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ESS 154/200C Lecture 15 The Inner Magnetosphere II 1
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ESS 200C Space Plasma Physics ESS 154 Solar Terrestrial Physics M/W/F 10:00 – 11:15 AM Geology 4677 Instructors: C.T. Russell (Tel. x-53188; Office: Slichter 6869) R.J. Strangeway (Tel. x-66247; Office: Slichter 6869) •     Date 1/4 1/6 1/8 1/11           1/13 1/15 1/20 1/22 1/25 1/27 1/29 2/1 2/3 2/5  • • • • • • 2/8 2/10 2/12 2/17 2/19 2/26 2/29 Day Topic Instructor M A Brief History of Solar Terrestrial Physics CTR W Upper Atmosphere / Ionosphere CTR F The Sun: Core to Chromosphere CTR M The Corona, Solar Cycle, Solar Activity Coronal Mass Ejections, and Flares CTR PS1 W The Solar Wind and Heliosphere, Part 1 CTR F The Solar Wind and Heliosphere, Part 2 CTR W Physics of Plasmas RJS F MHD including Waves RJS M Solar Wind Interactions: Magnetized Planets YM W Solar Wind Interactions: Unmagnetized Planets YM F Collisionless Shocks CTR M Mid-Term W Solar Wind Magnetosphere Coupling I CTR F Solar Wind Magnetosphere Coupling II; The Inner Magnetosphere I CTR M The Inner Magnetosphere II CTR W Planetary Magnetospheres CTR F The Auroral Ionosphere RJS W Waves in Plasmas 1 RJS F Waves in Plasmas 2 RJS F Review CTR/RJS M Final Due PS2 PS3 PS4 PS5 PS6 PS7 2
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Introduction • In previous lectures, we showed how the solar wind interacted with the magnetosphere, causing the plasma in the magnetosphere to circulate. • In steady state, a slab of magnetized solar wind reconnects with a sector of the magnetopause, transferring magnetic flux into the tail. That flux then reconnects in the tail and returns to the dayside. • It may appear that an electric field has been applied to the magnetosphere by the solar wind as if by capacitor plates along the flanks of the magnetosphere, but this is not correct. • At all times the magnetosphere is being pulled by the connected solar wind against the drag of the ionosphere and the atmosphere at low altitude. 3
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Field-Aligned Currents The correct approach to understanding both the corotation and solar wind-driven convection of the magnetospheric plasma considers the magnetic and plasma stresses in both the ionosphere and magnetosphere. Plasma momentum equation – force balance – leads to a fundamental driver of field-aligned currents that couple magnetosphere to ionosphere. B• j•B B2 =2 B•PB B3 V A2 dU 1 + 2 B • 2 dt B VA  + 2 B• d  • dB dt dt B Pressure gradient term Inertial term Vorticity dependent terms (U) Assumptions: •j = 0, E + UxB = 0. 4
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Region-2 Currents – Shielding Integrating over a flux-tube, slow flow: 1ˆ j||  b  V P  2 where V is the flux tube volume. If gradients are not parallel then fieldaligned currents flow. Currents close in ionosphere - imply electric field in ionosphere. If mapped to magnetosphere opposes convection. The idea of simply mapping the electric field down on the ionosphere is popular but incorrect. 5
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Inner Edge of Ring Current Data from Polar and ISEE to determine current intensity in Inner magnetosphere The inner edge (L ~ 3) has eastward current Also evidence or partial ring current (nightside currents stronger than dayside) 6
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Particle Drift Paths or LT-R Treating particles as test particles drifting in prescribed electric and magnetic fields, the particles conserve their total energy. For 90˚ pitch angle particles µ is conserved Assuming corotation and uniform convection electric field: Potential:  = 91.5/L - EconvL sin  Energy: µB + q = constant specifies the local time, 0˚ at noon, 90˚ at dusk Electrons: positive slope in space Ions: negative slope in space 7
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Electron and Low Ion Magnetic Moment Drift Paths • In Ф-B space, our trajectories are straight lines. • Electron paths are either horizontal or slope upward. • Open trajectories are on the left. The Alfven layer is tangent to dusk. • Trajectories to the right are closed corotating. • Low μ ions are similar. 8
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Ion Drift Paths: Medium μ and High μ • Trajectories all tilt down from left to right. • Proton nose ions refer to an early local time arrival of medium energy protons in data obtained by Explorer 45. • Closed banana orbits circulate within the Alfven layer. • Lines joining Dawn to Dusk describe closed drift paths, mainly gradient drift paths. 9
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Near-Geosynchronous Data Near geosynchronous orbit many energetic particles are drifting through the magnetosphere rather than trapped in periodic orbits. 10
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Radiation Belt Ion Energy Distribution • • • • Electron Slot Energetic Protons The flux of low energy particles is quite variable at all distances. The very energetic particle fluxes in the inner magnetosphere are rather stable and change only under unusual circumstances. At high latitudes or L-values, the fluxes of very energetic particles are quite variable. Particles can move radially by diffusion (scattering) across magnetic field lines. If they do this slowly they conserve their magnetic moment and gain energy as 11 they reach stronger magnetic fields.
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Gyroradii of Radiation Belt Particles Gyroradius in km • The gyroradius of a charged particle is mv or qB E 12 100nT (46km) A ( ) ( ) 1keV B 1 2 where V  is the perpendicular velocity, A is the mass in amu, E is the perpendicular energy and B is the magnetic field strength. • When the particle gyroradii are small compared to the curvature of the field lines, the particles remain trapped. 12
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Time Scales of Radiation Belt Motions Gyro Period Tg  2 2m 100nT  (0.66 s)( )A g qB B Bounce Period B  1 1 2lb l 2 1keV 2 (5 min .)( b ) A ( ) v  10 RE W Drift Perpendicular to B VD  E B Fext B W B B 2W11rˆc B    B2 qB 2 qB 3 qRc B 2 Drift Period D  2r 2qBr 2 r 2 B 1keV  ~ (56h)( ) ( )( ) Vgc W 5 RE 100nT W 13
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• Time Scales Continued Three motions can be studied separately through the use of adiabatic invariants: is conserved under slow changes of the system pdq where q is the coordinate and p is the momentum 2 • 2m mv p v dt  m  v  T  ( ) x x x g  q B The first adiabatic invariant is mv   2B • The energy of a particle is conserved 1 2 2 W  m(V  V constant • 2 2 1 )  mv 2 2  B  Particle must mirror when particle reaches a critical value of W Bm   • Second adiabatic m2 J p ds 2 2m  W  B( s )ds m1 is conserved on periods long compared to the bounce period. • Plots have relativistic corrections. 14
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Radiation Belt Electrons Annual Variation of energetic electrons versus L-value at low altitudes and high • • • • Diffusion can occur along the magnetic field when waves resonate with the gyromotion. Diffusion can occur radially across the magnetic field when the magnetic field changes on the time scale of the drift of the particle around the magnetosphere. SAMPEX was a polar orbiting, low-altitude spacecraft. POLAR was an excentric orbiter in polar orbit with apogee at 9 RE. 15
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Proton and Electron Radiation Belts • The electron radiation belt contains a slot of low flux caused by enhanced loss rates due to whistler-mode waves (both lightning-generated and instability (self) generated waves). • During large disturbed periods, the radial diffusion rate can be much greater and the 16 particles can fill the slot and move into an inner stable radiation belt.
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Loss of Particles from Radiation Belts: Electrons • Particles that drift into the magnetopause or tail can be lost from the magnetosphere. • If the drift paths do not intersect a boundary, the particles can be trapped for a long time. • If the gyroradius is much smaller than the scale size of the field changes and no time variations occur near the gyrofrequency, the first adiabatic invariant is preserved  W / B W / Bm • If Bm > Batm, then the particle will be lost. Sin (αe) has to be < (Be/Batm)½ • If waves do exist near Ωe, then the pitch angle can change. If the pitch angle moves toward 0°, it will hit the atmosphere and be lost. • Sources of such waves include lightning and natural instabilities in the plasma. 17
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Loss of Particles from the Radiation Belts: Protons Height H Density 3 RE 800 cm-3 4 RE 300 cm-3 5 RE 150 cm-3 3 keV 30 keV 2.2 3.2 5.7 8.5 11.5 16.8 100 keV 40 110 215 Lifetimes (Hours) for charge exchange for H+ with α = 45° • Protons can decay like electrons by being pitch angle scattered into the loss cone. This can be due to externally caused signals or by instability. • They also can be lost via charge exchange which creates a fast neutral not tied to any magnetic field line. 18
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Loss of Particles: Cyclotron Resonance and Scattering into the Loss Cone • When circularly polarized waves resonate with the cyclotron motion of a charged particle, the interaction exchanges energy between the wave and the particle. • The resonance also changes the pitch angle of the particle. If the change in pitch angle forces the particle into the loss cone, it will hit the atmosphere and be lost. This maintains the pitch angle anisotropy despite the scattering that otherwise would lead to isotropy. • The maintenance of the anisotropy can lead to sustained wave growth by the “loss cone instability” mechanism. Particle Type Energy Change in Resonance with Right-Hand Cyclotron Waves Resonance Particle Wave Parallel Perpendicular Pitch Energy Energy Energy Energy Angle Electron Head-on Positive Ion Decrease Increase Increase Decrease Decrease Overtaking Decrease Increase Decrease Increase Increase Electron Head-on Increase Decrease Decrease Increase Increase Positive Ion Overtaking Increase Decrease Increase Decrease Decrease An analogous relationship exists for resonance with left-handed waves. 19
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Loss of Particles from the Radiation Belt: Radial Diffusion • Particles drift around the magnetosphere on closed drift paths that contain a fixed amount of magnetic flux. • If the magnetosphere changes its magnetic configuration as the particle drifts around, it can move in or outward. Net diffusion will occur if there are gradients. • The first and second invariants remain the same unless there is noise at the gyro or bounce frequency. • If the particle moves to higher fields then it must gain energy if  W / B is constant. • The parallel momentum integrated along them 2bounce path is the second adiabatic invariant. J P11ds 2m(22 m) m1 ( w  B( s)) ds J 2(2where m ) 1 2 I I  ( Bm  B( s )) ds or m1 This is independent of the energy of the particle. • If the field line becomes shorter the parallel momentum increases. 20 1 1 2 1 2 2
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The Radiation Belts • Energetic particles can be trapped in the dipole mirror geometry of the Earth’s magnetic field. • These intensities build up and can be dangerous to spacecraft. 21
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Summary • Field-aligned currents transfer solar wind momentum to the ionosphere and the atmosphere. • The inner magnetosphere can store much energy from the solar wind in the ring current. • At low energy, particle motion is affected by both the electric field and the gradient drift. • At high energies, the curvature and gradient drift are dominant. These are the radiation belts. • Particles can be lost from the radiation belts by radial drifts and by pitch angle scattering into the loss cone. • Charge exchange can turn ions into fast neutrals. 22
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