ESS 200C Lectures 9, 10 and 11 The Magnetosphere

Transcription

1 ESS 00C Lectures 9, 10 and 11 The Magnetosphere

2 The magnetosphere Back in 1930 Chapman and Ferraro foresaw that a planetary magnetic field could provide an effective obstacle to the solar-wind plasma. The solar-wind dynamic pressure presses on the outer reaches of the magnetic field confining it to a magnetospheric cavity that has a long tail consisting of two antiparallel bundles of magnetic flux that stretch in the antisolar direction. The pressure of the magnetic field and plasma it contains establishes an equilibrium with the solar wind. The solar wind is usually highly supersonic before it reaches the planets. The wind velocity exceeds the velocity of any pressure wave that could act to divert the flow around the obstacle and a shock forms.

3 The Earth s intrinsic magnetic field To a first approximation the magnetic field of the Earth can be expressed as that of the dipole. The dipole moment of the Earth is tilted ~11 0 to the rotation axis with a present day value of 8X10 15 Tm 3 or 30.4x10-6 TR E 3 where R E =6371 km (one Earth radius). In a coordinate system fixed to this dipole moment 3 = Mr cosθ B r B B θ ϕ = = Mr 0 3 sinθ 3 B = Mr (1 + 3cos θ ) where θ is the magnetic colatitude, and M is the dipole magnetic moment. 1

4 The dipole magnetic field in Cartesian coordinates Alternately in Cartesian coordinates B B B x y z = 3xzM = 3yzM = (3z where the z-axis is along the dipole magnetic moment. This can easily be generalized to a dipole moment with an arbitrary orientation. r r Bx ( ) = ( ) z z r r r 5 5 ) M z r 5 3x r 3xy 3xz ( ) 3yx 3y r 3yz ( ) 3zx 3zy 3z r r m

5 Magnetic field lines and the L parameter The magnetic field line for a dipole. Magnetic field lines are everywhere tangent to the magnetic field vector. dr dθ = r dϕ = 0 Br Bθ Integrating r = r 0 sin θ where r 0 is the distance to equatorial crossing of the field line. It is most common to use the magnetic latitude λ instead of the colatitude r = L cos where L is measured in R E. A trapped particle conserving the adiabatic invariants will be confined to a surface specified by L. λ

6 Generalized planetary magnetic fields Although a dipole field is useful for many problems the actual internal fields of planets are more complex. Gauss showed that the magnetic field of the Earth could be described by the gradient of a scalar potential r B = Φ = Φ ( + Φ ) where Φ i is the scalar potential due to sources within the Earth and Φ e is due to external sources. The scalar potentials can be expressed as a sum of associated Legendre polynomials Φ i Φ n m m m ( r, θ, ϕ) = a [ r a] P ( cosθ ) g cos( mϕ) + h sin( mϕ) e n= 1 m= 0 n n 1 n where a is the planet s radius, and θ and Φ are to colatitude and east longitude in planetographic coordinates. The P nm (cos θ) are associated Legendre functions with Schmidt normalization. i e ( ) m m m ( r, θ, ϕ) = a [ r a] P ( cosθ ) G cos( mϕ) + H sin( mϕ) n= 1 m= 0 n n n ( ) n n n

7 P m n ( ) ( ) m m cosθ = N 1 cos θ d P ( cosθ ) d( cosθ ) m nm where P n (cos θ) is the Legendre function, and N n,m =1 when m=0 and [(n-m)!/(n+m)!] 1/ otherwise. The coefficients g nm, h nm, G nm, and H nm are chosen to minimize the difference between the model field and observations. In this representation the dipole moment M=a 3 [(g 10 ) +(g 11 ) +(h 11 ) ] 1/ The dipole tilt becomes α=cos -1 (g 10 /M) n

8 Properties of the Earth s Magnetic Field The dipole moment of the Earth presently is ~8X10 15 T m 3 (3 X10-5 TR E3 ). The dipole moment is tilted ~11 0 with respect to the rotation axis. The dipole moment is decreasing. It was 9.5X10 15 T m 3 in 1550 and had decreased to 7.84X10 15 T m 3 in The tilt also is changing. It was 3 0 in 1550, rose to in 1850 and has subsequently decreased to in In addition to the tilt angle the rotation axis of the Earth is inclined by with respect to the ecliptic pole. Thus the Earth s dipole axis can be inclined by ~35 0 to the ecliptic pole. The angle between the direction of the dipole and the solar wind varies between 56 0 and 90 0.

9 The Magnetopause In the simplest approximation the magnetopause can be considered to be the boundary between a vacuum magnetic field and a plasma. Charged particles in the solar wind approach the Earth s magnetic field B which is pointed upward in the equatorial plane. Return Current North The Lorentz force q(v x B) on the particles deflects protons to the right (left hand gyration), and electrons to the left (right hand). Magnetopause The opposite motion of the charges produces a sheet current from left to right (dawn to dusk) Magnetic perturbations from this current reduce the Earth s field Sunward of the current and increase the field Earthward Solar Wind B V F=q(VxB) Chapman-Ferraro Current Dusk Above the pole the field points in the opposite direction so the current does as well. This is the return current

10 A Particle View of the Magnetopause When an electron or ion penetrates the r r boundary they sense a u B force. After half an orbit they exit the boundary. The electrons and ions move in opposite directions and create a current. The ions move farther and carry most of the current. The number of protons per unit length in the z- direction that enter the boundary and cross y=y 0 per unit of time is r Lp nu. (Protons in a band r Lp in y cross the surface at y=y 0.) Since each proton carries a charge e the current per unit length in the z-direction crossing y=y 0 is nmp I = rlp nue = u B where r Lp = ( ump ) ( ebz ) Applying Ampere s law and noting B z = µ 0 I Bz µ 0 = nm p u z = ρ sw u sw I = jdx

11 A Fluid Picture of the Magnetopause The location of the boundary can be calculated by requiring the pressure on the two sides of the boundary to be equal. The pressure in the magnetosphere which is mostly magnetic must match the pressure of the magnetosheath which is both magnetic and thermal. The magnetosheath pressure is determined by the solar wind momentum flux ρ or dynamic pressure. sw u sw r j The current on the boundary must provide a force sufficient to change the solar wind momentum (divert the flow). The change in momentum flux into the boundary is ρ sw usw (we are assuming perfect reflection at the boundary) ρ r r sw u sw = I B = B µ 0 r B

12 Currents on the Magnetopause Near the pole there is a singular point in the field where B = 0. This is called the neutral point. The Chapman-Ferraro (C-F) current circulates in a sheet around the neutral point Neutral Point North Magnetopause Field Line This current is symmetric about the equator with a corresponding circulation around the southern neutral point The C-F current completely shields the Earth s field from the solar wind confining it to a cavity called the magnetosphere Solar Wind Chapman-Ferraro Current Dusk

13 The Location of the Magnetopause The standoff distance to the subsolar magnetopause is determined by a balance between the solar wind dynamic pressure and the magnetic field inside the boundary The collisions of particles with the boundary may not be completely elastic hence a factor k is introduced The magnetic field inside the boundary is the total field from dipole and boundary current. For an infinite planar sheet current the field would be exactly doubled. Inside a spherical boundary the multiplication factor is 3. The factor f must lie in this range. Equate and substitute for the dipole strength variation with distance Solve for the dimensionless standoff distance L s. p p p dyn dyn B = = p B = kmnu ( fb ) D µ 0 kmnu Where k~0.9 is the elasticity of particle collisions and f is the factor by which the magnetospheric magnetic field is enhanced by the boundary current. R s is the subsolar standoff distance. L s R = R s E = f k B D = = R B0 f B µ E B0 µ 0mnu D 0 R s 3 1 6

14 The Shape of the Magnetopause Half of the noon-midnight meridian plane is shown above the axis and half of the equatorial plane is shown below Dashed lines show different solutions while the solid line shows the final shape obtained by iteration The equatorial section is quite simple with no indentations. The subsolar point is at ~10 R e for the most probable solar wind conditions The equatorial boundary crosses the terminators at 15 R e The meridian boundary is indented at the neutral points where the Earth s magnetic field is too weak to stand off the solar wind

15 The Effect of the Magnetopause Currents Close to the Earth the dipole field dominates and there is little distortion Further away there is a significant change in the shape of the field lines with all field lines passing through the equator closer to the Earth than dipole field lines from the same latitude. All dipole field lines that originally passed through the equator more than 10 Re sunward of the Earth are bent back and close on the night side The neutral point separates the two types of field lines

16 The Shape of the Nightside Magnetosphere At every point along the magnetopause the component of dynamic pressure normal to the boundary must be balanced by the pressure of the tangential magnetic field interior to the boundary Far downstream the solar wind velocity becomes parallel to the magnetopause and the normal component of dynamic pressure becomes zero This would lead to a cylindrical tail But both the thermal and magnetic pressure of the solar wind exert a transverse pressure that eventually becomes important At the distance where the dipole field pressure equals the sum of the solar wind thermal and magnetic pressure the magnetosphere should close giving it a tear-drop shape The solution in the previous page treated the normal stresses correctly but did not include tangential stresses.

17 Tangential Stresses on the Boundary Tangential stresses (drag) transfer momentum to the magnetospheric plasma and cause it to flow tailward. The stress can be transferred by diffusion of particles from the magnetosheath, by wave process on the boundary, by the finite gyroradius of the magnetosheath particles and by reconnection. Reconnection is thought to have the greatest effect. Assume that one tail lobe is a semicircle, then the T magnetic flux in that tail lobe is Φ = B where R T is the lobe radius, and B T is the magnetic field strength. The asymptotic radius of the tail is given by RT = where p sw includes both the thermal and magnetic pressure of the solar wind. T π R T [ Φ ( π µ p ] 41 T 0 sw )

18 The Tail Current The stretched field configuration of the magnetotail is naturally generated by a current system. The relationship between the current and the magnetic field is given by Ampere s law c where C bounds surface with area A r r B ds = µ 0 r r j da For a 0nT field I=30 ma/m or X10 5 A/R E B T = µ 0 I where I is the total sheet current density (current per unit length in the tail)

19 Observing the Magnetopause Boundary normal coordinates are frequently used to study the magnetopause The boundary normal coordinates have one component normal to the boundary ( nˆ ) and two tangential ( Lˆ northward and Mˆ azimuthal). The dayside magnetopause can be approximated as a tangential discontinuity when IMF Bz >0. In this case there will be no field normal to the boundary on either side and the normalized cross product of the two fields defines the normal. When IMF Bz < 0 the boundary is a rotational discontinuity with a small normal component. In this case minimum variance analysis defines the directions of maximum, intermediate, and minimum variance with the minimum variance determining the normal.

20 Observing the Magnetopause Data from two spacecraft show two crossings of the boundary. Initially both spacecraft are inside the magnetosphere (strong field). The boundary moves inward and crosses first the ISEE-1 spacecraft (thick line) and later the ISEE-1 spacecraft (thin line). Some time later the boundary reverses and moves outward appearing first at ISEE- and later at ISEE-1. Assume a planar boundary moving with constant velocity along the average normal during each crossing. The spacecraft separation along the average normal divided by the time delay gives the boundary velocity. The time profile scaled by the velocity gives the spatial profile of the boundary The thickness of the magnetopause varies from 00 to km with a most probably thickness of 700 km.

21 The Magnetotail

22 The magnetotail is the region of the magnetosphere that stretches away from the Sun behind the Earth. It acts as a reservoir for plasma and energy. Energy and plasma from the tail are released into the inner magnetosphere aperiodically during magnetospheric substorms. A current sheet lies in the middle of the tail and separates it into two regions called the lobes. The magnetic field in the north (south) lobe is directed away from (toward) the Earth. The magnetic field strength is typically ~0 nt. Plasma densities are low (<0.1 cm -3 ). Very few particles in the 5-50keV range. Cool ions observed flowing away from the Earth with ionospheric composition. The tail lobes normally lie on open magnetic field lines.

23 The Magnetotail-Cross Sectional View Green hatching near the upper and lower tail magnetopause is the plasma (polar) mantle created by solar wind particles entering the tail. The clear areas are the tail lobes, regions of very low plasma density due to loss to the solar wind along open field lines The two regions of blue hatching on the upper and lower edges of the plasma sheet are the plasma sheet boundary layer (psbl) Red stippled areas on the left and right side of the plasma sheet are the low latitude boundary layers (llbl) Red horizontal hatching just inside the llbl is central plasma sheet (cps) with return flow from the llbl Vertical yellow hatching in the center of the tail is also cps with return flow from the distant x-line

24 The Magnetotail - Noon-Midnight View

25 The distant tail is aligned with the solar wind velocity because of dynamic pressure The inner tail is connected to the magnetic equator The location of the equator relative to the Earth-Sun line depends on tilt of the rotation axis towards the Sun (hence on season) It also depends on universal time as the Earth rotates and the dipole wobbles about the rotation axis. This causes the equatorial plane to tilt around the Sun vector The tilt of the equator raises or lowers the neutral sheet at midnight by some amount But the equator at dawn and dusk is in the ecliptic plane and also connected to the tail. Thus the neutral sheet is warped so its edges are in the ecliptic when its center is high MAGNETOTAIL Y-Z CROSS SECTION AT 15-Aug :30:04 10 Cluster Zgsm(Re) 0-10 DAWN Plasma Sheet DUSK -0 XGSM = thps = 1.4 dyp = 0.8 tilt = 7.0 Magnetopause Ygsm(Re)

26 The Magnetotail - Structure The plasma mantle has a gradual transition from magnetosheath to lobe plasma values. Flow is always tailward Flow speed, density and temperature all decrease away from the magnetopause. Ions in the plasma sheet boundary layer (PSBL) typically flow at 100s of km/s parallel or antiparallel to the magnetic field. Frequently counterstreaming beams are observed: one flowing earthward and one flowing tailward. Densities are typically 0.1 cm -3. The PSBL is thought to be on closed magnetic field lines. The central plasma sheet (CPS) consists of hot (kilovolt) particles that have nearly symmetric velocity distributions. Typical densities are 0.1-1cm -3 with flow velocities that the small compared to the ion thermal velocity (the electron temperature is 1/7 of the ion temperature). The CPS is usually on closed field lines but can be on plasmoid field lines.

27 The low latitude boundary layer (LLBL) contains a mix of magnetosheath and magnetospheric plasma. Plasma flows can be found in almost any direction but are generally intermediate between the magnetosheath flow and magnetospheric flows. The LLBL extends from the dayside just within the magnetopause along the flanks of the magnetosphere forming a boundary between the plasma sheet and the magnetosheath. Note there is a region in the tail where the plasma mantle, PSBL and LLBL all come together. The origins of the plasma mantle and the plasma sheet boundary layer are clear but the origin of the low latitude boundary layer is less clear.

28 Typical Magnetotail Plasma and Field Parameters Tail Lobe Magnetosheath Plasma- Sheet Boundary Layer n (cm -3 ) T i (ev) T e (ev) B (nt) β.5 3x Central Plasma Sheet

29 Reconnection Z X

30 Reconnection As long as frozen in flux holds plasmas can mix along flux tubes but not across them. When two plasma regimes interact a thin boundary will separate the plasma The magnetic field on either side of the boundary will be tangential to the boundary (e.g. a current sheet forms). If the conductivity is finite and there is no flow Faraday s law and Ampere s law give a diffusion r equation B 1 B = x t µ 0σ z Magnetic field diffuses down the field gradient toward the central plane where it annihilates with oppositely directed flux diffusing from the other side. This reduces the field gradient and the whole process stops but not until magnetic field energy has been converted into heat via Joule heating (the resulting pressure increase is what is needed to balance the decrease in magnetic field pressure).

31 For the process to continue flow must transport magnetic flux toward the boundary at the rate at which it is being annihilated. l J Y E Y E Y E = u An electric field in the E y ( y z0 x0) direction will provide this in flow. In the center of the current sheet B=0 and Ohm s law gives E = y j y If the current sheet has a thickness l Ampere s law gives j σ y = Bx0 µ 0 l B

32 Equating the E Y expressions ( µ ) l = σ u 1 0 z0 Thus the current sheet thickness adjusts to produce a balance between diffusion and convection. This means we have very thin current sheets. There is no way for the plasma to escape this system. However, if the diffusion is limited in extent then flows can move the plasma out through the sides.

33 When the diffusion is limited in space annihilation is replaced by reconnection Field lines flow into the diffusion region from the top and bottom Instead of being annihilated the field lines move out the sides. In the process they are cut and reconnected to different partners. Plasma originally on different flux tubes, coming from different places finds itself on a single flux tube in violation of frozen in flux. The boundary which originally had B x only now has B z as well. Reconnection allows previously unconnected regions to exchange plasma and hence mass, energy and momentum. Although MHD breaks down in the diffusion region, plasma is accelerated in the convection region where MHD is still valid.

34 Acceleration due to slow shocks Emanating from the diffusion region are four shock waves indicated by dashed lines (labeled separatrix). At the shocks the magnetic field and flow change abruptly. The magnetic field strength decreases The flow speed increases but the normal flow decreases. These r structures r are current sheets. The flow is accelerated by the J B force.

35 Reconnection driven convection By the 1950 s it was realized that plasma flows observed in the polar and auroral ionospheres must be driven by magnetospheric flows. Flow in the polar regions was from noon toward midnight. Return flow toward the Sun was at somewhat lower latitudes. This flow pattern is called magnetospheric convection. If all flux tubes remained within the magnetosphere then the flow pattern is like that in a falling rain drop caused by viscous effects. Dungey in 1961 showed that if magnetic field lines reconnected in front of the magnetosphere the required pattern would result.

36 When IMF B z driven by the solar -wind flow against the dayside magnetopause is southward reconnection occurs between field lines 1 (closed with both ends at the Earth) and the IMF field line 1 This forms two new field lines with one end at the Earth and one end in the solar wind (called open). The r solar r wind r will pull its end tailward ( E = u sw B sw ) In the ionosphere this will drive flow tailward as observed. If this process continued indefinitely without returning some flux the Earth s field would be lost. Another neutral line is needed in the tail.

37 At the tail reconnection site (called an x-line) the lobe field lines (5 and 5 ) reconnect at postion (66 ) to form new closed field lines 7 and new IMF field lines (7 ). The new IMF field line 7 is distorted and stressed and moves tailward. The new closed field line 7 is stressed and moves earthward. The flow circuit is finally closed when the newly closed field lines flow around either the dawn or dusk flanks of the magnetosphere to the dayside. The insert shows the flow pattern in the ionosphere that results. This flow pattern is highly simplified. Magnetospheric physics is the attempt to understand the dynamics and transport associated with this flow.

38 The electric field across the magnetosphere The process of reconnection causes plasma to flow in the magnetosphere and therefore creates an electric field r r r E = u B E = φ = φ R where R PC is the radius of the polar cap, u PC is the plasma flow speed and B PC is magnetic field strength in the polar cap. For typical ionospheric parameters. The solar wind electric field across a distance equal to one diameter of the tail (50R E ) is about 640 kv. Thus about 10% of the flux that impacts the magnetosphere interacts with it. The rest goes around the sides of the magnetosphere. PC φ 53kV = u PC B PC

39 The Plasma Mantle The plasma mantle is populated by a mixture of magnetosheath plasma and ionospheric plasma. Magnetosheath plasma is thought to enter along open field lines in the cusp. Ionospheric plasma is thought to flow upward from the ionosphere in the polar wind Reconnection is assumed to occur at the nose of the magnetopause. Magnetosheath particles flow along the newly opened field lines After mirroring near the Earth they move back up the field line joined by lower energy ionospheric particles. The field line moves tailward. The velocity filter Lower energy particles move slower and thus take longer to reach a given distance down tail In this longer time the particles will E r B r drift farther from the boundary creating an energy gradient. Cusp Mantle

40 A neutral line in the distant magnetotail can lead to the formation of particle beams. Charged mantle particles E r B r drift and move along field lines across the lobes toward the current sheet. Some will cross the separatrix and enter the plasma sheet. If the radius of curvature of the field line at the equator is small compared to a particle s gyro-radius it will begin serpentine motion across the tail This causes them to move along the E field gaining energy. Eventually they are ejected onto a closed field line near the separatrix after gaining energy from the motion across the electric field.

41 The Plasma Sheet Boundary Layer What particles enter the region earthward of the x-line? Time for a particle to move down the field line to the x-line t x where L X is the length of the field line and is the parallel velocity. Time for a particle to convect the radius of the tail (R T ) in electric field corresponding to potential and magnetic field B T = L v v The velocity of a particle that just reaches the x-line The critical energy is W R T B t = T φ c m = φ L x RT BT Particles entering the plasma sheet earthward of the x-line ee y will gain an energy W = = W and end up with W E 4 y = + 1 W v B Z ' energy where Ω is the gyroperiod. Ω v y 4 v E B z φ φ L x v = c RT BT

42 Particles ejected from the weak field region near an x-line travel along field lines towards the Earth Particles closest to the separatrix have the greatest energy because they have gyrated around the weakest B and hence travel a long way along the E field Particles ejected closer to the Earth have less energy because they gyrate in a stronger field However the reflected particles are displaced towards the neutral sheet by electric field drift. When the particles return to the plasma sheet they are scattered by the sharp kink in the field at the neutral sheet forming a hot isotropic plasma This effect structures the Earthward beam as shown in the diagram At the Earth the particles are reflected by the converging magnetic field and they stream backwards through the inward beam.

43 The Low Latitude Boundary Layer The origin of the low latitude boundary layer (LLBL) is less clear than the PSBL or the plasma mantle. During northward IMF the LLBL seems to be a simple mixture of magnetospheric and magnetosheath plasma. For southward IMF some heating by reconnection may be required. Reconnection may be important for both northward and southward IMF (the neutral line moves to the cusp for northward IMF). Diffusion may also be important. Mechanisms other than reconnection ( viscous interactions) may account for 10% -0% of cross magnetosphere potential.

44 Magnetopause Reconnection Direct evidence of quasi-steady reconnection at the magnetopause. ISEE spacecraft was moving from the magnetosphere to the magnetosheath. The magnetic field in the magnetosheath had B Z <0 and B y >0 As the spacecraft passed through the LLBL and the boundary there were large dawnward flows and antisunward flows The spacecraft made several incursions into the LLBL which gradually increased in length.

45 Field lines at the magnetopause for B z <0 and B y >0 (top, right). Magnetic tension will move the plasma along the direction given by the heavy arrows. ISEE was pre-noon so in the LLBL and magnetosheath the flow should be northward, dawnward and antisunward as observed. Reconnection at the magnetopause can also be patchy and localized in space. The left figure shows a localized reconnection event called a flux transfer event on the magnetopause.

46 Observations of northward IMF reconnection tailward of the cusp (Reiff et al., 005) A fundamental problem in reconnection studies is what balances the E field at the X-line where B is zero. Cluster Trajectory J_y The divergence of electron pressure tensor can provide this. me E = E + v B c = j σ + ne j + t ( vj+ jv) j B ne c p ne e Interplanetary Magnetic Field Z_GSE X_GSE Examined Cluster data in cusp for northward IMF on March 18, 00. Observed a series of magnetopause crossings where B X and B Z change sign together- magnetic null crossings.

47 The structure of the reconnection region. The diffusion region has two parts the ion diffusion region where ions become unmagnetized and the electron diffusion region where electrons are unmagnetized. The Hall effect is the term whose inclusion unmagnetizes the ions. r r J B The Hall effect leads to currents and quadrupolar B Y

48 1.5 x 10 5 Hall Currents with B y Magnetic Field J x By using magnetic field observations from the 4 Cluster spacecraft the currents can be calculated. The large J Z (red) shows the Hall currents. Cluster was in the ion diffusion region. By using electron observations from the four spacecraft the divergence of the electron pressure tensor can be calculated. The pressure divergence electric field reaches 1 mv/m. current density (A/m ), magnetic field strength (10 7 nt) Electric Field (V/m) J y J z B y :54:48 14:55:37 14:56:6 14:57:16 14:58:05 14:58:54 14:59:43 15:00:3 15:01:1 15:0:10 6 x Pressure Divergence Electric Field Student Version of MATLAB :00: :00: :00: :00: :00: :00: :00:18.15

49 00 The spacecraft with the smallest B was used to determine the relative positions of the four spacecraft A B :59:57.65 UT 15:00:14.15 UT cluster 0 cluster 1 cluster cluster 3 cluster 4 Magnetic field vectors for four times are shown in black. Z Distance from X Line (km) Student Version of MATLAB 150 Cluster moved from the mantle close to the X-line and into the magnetosheath C :00: UT Student Version of MATLAB 100 Estimate that Cluster entered the electron diffusion region and was within 1 km of the X- line D :00:0.875 UT Student Version of MATLAB X Distance from X Line (km)

50 The Radiation Belts and Ring Current The radiation belts consist of charged particles that circle the Earth from about 1000km to a geocentric distance at the equator of about 6R E Because is it easy for particles to move along the magnetic field the radiation belts are mainly field aligned features. The ring current is an azimuthal current circling the Earth at equatorial distances of 3R E to 6R E. There is no clear distinction between the ring current particles and the radiation belt particles however some people use ring current for those particles contributing most to the current and radiation belt or Van Allen belts for penetrating radiation. Penetrating radiation refers to particles that penetrate deeply into dense materials. Electrons which contribute little to the ring current contribute importantly to penetrating radiation.

51 This figure shows fluxes of electrons and protons in the radiation belts. Above 1MeV there is a slot in the electron distribution separating the inner belt from the outer belt. There is no corresponding slot for the protons.

52 Both gradient and curvature drifts cause ions to move around the Earth westward and electrons eastward. The resulting ring of westward current decreases the strength of the northward magnetic field at the surface of the Earth.

53 The Ring Current Assume all ring current particles are equatorially trapped at a distance LR E. The gradient drift gives r 3mu L ug = eˆ ϕ q B R If the total number of ring current particles of type t is N t,, the total current, I ϕ is 3 L mtut Iϕ = N t π The total energy of ring current particles is For a ring of current Ampere s law gives W I ϕ RC B E R The magnetic field perturbation at the center of the Earth due to drift motion is 3µ WRC B r E = N t E t= e, i mtu 3LW = π B drift r B = µ 0 t RC ERE I ˆ r 0 = 4π B e z E R 3 E E eˆ z

54 There also is a contribution from the gyrational motion of the ring current particles about the magnetic field. Each particle has a magnetic moment r WL 3 µ = e ˆ B where W = 1 mu is now the energy of each particle. This produces a field at the center of the Earth µ 0 µ µ 0 W B r gyro = eˆ ( ) z = eˆ 3 3 z 4π LR 4π BER E E Since the contribution from the gyrational motion is opposite to that from the gradient drift motion and since B depends only on the particle energy µ 0 WRC BRC = eˆ 3 z B R π E E E z

55 The total energy in the Earth s dipole magnetic field 3 ( B d x µ 0) above the surface of the Earth is 4π 3 Wmag = BERE 3µ 0 B r W Therefore RC = eˆ z B 3 W E This is called the Dessler-Parker-Sckopke relationship mag The change in the magnetic field at the Earth is used as a measure of the amount of energy in the ring current. The parameter which gives the change in B is the D ST index and is a standard measure of magnetic storms. After some corrections for the conductivity of the Earth we get that 100nT depression in B is equal to.8x10 15 J.

56 The Plasmasphere and Alfven Layers 3 B0RE Assume that the Earth s magnetic field is a dipole BE = 3 r where rr E is the equatorial distance and B 0 is the equatorial field strength of the Earth s field. Assume equatorial mirroring particles (ie pitch angle) E r B r Plasma in the equatorial plane drifts toward the Sun. This corresponds to motion in a dawn-dusk electric field φconvection = E 0 r sinϕ To this cross magnetosphere electric field we must add the effects of the Earth s rotation The corotation electric field causes particles r to rotate eastward with the Earth ( φ corotation) B = ω Ereˆ ϕ B ω π 4 where E is the angular velocity of the Earth ( is ê ϕ eastward. The corotation potential equation becomes d φ corotation dr = h) and ω E W = µ B E B r 0 R 3 E

57 The corotation potential becomes We can write all of the drifts of equatorial particles in the following form where φ eff r u D = = E0r sinϕ + r B φ B µ B0R 3 qr eff 3 E φ ω B E r corotation 0 R 3 E = ω E B r 0 R 3 E

58 For zero energy particles ( µ = 0) φ eff ω EB0R = E0r sinϕ r Contours of constant Near the Earth the corotation term dominates the effective potential while far out in the tail the convection potential dominates. On the dusk side the two terms fight each other and at one point the velocity is zero. The solid line shows a separatrix inside of which plasma from the tail can t enter. 3 E φ eff Cold particles that lie inside the separatrix go continuously around the Earth. They form the plasmasphere. It is filled with dense cold plasma from the ionosphere.

59 For hot particles the effective potential becomes 3 hot µ B0RE φ E ϕ + 0 sin qr where we have assumed that the azimuthal motion of the particles is greater than rotation. eff In the far tail all particles move earthward Near the Earth hot positive particles move westward. Near the Earth hot negative particles move eastward. Negative particles are closer to (farther from) the Earth at dawn (dusk) than are positive (negative) particles. The surface inside of which particles can t penetrate is the Alfven Layer. 3

60 The emission at high latitudes is from aurora and is thought to be caused by 53.9nm emission from atomic oxygen. These images of the Earth s plasmasphere were taken by the EUV camera on the IMAGE spacecraft on May 4, 000. The 30.4nm emission from helium ions appears as a pale blue cloud. The bite out in the lower right is caused by the Earth s shadow. The helium is excited by sunlight.

61 Field Aligned Currents There is one more major set of currents in the magnetosphere-field aligned or Birkeland currents The field aligned currents extend from the magnetosphere to the ionosphere. Region 1 currents are at high latitudes and flow into the ionosphere on the dawn side of the magnetosphere and out on the dusk side. Region currents at lower latitudes flow into the ionosphere on the dusk side and out on the dawn side.

62 Summary of magnetospheric currents Magnetopause currents Ring current Parallel currents Tail currents with magnetopause currents removed. The red and blue currents occur during disturbed times and will be discussed later.