s r t t r F r tr r t B t rt r t t t r t t a = F /m. t s t s t tr str t 2 r r t B t s E B. t s s t tr t r2 t r rt r t r s t r s ts r tr s 3 r 2 s t r t3 tr s r t s t E B t tr t s s r r r r s t 2 s r r r r t r s t t t t2 v r s r r t st rt s v/c 1 s r 1 r ss s t rr t t rst r r v/c. tr t s t r r r r 2 t r t3 tr s r t s t rst r r r E = E+ v c B B = B v c E s t t t E = 0 t E = v c B t s B = B t rst r r 2 s t s tr s r t s r rt t t s s t t t B tr E B s s r t r t t 2 t t tr r r t B s r t r t t s t t2 v = V D t r s t t V D = c E B B 2 t r r s t tt r r r r s E B = E B+ V D c B = 0 t s r r r t t t r r t B r s t t 2r t t t t t r r t B s t t s r s t t 2r t t s r t t2 V D t t t t s t2 r t s t s r r rt s t s s s r s t t t r r s 2 s 2 r t t r qe q t 2 r r F t r s r t V D = (cf/q) B/B 2. r t t s r 2 r s s r t r t2 s t s t r st q t t 2r r s t t t E B s r r t B t t v. rs s r s

P 2s s r t s s t r t s r r t q t t rs t 2r r q 2 t t r 1 t 2 t 2r t s r r t s s 2 st t s tr 2r t s t tr t rt t s t s t r rt s 2r t r t t s t r t t r t t r s t t t s t2 ts s t rr r t tr s rs t r t r s s tr s rs r t r r t r st t s ts s r rr t 2 r r t t s rt s t r s s t r 2 s r t t rt s P s s s st t s r tr rt s ss s t st t t s s2st s 2 t s t r t2 v rt t t t t t s t r 2 t q t t r rt t s r t r t rt s rt s s s r s r st s st t st r t 2 rt s r s t t t2 s st r t t2 str t t r rt s s s r ts t r t q t t r rt 2 r t q t r t t2 str t t2 str t t r s s s f s (r,v,t), s s t t t r rt s t t [r,r+d 3 r] t t s t r [v,v+d 3 v] t t t s d 6 N s = f s (r,v,t)d 3 rd 3 v st s r t t st t t s s 2 s t s r t s t r s s s t r s t2 t r t2 t t r 2 r t r r r ts f s t2 s r s t2 n s r t t2 s rt s s n s (r,t) = f s (r,v,t) d 3 v V 3 r t2 v s s v s (r,t) = 1 f s (r,v,t) v d 3 v n s (r,t) V 3 t r 2 t s t r r r t t2 v s (r,t) s < 1 2 m s(v v s ) 2 >= 1 f s (r,v,t) 1 n s (r,t) V 3 2 m s(v v s ) 2 d 3 v P s s

P 2s s r t s s t r t s 2 r st t rt r ss r rt s s s s s r t t t r r r r 2 2 p s n s = 2 3 < 1 2 m s(v v s ) 2 > t s t r 2 q r t t r t r t t2 str t t s ss t r t t2 s t s s str t s t 1 t3 str t m f s (r,v) = n s ( )3/2 exp [ m s(v v s ) 2 ] 2πkT 2k B T s r k B s t t3 st t t s t 1 t3 str t t t r s s v th,s = 2kB T s m s t t r t sq r t r s s < v 2 >= 3k B T s /m s s t r t r 2 r rt t r r r t t2 v s s W =< 1 2 n s(v v s ) 2 >= 3k BT s 2 s st t t s r s t t r s t r r f s t r ts r t t s rt s q t r 2 t s s t s r t r s t t st s s r t r s s s r s 2 st t s s s t r rt s s s s s tr s s q s tr 1 ts t r r ss 2 r rt s t q 2 s s t rt s st r 2 t r r s r t s s r 2 rr t t r t s s t s s s s t r 2 t t r t t t rt s s r t 2 t r t r rt st < r > s s r t t t r t r 2 r rt e 2 < r > k BT < r > n 1/3, t r t r Γ t r t t r r 2 t t r t t k B T Γ n 1/3 e 2 k B T rs s r s

P 2s s r t s s t r t s st s r t t2 r t s t q 2 s s t s t s r s Γ r s t 10 8 10 7 t r s 2 t tr st r t r rt s s t tr tr t2 t t r 1 s t rt s r 3 t s tr t2 t t t t ts t r s t s r s t t r t 1 t 2 tr t t s s t t t tr st t t t t st r r r q q r tr s s Φ(r) = q r e r/l D r L D t 2 t s kb T L D = 4πne 2 t st s r L D t tr t t r t r q s r 2 t r s t r L D t r s t 2 s 2 t r s t t s t t t st s s r r t s s q s tr t s s r r t L D. s r t r t s r t r 3 2 r s t2 n 5 10 6 3 T 10 5 s r s t t 2 t t s r t s t s t t s rt t t t t 2 s r q r s t t r s 3 D t s r r rt s nl 3 D 1. t t t t Γ L D t tt r t s r s s (4πΓ) 3/2 1. t s t 2 t q r s rt r r st 2 t r rt r t tr t t r s r str t t s s s 2 t r st r t 2 s tr s r st r t t s t 2 s t t t s t s t t s s T = 2π me 4πne 2 2π w pe r w pe s t tr s r q 2 t r s t2 n 5 10 6 3 t s r tr s t r q r t 5 10 5 s t r st r t 2 s s t r st t t s s t r t tr s s tr s rt s t r t 2 r s t s t s r t 2 t s rt r r s r 2s t t t r rt st s r 6 r r r st t t t s t s r s t2 t s r s t s s r r t t r st t rt s t s t t t2 t rt s P s s

P 2s s r t s s t r t s str t tr t r s t 2 t t r t s t s s q t r t s t s s t t r t s t rt s r tr t t s t 2 r r r 2 s s t t s rt t r ts t r r t r rt s t t s r t rt s t t r s t t r ts t t 2 t r t r s tr t s t tr t s t st t st s tr t t s r r rt s t t s t t r r s s t s tr st t t tr s s t t s t t 2 3 s s s ss s t s t t s t r rt s r t r tr t r2 t t t s 2 t t tr t s 2 r r t t t 2 3 s s t s t s s t t rt t s r t t s t 2 t t s s t 2 str s t s t 2 s ss s t s t t t s r s s t s t r s t r t r rt tr r t r s s s λ mfp = [ 4π 3 nr2 l ln(1/γ)] 1 r r l s t s r s s q t r l e2 k B T s ss 2 3 s s r t t s r rt tr t r2 s 2 t r 2 t t tr t r s 2 t s s s s t s 2 t t t s r K n λ mfp /L s r r t t t2 t L t r t r st t s t r st 2 P s t s r t st s r r t t t s r 2 1 s q t s t t q t t tt r t r t t t f s (r,v,t) r t str t t r t s s s t t r s r r r s t s s r r q t 2 s r 2 t r 1 t 2 t s t r t r st t s r t t tr st t r s r2 t s r r t t rt r s t s t2 str t t r t t r 2 q r 1 r s st t s t t r 2 1 str t s r r s t rs s r s

P 2s s r t s s t r t s q t s t s t q t s t t 2 r rt ss t s r r t q t r t s t r t r s t st rt t s r ss s r t rt t r t s s s t t2 s t r r t s s s r r t s t 1 r 2 t s rt s 1 s t s r 2 1 r ss s r t 2 tr r s t s st t s r r 2 1 r rt s t t2 str t t r r t st s s t r r t t t3 q t s f s t +v f s r + q s m s (E+ v c B) f s v = f s t c r q s s t r t s s s rt m s s ts ss t r t s r r s ts t ts s rt r s s s t r s st t s r t s r t r t s q t t t t t r t t t t s t s s t r t t r2 s s s s r r2 r r t s r t s s t r t s r t r q t s t t s q t f s t +v f s r + q s m s (E+ v c B) f s v = 0 s s t t q t s r t r t t s t s s t st r q t s t r t t2 s t 1t s t r 2 s r t t 2 r 2 s t r2 r s s t 2 r 2 s r ss s t t t s s t s t r 2 q r q t s s r t s s t t t 1 r s tr t r s s r t r 3 2 r r rt s r t rt s s r q t t s t s ss t r 2 s r t t r r q t t s s r s s 2 3 2 r s s t t s tr s r t s ss sm e m p r s t 2 q t s t t2 r t s t s s ss r t st s r t r t n i,e t + (n i,e v i,e ) = 0 P s s

P 2s s r t s s t r t s s q t s t t s r 2 ss t t tr s r t s r t r t r str 2 2 t st t 2 s 2 t r t r s 2 1 t t r t rr s q t s r r s t t r t r [ ] vi m i n i t +v i v i = q i n i (E+ v i c B) p i +R ie [ ] ve m e n e t +v e v e = q e n e (E+ v e c B) p e +R ei r R jk = m j n j ν jk (v j v k ) s t r ss t t s s t rt s t s s ν jk s t s r q 2 t s s s t s t t R jk = R kj. t s s ss t t t s s s t s s t q s tr t2 t r n i = n e = n r r 2 s t s ss t t t t t tr rr t s t2 s tr s r t s s J = en(v i v e ) t t s r t t t 2 r s s t s s t rst r 1 t s r t s t r s 2 s s r t r 3 2 ss s t2 ρ t2 v ρ = m e n e +m i n i m i n t t r ss r ss s tr r ss r v = m en e v e +m i n i v i m e n e +m i n i v i p = p e +p i r t r 1 t s r t t t t t t m e << m i r t r t t t t2 q t s r r t s tr s q t r t ss t t2 q t t t s ρ t + (ρv) = 0 s 2 t q t t r t s s t v t +v v = p ρ + J B ρc rs s r s

P 2s s r t s s t r t s t 2 1 s q t s t s2st r B = 4π c J B = 0 E = 1 c E = 4πρ c B t r ρ c s t r s t2 r 3 s s r t 2 r s s s 2 r r t q t t ts tr s t t s [ ] ve m e n t +v e v e = en(e+ v e c B) p e +R ei t t ss ss tr s t t r s s q t s st t s 2 s s t t r s t 2 t r s s s r ss s t tr s q r t t s r r t tr rt 0 = en(e+ v e c B) p e +R ei 2 s q t s s st t t t t2 t tr s 2 r t t t E+ v c B = 1 en v e = v 1 en J ( ) 1 c J B p e + 1 σ J r σ = ne 2 /m e ν ei s t tr t t2 q t s t r 3 s rst t t r s t t s q t s r t tr r ss r ts r s t 2 s ts r s s t r r r s ts t t s t r s r t r r r s t r t s s s r t t t t2 s t s s ss t t t r r st 2 tt r t r t s t ss t t t tr t t2 s r t s s s t r 3 s r s t E+ v c B = 0 P s s

P 2s s r t s s t r t s t t t E+ v c B s t tr t r r r t s r t r r t t q t s s st t t r t st r v << c r t s t t t r 1 c q t s t s r r v 2 /c 2 r t t r st t t r s t s t t q t s r r t t2 r s t j = 0 s s q t s rr t r s t t r s t s r 2 t t r t r 3 s s q t t t t t q t E t [( B t = v 1 ) en J B 4πη ] c J r η = c 2 /(4πσ) s t tr r s st t2 ss t t t tr s s t s 2 tr q t p e = p e (ρ) t r r ( 1 n p e) = 0 t t t r t2 q t s t 2 t r t r t t tr t rr t s t2 s st t 2 r r q t s s s r t r r r s ts r t t t q t s B t = (v B)+η 2 B s t s t s s rs s t t s r t 2 t rt 2 s t r t r t rt t s t ts st t 2 s t t 2 s r s R m = L ov o η r L o 2 v o r r s t 2 r t r st t t2 t t s s t t2 R m >> 1 t s t s r t t t t s t t t t q t rt r s B t = (v B) t s t t t tt r q t s t t t t s t t r t t s s t r t s é s s t t r t s t s t t s r r 3 t t r 2 t s ts t s r r t t t t s t r 2 t r t t s 2 t t s rs s r s

P 2s s r t s s t r t s 2 s s t s t r q t t t r r s ts t s r t r 2 t 1t s t s t t r 1 t s r2 t t s r t r t q t s s s s r t r t st t s t r 2 q r s s ss t tr s t s s r r t t L D t s s r r t t w 1 pe. r t r st t t r ss r st 2 st s 1 t t t s s t 2r r s T T coll,2πω 1 ci,2πω 1 ce t s t t t2 str t t s q t 2 t r ss r r s tr t s t s s r st 2 r r r t t r r r s t s t t t tr r ss r t t t t r 1 t t s t s t t s r s t s st t t t r t st s r 1 t t t r 1 c t r s E t st tr t t2 σ s t t r s t tr s r q 2 σ tr s q r t t s t E = v c B, t t s t r t s r r t L t t s s s r t s ss 2 s s s t q t r r s t t r 2 s r t t r 1 t 2 t s q t s st t t r r st 2 r ss ρ = st t 2 v = 0 s t r ρ p t pρ 5/3 = st t t 1t s t s r t r s s t s t r 1 t t t s P s s

P 2s s r t s s t r t s t 2 r 2 s st 2 t r rt s t r s r t t s st t t s rt t st t r t ts t t r s r t t t st r r r rst t 2 q r st t t s r st 2 t rt r t s t 2 s t t t t s ts 2s r s r s r t t r q r s t s s r r st t q r 2 ρ = ρ o = cte, p = p o = cte, v = 0, E = 0, B = B o ẑ t s s r s t s t s r s f = f o +δf r δf << f o f 2 t 2s r s ss t t t s s t2 s s t tr r s st t2 t s r s t 2 s s t t t rst r r r 1 t t r s t r 2 ss t t 23 t r t s t s ss t t t r r q 2 s r t t t t r 1 t pρ γ = cte, γ = 5/3 t t t t s st t s r 2 q t s q r s t t q t s 1t r 2 rt r t s q t s t s r t t t rt r t s s q t s r t t δρ = ρ o δv ρ o t δv = δp+ 1 4π ( δb) B o δe = 1 c (δv B o) t δb = (δv B o ) δb = 0 δp = c 2 sδρ, c 2 s = γp o ρ o s s t q t s s s r t t s δρ δu δe δb δp s t ts r st t s ss r q r s s q t r t s t t r δf = f exp[i(k x wt)] rs s r s

P 2s s r t s s t r t s t t ss r t2 s t ˆx 1 s s t t k = ks (θ)ˆx+k s(θ)ẑ. t t t t q r s s tr s B o s r t t ẑ 1 s t r s t t r s q t t t t s r s t t q t s t t s rs r t s w 2 = k 2 v 2 Acos 2 (θ), v A = B o 4πρo w 2 = k 2 [ v 2 A +c2 s 2 ± (v 2 A +c 2 s) 2 4 v 2 A c2 scos 2 (θ) ] q t s t s rs r t r t s é q t s s t s rs r t r t t st t s s t s t s t s t s t r st 2 t r s s r t s r t r t r tr st t ss tr s r 2 s s s r s t 1t t r t ss t t rs 2 r t s rs r t s q t s r t r t t s t2 t t r r s s v φ v φ = wk 1. r s s r t t s t2 t é t st s t s s st t t t s r s t r r t s s s t s t2 ss t t t r t θ. s s s r r t r t t B o = B o ẑ. q t s r r δb x Bv 1 φ cos(θ) 0 0 δv x δb y = 0 Bv 1 φ cos(θ) 0 δv y δb z Bv 1 φ sin(θ) 0 0 δv z vφ 2 v2 A c2 ssin 2 (θ) 0 c 2 ssin(θ)cos(θ) δv x 0 vφ 2 v2 A cos2 (θ) 0 δv y = 0 c 2 ssin(θ)cos(θ) 0 vφ 2 c2 scos 2 (θ) δv z q t s s t t t t t t2 rt r t t t B o δv z s t 2 t t t rt r t δb. t 2 q t s s t t δv y s t t δv x δv z s t s r q t t r t2 r t é s s (0,0,±v A ). t r r s t s r s t2 t t s r t t P s s

P 2s s r t s s t r t s 120 90 1.5 60 1 150 0.5 A F 30 180 0 S 210 330 240 270 300 r P s t2 t t r r s r 3 t t é t2 s é st c 2 s = v 2 A q r t t s t2 q t v A r r ss t r t r t t rs t s 1 r ss s 0 0 δv = 1, δb = Bv 1 φ 1 0 0 δv δb r r r t t t t B o t t r k. r r δv s r t δb. t rs r t r r s 1 r ss s s vφ 2 c2 scos 2 (θ) cos(θ) δv = 0, δb = Bv 1 φ (v2 φ c2 scos 2 (θ)) 0 c 2 scos(θ)sin(θ) sin(θ) t s s t t rt r t s r r t t t r s s 1 t r q t rs s r s

P 2s s r t s s t r t s s t r t rs t t r rt s t s r é s r tr s rs t t q r t r ss t s t r st r r s t t s ss t t t t s tr st t t t st t s s r r ss δρ 0 2 s s 2 t t t s r t B o r t s t r t t t str t t s r ss r r s s s r t st r t t s t s s s r s t r t s t t s t2 t t t s r ss r t s r t s rt r t s r t s t s r t s r t t t s s t t s s t s t t t st 2 s 2 3 2 r t t s t q t s s r ts 2 s r s t q t s r t q t s s r t t t 2 r s s s t s t t s r s t2 r t s tr s q t s r t r r s t s s ss t t t s s s t s 2 tr r t t s s p i,e = p o i,e ( ) n γ s t t t 1 s q t s t r 3 s t σ s q t t s s ss rs t q t s n o n dv dt = ( B) B β (nγ ) E = (v ε n B) B ε n βe (n γ ) v e = v ε n B r t ss t ts r n o p o i,e L o B o v o = v A = β = po i +po e m i n ov β e = po A 2 e m i n ov A 2 ε = c w pi L o = v A Ω ci L o Bo 4πmi r n o P s s

P 2s s r t s s t r t s ε r t r s t s r t r s r s t r t rt t s t t t ε 0 r r t q t s 23 t r s s t r s s s t t r s s t s t 2 rt r r q r t s s ss ts t s q r s 2 n o = 1 p o = 1 B o = ẑ v o = 0. s r s t r tt s rst r r r 1 t n = 1+δn v = δv B = ẑ +δb p = 1+γ δn r s t s t q t s s s r t rt r t s δn δv δb s t ts t s q t s r st t s ss r q r s r s t t s t s t t s q t s t t r s q t t w δn = k δv k δb = 0 w δv = γβkδn (k δb) ẑ w δb = k [(δv iεk B) ẑ] ẑ 1 s s t ˆx 1 s s t t k = ksin(θ)ˆx+kcos(θ)ẑ r B o s r t t t rt r t δb r tt s δb = (δb cos(θ),δb y, δb sin(θ)) 1 r ss t t 2 s t s s q t t t r t t2 rt r t s r r s t t 2 δv = (δv cos(θ)+δv sin(θ),δv y, δv sin(θ)+δv cos(θ)) r q t s t v φ 1 0 0 0 0 δn γβ v φ 0 0 0 sin(θ) δv 0 0 v φ cos(θ) 0 0 δv y = 0 0 0 cos(θ) v φ 0 iµ δb y 0 0 0 0 v φ cos(θ) δv 0 sin(θ) 0 iµ cos(θ) v φ δb rs s r s

P 2s s r t s s t r t s r µ = εkcos(θ) v φ = wk 1 t t ts µ = 0 s t t r r t r s tr δv y,δb y rr s s t r 2 r 3 é s r s st t r s t r r t r 2 r 3 é s s t s r 2 t r r t s sin(θ) = 0 t r s q r t t s t s r t t r r t t st s t s s t s r t r r t B o t r s t s s(θ) = 0. t r st 2 t t s t t ts t t rt r t t r δb y,δb t t r r r 2 r 3 s t r t t t r t t tr 1 q t t s rs r t s t vφ 6 v4 φ (1+γβ +µ2 +cos 2 (θ))+vφ 2 (µ2 γβ +(1+2γβ)cos 2 (θ)) γβcos 4 (θ) = 0 r r t s 1t t s r r t k ẑ cos(θ) = 1 t rt r t s s t st s r t t r s s r t r 3 2 s ss s t2 v ± φ = ± (γβ) r r t s t2 s s 2 t s s v ± φ = ± ( γpo m i n o ) t t r t r r s rr s t st rs st t s r s r 2 tr s s t s r s t2 t s r s s vφ σσ = σ µ µ 2 2 +σ +1 4 r σ = ±1 σ = ±1 r t t s r r t µ = εk s t s s r r r 2 r 3 r s rs P s s

P 2s s r t s s t r t s r 2 tr s s r 2 tr r q 2 σ = σ s2 t t 2 s t t r t 2r r q 2 k. vφ IC = w k = σ [ εk 2 + εk 1+ 4 [ 2 ε 2 k 2] εk 2 + εk 2 ( 1+ 2 )] ε 2 k 2 = ± 1 εk w(k ) ε 1 r r t r q 2 t s s t s t t t rr s s s s w(k ) v Aw pi c = Ω ci r t t r t r r t s s s t r 3 t t r k t s s vφ IC 0 t s t r 1 t t s rs r t 2 v 2 φ (µ2 γβ +(1+2γβ)) γβ r t r s t s r v IC φ σ kε, σ = ±1 2 r t s 1 r ss r t s t2 t tr 1 q t t δb = (1, iσ,0) δv = (1, iσ,0) r ts r t r t s2st (ˆ k,ŷ,ˆk) 2 t t t q t s t s t t w > 0 σ = 1 δb = (1, i,0) r t t s t s s s s t r t t 2 t s t w < 0 σ = 1 δb = (1,i,0) s t s s s r t t s r r r t r s rr s t r r 2 r 3 t t r t t s r B o t t s s s s s t s s r s s t r 3 s w > 0 t r t s r t ẑ w < 0 t r t s t r t ẑ. st rs t s s r t st r σ = σ t t k s t2 t s t s t r 1 t s vφ WH = w k = σ[εk 2 + εk ] = σεk 2 rs s r s

P 2s s r t s s t r t s w(k ) σεk 2 r r t r q 2 t s t ts rr s s s s w(k ) σ v2 A k2 Ω ci st 2 t r 3 t t s k t s s vφ WH σεk t s 1 r ss r t s t2 t tr 1 q t t t t δb = (1,iσ,0) δv = (1,iσ,0) w > 0 σ = 1 δb = (1,i,0) r t t s t s s s s tr r t t t t r w < 0 σ = 1 δb = (1, i,0) r t t s t s s s r r t r s rr s t r r 2 r 3 t t r t t s r B o t s s s s tr s s r s s r t r 3 s w > 0 t r t s r t ẑ w < 0 t r t s t r t ẑ. s r2 t t rt r t s rr s t t 2 tr st r s r r s t 2 s t r t s s δb IC/LH = [cos(kz wt),σsin(kz wt),0] δb WH/RH = [cos(kz wt), σsin(kz wt),0] r δb IC/LH t s t 2 tr s r t r 3 s δb WH/RH t s t st r s r r t r 3 s σ = 1 r w > 0 σ = 1 r w < 0. r s 2s t s rs r t r t s r t r r t s ss r ss r rt r s s t t s t s r st s w R r t s s s s t r s st t s r r s t s s t s s s s r t 2 tr s r r s r t r t t 1t 1 s r s rs s t s s s t r st r t t s r s t r rt r s t t s t s s t r 2 r s t t s t s t s t s s r r rr t s r t 2 tr s 2 s t r r q 2 t r r r t s r t t t s r t s s t t r t 2 tr r q 2 P s s

P 2s s r t s s t r t s 5 4 WH 3 w (k) / Ω cp 2 1 0 1 IC IC 2 3 4 WH 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 k c / w pp r s rs r t r t 2 tr t st r s t r r t r ss s r r s rt r s t t s r r tr r 2 ss t t r s r s r2 t s r 2 tr r s s r rt s r t st t r t r r 2 r 3 s t r t t s t 2 r s rr s 2 r t r 3 s t r t t t s s 1 t r r s t s s r t t r t t s t 2 r s t2 r t B 0 s t 2 tr r t r t B 0 t t t r s t t t r s s t t r 3 t st t t 1 r ss s δb LH = [cos(kz wt),sin(kz wt),0] rs s r s

P 2s s r t s s t r t s t w > 0 t t r t tr t r2 t s r v > 0 z +ion = v t r +ion = r L [cos( Ω ci t),sin( Ω ci t),0]. t Ω ci > 0 r r t r r r t t r s2st z = z +v t r +ion = r +ion t s r s δb LH = [cos(k(z v t) wt),sin(k(z v t) wt),0]. z = z ion (t) t r r z = 0 t rt t s s t r s t r s ts kv t wt = Ω ci t r t s st t w +kv = Ω ci r t s t s r s t 2 s r r s t r t t s t 2 r t r 3 r t st t r t r t t t s s s rst t r s t r t r t s r t r q 2 t t r 3 s s 2 t r rt t r s t t t 2 r r s t s q t t 2r r q 2 r t s r s tr r t r 3 r t t r s t r r s r s t s t s t s r t s s t t r t t t 2 r t t t2 r t B 0 r t r 3 s r t s r t B 0 t r r r t t δb RH = [cos(k(z v t) wt), sin(k(z v t) wt),0]. t v > 0 z = z ion (t) t z = 0 t rt t s s t r s t s w +kv = Ω ce r t t s r s t 2 P s s

P 2s s r t s s t r t s s r s t s s r rt s t r t r r t t s t 2 t t s s 2 tr r s t s s t s t 2 r s t r t t r t r 3 s t 2 r s t r t t t r 3 s ss s rs t s t 2 r s rt t s v > V ph t rt s s r t t s r t s 2 t t t s t t t s r t r 3 s s r t t t s s s s t t r 3 s t s t r t s t s t s s r t s s r t r t s t 2 r s r t r 3 s r r t t s r t r 1 t ẑ 1 s r r v > 0 t s r t r r r s δb RH = [cos(k(z +v t) wt), sin(k(z +v t) wt),0]. r s t s w kv = Ω ci r t t s r s t t s s t r s t t r t t s t 2 r r t r 3 t t 2 r t t s r t t 2 r s t v > V ph = w/k t r q 2 s 2 t rt s q t ts 2r r t r 3 t s r rs r t r 3 s s r t r r r t s t t t r 3 t s s r s rs t tr s t r 3 s v > 0 t s r t tr r r r r s ts δb LH = [cos(k(z +v t) wt),sin(k(z +v t) wt),0]. r s t s t w kv = Ω ce r t t s r s t r t s s t s rt t t str ss t t s t t r 3 s r q s t s r r r t r t 2 tr r q 2 r s t tr s r t2 2 r t st rs s r s

P 2s s r t s s t r t s ts s s t s t r t ss t 2 s t t t s ts t t r t r 2 r q t s s r 2 tr t r s t s s t s ss t t t r ss s r s r t r t r t t s t rt str t s r r t r t r s tr s r t rt t t st r t r ss s st t t t s r s s r 2 s 1 str t r 2 t 1 str t s t r t s ss q s tr t2 s tr t r t r s t t s t rr t t r s s r t st ts t r r s r r t r s t tr t t s r t rs s s t r t s t t r s s s r r s t s s r s t q t t r s str t r s t r r t 2r r s r t s t r r r rr t s s 2 p e s s q t t r s t st t s s r rt t r t rs ss t t s t r 2 ss t s s r s r s rs t t r t r ss t s t t2 t L t str t r s s r t t t t s t ss t s s s 3 s r t r s t t s r r rs s r + s t t s s t r s t r2 s s t t t r t ss t s t s t s s t r r = r ss s rs t L λ D /L 10 7 10 6 10 5 s tr t2 λ mfp /L 10 4 10 5 10 9 s r (c/w pe )/L 10 4 10 3 10 3 tr s t (c/w pi )/L 10 3 10 2 t r L /L 10 2 P rt t2 s tr s r s s r t s s 3 s t s rs t t t r2 r s 1tr t r t s s t r t t t 2 t t t r2 s s P s s

P 2s s r t s s t r t s λ D /L 1 t s t ss t q s tr t2 t s s s r s t r t s t t t r2 s s 3 λ mfp /L s s t t 1 t r t s r s t t s r s t s s s ss t s r r t s t s s t r r t 2 t s s t t t s s 1 str t s tr r ss r 1t t t s s (c/w pi )/L (c/w pe )/L r t r t r st t s s s t r q s r t tr s r q s t s ss t t t s t r q s t r r t tr s r q 2 t s t r r t s r q 2 s s 2 tr s s t t s s r rs t r s t 2 r s st r t t r L /L r s t r r r s s r t s r s t str r s rs s t t r t s r s t s r t t t 2r r s ts t s s t r s r 2 t rs t 2 t t 2 t s rt t t t t t t s s r r r s t t t + s t s r t t 2 s 2 s r t s r r s t 2r r s t r2 s r r t t s s t r r t str t t t t r t t r2 s rs s r s

P 2s s r t s s t r t s s st s s s s s s r t s s 1tr t t s st s rtí s 3 s q r t r t r s t s 1tr t s r q r t r í 2 2 s tr s r s tr rtí s r s 2 r r s r t s s r3 r s s q s t r r st s s r3 s r í q r s t r s s rtí s í s t st s t s rtí s 2 s r s tr s rtí s r q r s r s r s s r 2 r t t s s t r s t s s rtí s s rt t s ás ú q s t r s t s s r 2 q s t 3 ét r 1 s tr r s 2 st t s s s st r s s s s s tér s s r ó t r st ít r s t s t s t ór s t s r s t rtí s s sí t é s r s ét s 2 í s s s s s s tr s t rtí s r s s ét s st t s 2 r s r s r ó ét s r ó t3 2 s t rí t r á t rí s t s s s s rtí s s t ór s s rá t 3 s r t r r t r s r s s í t s s t s P s s

P str ts t s 2s s s r t s r ts s t r s r s t t t s t str ts t t r s t t r t s t s s r 23 t r t t t rs rt r 2 s t rs r 2 r t ss ss s s st t r s ts r s t r r rs t t s t r s s r 3 t t s 2s s s r t s t s r ts s t s t s s rs r 2 r ss rs r 2 r s t r t s str t s r t t r t r t r rs t r t r t r t r2 tr 2s s t s r ts r r2 ss r r t r 3 t s r t r s r ss s rs t r t s t str t 2s r rt s s r r s r s

str ts t s 2s s s r t s r ts t r t t r 2 t s r t t st s t t r t t s t ts t r t t t s r t r t r t t r str t r t t s r t 2 t r t s t rs s r t t s r s t r 1 s st 3 s r t q t s r r t s t str ts t rs r t r t r ss tr t r t rs r t s r t t r t 1 r t t t t r tr t t r t t s t s s 23 t r 2 t st t r s r t s t s r t r t tr2 t str ts t r t s r t s r t t ñ t r t tr2 r r t ss s st s s t t r t r2 tr t s rt t r t r rs t r r s t s r 2 r r t r ss s s s s t s s s t r r t r ts r t t t r s s t t s s t 2 s t t t r t s 2 t rt t s r s t s t 2 s t s r t r ts s s r t r r s t r r r t s t s s r r r ts t t r t r rs r t t t r r s t r s s r t P s t 2 rt r t s t s r t r t t rt r t s r s s r t r ts ttr t t t 2 t t s r s s s r s r r t r r r t 2s s t s st ss s t s s t s t 1 ss 2 r ss r s r t s r t r t t r s t t r t r 2 r st 2 t s t r r s s t t t r t t r t r r r t s st r t rr str 2 r r r t r s r r t t t t 2 s r t s s s t t st s tt r t st s r s r t 2 r s P s r ts P t r r s s s r t r s t t s s P s s

str ts t s 2s s s r t s r ts r r t r s t t t r s t t r2 r t tr2 t s t s st t s s r 3 t s s s t r t r t s r t s t rt s r ts t s r t 2 t t t rt r st t s s r t t t r r r t t r 2 r t r rs r r t 2 rs r r t r 2 2 rs t t t 2 t r s r t s t t t t t st t t t rt t r 1 r t t t r tr t t r r t r t t s r t r rs r s s t t t str ts r s t s str ts t r t t s r t tr 2 t t 1 t t t t rs s s s rs r t t t t r s t s r s t s t 1 r t r ñ t t r t t r t rt t rt t t t s r t r 3 t s t st s t r rs tr s t rs s r s

str ts t s 2s s s r t s r ts r str ts r t s r t t s r s r t t r st s r s st 2 t t r t t s r t t r t s r s r r t t t t t rs t t r 1 r t s st t tr 1 1 t t t rs t t r s t t r s r ts t t str t s 2 r ± t ± t t t t r r s t t t r r t str t t r t s t t t r s s s t t t r t s s s 1 r t r s t t t t t s r t r s t ss t tr2 r t ñ t P s s

str ts t s 2s s s r t s r ts t t t r s r t t 2 s t r t s r t t s r t t t r s tr t r t t ñ t s s t r r2 s r rt t2 t t s t s r ts r r t t s r t s t r s r 1 tr t s r t t s t t ñ t 2 s r t s r t P r ts t s tr t s st s s t s t r t s r 1 t 2 s s t r r t t r s s s 2 t t t t ss t r t t t s t r r t r s t s r t t r t 2 r r t s t s tr t t r tr r t t r s tr s tr t r s r t t tr 1 s t r 2 t t s st t t s r tr st t 23 r t π r s 2 s t rs ). str t s t t r s r s st s t s t t r t 2 s r 2 s r r t tr 1 t t s t r 2 s t r r s t t r r s r 2 r s t s E E = t 1 t r t r s t s s t t r s 2s s t t s str t s ts t t t t s r t s r t 2 t s s r ts r t r t t t t r t t t str t t tr s t r s r rt s r t r r s r t t t rr r t 1 t t str t tr s r t r r t t t r s t t str t t t t r t r r t t 2 r r t t tr s s t s s t str t t t r 2 s tr t tr s t s s r t t r t 2 23 t s t t t t t t ts tr s t t t r t r r t 2 t s r t t t r t t t t s rr s t t t t s r t s r t t s r tr r r t s r r s t tr s r s r t t r s s t t s r t t tr s s r t t t t t tr s r r s t t r t t r s 2 r2 s r r t t r t t r s s ss t t t rs t r t s r rs s r s

str ts t s 2s s s r t s r ts r t t tr r t t r s t tr s r t t s t t s t s s t t t s r t2 2 tr s st t R M. t s t s s 23 t r t 1 s r r r t s t r s r t 2 t s s rt t t t t t t str t s r r rt s t s r r r t rs s s t s r s t2 t r t r s t2 r ss ss ss 2 s ss s r t t t r 2 t t 2 s t 1 r t t r s2st ts r s s t s s t t r ts t r s 2 r r 2 t t r r t2 ss st rs ss t r t r t r t r 2 t t 1t s ss t t s r t r ts r t t ts s t t P s s

str ts t s 2s s s r t s r ts t s t t s ss t t r t t t r s str t r 2 r t r s t t s r t r s s r t r 3 t t s r t s r t t t tt r t s t st 2 t s t r t t t r s t s r ss s r 2 t r r t 2 2s t s t ss s 1t t t 2 r 2 2s t t t s 2 ss s t r t t 2 2s q t t str t s ss s t r t s r ts t s r t2 t s r t s t s tr r t ss s r t s r s t r 2 t r t r s st s st r q t r s r q t t tt t t st r t t s P t t s P rt s P t t t r s t str ts s s t 2 s Pr s t ts rr2 st t s t str ts t t r s t t r q t t s t s s s r t s t r s r str ts r ss 23 t s r t s r t 2 t ss t t r rt2 t t s t s r t r t r t ss P s tr t r P t tr r s t2 s r t t t r t r t P s r Pr str t P P r tt t t r s t r s r t t s str ts t t r ss t 1 r t s sts t r t t r 1 t t t r s r t t t r r ± ± r s t 2 t r s r ts r 2 t t r s t 3 3 r s t 2 rt2 t s t 2 t t t t r t s t t t t t t st r s s r ts r st t t r t s t s s s s r t r t s r ts rs s r s

str ts t s 2s s s r t s r ts r r t ss s r t 1tr t r tt s t r s ss P rt tr t r tr tr t r s r P ss P rt tr t r tr tr t r s r P s s r tr st t 23 r t t t ts tr s t r 2 r t r 2 r s t E/E = 0,17 r r s t P s 5,2 160 t t s t s s s tr s t2 st t s r r t tr str t t t t s s t ss P rt tr t r ss tr t r P P s s s t r s t rs s t s t r st t s 8 20 s s r s t 2 t r t t t rt t s r tr st t 23 r t r t r t t t r tr s r t s tr t t t t t ts s t t t 23 r s t t 2 P s s

str ts t s 2s s s r t s r ts rt s t rt r r r 2 r r r t rr r tr s tt t r t t t 23 r P t s s s t rr s t r 2 r r s tr r r t t s tr r s t st r 2 s s t s t q r t t r r tt t r 2 s s r str t s t r t q s t 2 s 2 r r t s t 2 sts s r r t P str ts t s t t s ss 2 1 t t r r t 2 t t t r s str t r t tr t 23 r r ts t r t s r t t r2 r ts tr s t s tr t s r r t s r t t t r s r tr s s t tr s t r t r t t r t str t t r rr r r t P r st rt t ts r r r t s r t t 2 r s s t 2 t r s tr s r t r t t r t s t s s r s r r t t r r t t t P s s s ts s t r 2 t st ss t s s s str t s s t r r t t s r t s t 23 r s s t r t s t 2s s s 2 r t 2 rs s r s

str ts t s 2s s s r t s r ts t t r s t rs r s t t r t r 2 st s r s t r 2 st s 2 sts s P s s rs r t r t t t r t t t P str t 2 180 r 1 s r t t s r t 1 s t r t r t P r r s t t rt t tt r t s t s s r t s r s t r t r 3 t t r 2 r t t s r t ts s t t r t ts st t t s s P s P P s P st t s sts t r r t tr t s t r rt s r t t s r r P r tt t t r s t st 2 s t P t r q 2 r s r t s s t 2 r t t st t s r t tr r s t2 r t P s r t s t t t P s r ts r st t s r t tr r s t2 t r t r s r t t t P t t 2 r st t t tr r s t2 t r s r ss s t 2 r s t t s r r t r 2 tr s t s s str t r r s t s s s s t t t s s rr r t s t tr st t tr st t ss s r s r 2 t t s r t tr s t2 s 3 r r t P str t r s r s r ts r s r2 s t t 2 t s t t s ts r t r2 r t r t r 3 t t tr s t2 t s t2 tr ts r t r ss s t r r s r t t str ts s r t 2s s t r s r r t st 2 t t r 2 s rr t P 2 st t t r 2 t t t r r t s r t st 2 r rt s s s t 1t 1 s r s 23 t r t t t r t 23 r P s str t P r s 1 r ss P s s

str ts t s 2s s s r t s r ts t t r t ts t s r t s t s r t s r s s t rr2 r s t s t t r t t t P 2 r t s r ts r r rr r s t r t r r s t 2 t t s r t2 t t t ss r2 s sts t 2 2 2 s t t 2 r t r t s 2 r r s t 2 t 1 r t t t r t r2 s r t 2 s r s st r s s r 1 t s2st s t t r s s rs t t t t s r s r t r s s r t t r s r s str ts 2 r ± s s t t2 r t t s t s s 23 r s t t s r ts 3 s 1 r ss t t r s str t P s 1 r ss ss r s t rst r s ss t t s t t r s r t s t t 2 t r r t r s s s s t r t r str ts t rr s t t r 23 r s s s r t t s t st t t s s r t t s 1 r ss t t r s sts t tr 1 1 t s s rs t t t 2 t t r r t 2 tt t t s r t s t s s s r s r ts t s ss t s r t t t t r t r t 2 t s r t r t t t r 2 t s r ts s s r q 2 t s r ts 23 t s t s s s 3 P str t r s s r s s rs t r t tr t s s rs t tr s tr t r t ss 23 r t ts s t r 2 r t q q t r r s r s s t r2 s t s t r s t s t s t s s 23 s r t rs r r r s 2 s 1 s 2 t s r t2 t r t s t2 r rr t 2 t s s 2 t t t t r 2 2 s r t r 23 t s t rs s r s

str ts t s 2s s s r t s r ts ss t r t t t t r r t s rr t s r t s t t r t r s t ts r r t t s 2s s t s r ts r 2s s t t r 2s s s t r s s r t t t r t st t r t r t r t s r r 1 t 2 s rr t 2 r r t r t r tr s t 2 r s 1t t t s t t r t t r t r ˆn r r 2s s t t r s r ts t 2 s r t s t s t r t str t r q st r st t ˆn t t t s t s t r t t r t t s t 4B (m) ˆn6 m = 1,...,M s t s st t r r s ˆn s t r 2 3 t σ 2 = 1 M M (B (m) < B >) ˆn 2 m=1 r t r < B > s 2 < B > 1 M M m=1 B (m) r t 3 t s s t t t r 3 t str t ˆn 2 = 1 r t r t r s t s t t r q t s r tt tr 1 r s 3 Mµνn B ν = λn µ ν=1 r t s s r ts µ,ν = 1,2,3 t t rt s ts t s2st Mµν B < B µ B ν > < B µ >< B ν > s t t r tr 1 r q t s t t t λ s r t s λ 1,λ 2,λ 3 r s r r Mµν B MB µν s s2 tr t s r r t rr s t rs x 1 x 2 x 3 r rt t r t rs r r s t t r t s 1 t r t r t t t r r s t 2 t t t t s s P s s

str ts t s 2s s s r t s r ts t t t rs r r tr r2 s t t r 1 x i kx i kx i i = 1,2,3 r t rs rr s λ s r r s t t t r s t s ts r t r r t r r t ˆn rst t r t tr 1 Mµν B q t t r s t s r t t ts t r s λ i t rr s t rsx i t rx 3 rr s s t t s st λ 3 s s s t st t r t t r r t t rr t s t r r t λ 3 ts r r s ts t r t t t t st t r t rs x 1 x 2 rr s t t 1 t r t r r t r r t t tr s t 2 r s t x 1 x 2 x 3 rr s r t rt r tr r s s t s s r rt r 2s s r r 2 r 2 s t t rs 4B (m) 6 t ss r 2 t r s r t r ss tr s t 2 r r r t t t r s t t r tr 1 M B µν r r t t r s t t r r t s2st t s 2 23 t t t s t t t tr 1 Mµν B s t t t r r r t s r t rs rr r st t s t t 2 r t rt t s t r t s t t rs (x 1 x 2 x 3 ) t r tr 1 M B M r st t 2 r r rt r t 2s s t t r q t r t s r st t s t 2 st r s (M + M) (x i + x i ) = (λ i + λ i ) (x i + x i ) r i = 1, 2, 3 rr s t 1 t r t r ss t t M r s t 2 r 3 rs t s q t s M x i +M x i = λ i x i +λ i x i q t s r tt t rt r s s M s r r t t t q t r s ts (λ j λ i) x ij = M ij λ i δ ij r x ij s t t t t t r x i. M M r t s2 tr tr s M ij = M ji s t s r q t x ij = x ji rs s r s

str ts t s 2s s s r t s r ts q t2 1 r ss s t t t t t rt r t rs st r r t r tr q t t r tt s x 31 = x 13 = M 13 /(λ 1 λ 3) x 32 = x 23 = M 23 /(λ 2 λ 3) x 21 = x 12 = M 12 /(λ 1 λ 2) x ii = 0 t t t t r r 1 t t q t t s x 31 x 32 s r r s t t r r t t s r s t t r x 3 t r s x 1 x 2 r s t 2 r 2 x 21 r r s ts t r r t t x 2 t r s x 1 t t s t t t rr rs t t r t t t rs r r t t r s M rt ss t r 1 r ss r M ij 2 r B (m) 2 B (m) + B (m) t t M r B (m) s t s t r s t t t s r ts t r r s t r r r r s r 3 t s t s t t s r r t t r s r r ǫ 2 [λ 3 /(λ 2 λ 3 )] 2 /(M 1) 2 r t t2 t r s t s ϕ ij = ϕ ji = << ( x ij ) 2 >> 1/2 =<< ( x ji ) 2 >> 1/2 = λ 3 (λ i +λ j λ 3 ) = (M 1) (λ i λ j ) 2, i j r <<... >> t s t s r ϕ ij r r s ts t r rt t2 t r x i r r t t t r r 2 r t r x j st t st rt t2 t t t r t t t r x 3 s s t r rts t rt t2 t r ss t t t rr s r λ 3 t t rt t s ss t t t r rr r st t s r x 3 ss t t t s rr rs r t r t t t t st t st rr r st t r < B > x 3 s λ 3 < B > x 3 = (M 1) +( ϕ 32 < B > x 2 ) 2 +( ϕ 31 < B > x 1 ) 2 r 1 r ss s r tt r t rt t s < B > x 1 < B > x 2 t t s rr r st t s r s 2 ss t r st P s s

str ts t s 2s s s r t s r ts t s 2 s t st t t r t r t r t ss t t t s r t t t s s t r t t t r k st 2 t r t s t t t 1 t r t r s t t r t r 3 t t s s 2 s r s t r s r t t s t r s s r t rs r t r t r t s2st s t s r t s r r s t t s r t s t 4B (m) 6 t r r r t s2st t t t r s s s ts t t t t r s q t 2 r s r s 2 t r t s t r r r s t rr s t t r r t k t r t t t s t tt r t r λ 3 λ 2, λ 1 >> λ 2 t r 3 t s q s r t s t r 3 t λ 3 << λ 2 < λ 1 t s r r r 3 t λ 3 << λ 2 λ 1 s s s t t r t t s t r t r s t t t t r t x 3 t ts t t t B 1 B 2 t r s t s s r 3 t t r r r t s r t r r s t r t t t r t r t t t t t t r k r ss t t t s t x 3 B o =< B > s t s θ kb s ) (ˆx3 B o θ kb = arcos B o r s 0 θ kb π/2 θ kb s t t r t s r r t r r r r q t t t t r r r t s r t s r t r r r s r r r tr s r s r t t s r s x(n) s s X(w) = x(n)exp( wni) n= r X(w) s s t x(n) ts r q t ts s t t t X(w) s r t r π. r t r st t r q t ts t t r r s t t 1 s t s r s r t s t t r r t s s ts t t rs s r s

str ts t s 2s s s r t s r ts r s tr s t2p(w) s t r r tr s r P(w) s s t r s t2 t s t r (w,w+dw) t s s P(w) = X(w) 2 t r r s P(w) s s t r str t t r q s t t r s st r q 2 t t st s t t t2 t 2q st r q 2 s s f Ny = f s /2 r f s s t s r q 2 t s r q 2 r s t t s tr s 2 t rs t r T r t s tr s t t r 23 s r ts s r r tr s r s t r s tr s t2 s t r t t t t r r q 2 t s s r ts 2 s 2 r r s tr s s tr r s s tr r s s st 23 t s r ts 2 r t t s t r s s r t r s tr s t2 s t t 2 r P(w) ss t t s t st 2 t t t s r t 1 s t r t s r t s s r ss rr t t s r t s s r ss rr t r xy (l) t t r tr r2 s r t s s x(n) y(n) t t N s s s N k 1 n=i (x(n) m x )(y(n l) m y ) r xy (l) = N 1 n=0 (x(n) m N 1 x) 2 n=0 (y(n) m y) 2 r i = l,k = 0 r l 0 i = 0,k = l r l < 0 l 1 s t r t r s t r t 2 m x m y r t s t rr s s r s s s r tsxy t s q r xy (l) t t s s rr t t r r r r 1 x r y t s t r t s q s s r t t r t s s t s q x(n) s t s t s q y(n) s s l s s s t t t s r t r r t tr 1 t s ts r 2 / s t r t r 3 t s t r s t t s s rr rs t t t r ss rr t r t r s t r t s s t t t s s rt t t st str ss t s t ss s t t t t s t x(n) y(n) r s t t s r q 2 s s t r t s r q s t t t r t tr r t t r r t ss r 2 t s r r t ss r2 t t r t t t s s t t t t r P s s

str ts t s 2s s s r t s r ts r r t ss t t t s s x(t) y(t) s 2 C xy (w) P xy(w) 2 P x (w)p y (w) r P x (w) P y (w) r t r s tr s t2 t s x(t) y(t) r s t 2 P xy (w) s t r ss s tr s t2 sp xy (w) = X(w)Y (w) s r t s r s t r rr t t t t s r s t r q 2 s t s r q t t r t t t t s s t r w 2 s t s t st 2 t r t s r t s t r t s r t r 2s s r r r t r r rr t s t r s r r r t tr s s r r r t r r 2 s s r 1 st r r t 1 r t t 1t r 1 t r t s t t r t q s st t r2 tt r t s t2 s s r rr t 2 r s r s t s s q t s r t r t t s ts t rst r r r 1 t t t st 2 t t tt r r t t t str t s r s s r t t tr s s r 12 r E t 2s s t s sts t r t2 HT t t st r s t s t s r ts t B s t2 v. 2s s s t t 2 t ss q s st t str t r s 1 st t t t r s r s s q t 2s s r 1 t r t 2 t r t t r t2 HT t t 3 s t sq r t tr D( ) 2 D( ) = 1 M M (m) 2 = 1 M m=1 M (v (m) ) (m) 2 m=1 r v (m) (m) r t s r ts s t2 t m s r t M M t r s r t s t r t t t r r st 2 s r t r t2 HT s s t r t2 s s r r r t 3 t t r D( ) s t t q t s t r HT HT = 1 0 < (m) v (m) > rs s r s

str ts t s 2s s s r t s r ts r K (m) µν = B (m)2 ( δ (m) µν B(m) µ B ν (m) B (m)2 ) (m) s tr 1 ss t t t (m) t t r ts ts K µν (m) r r t t t µ,ν t ts B µ (m),b ν (m) t t t t s t2 B (m) 2 t 1 r ss s q t δ µν (m) s t r r t tr 1 r ts <... > t t r t s q t t2 r t s t s r ts 0 < (m) > r t r 3 t t q t2 t t r t t r 1 t r t r t t r t D( HT )/D(0) t rr t t R HT t t t tr s c (m) = v (m) (m) (m) HT = HT (m) r r r é st t t s r s r 1 t t rt t r s r é str t r s s s r t t s t t s r rr t 2 rs r r s t t s str t r s t ts t s t2 t t t t s 2 rs r s s t t n r r n = ˆn ˆn s r t t s t t2 s st t P s r s r ss s str t r s s t s s t t = ± A r A r t r t s t s é t s r s t 2 q t s t s é r t s r t s s r r t t r r r r r r t s r r r t é r t r tt s s 1 r P s r = ± A r A r t s t2 t é t2 t r r s t 2 s s q t s s t t t 2s s t t r t é t st r r r s s 2 t st 2 s r t ts t r s s t t s r rr t 2 rs t st s t r t t t s r s t r t s t t r 2 t s s r s t t é t st s sts r 1 t r r r t tt t st t s t2 ts t r P s s

str ts t s 2s s s r t s r ts tr s r t t t r st t rr s ts t t é t s t é str t r t s tt r t s s rr t t s ± t r 23 ss s s r ts s t 2s s t é t st t t r t t s s r s s r t s s r t t r 2 t s t t t rs s r s

str ts t s 2s s s r t s r ts s st st ít s r s s té s s str t s q r 2 r s t s r r s t t s s 3 s r s s t s ít s s tr s r t s s s rs r 2 r 2 ss q 2 rí s r s t s r s t s r rt 2 tá st ít t é r s s s ét s á s s s s s t r st s r s s s s s t 3 s st t s s s t s ó rs r 2 r s s r r s s t s trí r t s rr s t s sí t é s s s tó tr 2 r tó tr tr s r ás s r s r t s t s s ó ss 2 t tó tr s tró tr tr s 2 r t s 2 str t s s 2 r q s r r st s r 3 s s s s s s 2 t 2 s r s s tó tr 2 str t s r s s 1 r ss 2 tó tr r s s ét s á s s q s s r t s s s s t s á s s r 3 í r s r r r s r t rr ó r 3 tr s ñ s s r t s r á s s r t st é P s s

P t t 2 t t s r s s t r s t t t st 2 t t t 2 t t r s ts r t t r t t t 3 s t s r t 3 t st r rt r 2 t r st t 1 r 2 t t t 1t r t t 2 t t t 2 s rr t s r t 3 t s 2 t r s t r ts t t2 t 1t r s r ts r t r t s q t r ss s t t t t ts t s 1 s2st t s t ss t s t 3 rt s t s r r s r ss s t r s ss t t t r s rr ts t st s t t s r s rr ts s s t r s 2 t ss s s t t 3 s r t t st t s r t s ss r s t str t r 3 t t s s r t t st t r t t t s t t t s r str t t r t t rt r t 3 s s t str s 2 r t 2 r s t t t r s s s q t r t t 1t r t 3 s

t t 2 t t s r s t str t s r r r t st s str 2 s t t t 2 t s rr s t s r t 3 t ts t s t r st 2 t r t 2 r t t r t s r t ts r t t r t s 2t s s t t r t tr t ss t t r t 2 t t 3 s t r t t s r t 2 r st 2 st t t s t s r t s r t r 3 t t r 2 s r t t t s r s t t P 2 rs s s r ts t 2 t s r ts r s t 2 t t t r t é s r s s r t 2 r s R t t2 σ t r ts t t 3 s t t2 V w rt r s t s t s r t rs s t s 2 t t 4πσRV w c 2, t q t t s r t 2 s r R m 1. t s t t t s t t r t 2 s r t t t r t t 3 s t s st t t r r t str t t tr t t t s s r 3 t t t t st s t 2 st st r t s t s s s t t s r t t 2 t t t s t t s 2s 2 t rt r t t s r t t t r t t str s s r t s r t s st s r t t t r t t t t 2 s r t 1 t r t t r2 s t s r s t r t r t r t t r2 t s s t r r t t r s s s t s s s r t t s t s 2 r t s s t t r r r t t r t st t r2 st t s s r 1 t t s s r tt s V = V(x)ˆx B = B(x)ŷ t t 1 1 s t r t t rt r t2 t x t st t t r t t 2 t s rt r s t r 3 t q t 2 s V(x)B(x) = constant r r s t 2 s r t t t t r s s r s t t st s s t t 2 s t r 3 r 1 t r s P s s

t t 2 t t s r s r t t t r t r t 2 t t s r s r t t tr t t 2 r t s t s rt s 2s r s t t s t t r s str 1 1 s r rr t t t 1t s t r t V w t 2 1 s s r t B w. t r s t t s t 2 é r 1tr t r 2 r r t t s s s s t s s t s r 1 t t st rt s t t r t t t t t s s s s s t tr rr t J r r t t r s r s rr t s r 2 t tr t r t 2 2 t t t t 3 s E = Vw c B w. r t t t str t r r t t t s rt t t str ss t t t 2 t r t t 1t r t t t s sts t s s t t r t2 r t 2 t t t rr s s s r t 2 r t2 r rs 2 r P s t t r t t s r rt s s r t s r ts t r s t r ss s s r rt t ts s s rst t t 3 s s s rs t t st t t r s r t s s t s s s s t t t t r s t s r2 s t t 1 t t s t2 r t t 2 r s t r s 1 t s s s t t t s r ss r s t st s t rt t t r t r ss r t r ss s t t s r t s r s r s2st s t t t t t2 r q r t t st t t 3 s r t s t 3 s s r 2 t r s r s r t r t 2 t s t s s rs s r s

t t 2 t t s r s r t s t r s s t t s r t 3 ts ss ss 1t 1 s r s t s s s s t r tr st t ts 3 r r t r s r s s s s t s r s r r t t 2 r r t 2 t str t t tr s r ss s t r 2 t r t 1t r s s t t t 3 s s s s r s t s t 1t r s s t 2 ss t rt s t s r r s t s rt r 2 rt t t s t ts s rs s t r 2 s r t s s r ts t s r s2st s t t t t r t r t 2 t t P s s t r ts t t t s r s s t 1 s r t s st s s t t s t rs t s t r r t t t 2 r t s ts r s t s s s t t t t 2 r t s ts r s t r t str t s s s q t r ts t s t2 t 2 t str s t r t tr s rs t t t t s r r s t r t r r s t t r t t s t 2 t t t t 3 1t r t r r s s s s t t t t t 1 t t r 2 t t t s r t s t r t t r r t s r ts r r 2 t t r t t r2 1 r r s r t t r r ss t t t t t t r t s t r t s s 1 t s t r t r s 2s t t s r s t t r r s s r t s s t s t t s r r t t r t t 10 4 tt r t t s t t s s t s s t s 1 r s t t r 2 t rt r t r t t t r r s r s s t t str t r rs s tr s r t t t s r t t s r t st rts s s s t P s r ss r t r2 r t s r s s r 2 s t r2 r 2 t s t r s t t s tr t s r t r t s r s s t s r t r2 rt s r2 P s s

t t 2 t t s r s r t s r t s r t t r ss t t t r t t r t r t t t t t t t r s s str t s t r t t r t s s t r t s r 1tr t r 2 r r t r t r rt s t tr t s s s t s rt s s s t t s rt r t t r2 2 s 2r r r r t t t s 3 t t s s t s t P t s r ts r s t s t t r r s t r t s r t r t r s s t t s r s s r r t str t s t t s t t t t r t t t2 r r t s s str 2 s r t str t t r s t s r t r s st s r t r s t r s t r s r ss t P r t ts rs s r s

t t 2 t t s r s Magnetic pile-up Magnetic pile-up r t s r ts t s rr rs t 2 rs r 2 r 2 t t r t r ss t P s r ts 2 t t t r r t rs r 2 r s r t ñ t s t t rs s t s t tr s t ñ t s r s t t r s r t t r t t t t 3 s r t t s r s r t t s s r t r s t t r t t s t 3 s tr 3 t r r t s s s rt t s t r t t t s r rs s s t t s r 3 s s s s t 3 t r 1 tr t s t r s r rr t s2st s t r t s rt r t s t str t r t r2 t t ts r r t rt t t s r r t tt r t rt t t s r st t t t r t t t P rs t t s r r 2 s rr t t q t t s t ts s sr t t s r ts s r s t s r tr st t t r r r ss r t t s t t r s s str rr t t t t ts r tr st t r s t t t2 s s sr t t s t r 2 r t t t t r t t 1t r s rr t t t r 2 r t t s r t P s s

t t 2 t t s r s t r2 st s s s t P s r ss t t s s 2 r 3 s t t t s t t s t t P t r 3 t s s s s r r s q t ss tr t s t t 2 s 1 s r r t r r t r t t s r s t t r2 st ts s r t r t rt r st t s t r st 2 t t r s t r s s s r r s r ts r r ss t r s r st t s r s t str t t r t t t t s t2 t t P t s s rt t t s t q t t P r t s t s P r s r t r P t t r t r s ts s r st t t r 2 t r ss r2 t P t s 2s t t r t s P s s s t s r2 s r ss t t s 2 s r 3 str 2 r s s t r s s t r t r t t str r t s st s r rs t s t ss r 2 ss t t str 5 5 t t t P s t rs 5 5 r s s t 2 t r r t t t r2 st s ss s s s t t P 2 tt t t P 2 r r s t t t r r r t t r s r ts t t r t r t r r s t r s s s r t t r r P r ss t 2s 2 tt r t t t r t t 2 t t tt r s t t r s s t ts r r t s s t t s t r2 st t t r t r s r t t t s t t t t P t r t t 2 s r t s r t r t r2 s 2 r t r r t s r r2 r t P 2 r t r 3 2 s r r s t t str t r t tt t r st s tt t t r t tr t t tt r rst t r r t rs s r s

t t 2 t t s r s t s sr t t s t q t tt s r ts t t t P r ss t 2s s r t s t t r2 t s t r t r s s t r r t P t str 2 r s t r s r ts 2 t 2 r t t r t s r s t 2 tr st t t tt t s t t P s t s r 2 t t t r s t t s s r s t r 5 5 t r P s r s t 3 t 2 s t r r s s 2 t t q s r sr t s st t st 2 t rr t t t B x t r ss B rad ts t t r t t s t q r s t rr t t B x B rad s 2 r s r s s t t str t s r 2 t t t t 2 t t t t tt s t t t s r t s t rst s t t str t r t2 s s r t r t t t r 1 t t s rst s r s s s r s r t r s s r s t r s r s 2 t t t r t s r s s r t r s t r t r tt r s t t r s t r r t r r r s ts r t t t t s r s t 2 r t t s ss t t t P ts t t t s r r t t s t r t rr t ts r t r r t t r s r r r t t t r t r t t t2 r ss t 2 ttr t t t P s t r t s t r s r t s r t r s t t t s t2 r s s r 2 +35 r r st r 10 5 t t 9,6 10 4 t t t t t tt t r r2 s r r s +20 r st 10 5 s r rt r t s t t s t t r s t t t t t t t t s t t s r s 2s t t rr t r s t r t t s s rr t P s s

t t 2 t t s r s 80 B CSE, VEGA 1 flyby at Comet Halley, 1986 Mar 06 Bt CSE [nt] 60 40 20 R CSE [x 10 5 km] 8 6 4 2 07:20 CA 0 05:00 05:20 05:40 06:00 06:20 06:40 07:00 07:20 07:40 08:00 08:20 M1 C1 C2 r t s r s r s t t str t t t t s t r s st r r r t t t s r s t 2 r t r t r rs r r t t t r s r s r 1 t t 1t r st t t t t t t r s s r t 1t t r t t r t r s t r s r rst s r t s r 1 t 2 s tr s t s t r t t t s t t2 s r ss t t t t r r t t t r r t t Bz CSE s s r s s t r t rr t 2s s r r t t str rr t s t t t r t t 2 s s s t s t s r t t tt s s s t s t s t s t s r s str t t t s t st 3,3 10 5 s r t t s t st 1,5 10 5 r t r t2 st rts r s s t t s t r s t r s r r t t r t t rr t t t B x B rad t s t str t t r s t t str t r s s r r t t t r t P r t t t rs s r s

t t 2 t t s r s 50 45 07:00:00 to 07:09:59 y = 0.70x+17.25 r c = 0.91 ns = 578; 1 av /(1 s) 40 20 07:10:00 to 07:15:59 y = 0.96x+13.40 r c = 0.99 ns = 360; 1 av /(1 s) 40 Brad [nt] 35 Brad [nt] 0 30 20 25 40 20 40 35 30 25 20 15 10 Bx [nt] 40 20 0 20 40 60 Bx [nt] etween and, for four intervals around closest approach, the color refers to the respective time interval in Fig. 7. For the inte r rr t t B x B rad r r t r s r s st r r t t r t rr t s t s t t t r s s t r t t t r r tr s t r t r rt st rt rr t r2 s t r 3 t t t 2 tt r r r s st r r t str t s t t t s t t t r t t t2 tr st t t r t r s t r t t t r t P t st t 3,4 10 4 t t t r t s t str rr t ts r t s r s t r ss t P t ts s2 tr r t t r s t t t t t P s r ss s rt r st t t s t r s t t 2 t t r s rt t t t t t t 2 ss t t t s r P s s

t t 2 t t s r s t 3 t r2 s t r t t t s s r t ts t t t2 s s r r r t t r r s s t t r t r t P t 2 s t s s 2 s r t rs t t t r r2 r tr s t r t r s t r s r t s r t 2 t r t s r ss s t s s r t tt t r st r t r r tr s t r t P t t P t t r 2 t t s t r2 2s s r r t t t 2 t s s t r rr s t t s r s s r ts t s r t r s ts t r r 2 t t t t str t r t r t t r s s r ts r 2 r ss t t t t r s s t t t r t str t r t s s t t t r t r t t t str t t t r rts t s t tr t t s r ts r t r r2 t s rs t s r t s r s t 2 t t t r r P s q r r r ts t rt r s t t t r t t t s sts 2 t r s t r s t 2 r s r t r t t 1t r r t q st t 1 st tr s t s r s t t t t t t rr t rs t r t t s tr s t s r ts r s t r t r 3 t r rt t r r t r s ts t t s 1t s 2 st 2 P s 1 r ss s r ts s t rs ss t rt r s t t r t r str t r s t t t r t s r R V, t R V = 6052 str r t t r P t t r s r t s s t rs t t t t t str t r s st t s t t s s r t 2 2 r s t s r t t t t r t t r P r r s r tt r t 2 t r rt s2 tr s t s t r s t t t r t t t t r t r2 t tr t t ss t t r s r t s r t r s r t t t P s t P t s t ts r t t t t r t t s s s r r t s r 2 2s t r t r st s r t rt rs s r s

t t 2 t t s r s t r r t 2 t s r s 2s s t r t 1t r str t r s t r t s t t r t t 1t r t t r st 2 t t t P t t rs s t st r r t s r t t t t P t r s t t t t t t r t 2 t t s r t t r t 2 t str t t2 ts t t t s s r t s t t r t t t 3 s s t ts s st 2 s r s t s r s r s 1 s s st s r rs P r r t t r t r t r r s r t r r 2 t r t r s t t tr t t r 1t r r t st t r ss rs P r r r t 2 2t 1 s t rst r t t rs r s2 t t s t s r2 s r2 r r t s r t t r t 3 s r t s r st 2 st t t s 2 s t t r s st t2 s t t r s r t s r r 2 r r2 t s t t t ss t t s s O(η 1/2 ) r η s t t s t2 r tr r s st t2 t s r t t rs 2t r t st 2 t 2s r ss s rr t r 3 t t s s r s r 23 t r t r st s t t r t s r t 2 t st s r r str t t t rt r s r t r t s r r t t t2 tt t t st 2 t s r rt s t s r rst r s t t t s r str t r r r t r 3 t t t t 2 t t r s ts r t t r t t t 3 s r s r t 2 r r tr r2 t t str t2 t str t t s rst r t 2t s t r t tr t s ss t t t s r r st 2 st t s r t 2t s r t t t r t s s r s t r 3 t t s s t2 V(r) rr s s t t t r s r r sr r st 2 P s s

t t 2 t t s r s st t t s rst t s rt t t t t t t s r s r t 2 t r s t 1t r s s t t 3 t r st s s2 tr2 t t 1 s r s r r tr r2 t r t r 3 t t t s s2 tr2 s st r 3 t t s r st t r ts r t r st s t r r2 t 2 s rs r r t rst r 1 t t t tr t s t t ts r s st t2 s t r t2 t s ss t r st 2 s r t s tr 2 r s st t2 s t t r t t tr s s t r t q t s t t s r t r st 2 st t t s r (V B) = 0 B = 0 E = V c B s t s s t q t s ts t s r r st t r2 t2 s ss t t rr t t V = 0 r ss V = 0 r t s r r s t2 t 2 t tt r s 2 t r t t t s t r r r t s2st t t t r t s r t 1 1 s t r t t t2 t t2 ss s t B 0 t t2 s t r r t t t2 V 0 ts t r s t s t 3 r t 1 s r s s t t r t s2st s t t2 s r r t s s 2 t 1 r ss V = (1 R 3 /r 3 )V 0 cos(θ)ê r +(1+R 3 /2r 3 )V 0 sin(θ)ê θ r r θ V 0 r t r st t r t t s t2 t t2 t t2 r s t 2 t t r t r p t t s t st p str r t 1 1 s r r s p = 1 R 3 /r 3 rsin(θ) rs s r s

t t 2 t t s r s Z B 0 Y R X B 0 r t t r t s2st r θ s t t t 1 1 s rt r s t r t t s s t π 3 t φ s t t 2 3 t s s t 2π r φ = 0 rr s s t t r t t 2 1 s q t s s t 1 r ss t tr t r s t tr st t t t Φ E = Φ t r r V Φ = 0 q t s t t t tr t t s t r2 t str s t r2 t s ss t t q t r t t t s r t s r s q t t s r t t t r st s r t t t tr s t s2 t t r r s ts t t 2 1 s s q t r r t s t s t t r2 t Φ(r ) = E 0 rsin(θ)cos(φ) r φ s t 3 t r t t t s r r t s2st s r t s st 2 s t t q t s st t t t st t r2 t q t s Φ = E 0 r 1 R 3 /r 3 sin(θ)cos(φ) = E 0 pcos(φ) s ts 2 s q t t t tr s r r t s r P s s

t t 2 t t s r s E r = E 0 [1+R 3 /2r 3 ] 1 R 3 /r 3 cos(φ)sin(θ) E θ = E 0 1 R 3 /r 3 cos(φ)cos(θ) E φ = E 0 1 R 3 /r 3 sin(φ) q t t t r t t t2 t tr s t t r t t ts r r t V t t r r r t t t t t t t t t t q t s s t s 2 t r t t t t r t t t 2 r 2 ss r t r t t s t r t t s r t tr t s t r t t t r t B 0 t t2 t t2 V 0 s 90 t r t t B 0 V 0 t t2 s 0 s t r t2 t 3 r t r s t t B 1 t t2 V t r s t r 2 ss t t s s s 2 r t t t s t s t s s t t t t2 s B 0 = B 0 +B 0 rst s r t s r r t t t r s t s t ẑ r t s2st 1 s B 0 s r r t s t s r tt s (B 0 ) r = B 0 sin(θ)sin(φ) (B 0 ) θ = B 0 cos(θ)sin(φ) (B 0 ) φ = B 0 cos(φ) s r ts t r t q t s r rs s r s

t t 2 t t s r s [ (V B)] r = θ [sin(θ)(v rb θ V θ B r )]+ φ (V rb φ ) = 0 [ (V B)] θ = r [r(v rb θ V θ B r )] 1 sin(θ) φ (V θb φ ) = 0 [ (V B)] φ = r (rv rb φ )+ θ (V θb φ ) = 0 B = 1 r 2 r (r2 B r )+ 1 rsin(θ) θ [sin(θ)b θ]+ 1 B φ rsin(θ) φ = 0 r t t2 V q t r q t r t r t q t r B φ B φ r + V θ rv r B φ θ = 3B φr 3 2r(r 3 R 3 ) t t r t t r B r B θ t 2 q t 2 r q t t 2 sin(θ) t t K r + V θ rv r K θ = 0 r K = rsin(θ)(v r B θ V θ B r ) r s t r s rst r r rt r t q t s s 2 t t r t r st s t s s r r s r t r t r t r st q t s 1 r ss t r s θ φ t r s r r r str d dr = r + V θ rv r θ s V φ = 0 s q t s str t t r t r p t t2 q t r r t db φ dr = 3B φr 3 2r(r 3 R 3 ) q t s dk dr = 0 P s s

t t 2 t t s r s t r t q t s t r2 t r t t t t2 q t r r B φ = B 0 cos(φ) 1 R 3 /r 3 r q t t t t K = pv 0 B 0 sin(φ) t t t q t s r t t 2 r t t q t s t r s ts r r t tr t s t t 2 t r B φ K t E r = V θ c B φ = (1+R 3 /2r 3 ) V 0 c sin(θ) B 0 cos(φ) 1 R 3 /r = E [1+R 3 /2r 3 ] 3 0 1 R 3 /r cos(φ)sin(θ) 3 E θ = V r c B φ = (1 R 3 /r 3 ) V 0 c cos(θ) B 0 cos(φ) 1 R 3 /r 3 = E 0 1 R 3 /r 3 cos(φ)cos(θ) E φ = (V rb θ V θ B r ) c r E 0 = B 0 V 0 /c K = crsin(θ) = pv 0B 0 sin(φ) = E 0 1 R crsin(θ) 3 /r 3 sin(φ) q t s t t ts B r B θ 2 s q t s 2 t t r t r st s str s t t r t q t s r B r B θ s s rs P r r r s r r t [ db r 2 dr + r 2r3 +R 3 ( )] 1 2r(r 3 R 3 1+ ) cos 2 B r = B 0 sin(φ)sin(θ) (θ) r 1 R3 cos r 2 (θ) 3 [ db θ 2 dr + r 2r3 +R 3 2r(r 3 R 3 ) + 9r 2 R 3 ] (2r 3 +R 3 )(r 3 R 3 B θ = 2B 0 sin(φ)(r 3 +2R 3 ) ) r 1 R3 cos(θ)(2r r 3 +R 3 ) 3 rs s r s

t t 2 t t s r s r s t r s rst r r r r2 r t q t s r s 2 t r t t r s t r t s q t s 2 t t ts B r B θ r B r = (r3 R 3 ) r 3 r cos(θ){c 1 B 0 sin(φ) pr 4 dr (r 3 R 3 p 2 r) 3/2 r 3 R3} B θ = (2r3 +R 3 ) r r 5/2 r 3 R {C r 3 (r 3 +2R 3 ) r 3 2 ±2B 0 sin(φ) 3 R 3 dr (r 3 R 3 p 2 r) 1/2 (2r 3 +R 3 ) 2} r t r s s r r t t r 0 θ π/2 t r s t π/2 θ π C 1 C 2 r t r t st ts t r t s t s 2 t r2 t s str r t t t t t r t ss t t t r r s q r r t t t2 s r t s B 0 = B 0 t r r B 0 = 0 t t t B = V = 0 (V B) = 0 t r2 t s s t t2 B 0 = B 0 V = V 0 r s t t r t t s t t 1 1 s r s t 2 s t s s s r r str t t r t t t2 t 1 r t t V B s r r t r 3 2 t s t 2 t 2 t s r r t r s t t ts t s s r B r = (1 R 3 /r 3 )B 0 cos(θ) B θ = (1+R 3 /2r 3 )B 0 sin(θ) B φ = 0 s r s 2 t t t r s t r 2 ss r t t t t t t2 s s 2 r t t t t s t s r s q t θ 0 s t t t r t t 1 1 s s r t B 0 = B 0 cos(θ 0 ) B 0 = B 0 sin(θ 0 ) r s s t t s r t s r st t 1 3 r t s r B 0 V 0 B 0 r t t 3 1 s s r t r rt s r s r s t t t s t2 t t s r t s r s t str r r t r st s r r t s rr s t Z = 0 P s s

t t 2 t t s r s Z(R) PRL V 0 X(R) r Pr t t s r t s r r B 0 V 0 s t t str t r s sts t rr r s2 tr t s r s s r t 2 t r t2 r rs 2 r t t Z = 0 t t r r s t r t2 t t t t s s t r s t t str t s t t s r t s r r t r s ss t t r r t r s s t t s r t s r st t 2 3 r t s θ 0 = 60. r r r s s t t t r t t t s2 tr2 s r r s t rs r t2 r rs 2 r P P s r r rr s s t t s t ts r B x = 0 r t t P r r t s s s t r r t 2 rs r t t t t r rs s ts r t2 t s 2 rs t P s t t Z = 0 st s t s s r t str t 2 r r B 0 s str st t t s t t s t P r s t θ 0 t 1t s t r r r t 2s s t r rt s t s 2 rs rs s r s

t t 2 t t s r s IPRL Z(R) PRL V 0 B 0 θ 0 = 60 X(R) r Pr t t s r t s r r θ 0 = 60 s t r s st t2 ts t P t P r s r s ts r t r t ss t t t r s st t2 ts r t r s st t2 ts r r 2 rt t t s rr s t P t 2 r t 1 t t t t t s t P s t 2 s r s t t t t t t t s t2 t t s t t t s s t P t r 1 t2 t P t r s t r s r t r s t 2 P r t2 r rs 2 r ss s t t t r t r t t rt t s s t t s r s st t2 ts t r r t t t t 2 s t t t tr st t t t r s t t t s s s t t p/r > O(Rm 1/4 ) r R m s t t 2 s r r r t 2 t r2 2 r t t 2 t t t r s t r s st t2 ts r r t s s t r s s t t s s t s r t P s t s 2s t t Z = 0 r r t r st P s s

t t 2 t t s r s t 2t t t t t t s r t t s s t2 ts s r rr t ss rs r t2 r rs 2 r t r s st t2 ts r t ss t t r r t P t r ts s t s r r t s θ 0 s t t r t r r s t t r s s t r s s t t tr2 t P t r θ 0 = r s s t 1 r t 1 s t t 1R < X IPRL < 2R t P s r r t st r s t s rt r str 1 < 3R t P s t t t 2 t str rt t P t s 2 r s r 2 s t t r r st s r t Z = 0 r r r s t θ 0 r s s t 3 r t rr s t t t t P t str r rt r r X IPRL = 3R r θ 0 [ ] s t s t t 2 t r r s t r r r θ 0 s s r r θ 0 s ZIP RL(R) X IPRL (R) r t t rs r t2 r rs 2 r P t 1 3 r r t s t t r t t r t s s t t t r θ 0 = 45 65 85 t r r 2 t t ss s r t r st s s r2 r r s ts s t t t 1t r t s str t 2 r r t t r t t t t t r str r t st s sts t rr r s2 tr t s r s s r t 2 rs s r s

t t 2 t t s r s 2.25 2 1.75 ZIP RL(R) 1.5 1.25 1 0.75 0.5 0.25 0 0 10 20 30 40 50 60 70 80 90 ( ) θ 0 ( ) r st t P 2 r r t Z = 0 t 3R s t θ 0 t t P s r t t r t t r ss t B 0 s s rs P r r r t s rt r s r t B 0 s 3 r t rr r s2 tr2 r s r s t t P s t s t r t t t r t rt r r s t t t P s t B 0 r t B 0 r s t t r t B 0 r s t B 0. t s r r t t t t s t ss t t t P s t s r s st t2 t t t t t s t r t t s t r s t t s t t r 2 r r t r 2 r s s s s t t t s t tt r tr s t r t t s t t t s r r s t s r s st t2 ts t r t rr r s2 tr2 s r r str t 2 r r s t s t t P r t r t r t t s r 1 t2 st t t s r t t t t t P t r r s ts s t s r s ts r t s r t r t t t r r t r t t s s t t r ss s r s t t r r r s t 2 s s r P r t s2st r t 1 s s t r t t 1t r t 1 s s r t B IMF s t t X DRAP < 0 t s s r P s s

t t 2 t t s r s B IMF XDRAP = BIMF = 0 t B XDRAP s r r str t t t Z DRAP > 0 s t r rs 2 s t B XDRAP s t t s r Z DRAP < 0 BXDRAP IMF = BIMF > 0 r2 t t Z DRAP < 0 s 2 s t B XDRAP r r s t Z DRAP > 0 s 2 t s t t B XDRAP s BXDRAP IMF = BIMF < 0 r2 t t Z DRAP > 0 s 2 t B XDRAP r r s t Z DRAP < 0 s 2 t s t t B XDRAP s st t t r t s rr t t t s t str t t t s t r t t s s r t t s r rs 23 t t r t ss s r r ts P t s r s t s r t r r t r ts r t s t t r s t t t r s 2s s r r s t t 1t s t t t t rt t s t r t s r t s r t 2s s s t r t r s r s r ts r t t rr t rs r r t r t s2st t s r q 2 3 3 s r t s2st s t r rs t t X MSO 1 s t s t t t s r r t t t r r r ss rr t 4 Z MSO r r t rs s r t s t t t t rt Y MSO t t r t s2st r r2 r t t s st 2 1tr t t s t t t s t P str r t rt s t t r s s t P ts 2 s t t t t r t t t t ts r st t s s t r s r s r ts rr s t P r t X MSO r t s r t 1,5R M st t r t s r t r s s t r 2 r t s t rs s t t t t r st t s t rs r t t s t 0,41R M rs s r s

t t 2 t t s r s Z DRAP (b) southern lobe B IMF PRL X Titan B X= 0 X DRAP B X IMF =0 SW Z Z DRAP B0 (a) current sheet B IMF IPRL PRL PRL B X = 0 SW X Titan X DRAP B0 B0 B IMF X >0 B X = 0 X Z Z Z DRAP (c) northern lobe B IMF SW PRL PRL IPRL Titan X DRAP B IMF X <0 r t s r r r t r t t s s r t P r t s2st s t s r s t r t t 1 s t t t s s t P s t t t t s r B XDRAP = 0 r r s rr s t BXDRAP IMF = 0 BIMF XDRAP > 0 BIMF XDRAP < 0 r s t 2 P s t t Z = 0 t rt r t s t r s r r s t 2 t P s s

t t 2 t t s r s t r t str t t r r t rst t s r ts ts t t s t t t s t r r r ts t t st t s r ts t 2 st t t r s r t s 2 t t s s r r s r s t t t s t r r r r t r2 t s s t2 2 tr s st t r r 1R M r r t t X MSO 1 s r t r r s s t r t t r 1 t 2 t s s t r s r r ts t s r s t t r t t s t r s t t t r t t s r t s t str r t rt s t s s r t rt t t rt r r t 2s s t s ss t t s r t t t s t r2 s t 2 r ss s t t t str t r t s r r r ts t t t st t s r tt r s t t t st t st t r t2 t t t s t 2 st t s t s t r ts t t r 2 r t st t s r t r st t r s r r r 2s s t t t s t t t t s s t s r s t t t r ts s t s 2 t s r t r r t st t s r 2 t s s s t t t r r t s r ts s t s t 2 t t t s r s t t r ss t t s r t s s t P r s s t tr t r2 t s t r ts t rr t 2 r r t s2st t r s rs t str r r r2 t t s t s r t t rs t rt t r t r s t t t s t X MSO r t s r t 4,5R M 3,7R M. t r t s s r ss t rs t t s t r s t P r t r s t s t s r2 r s t s r ts t rt t s r t t t r s st r s r r ss s t r s r t r s t t str r r t st t s t t 3 t P r t s2st 23 s r t s t t t r s r r t st t s t s r r r r t t t r t s2st s r t s2st r 2 r rr t s t P r t s2st r t rt t s t t t t r t s s t t2 s s r ts r rt s ss t t t s r s t rr t rs r t P r t s2st s rs s r s

t t ② t t s r s 13 12 11 10 [Y2MSO+Z2MSO]1/2(RM) 9 8 7 6 5 4 3 2 1 0 5 4 3 2 1 0 XMSO(RM) 1 2 3 r tr t r② r t s t r ts s t rr t ② r r t s②st s r t s②st t r t rs s ts XM SO ① s t s t t t s r r t t t r r r ss 4 rr t ZM SO s r r t rs s r t s t t t t rt YM SO t s t r t s②st t t r r s s XDRAP = XMSO [0, BYMSO, BZMSO ] ZDRAP = q B2YMSO + B2ZMSO P s s

t t 2 t t s r s Y DRAP = Z DRAP X DRAP r B YMSO,B ZMSO r t Y Z ts t r t t t str r rs t s r ts t t st t s t t r t t t rs 2 r t t t P r t s2st s r t t t r t s t (X Z) DRAP t P r t s2st B IMF ZDRAP B IMF XDRAP 3 r s 2s s t s q t t t X t t BIMF YDRAP s t t t r t t t P r t r r r r q r s t t r t t t s t t t t s t2 t r t r 3 t rt t t str t r s s r ts t r r t r ts t r s t r t t t r s t t t t X DRAP r t r t r t t t 2 t s r t t X DRAP 1 s s θ t s r t t t s t2 s r t t t t t s s rs ñ t t B 1 t θ t t s rt t s θ = ± s[ 1+B ] t s 1 r ss 2 t t s r ts r r 3 t s s t rt t2 t t t r t r2 t s t θ IMF ± θ IMF t 2 t 1 t t r t t t = BZDRAP IMF s α = t (BIMF ) 1 t r r t t X DRAP 1 s B IMF 1 r ss B IMF r s 2s t s t t r r t t P r t s2st rt r t r r s ts t r t t t t (X Z) DRAP t r s s t r t t t (Y Z) DRAP 2 t B IMF s 2s r t t +Z DRAP r t t r rt t2 t t r t t s r t α r t 2 t s r t s s r r t s t Z DRAP t t r s t s s r s s r r 2 s 2 t str t s Z DRAP = Y DRAP /B IMF Z DRAP = Y DRAP /B IMF. s ss s t t t t 2s s r r t t t t s r s t t 1t s t s t r ts r t t s s r ts t st t s t t θ IMF ± θ IMF s t t t s t B IMF XDRAP t r s r t s s r r ts t r t t B IMF XDRAP s s s t r r s t r r t r t t t s r st t s t rs s r s

t t 2 t t s r s AL.: DEPENDENCE OF THE MARTIAN MAGNETIC LOBES LOCATION ON TH IMF r s t t P s2st r r t t t (X Z) DRAP t t t X DRAP 1 s s t 2 θ IMF. r r t t t (Y Z) DRAP 2 t t P r t s2st B IMF s t t +Z DRAP r t α = t (B IMF ) 1 t B IMF s t rt t2 t t r t t s r t t P s s

t t 2 t t s r s 1 r ts r t 2s s t t s r s t t t r r t s t s t rt s t s 2 r s t s t t s t t st t t s r r t s r t t t s t r ts r r st t st 2 s t s t t t st 2 t t t t rt t s t r t t t t t t t r t s s rt r t s s t r r s r t s t t ts ts t t t 2 s t r t t st t st r s ts r s t t 1t s t s ts t t str t r B IMF XDRAP r t r t r r s t t r s s t t r t r 3 t t s t r ts r t t θ IMF t r t t t P r t s2st t r s t rr t t t 1 r t rt t2 θ IMF rst ss 2 t s r ts t t r s t θ IMF ± θ IMF r t s t s s t 0 < θ IMF ± θ IMF < 90 t t r t s t s s t 90 < θ IMF ± θ IMF < 180 rst r s s r ts t BXDRAP IMF > 0 r s r t s r ts s r t s r ts t BXDRAP IMF < 0 t t r s t r t s r ts s r 2 st t t r s s t t r rt t2 α t t t r t t t rt t s s 23 t t s t P t s r t t s t r t 2 t str t s Z DRAP = Y DRAP /B IMF Z DRAP = Y DRAP /B IMF t r 2 r s t r r t t 2 s t t r2 r s 2s t tr t r2 s t P r t t t (Y Z) DRAP t (X Z) DRAP r t r r r s s r t t s r ts r s t t B IMF XDRAP t s r s t 2 t r r s ts s s r t s r r t t s θ 0 180 r s ts ss t r rt t2 θ < 20 s r t t t r r t s t 2 s 1 r t rr rs rs s r s

Z DRAP (R M ) 2 1.5 1 0.5 0 0.5 B X IMF >0 t t 2 t t s r s OP IP IN Z DRAP (R M ) BINS T A 2 51.44% 48.56% 1.5 1 19.24% 80.76% 0.5 0 94.41% 5.59% 0.5 1 1.5 ON 1 1.5 100.00% 100.0% 0.00% 2 2 1.5 1 0.5 0 0.5 1 1.5 2 Y (R ) DRAP M 2 4 3.5 3 2.5 2 1.5 X (R ) DRAP M B X IMF <0 2 1.5 OP 2 1.5 0.00% 100.00% Z DRAP (R M ) 1 0.5 0 0.5 IP IN Z DRAP (R M ) 1 0.5 0 0.5 9.80% 90.20% 93.50% 93.65% 6.50% 1 1.5 ON 1 1.5 90.41% 9.59% 2 2 1.5 1 0.5 0 0.5 1 1.5 2 Y DRAP (R M ) 2 4 3.5 3 2.5 2 1.5 X DRAP (R M ) F igure 4. MGS locations inside the MPB projected onto the DRAP coordinate system. θ ( ) 0 20 40 60 80 100 120 140 160 180 r tr t r2 s t P r t t t P r t s2st r r rr s s t r ts t BXDRAP IMF > 0 BIMF XDRAP < 0 t r t s 2s t r t t tr t r2 t (Y Z) DRAP (X Z) DRAP s s r t ts t t r t r s s t P r t r t t r t 2 r t P P r s r t rs s t t r t rr s t s r t t s st t r r r t t s rr s t s r ts r 0 < θ± θ < 25 155 < θ± θ < 180, r s t 2 t P s s

t t 2 t t s r s st t t r t r s r t s t t s t str t t rt t s t r t t tr t r2 r t s t 2 r r s r t Z DRAP rst t r s r t s t s r t r s t P r t r s t 0 < Z DRAP < 1 1 < Z DRAP < 0 r s t 2 r t r s r t ts t t st t t P s r t t r s t P t r t r s t Z DRAP > 1 Z DRAP < 1 r s t 2 t r s r r 2 t r t s ts rst t t st t s r ts t r s r Z DRAP < 0 r r t t r t t s 2 s r ts r t 2 r rs t t r s r Z DRAP > 0 s s s t t s r ts r q t t r t t t s s r s t r 2 t s 3 r t r r r r s r t t r t t t t t P P r s r Bx IMF > 0 Bx IMF < 0 r s t r st t r s rt r s r t rr s t r 2 r t 2 r θ ± θ = [155 180 ] t r t t r r θ ± θ = [0 25 ] t t r t t t t r 100% t t s r ts t t t r r s t B IMF XDRAP t s t r 10% t s r ts t t 2 r t B IMF XDRAP t s t P r 100% t s r ts t t r t B IMF XDRAP t s t P r 50% t t s r ts t t t r r s t B IMF XDRAP t s s st t st r s ts r s 2 t r t r t rs t t r t r t r st 2 t s r s ts s st t 2 s t 1 st s t t rt t s t r s r r s Z DRAP t r s t t t s t s t r r t B IMF XDRAP t s r s t 2 s t r t 2s s t rr t t P r s r s t s r s t t tr s r t s s r s t s s r t t r r s t P r t t r 2 s r ts r s r r s t BXDRAP IMF t s 19%, 81% t s s t 1 s ss t t t P r t st r 2 s s t r t rs s r s

t t 2 t t s r s s r ts t t t rt r s r r s s 1 s r ts t r Bx IMF < 0 93,5%, 6,5% t r s s r r 1 r t t r r t s r r t t r t ss t t t r t t t r t Bx IMF < 0 s rts r s r s ts r 2 t s r 100% t ts t t t t P r s Bx IMF < 0 t r s Bx IMF > 0 r s t 2 r s r r t s r t s s 90,2% r t rst s 94,41% r t tt r s s r 100% t s s t 1 t s s rt r 2 r t Z DRAP = 0 Z DRAP > 1 t s B IMF x < 0 Z DRAP < 1 t s B IMF x > 0 s ss s s r s ts r t s t r r t t t t t rt r t s t t r s t r t t r t t t s r t 3 ts r t ts t r r 1 t 2 t s t r t t t s t s s ss t t t tt r ts r r r t t t s t r 2s s s r t s r t P 2 s s st t t t P s t 1t r r2 r t r s s r t t s t t s r t 2 s t s s rs r s s r r r t t t t r 2 s r t t r r s s t rt P s t t r s t r t s t t t 1 t t s t r r s r s r 2 s r s st t t t s t t s t t r s t t rr r 2 s t s s s ss 1t rst s r s t r rt s t s r s s str t s r t r t s r t t t s t rs t s t t t t rs r t r s t P r t s2st r t t t r s t t t rr t r t s2st s t r t t s s t s s t t t r t 1 t tr t t st rt 2 t r s t t t t t 2 t t rs s ss s s r t t t r r t s t 23 t r 2 2 s r t t s t ss t s r t s s t P t s r r t r r r st 2 t t 23 r ts t t P s s

t t 2 t t s r s r t s t t t s r s t s t Bx IMF t r ts t r t t r r t s t t 2 r t s r s t ss s r t s r rr s t t P t r r t t t t t s r s s t t s t r r t s t s r r r s t s s t s st t t t t s t q s q r r t ss t t r t t r 1 t 2 t s t r st 2 t rr s 2 r s t t t r s t t t t r s 2 r t r t r t r rt r t r t 2 ss t t t s s r rt r s r t s 2 t s s r s t r t t s r t 1 t tr r t s t2 t r t t t s t t t rt t s s t t t t r s r r t s s t P r Bx IMF > 0 t t Bx IMF < 0 s t s r t t ss r t r s s t 2 r r t s s t t r Bx IMF < 0 t t Bx IMF > 0 s r r t s rr t s s r r r r s r r s st t st st 2 t t r s t t r s s t r t r r s θ± θ = [0 45 ] θ± θ = [135 180 ] t 2 s t r t r s s t t t s s r t s t r s t t t 2 t ts t Bx IMF > 0 t P Bx IMF < 0 r s t t s t t t r s r t t r r s ts t r s t r t s r s t r r t t s r t t r s 2 s st s r rt t t r t t t t t t P t P t t t t t s s t 2 t s t r st t t t t t s t t t s t r t t t s s s q s t t t r r t r2 rt r t s 1 t r r t s t s t t t t s t r st t s r t t r2 s s r t t st s t t r2 rs s r s

s st t t 2 t t s r s r s t ít stá st t í ét q r s t t r ó tr s t 3 2 stá t s ér t 3 st s rt r t t r s s t r r í 2 t t tr 1t r 2 t t r t t í ét q r t t s ér t 3 s r t r s t r s r t s 1t r s r t s s s 3 s s r s s q s s t s st s st s s 2 ó rtí s 3 s r t s ér s r s r s s r s r r3 s r s rr t s r s t s s r t r t stá st s rr t s sí t é 2 ó s r t s t 3 r t stá s r s ré s s á ét s s r t r ó st t s t s í s ét s st r s r ó t 1t r tr s s t r t st ít st s t í ét s r r s t s t s ér s t r s t 3 s s t s st t ór s 2 s r s s t st t ór s rr s ít q r t t r r tr ét s s t 3 r t t t r t r t s r t r s st r s s t st s r r t r 3 s r í ét s r tr s tós r s s t 2 2 rt sá s s r s t s r s s s s s 2 r s t t s tr s r 3 s r t st t s s r r s s t s s rt s r t r2 r t t 2 P t ó 3 rt t 2 st t t 2 r 2 r t 3 t s r str 2s r rt ó 3 3 t rt t s t t t r t r2 t r t s r t s r rs r 2 r 2s s P 2s s r ss P s s

P Pr t 2 tr s str r rs s s t r s s t st 2 r q 2 tr t s s s r t 1t 1 s r s rs s r t r 3 t r r r t s r q 2 r 3 t r t s ss t r t t t t t t r2 1 s r s s t2 t r t r t r t r s t r t r ss s t t r r t t s t 1t t r r s s s t s 3 t t t s r r t rs r t r 3 t s s r t r t s t r t t t t2 t t2 str t t s s t t r s r t t r t r rt s s r2 rt r 1 s r ss s t s t str r t ts str r t r r s t s s 1 s r tr rt s r t 2 3 s s q t 2 2 t s r s s r s s t st r s P s s t rt t s t t t r t t rs r s s t t s t t s t 2 r t 1 s s rs s r t t t r t t r2 s r r s t 2 t

Pr t 2 tr s str r rs s t r t r s tr s r r 2 t t t t t r2 rt s t t s 1 s r t t s s s t rt s r t r q t t r r t 2 t 2 s t r t 2 s t s2st t s t tr t t t s t t s s t rt s s s t rt t s t r s t t t t t r t s st t s t t s r s s t r s r s rs r t 3 s ss t tr t s s r t 1 t s r t str r s rs s s t ts tr t s r t r ss s r ts t t tr s t s s s s r rs t 1 s t tr 1 s r s t t 1t 2 t r r s t s s s r t s r t t r t r ss s t t t t t 3 t t t r t t t s r t st rts r 2 t r rt s r t 1t 1 s r 2 2 r t t r t r s t t t r2 t s r s r 3 s r t r2 r 2 r t t r 2 t r t r2 tr s r 3 2 t 3 t r 1 tr t t t s rs t s rt s r 3 st 2 t r t rst t r ss s t s 3 t s s s t r 2 t t s t r s t t t r r t tr s s t tt r r r 1 t 2 t r st t r s t t t t t s r t t s t2 s s 1 r rs t t tr t s t s r s s r s t t r t tr s 3 t r r rt s t t t r t t2 s t V SW t s s r s tr t r2 r t t r t r2 t t r r t2 V SW sin(α V,B ) r r t V SW cos(α V,B ) r t t t t2 t α V,B t t t t r s t t t t r s t s s t s s r s t s s r t s t t2 str t t t r t r2 s r t ss t r t r s r r str t s s2 t t s s r s s r t t rt s s s r t t t r2 r r t t r t r s t 2 t P s s

Pr t 2 tr s str r rs s r r str t s r cos(α V,B ) = 0 r str t s rr s t sin(α V,B ) = 0. + r P r r r t2 r 2s s t r2 t 2 s r r t s s 1 t 2 t s s t r s 2 st t ts s r st 3 r s r t t s r t r2 r r s t r r t r s t r2 s s r s rt s t t r r t2 r s 2 t 2 st str t s r t r2 s 1 r t r t r t rs ss t t r tr t s st t2 t t r s ts r t t r t t r t 3 s str t s s st 2 s t r t s t s 2t s t t s s t r s t s t2 r t s 2 st r t t r r t r2 str t t s s tr t st t s r2 t r r 2 r t r t str t t t s t t t s r r s r t t s r t t s s t t t α V,B s t r s t t r s t r t 2 2 r t t r s t r q 2 t r t r t 2 st t t st t2 r 3 t t α V,B t t t s r 3 s s V SW s r t t t r s r t s r r t tr t rs s r s

Pr t 2 tr s str r rs s r t r s t st t2 r t r2 t t r V SW s r r t t t r r str t t r t tr t t st t r t s α V,B t st t2 s st r t r s r t t t t 1 r t r t t st t2 s r r t t t t st t2 r α V,B > 75 r s r t r2 r2 s s r2 t s t s α V,B = 90 s 3 t t s ts r t s st t s t t st t s r rt t s t t r 2 tr r s t st t s s 1 t r 2 tr r s t st t2 rs t t s r s t t t r rt s s s t s s t r s s 1 r tr t r q 2 ω t r k t r s t r q 2 s t t r 2 tr r q 2 Ω ci r t t s r q 2 r 2 tr r s t r tt ω k v ion ±nω ci = 0 r v ion s t r t2 t r t B Ω ci s t 2r r q 2 t s s + t r 3 t t s + r r s t 2 tr r r r 2 tr r s s r ss t t n = 1 n > 1 r s t 2 r r t r s rs t s s s t s t r r r r s t r 3 t t s t tr r t t t s s s s t r 2r t t t r t s st s s str rt t r t t t r 2 1 t t t r s t st t s 1 r t r t s t k B = 0 r k s t r t r r s r t t s s 2 t t 2 tr r s s ss 2 n = 1 s t s r q t r t t t t st t2 r r t r t B s t s s t 1 r ss ω k v ion +Ω ci 0 r r t α V,B r s ω k s t t s t 1 r r t r t s r2 t r t t t t t r ω ion = ω k v ion s t r q 2 t tr t s r q 2 ω t r k t r s r t r r r r t s s r ts s r s r rt s r rs r s t tr t s r t t t P s s

Pr t 2 tr s str r rs s t t 1 r ss s s ω sc = ω k v sc ; where vsc = [V sw ˆk]ˆk r ω sc s t r q 2 t s t r ˆk = k/ k s t s t rs s t t t2 t r t t r2 r s s t r s t t V sw t s s s ω sc Ω ci r r s r t 2 t st t2 tr r t r 2 t 1 s r s t r t t t s r r t r 3 2 r q 2 t r st s t t r 2 tr r q 2 t t r 3 t t s s s r t r r t st t2 r s t r rr t s r2 s t r r t s s r t t r 3 t t t s r s t t r 2 tr r q 2 s t s sts t t t rr s t t 2 tr r q 2 rt r s s t r ss t t t rr t s s t s s s t r s s s s r r t 1 st 3 1 s r rt s rt t st t t r 2s r rt s 2 tr s r rt t rs ss t r t 3 t rt t t s t t r t t ts s r t t st t ss r t s r t 3 r t s rs t rst s r t s t t r t 2 tr r q 2 str t s 2 t P s s r t ss t s s s t s t 2 r t t 2 r 3 t r r t t s t t t P s s s r 2 r t 3 t r t r r st t st 2s s t r rt s t s s r t r s s t t s t r q 2 r 3 t r t t s t t r s r t t s t r r P s s r t s r t s r r t t s r t r t tt r t t s 2 rs t r ss 23 ts r t s s ss t r t s s t r st s s s t ss str t s t r t t t tr s t r2 2s s t t s 2 ss r 2 t t P s s r str r t s rs s r s

Pr t 2 tr s str r rs s s t s st 2 t t s r ts rr s t r ts r t 2 t str t t s t r rr2 t st 2 t P s t t 2 t r str r t rt s r t r s s 23 t r q 2 r t r 3 t r rt s t s s t ss t rr r t s ss t r t s s t r r t s t t tr s t s t t 1 s r rs s 23 t s t str t t s s t tr r t s2st t r rs t 2 s st 2 t r rt s tr t s s s r 2 P t str r s s ss t t s r r s ts r t t r t st s s str r rs t s st 2 2 23 s r ts t t r s t s 3 t s r t s s r s r t str t t s q t r r r t s s r t r 1 s r r t s t r s r t s 1 t r s t s s t s r 2 t tr str t t s t 2 s r t t tr s 2s s r r t s sts r t r 3 t t r s tr r rt s t r r 3 t t r r r t r t t t rs s t r s t str t tr t r t s2st r t s r t s t s 2s s s t t q s r t r 2 s tr rr t r t 2 r r s tr t t ts t r t s2st r t r s t t t r rt s t s r P s s t t r ss rr t t t t t s r s t t tr 1 s r ts r s r 2 s t t t t ts P r 3 t r t r tr 1 t t r r 3 t P s r t 2 2 t 1 t r t s r t r r r r P s s

Pr t 2 tr s str r rs s t t t t 2s s s t t t r tr 1 t t r 3 t r r t r t 2 tr r q 2 r tr t s r t s r t P rr t ts t s tr 1 r r t t t r s r t t r 3 t t t2 t t s t r q 2 r s r t rs r 1 t 2 t q t s rt3 r s t 2 t 2 s t t s 2s s t t t2 t t rt s t r t s t t s r t s t r s t t t rt r s s t s st 2 s s r t r t s s s r t r r 1 s r s 3 t r t s r s s st t t s s t r t rs t t t t s 2 t s r t ss r t str t s s r t r t st s t s st t s t str t s t t tr E st t s r tt r s t str t s 2 ss V SW = 400 s 1 ˆx MSO st 2 t s t str t s t r t t r s t t t r t t t tr E = V SW c B 2 tr tr t r t s2st s t r t rs t t Z MBE 1 s s r t E X MBE s t r t V SW Y MBE t s t r t tr s s t s 2s s t s t s s t t t r s t str t t r rt s t s s t t r t r s t st 2 s t r rt s t s s t tr t r2 r t t s s ts s s s 2 t t s t r r t 2 tr r s 1 s s r t s r s s t2 1 s t t2 r s t s r ts r str t s 1 P s s 2 str r t rt s t t r s s t t ts t r r r t rst t s t s s r q 2 rs s r s

Pr t 2 tr s str r rs s r t s t r r t s t r t r t B o s q t st 2 ts t s s t 2 ts r t t s 34 t r s t t t rs r t r s s t r t tr 1 s r ts 2 r r s t t r s t s s t s s r t t s s r 2 s t 2 r s r r 2 s ss t t t 2 r s r s t t t t tr s t2 Bx (nt) By (nt) Bz (nt) 10 8 6 4 1 3 5 7 6 4 2 0 Orbit P216 B (nt) 10 9 8 7 10:37:00 10:37:30 10:38:00 10:38:30 Universal Time (hours) r t s r ts r rt t r t P r t s r t 2 s tr rr t s t s s r ts r r t t t t t t r t B o t r t tr 1 s r r t r s r s r s s t t t s t r t t r t tr 1 t r r rt t r t P r ss rr t t t t s r s s t s s 2s t 3 r s t t rr t t t ±2 s r t t s 2s s r t r ts r r t r 2 s t s r r s ts s s st t t t t s r s s s r P s s

Pr t 2 tr s str r rs s 3.10^4 Orbit P233 Flux (part/(cm 2.s.ster.eV) 10^4 314 ev 191 ev 116 ev 10^3 17:33:00 17:34:30 17:36:00 17:37:30 17:39:00 Universal Time (hours) r tr 1 s r ts r rt t r t P r t rr r ±2 s ss t t t t str t s t t st t s s r 2 r q s t r t t r t 2 tr r q 2 Ω cp t ±1 rt t2 r s s 2 r r s tr t Y MSO t t t r rt t r t P t r q 2 t s t s s s2st t 2 s t t t r t 2 tr r q 2 r s r rs P r 3 t s s t t t s r r r t st r t t r t t r r r 3 t t r t r s t t B o r s s 1 t r s ts 2 tr r s t t s s 2 s λ 2 /λ 3 r t t t t t s r r s t 2s s 2 s s t k B o θ kb = 8 s t t t r r t s q s r t r s t t t r r s r t 1 t r t r ts r 2 s s t r 3 t s t t r t s t r ts t t t rs s r s

Pr t 2 tr s str r rs s 0.5 Orbit P232. δb par and δflux (E = 116 ev) δb par (nt) 0.25 0 0.25 δflux (part/cm 2.s.ster.eV) 0.5 3000 1500 0 1500 3.000 0.5 18 12 6 0 6 12 18 Time displacement (seg) 6:40 6:41 6:42 6:43 6:44 6:45 6:46 6:47 Universal Time (hours) 1 0.5 0 Cross correlation function r t t s t r t t t t tr 1 s r ts r rt t r t P r t s s r t r t r rt s t s r r s r rs s r s t st t θ kb r r t 2 tr r s r λ 2 /λ 3 > tt r t 2 s θ kb 9 s st t 2 t s r s ts t t t s s t2 2 r r t r t r r t t r t t t t t t t t r k s s t r t t t r t P r 3 t r r tr 1 r t r t s s r s r t st t t r t r 3 t r r t r t 2 tr r q 2 r s s 1 s r t s s t r s r r 3 t 70% r t r r t t2 t t s t t r 3 t < r 2s s t t r r ts 2 s r r rt s r r r s t t2 2 r s s t t t t s r s t r st r t t P s s

Pr t 2 tr s str r rs s r r r 2 s tr B YMSO r t P r t r t 2 tr r q 2 r t s tt r r r t s t t s s rr s t t rr r rs ss t t t s r t s t P s t r s tr s t2 t r s rt t t t rs s t s r t s s r str t s t s s r r t P s r r s s r r t r r ts t t t rt s r rt s P s r t s s ts t rt r s r s ts r s r 3 s s t r r rt s P s r s t r ts t t r s s t r rt r 2 s r 3 t r r 1 r ts P P s r r rt s t 2 t r r t r 3 2 r r 3 t r r t t t2 θ kb s ss t 15 t r s r r 1 t 2 8 rt r r t s s t s r s r t s r r 1 t 2 t R M R M r t s r r s P t t s r t t t s t s s t r P r r s s s t rst s B o s r 1 t 2 t s str 2 s st rs s r s

Pr t 2 tr s str r rs s 2 Orbit P216 April 3, 1998. 10:37:11 10:38:42 1.5 1 0.5 B 2 (nt) 0 0.5 1 1.5 2 2.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 B (nt) 1 r r rr s t 2 tr r t r r r t P t ts t t B o = [ 1,02, 0,18,8,27] r ss t s t st rt t t s r s 23 t t t t s r t ss t t str s 2 r s t t t rt r s 3 t r rr r t 2s s t r rt s s t t rt r ts r r t st 2 t rr r t t s ts t r s s s r t s t str t r t r t P r r q r t 23 t P r t str t s r t t s t s P s s t s s t t r q 2 s t t t r t 2 tr r q 2 ±1 ts t λ 2 /λ 3 10 ts t r t t2 r r 3 t % P s s

Pr t 2 tr s str r rs s Degree of polarization Ellipticity Coherence 100 90 80 70 0.5 0.6 0.7 0.8 1 0.9 0.8 0.7 Orbit P204 15:30 15:45 16:00 16:15 16:30 15:30 15:45 16:00 16:15 16:30 15:30 15:45 16:00 16:15 16:30 Universal Time (hours) r Pr rt s t tr r q 2 s s r 2 t s r t r rt t r t P r t s 1 t st 2 t t r r t t r t r rt s r t s r s t t r r t s ts r s s t t rs s t tr st str r t r P r ts t s st t r t r s tr s t2 t r t r t t r t 2 tr r q 2 t t 3 2 r ss s rr s t t P s s r r s t P ts r s 2s t r t s r R M s s r r s t s t r s st ss t t t s r r t s s r 1 s r r t s t t r s t s t 1 t r t st t r s s t s t2 r s s t st r s r t t s s r t t r s t 2 r t str 2 t r s s t t t s st t t s 2 s r s t t s r r P r ts t s t2 t r s r ts α V,B s t ss t tv SW s r t t rs rt r r s r s r t t t r t s t t2 t s t s t r s t t r t2 str t t 2 r ss s rr s t P t r rs s r s

Pr t 2 tr s str r rs s 0.35 Orbit P216 0.3 0.25 δb/b o 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Altitude (R M ) r r t t s r s t r st r t t r t P r 1 t t y = A 1 ( r a ) 2 s s t a = ( ± R M t r s t P t r s 2s t r t s r 10 s s r s t s 2 st t st s t t t s t t s 10 r s s s t s t t r s t s s t r s s s tr s s r t t r t s t r t t t st t2 s t r t s st t t t s t r t s t 2 t r t str r rs s t ss r 2 t s r t s s r 2 r s t s 2 t s st t2 t α V,B str t t α V,B st t rr rs r t s r s s r t r s r s r t r s ts t t r r r s ts s t str t r r s 23 t s t str t t r t s ts r s r s t r t s2st r s s t t s r r t r t t tr t r2 t Y MBE,Z MBE r P r ts r s s t α V,B st t r s s r s rr s t P P r s t 2 2s s t s 2 r r t s t str t t s t t s t s s s P s s

Pr t 2 tr s str r rs s r t P λ 2 /λ 3 θ kb 5 5 α V,B t s s s t t t s s s st s t r ts r t r r rt s r t t r t r r 3 t t t2 r λ 2 /λ 3 θ kb 5 5 α V,B t t t rt s t s s t t s r t Z MBE = 0 r t t s r t s t t s r s r s t t s t str t P s tr st t t s t str t s s t s t t 2 t s t tr t t s t rr t t s t α V,B r t t 2 t tr t r r r t s s r s r E s r t 2 t r t r st s t t s st 2 s t r r t rr r t t s t P P r s P s r r s t t P str s r t s t 2 2 r t t s t 2 t str r r P s t s r P st r r r r 3 t r t t s s r P s r t rr P s s r t t s t α V,B s t str t s r t s s s t r 60 P r r s s r t rs 55 t rs s r s

Pr t 2 tr s str r rs s Amplitude (nt) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Altitude (RM) r t t P s s t t t t r P r ts r t r st t t t s t t 2 r ss s rr s t P s r t s r r s rr s t P ts st r t 19 s st t t t tr2 t t s t 2 r P t P t r t rr t s t P P t r t t t r s t r rt s t rt 2 r 1 s r r 3 t r t s t t t r t s t s t2 r t s s rt r 2 t s s s st t t 1t s t r r t2 P s str r rs t s r rs st t 2 r 1 s r P s rr r t r r t r t t r r r r s st 2 23 t t P r ts s r ts t r t r r s r r s t Ω cp s t r t r t st str s ts r2 P r t t t t R M s t s s P s s

Pr t 2 tr s str r rs s Amplitude (nt) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 70 80 90 Cone angle α V,B ( ) r t t P s s t t r P r ts r t r st t t t s t t 2 r ss s rr s t P s r t s r r s rr s t P ts s 2 t s r s t t r t r t t r t r s str rt s r t s t t r s t s s st s t t t s r t st r t t t r t r s t t 2 t t s r t s t s s t r r r s tr s t2 P t tr s rs t t r s t t t δb P δb s t r t r s ts r t r s tr s t s t ts δb st s r t P s st t r s t t r s t s r r r r s s t s t t r s r t t t s t Ω cp r t t t r P t t r q 2 f cp ± 0 015 3 r Ω cp = 2πf cp 3 s t rr r f cp ss t t r s r t s s r r t t r P r r q s f > f cp + 0 015 3 s ts st r t t 2 st t f N t 2q st r q 2 rs s r s

Pr t 2 tr s str r rs s 6 4 Amplitude (nt) 0.8 0.7 Z MBE (R M ) 2 0 2 4 0.6 0.5 0.4 0.3 0.2 6 6 4 2 0 2 4 6 Y MBE (R M ) 0.1 Z MBE (R M ) 6 4 2 0 2 4 6 6 4 2 0 2 4 6 Y MBE (R M ) α V,B ( ) 80 70 60 50 40 30 20 r r t r2 t s r t P r ts t P s r t r r r 2 t t t s r 2 r 2 t ss t t t s r ts r t s s r P s s r s rr s t P P r s t 2 t P s s

Pr t 2 tr s str r rs s 3 r t t r q 2 s s r t s t s t s < PSD(f) > fcp+0,015hz f cp 0,015Hz > k{< PSD(f) >f N fcp+0,015hz + < STD(f) >f N fcp+0,015hz } s s 2 r 2 s t s r r ts t t t r s tr t Ω cp t t = s t s s t r ts s s t r s t Ω cp t r r s q t r st t st r s s r r t r s r ts t r s s 1 s t t t s t t r t 2 tr r q 2 t s s t P δb s t t r q 2 f r t t r r s tr s s t f cp = 0 125 3 t r r t t 3 s s r t t r r t t r r q s r 2 s s ts r 2 s t q t 2 t t r r t2 t P s rst str rr r t ss t t r t s s t r t r s t t r t r 2 t t t r t r s r ts r t r s t t r2 t rs t r t s r r t st t t t r t r r t2 t s r t r t t r r2 r ts t r t r r rr r t s t s tt r s t t r t P s rr r t r s rt s s s s r s t t r t r r 1 t 2 rt 2 r r s r t s rr s t t P tr s t t t r r2 r t s r t t s t r 2 t s s r t r t r r t s t r s r q 1 t r r s s t 1 t t r t r r t rr t r 2 r r s str r s s r rs r r2 r s r s r t t t r r2 t r s t t ts t rst t r t t r P s r r s r t r s r t r r r s s s r P t s r r r 2 s t r t r r s t t t t r str t t r t r rr r t s r s st t t st t s t t r s s t s 2 r t r r t str r rs s r s

Pr t 2 tr s str r rs s f c r P δb r r r s s t t t s t Ω cp s t t r q 2 r rr s t t rr r t st t f cp t s r t s ñ t r r s t2 r r q s r t t r t t t r s t r 2 s s r 2 s s s t r s t tt r s t s s r t t r t t r r Ω cp rt t r r ts t s r tr2 t s st t t tr r t r t r s rts t 2 t s s t t 2 r t2 t rr t Ω cp t t t ttr t t t r ts t s r t rt 2 r 1 s r 2 t t r t r t r s rr t t t s r s < R > t st t t st t rt 1 s r r q r t r 2 t r 2 r rt s s s ts r s t2 t r t r s s t 3 t r t s r ss s t s rt t 2 t r r r t rs 2 s r t t t s t r r t t s r s ts t 1 s t s r s t t rs s r 2 r P s s

Pr t 2 tr s str r rs s r rr str s t Ω cp t t r t r t r t r t s r r t r 2 ts r t r ts r s 2 s t2 rs t P 2s r s t2 t t t r s r t t2 r st t t r rs r P r2 s t r s r s r q 1 t r s t r s r s r s st r r2 s t r s r t q 1 2 r t rt t t r r s t str t r t r t s r 2 st t r r t s r t s r r s t s st t r s s r r s s t r q r r t rt r t 1 s r r s t2 s r s 1 t s s t s t t 1 s t r t r s t2 r 2 s r s r t s s 1 s r s t s t t r t s s r r t r r t s rs s r s

Pr t 2 tr s str r rs s 2 r tr t t t rt t r s r s r s t s r 2 s s s r 1 t r t 2 t 3 t s s t t rt 1 s r t t s rt t t t t s t t t r t 3 t r 1 r t s t s r t t2 r t r s s t2 r r t s s sts t t t 3 t r t s t 1 r r t r t s r t st r r t t t s st s s t r t P s t rs ss st t 3 t r t s t t t t s r t t2 t s r st s rt t r 2s s t t t t r t r t t r t s r 1 t rs t r2 s t 2 ± 2 s 1 s st t t tr s t ts s s t r t r2 r ss t s r r t t t s t t r r t2 s r t r rr t s r t s t t s t t r r r s t t t r s s t Ω cp s r t tr s t2 r t s t t s sts t t r s t t s t Ω cp s t r s t r s t s t2 t t r t str t s r t t r ts t 1 s r tr s t s t r ts t r s t2 t t r t s r rr r t s t Ω cp r t 1 t t s s t 1 t rs s s r ts t r t s tr t t t t r s s r2 t s t r s t P s r t t s t 2 r 1 s r s t s t r 2 ss t s t t r t 2 s t s t2 t t t 3 t r t s r st t r t s r ss 2 t t t t s 2 t s s t r t rt 2 r s t s r s r t t2 t s 2 s 1 s r r 2 t s r r t s r s t s t r t r s t t 1 s r r t r été r 2 q t 3á 3 t s t 2 s t s r t r t rt t t s r s r s 2s t r 1 s r s t2 t t t t rt t P t s t2 r r t t r 2s s r t t s t t t st t r s t t s s s t r t t r t s t s t r t s t r s r rt s P s s

Pr t 2 tr s str r rs s t 2 r t s t s r s t s r t t2 r s t tr t t r s r s r t tr st s st s t2 r s s 2 1 r rs r s t r s r s st r r2 r s r s r t s t s r t s2 tr r t r 1 s s r 2 t tr st ts r rr r2 r r s t 2 t t t s tr t r ts s t s s t2 t s s t s t t s s t s s s r r t 2s r s r 2 t s s t s t s t t r t r t s s r t rs t2 tr 1 s r s t2 3 t r t s t s r r t2 < R > r t t t s s s t r r t 2 r 1 s r rst t r rr t s t2 r s s 1 r r s t r s r s st s 2 r s r t q 1 s s st t t t rr s 2 t 1 s r tr t t t s 1 s r r s s t s s s s r t rr s t2 r s s 2 s t s t s s t r r t s r t s s t t s s t s t2 s t s r t 2 t 1 s r s t r r 2 ss rr t r s t s r t t P 2s s s r rs s st t t t t s t t s s t2 t t 2 rr r s s t t r t r t s s s 2 t ss s r t t2 r s s s s r s 2 st t t r t2 t 1 s sts t t s r ts t t r s r t s r r t r s t t t t s 2 t r t r t t st t2 t s r P s t 1t s t r r t 2s s t r 2 t str r s rt r P str ts r s r t t s r r rt s t s r t str r t s s t str ts t r r r t t t 1t r t s r r t r s t s tr r q 2 s s rs s r s

Pr t 2 tr s str r rs s s str r s t s t st 2 t P s rr r t str r t s s t t r s rt t r r t t t t s s t r s s t t P s rr r t t rs rs t rr t t t rt tr st r r t s r t t2 t t ts t s t ss t q t 2 ts s s r ts r t r s r t s tr st t t s s t t tr st ts s r t 1 t t s s t s t rt s t tr t2 t rt r t s t tr t2 t s r t s r t r r r t s r t t2 r s t r r t ss ss t st 2 t r r t ts t s s t 23 t P s t r s t t r t ss r t s 2 rs 2 st r s r t s t s 2 rs t r s s t r 2 r 2 r t s s t s r 1 s s t t s t t r t r t r r r t s t 2 t P s r t s s r t t s t t 3 s r rt s t t r t r t r s t t s r t t2 r s t t r t t s r r t r r r t s r q 2 3 r r r s t r t s t t X VSO 1 s t t r s t s t t t t2 V SW s t t r 2 t r r t t Z VSO 1 s r r t s r t s t t t rt Y VSO 1 s t t r t s2st s t s rs s st t t s t t t r t t s s t t str r s s t t r t r t r t r ss t t r s tr s t t s r t s r s ts t r s st s t 2 P s t t 2 s t r r q 2 t r r t r t 2 tr r q 2 s t t s t s rst t 2s s t t P s t s r ss s s t P s t rs r t 2 r s r t st s r t t r s 10 6 10 6 r rs s r s t 2 P s s

Pr t 2 tr s str r rs s r 1R V = 6052 r t s t t s r t t2 r s s s r s t r t t t r s t t r P s r r s r 1 t s 2 P s ts t s s t s r t s t t s r r t rr r s s t q st t r t t rs t t P s t s t r r q t 2 s r t s r 1 2 t r r 1 t 2 t t s r t r r t 2s s t s r t s t s t s tr2 t rst t r t 2s s s t s s r r s r t t s t s rst t st t2 t t st r s r s 30 s r t s r 1 t t 1t r t s r r r t t t t s r t t2 r s t s r t r st t 30 t r r r t t st t s r r r r s t s ss r P s r s r r q s t r t s t t s r t2 s 1 t r t r t s s r s t t s s r t s r t st t2 r t t r P s r s r s r tt t t r s ss s t s r rt s t s t r s r t s r t2 t s r r t s t2 t s r 2 P r t2 t s t s s r t rt s ss t t t t2 s r 2 t r r t r s t P str t r s t r t r t s r s t str t s r t r 2 st r s V SW r s t r s t s r r t r s r 1 s t t V SW s t s 1 r r s r 1 t t r t s r s r 2s t P rr r s r s 2 st r s t r t rr P s s t V SW s t s s r P s r r r q t 2 r r t r V SW s 1 r s r 1 s r r s t r s s 1 t t s s t r s tr r s s t r r r 2 rr s r V SW r t s 1. rs s r s

Pr t 2 tr s str r rs s 50 2006 05 10 to 2007 08 10 (2006 DOY 130 to 2007 222) 50 2011 03 01 to 2012 05 31 (2011 DOY 60 to 2012 152) No. of occurences [%] 40 30 20 10 PCWs (ns=153) Vsw (ns=452) No. of occurences [%] 40 30 20 10 PCWs (ns=439) Vsw (ns=457) 0 100 200 300 400 500 600 700 800 Vsw [km/s] (1 val/day) 0 100 200 300 400 500 600 700 800 Vsw [km/s] (1 val/day) r st r s r s r s P P t r s r s t t s r s r s r t s r r t r s r 1 t s r s t t t r r ss t s r t t2 P s r r r q t 2 s r r s t s r s s s 1 s t r t r s r s t s t s s t t t r t r t t s r s s t r s r t t2 t t r s t t t r s r2 t P s r t s t s t r t t t s r t r t s 2 t r s t t t r s t r r s t s 2 r s t t st t2 s t s t r t 2 s t s r t s r r V SW r t s t r ss t t r r r s tr t t t r r r 2 t t r st t2 r r t 2 ss t t s r s r s t r t r t s s t 2 r t r t s r P s r s t2 t s t s r t r t s t2 r r P s r ts 2 r s t s t t t t t t str t t t s s s r t rts t s t s r t r t t r s t2 st t s t s s t s r r t r t P s s

Pr t 2 tr s str r rs s t s t r st s t s r r st t 1 t t s r st t t r t r s r 1 t s r s s t r rr s t r s r 2 s t t P s r r t s t2 n p r t s t s t s r r t 2s t t P s s 2 n p s r t 3 r r P s r 2 r s t s r t 3 r s r 1 r r t t r s r r t r s t2 r t s t t P s r s r t 3 tr r r P s r r s t s n p 3 s s r 2 s s s t t s t t P s r r r 2 r r r s r s t2 s s s rts t t t t t r t s t2 t r t r2 r t s t r s t t t r r t s 2 s t r t s t t P s r t s s t s r r t s t2 r s r 2 r r s r 1 2 t r t r r P rr s s r t t t s r s t r s r r P t r s r 2 s t t r t r s t2 P r t s r r t r s r 1 r t 2 r P s r r s t2 s s t s s t rs s r s

Pr t 2 tr s str r rs s t t s 2 r 1 s r 2 r r s t s s t t t r2 s t s s s t s r r t s t2 r s t t r s r 2 tr s t r r t s 2 r s r st t t s s t st r r t r s r t s t r s r t s r t t str P s s r t t t r t t t r2 r t s t2 t t r s r r t s t2 t s s t s rt r t t s r t s r r 2 r st t r t s t s s s t q st t s t t r t r s r 1 r t t t r r st 2 t t 1 s t r r t r s r t rt s2 t r r t 3 t r t t t s 1 s r r s s s s 1 t t rt t t t r s t2 r r t s t 1 s r s r t t r s r s t t r s t2 2 r t t t r r t s s r t t2 r t r r s r 1 2 t t t s r 1 t s s t s t r s r r s ts t r t t t 2 r r t t r2 + s t2 t t t R V t st rt r r 2 r t r s r s t2 r s r 1 t r s r 1 s t r s 3 t r t t t 2 r s r s ts s t r r s t2 r + t r t t s t r t s t r t s r s r r s t2 2 t r t s r r t s t r s t2 1 s r r t s r s 2 t r r t r s r s s r t t2 t 1 t t t r t t t s t2 t r2 r t s t t s r r 2 t r r r r t r2 s r st t tr2 s 2 r r 2 t t r s t r rr r t P s r s r 1 s rt r str P s t s r s r 1 r t s r r t r s 2s s t t t t t q s t r t s t t t2 r t t r r t s t2 s 1 s r r t s t r s t t t r r t s t2 s t 2 r t r r t r r s r r t 2 tr s r s r 1 P s s

Pr t 2 tr s str r rs s s ss s s rst t t t t s t t r s 2s s s t t t s t r str t rt s s s r s r t r t t r t 2 tr r q 2 r t t 2 r 3 r s r s s s t t r r t t s P s s t r s t r t r ss r t s r t 1 s r 2 r rs s 1t 2 t r s s ss t s r st s r s r t s t t r str t s r 2 s r s r s s st 2 r q 2 s r t 2r r q 2 t s t t r2 r r rt r r st s t s s t s r r t t s v ion r2 s t t t r q 2 s r s t 2 t r t t t t t r t t Ω ci. s r t r 3 r t t r t v ion st t r r t r 3 t s s r t t2 str t s r t r t r 3 r t 2 tr t r s t t t st st t r r s r s t t s s t t str t t t r t s t r s t t r s s s t s s s t st tr t r r r r s r 2 t t t r 2r t t s r t s rt t r t t s r s t t r 3 t t st s r rs t t t s s t r r t s t t 2s s r r t t t s rs t t s t r V SW s ss t t rs r t t s t t r t s r s t s r t s t s s r ts t s ss t t r t s t2 t s s rt r t t k V SW t t s ss r2 t t t r rr t t t r 3 t s r s r t r t r s ts t ss t t t s s s t r r t t V SW s t t r 95 t t s st t s s r t rr s t t s s r t t r r r t r s r 90 t r r s t r t 2 2s s s s t t t P s s r t rs r r r t st r t B s 3 r θ kb t r s t r ts rs s r s

Pr t 2 tr s str r rs s t r ss t s st 2 3 t s r s s r s r ss t2 t2 2 δb par /B 0,25 r ss t2 t s s s st r t r ss rr t t t t t tr 1 t t tr 1 s t s r 12 t tr s t2 t r t t 1 s r t r ss rr t t t t t s r s r ss t t s s ts t s q t2 t s r s t s t 2 t t t rs t t t s r t 2 t s r t t t r s t t str t s s t s r s rr r s tr r t t t st ss r ss rr t t t t t s r s t t s t t r ss rr t r s r t r s t t s t r t s s s r t r s ts t 1 t rr t t t t s r 3 r t s s t t t r s s2st t rr t t t t t s ts t t rr rs s 2 t s r t s t t r s t t s t s r s ts t t t t rr t s t ss rr rs r t s s r t 2 tr r 2s s s r ts s s s t t t r q 2 r 3 t r t s s t s t t r t t rt r t t t t s s t s t t s r r s t t t s r s r t ss t t t r s r r t s r t 2 str s t q s r t t r r q 2 t r s r r t r t 2 tr r q 2 3 t t t t t t s r s s s r s s t t t r st r t t r s tt r t s rts t t t rs s t s r t s s t r st t r t s r P s t rs s t r r t t r s t t s r r t s t r r s r st s t t s st t t t s t r s t r rt t r t r 2r t str t s str r t rt s s s s r t t rt s r s 3 t 3 t t r t 2 r t s s s st r t s t r r r t s t t tt r s r t s t 2 t s r s t t 2 r t s t r q 2 s t t 2r r q 2 t r r s r t str t s 3 t t 2r tr str t s t s r t t s t P s s

Pr t 2 tr s str r rs s t t tr E t s t str t s s t t t P s s r t str r rs s sts t t t t t s t str t t s t s s t s t t t t s t ss st t rr t r s s r r r r t t t s t t t t tr 2 s r t t t P s t r st s ts r s t r ts t B > 5,6 r t r tt t 2 r t 2 t s r r E ts 2 r t t s r r r t 1 t s r t t rs r s s r 1 s r 2 r t s 3 t r t 2 t t tr r 1 s t tr s r t t st tr t r st t r s t t t t t tr s 3 r t s 2 tr s str t t t s r tr st t t s r s t t t r P P t s t str t r st s s r t rt r s t s t t r t t t t tr t r r r str t r t r rt r r s r E s r t 2 s s r P s r 2 t t s r t t r s s t s t s st t tr 1 t t t s s t t t str t s t ss r 2 t t s t s rt t t t t t s r t s s t s r t r2 s rt s t2 s t 2 t s r s r s t st s r t t r s ts 2 ss t s r s t r t t t t t s r t r s r P t t r t s s rt t t t t t t t rr t t t s t str t t P s t t tr s s s r t s t 2 t 2s s r r t t s t r st r s ts r r t rr r t r t2 t P s s r t str r s rs s r s t 2 t s rs r2 r r t s r t s s t r rt s P s r s r t s t r t P P s s s r r st t st st 2 t t s 2 s t r t t r s t s s st t t t tr2 t t s t 2 r P t P t t 2 t s s r t s st t t r r t2 t s s r t s t t t r 2 rt rt r r rt2 s r t t r t r 1 s r t 2s s t rs s r s

Pr t 2 tr s str r rs s rr str tr s rs t t s t Ω cp t s t r t t s s s t t t t s s r s t t s r t s s t t t s r t s s t 2 r r t rt r r s t r s r t r t s r t q 1 s r r t s r t2 s t s 2 s r t r tr s t s t s t s 1 s r t r s t t t t r s r t 2 s r r t t t r r s t t 1 t2 t s r t t r ss s t s r s ts s st rr t t t rr t s s t t r t t st t rt r ss t t r t 2 s t s t2 t t 3 t r t s r st t r t r st r t s r s ts t s s rt t t t t t t t s r ts r r r t r s r t s s t t ss ss ss s r t t2 s t rt 1 s r t r r t P s rt t 2 t s s t t s r s r ts t r s t t s r 1 t s s r tr st ts t P s rr r t r t 1 t t s s t s t rt s t r t t r s r 1 t 2 t s r t r t rs t t t s r t 2s s r r P t r rr P s r t t t s r ts r t t s r 1 r t s r s r s ts s s st t t t t q s t r t s t t t2 r t t r r t s t2 s 1 s r r t s t r s t t t r r t s t2 s t r s s r t r t r r s r r t 2 tr s r s r 1 P s s

Pr t 2 tr s str r rs s s st st ít stá tr st s tr ét s s r s r s s 1ós r s 1t s rt 2 s s í t r t r 3 s s s r s r r 3 ó r t 2 s t s s 1 ó q s s 1ós r s t r s s t r t r 2 s r t s r s s t r ó r s ó s q r s r ó st t 1t r r s ó s t 3 r t 3 r q r r s rá tr s r t r 3 st s s t s r t t s t r ó t ó str ó s s s r s s s rtí s r s t r t t s r2 rt r st s r s s t r r ó s rr s t s s r s rr s s r s t s s q rtí s 1 s ér s tr s s t 3 s 2 s s t t t r s r t s r q r s s r s s r s t st s r s s r tró r t s s t t rt t s tr t t r ó tr t s r 2 rt s 2 q q s t t s s r s tr és 2 r s s tr s r r í 2 t t tr t s r 2 s rtí s t r s st s t t s 1 s ér s s s s tr rtí s s r t s 2 r t t t r s t á s st s tr s r 3 s r t st t s s r r s s t s s rt 3 3 Pr t 2 tr s str r rs s r t s r rs r 2 r P t rt r 2 3 3 3á 3 r r r t2 s t t r t 2 tr r q 2 str r rs t r rs s t t 2 r 1 s r 2s s tt rt r 3 str r t 2 tr s t s r s r 1 2s s P 2s s s 1 s s rt 2 s stá 3 s 2 tr 2 t t r s t t t r r tó t r rt 2 s s r 2 r r t rs s r s

Pr t 2 tr s str r rs s P s s

P t s s r t t 2 s r s r t r ss s s t r s t t t st 2 t s r rt s s rr t r s r st s t t t t s r s r t r ss s t ts t t r t r ss s r t rt st t t t t t s r s t ts t r t t ts s r t s ss t s t 2 2s t t r ss t s t t 23 t s r s r r s s r s r s t t r 2 t s s t 2 r r s r t s r 1 s 2 r t r t s 2 2s t t r t 3 s t t r st t r s r s t st 1 1 t t r t t t s r t 3 t ts s r t r s r s2st s 2 t t t t s r t r t r ts t r st t r r R s t r r s r t r t t s s t t 2 r 1t r t s rt

t s s r t t 2 s r s r t r ss s t s s rt 2 t r s t t r r r t2 t t r r s t s s 1 r rt s + t r r s + s t + + 2 + 3 + r r t t r t s r t rst r r r 1 t r t t s t t t s ts t t s t r s t t 2 t r s t t t s t s r t r t t s r t r t r t t r t t r t t2 s 1, t r s t t s r t s r t2 s 1. r 2 t t s s rs s s t ts rr ts s t t s 2 t s r ts s st t t s t t t 1 s r ss tr s t 2 t r s t r t tr st t t t t r t s r t 3 ts t r s s s s s s r str r t s t t s t s st t r s t t r t r t r t t s r t r st 2 t t r t t r s t r t t s t t t s t ts r t s s r s r s t t r t t t r t r s t r t r t t t t s r r t t s s s r t s r ts r t s t t s r r s t r t t r t t s t t r s t t t r t r r s r r t r t s r t rt r t r t r t s r r t 1 s s s t s t r t s 2 r r r t s r t rs s ts t r r s t s s t s r t r t r s t s t s r t t r t t s s r t t r s t s s ts r r ss t 2 s t s t t s st st r t r s s r 2 str t t s t R s. r r s r s 2 t t s st t t t t t t s r t r rt t st t t t t s s t s r t t t r t s r 2 r ss r s s t 2 r t s t 2 s t t r t s t rt t r t s r s rt t t r st 2 2 t tt r s t r s t t s 10 28 3 580 t s t t t t rt t s r t tr t2 s t r t s r s r t t t t r q t r P s s

t s s r t t 2 s r s r t r ss s s t s s r E = (v B) r t r t s rr t r t t s t r t t s r t s r t r s ss t t t r s t r s t 2 s ss t t t s r r t r t r 1tr t r t s t s t t 1t r t r t r 3 t t s t r t s s s r rst t t r rts t r s t s r t t r t q t r s 2 str t r s s str t r rr t s 2 t r t s t s t t t s t 2s tr s t s t t t t t t s r t s t r t 2s t t s r s r ss 2 t s r s st 2 s t t s st s s r t R s s t t ts s t t s r t t s s 2s r s t t s s t ss t t t t r t s r s ts s t 2 t r t s r rr t r r s s t t s str t r s s s r s t r s 2s s str t t st rs t rs s r s

t s s r t t 2 s r s r t r ss s r s t s r t t r t t s r t t r s t s t s s t t s t rr t s t t t r t r s ts t t r s str t r t rr t s t t t r t t s r t t s s t s r st ss rr r t r s rt r s r t r s r ts t t s s t2 t r t t t s s t t s r rt t q t r r t t r t s s s t r s s t s t r s t s r s 2 r ss t s ts r t r r t t r2 r t t s r s t r t r s t r t s t r s r 2 r t t t s t r2 r t t s t t s r str t r t t r t s r r t r ts ré t s s r t t t t t t s r t r s t t r s s t t t r2 r r t t r s t s r t s r r s s t t r s t str t s t t s t t r rt t 23 ss t str t t t t r t t t t str r t r2 2 t r t s t r t r s t s r rr t s t r t s t st t t t rr t s t r t t r s t t s r s t s t t r t t t rr t s t t r s t t t r t t q t r t s r t rr t s t t r t r t t ts 2 r r t r s t r r s t 2 t s t rr t s t t r t s s t 2 r t r t t 1t r s s tt r t r t s r t t r s s st 2 t t s t q t 2 t r t t t rt r ss r s t t s t s r t s t t t t 1t r r t s t ss s s 1 t s r s r str2 r t s t s r s r2 s t s r r ss r s r t t s r r ss r rt t r t2 t s 2 s r t rt t r s r 1 t 2 t t s r s r t r t s s r t t rt s s r r t t t s r s sts r tr 2 r r s r t t t t t r t t ts r t t 1 s s ss t r r t t t s s r r s t r r t s 2 t r s 1 t t s P s s

t s s r t t 2 s r s r t r ss s r t s str t t st rt t r s t s r t st rt s rr t s t t s t t r r t t r s t s st rt t r s t s rr t s t rr s t t r t t r s rt r s r r ts t 2 r r s t t t 2 r r t t s t r 1tr t r rr t 4 s r t t s r t r 2 r 2 s t ts tr st t s st t t s str 2 s t 3 t r t s r r t r t tr s t r s t s r t tt r r rt t r t ts t s t s r 3 t r rts t s t s r r t ts s r s s q t t t r s t 1 r t ts t s t r t t t s r t s r t r st 2 t t r t 4 t r t s r t t s tr t t r t s r s 2 r r s t r 1 s st t s s t r t s r r t t t t 2 6 2 + 7 t 2 2 4 2 + 5 t2 2 2 2 + 3 s r t t t t s s r r q 2 r r s r r rs r t t t 2 r r 2 r r s t tr r t r s s s 2 r 2 2 + 2 r 2 t t r t t r s r 2 rs t r t s 2 rs t s r t 2 t t s s r t t r2 r t r 2 r t t 12 t s rt t t t s t s rs s r s

t s s r t t 2 s r s r t r ss s r r s t t s r t t st t r s t s r str t r 2 r ss t s ts s r s t t r r t r s t t s t t t r 1tr t r s t 2 r tr r r s t t s t s r r t s t r s rt s s r t t t s r t P t 2s s t s t r t rst t 2 2 s st t r s + + 2 + + 2 + 4 + 2 t ss tr t + 3 + 5 + 2 + 5 rt t r 2 t t t r t s r t 3 ts rr ts s t t s s r tt t t r t t 1t r t r s t r tr t t r t rt r s t s t 1t r s s s r 2 s s r s t ss 2 t s 2 ss s r r t r t s r s t s s t s t t t t t t s t st t s r r s t t s rs rt t s s q t s r t t r t 3 s t s r rt s r 2 t t r s s t s r st t s s rr ts s t t s s r r t s t 2 str t st t t 3 s s r s t t 3 s r s s 2 s r P s s

t s s r t t 2 s r s r t r ss s t s t s r 2s s t r s s r rt s str r t r s 2 st 2 t s t t r 2 t s t s r s t r t s t r t r ss t t s r r r t t s r r 2s s rt s s t t r s r ts r 2 ss r s t t 2 2s r ss ts t t s r s t s t t r s r t r ss s r s r t s t s t s t t s r s t s r tr s rt str r t s r s t t t r t t t r s r tt t st t str t r t s r 2 r s r ts s st t t t s s r t tr s t s r t t t s r t r tt t s st t t t t t t ss r t s r s s t 10 24 s s 1 r r t 2 t 23 t s r t r t r t rst s r t t r t r r ss s r t s t s s s t t t 10 25 s s 1 t s t 3 t r rt t r s s r s t s r t r t t r r ss 2 2 t st t ss t t r t 10 25 s s 1 tt r t st ss t r t 2 2s st t t t t s r 1 2 r t r t s t r t 2 2 s 7 10 6 2 s 1 r t 23 P s r Pr s r t s r s t s r ss t 2 2s 2 r t 3 s s t s t t ts t t t s r r ss 2 rt r t r ss t ss 2 s r t r r s ts s st 2 str t r s r s s r t t r t s st t r ss r t s s tr t t t s s r t t 2 t s s r s s r t s r r t ss P s tr t r tr s r t s t t s st t t r 2 2s s st t 2 t s t 2 t t r s s r s t t r t tr s tr t r t t t t t s 2s s r s r t s r 2 q s s t q t s str t rs s r s

t s s r t t 2 s r s r t r ss s t 2 s st t t t r tr 2 t r r t s 2 st t t t s ss r t s r t t r r 10 24 s s 1 r t t r 2 2s t t t r s st s t r t t ss r t r t 10 25 s s 1 s s r ts r s t rs ss t t s 2s s t s r s t r 2 2 s t t st t s ss tr ss tr t r s r t s t t t t s r t t t rs s t s t s + 5 + 2 + 5 t t t s s t s s t t s t 2 s st t t t s s st r t t 1 s tr s rt t t t t t t 2 t t r r ss r t r s 2 s t t t t t s t r t t r t t 2 s r t t r st t t st t t r t t t s r s t r t s r s t t s s t r t s r s r 1 t t rt t r t s s s t s s r s r é str t r s r r s t r r t s str t r s t ts t s t2 t t t t s 2 rs r s s t t t t s r s s t s 2 t é r t t s st 2 23 ss s s r t s t r 2 2s s t s s s ss s tr t r2 1 r t s t t s t r t r 3 t s s t r s 2s t tr t r2 ss r t t r 2 2s t s r t r t r t s t s t t r r t s2st t X TIIS 1 s ts t r t r t t t Y TIIS 1 s ts t r s t r t Z TIIS 1 s t s t r t s2st s t s ss s t t s r t t t s r 1 t 2s s 1 s r str t ss s t r 2 s tr s t st t t s t2 t s s r t t tr r s t2 t s r t s 2 s t é s t s r 1 s 2 r t t r r 2 t t t r s r t s r t s ts r r é t st t 2 r r t t s r ts t t r t 2 s 2 s t r s t 1 s t rr t 2 rs t t t s r s r 1t s t r s ts ss s r t s 2 st 2 st s r t t t s r t t 1 t t t 2 s rr t t s r t r P s s

t s s r t t 2 s r s r t r ss s 2s s rt r t s st t t 2s s r r s t r t 2 2 t s r st s r r r 2 2s data1 T1 T4 T1 4 2 T17 T19 Z TIIS (R T ) 0 2 4 4 2 0 Y TIIS (R T ) 2 4 T40 4 2 0 X TIIS (R T ) 2 4 r r t r2 ss r t s r 2 2s s r t s ss s t 2 2 t r2 t t s st r t t t t t r t s s r s t t t t s ts t s r t t s s t r s s P P P s r t s r t s 2 2 t t t r t s s t r t P s s s r t s s 2s t tr r s t2 r 2 P t t r s P 2s s r r s r t r 2 r r q 2 r r s tr r s t2 r t t t r t r t s tt r s ts t t ts s r 2 r t s r r r s s t Bx TIIS By TIIS Bz TIIS t ts rs s r s

t s s r t t 2 s r s r t r ss s r s t 2 t r s 2s t t t s t2 B TIIS Magnetotail r P P s r t s r 2 2 s s t s r t P s r t s s 2s t tr r s t2 r 2 P t t r s P 2s s r r s r s r t s r r s tt r s ts t t ts s r 2 Bx TIIS r By TIIS r r Bz TIIS r r t t t s t2 B TIIS r t ss s t t r s t s r t s s r s r t r 3 2 tr r s t2 r t 3 t t ss t rs t s t s r t tr s t2 r s s t s r t r s t s s r t t s r r 2 t s s t 2 r s s r t t t s t s r ts s t t ss s t 2 Bx TIIS > 0 t s t t tr2 t t t s r t r t r t Bx TIIS t t r t ts r s P s s

t s s r t t 2 s r s r t r ss s t t t t s t s r s r t t t r t t X TIIS t t s t s s t r t t 1t r s ss r s t 2 t s t t t t r rs t Bx TIIS t t t t 2 ss s t s t s r t t r t s st 2 t st t s r s t t r 2 t s r t ss t t t t s r s r s t r t s t t r s 1t s t s s r t 2s s r r P P s r ts r r t st t t t2 t s t é t2 t s t r r t r s s t 2s s r rr t t r tr r r t r t s2st s r t s2st s t r t t r t t X KSO 1 s t t r s t t Z KSO r r t t t r s r t t t rt t t Y KSO t t r t s2st P s r t t r t t r t s t r t P s s t s s t st t s P t t t r s t t s r t r t t r s ss s r t t t t t 3 t r t s s t r str t t r str t r t t r s t str t s t r r r t ts tr t s s t t t 2π st r s r 1 s r t r t t s 2 s 2 t str t s r tr 3 2 t r s r r t s δ θ t t δ s t t t Z KSO = 0 t s t r t r s r 90 t +90 t θ s t t X KSO Y KSO t s s t 180 +180 r θ = 0 rr s s t t r t t X KSO 1 s t t t tr s r t t 23 r t t t r t t s r t r t t r t s t r t q s t t 2 s t 2 t r t r r 2 s st t t t t r ts r r t t t P tt t s r t δ θ r s rt t t r s 2 t t r s s t r str t t r str t t s t s r t r t r t s2st r t s t r t r t str t t s s r t t s s δ θ rt t s t s r r t s r δ = 20 θ = 20 r s 2s t s 1 s s r 2 P r rs s r s

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2024 © DocPlayer.gr Πολιτική Απορρήτου | Όροι Χρήσης | Σχόλια