Lecture 9

Solar Wind-Magnetosphere Interaction

Structure of the Magnetosphere

Solar Wind-Magnetosphere Interaction:Reconnection and IMF Dependence

The MagnetosphereThe Magnetotail - Noon-Midnight View

The MagnetosphereThe Magnetotail

The MagnetosphereThe Magnetotail

• 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 a periodically 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 ~20 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.

The MagnetosphereThe Magnetotail-Cross Sectional View

• Green hatching near the upper and lower tailmagnetopause is the polar mantle created by solarwind particles entering the tail.

• The clear areas are the tail lobes, regions of verylow plasma density due to loss to the solar windalong open field lines

• The two regions of blue hatching on the upper andlower edges of the plasma sheet are the plasmasheet boundary layer (psbl)

• Red stippled areas on the left and right side of theplasma sheet are the low latitude boundary layers(llb l)

• Red horizontal hatching just ins ide the llbl iscentral plasma sheet (cps) with return flow fromthe llbl

• Vertical yellow hatching in the center of the tail isalso cps with return flow from the dis tant x-line

The MagnetosphereThe 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.

The MagnetosphereThe Magnetotail - Structure Continued

• 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.

Magneto-sheath

Tail Lobe Plasma-Sheet

BoundaryLayer

CentralPlasmaSheet

n (cm-3) 8 0.01 0.1 0.3Ti (eV) 150 300 1000 4200Te(eV) 25 50 150 600B (nT) 15 20 20 10 2.5 3x10-3 10-1 6

The MagnetosphereThe Magnetotail - Typical Plasma and Field Parameters

The MagnetosphereReconnection

XZ

The MagnetosphereReconnection

• 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 equation

– 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).

2

210 z

Bt

B x

The MagnetosphereReconnection Continued

• For the process to continue flow must transport magnetic flux toward the boundary at the rate at which it is being annihilated.– An electric field in the Ey ( ) direction will provide this in

flow. – In the center of the current sheet B=0 and Ohm’s law gives – If the current sheet has a thickness 2l Ampere’s law gives – 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. If the diffusion is limited in extent then flows can move the plasma out through the sides.

xzy BuE

yy jE

lBj zy 0

The MagnetosphereReconnection Continued

• 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 Bx only now has Bz 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.

The MagnetosphereReconnection

• 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 increase but the normal flow decreases.

• These structures are current sheets. The flow is accelerated by the

force.

BJ

The MagnetosphereReconnection

• 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.

The MagnetosphereReconnection

• When IMF Bz 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 solar wind will pull its end tailward ( )

• 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.

swsw BuE

The MagnetosphereReconnection Continued

• 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.

The MagnetosphereReconnection Continued

• The electric field across the magnetosphere– The process of reconnection causes plasma to flow in the

magnetosphere and therefore creates an electric field

where RPC radius of the polar cap, uPC is the plasma flow speed and BPC 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 (50RE) 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.

PCPCPC

BuR

E

BuE

2

kV53

The MagnetosphereThe 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 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 farther from the boundary creating a energy gradient.

Cusp

Mantle

BE

The MagnetosphereThe 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

where LX is the length of the field line and is the parallel velocity.

– Time for a particle to convect the radius of the tail (RT) in electric field corresponding to potential and magnetic field BT

– The velocity of a particle that just reaches the x-line

– The critical energy is

– Particles entering the plasma sheet earthward of the x-line will gain an

energy and end up with energy

vLt xv

TT BRt

22

TT

xc BR

Lv

22

2

222

TT

xc BR

LmW

WBv

EveEW

z

yy 42

W

Bv

EW

Z

y

1

4'

The MagnetosphereThe Plasma Sheet Boundary Layer

• 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

• 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.

• 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

• A neutral line in the distant magnetotail can lead to the formation of particle beams.

• Charged particles drift across the plasma sheet

• If reconnection is occurring they cross the separatrix and enter the plasma sheet

• Inside the plasma sheet there is also an field

• 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 drift 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.

BE

E

The MagnetosphereThe 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% -20% of cross magnetosphere potential.

The MagnetosphereMagnetopause Reconnection

• Direct evidence of quasi-steady reconnection at the magnetopause.

– ISEE 2 spacecraft was moving from the magnetosphere to the magnetosheath.

– The magnetic field in magnetosheath had BZ<0 and By>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.

The MagnetotailMagnetopause Reconnection

• Field lines at the magnetopause for Bz<0 and By>0 (top).– Magnetic tension will move the plasma along the direction given by the heavy

arrows.– ISEE 2 was post 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.

The MagnetosphereThe Radiation Belts and Ring Current

• The radiation belts consist of particles that circle the Earth from about 1000km to a geocentric distance at the equator of about 6RE

• 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 3RE to 6RE.

• 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.

• Both gradient and curvature drift 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.

•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.

The MagnetosphereThe Ring Current

• Assume all ring current particles are equatorially trapped at a distance LRE. The gradient drift gives

• If the total number of ring current particles of type t is N t,, the total current, is

• The total energy of ring current particles is

• For a ring of current Ampere’s law gives

• The magnetic field perturbation at the center of the Earth due to drift motion is

.

eRB

L

q

muu

EEG ˆ

2

3 22

I22

3 2

,2

tt

iett

EE

umN

RB

LI

2

2tt

tRC

umNW

22

3

EE

RC

RB

LWI

zer

IB ˆ

20

zEE

RCdrift e

RB

WB ˆ

4

33

0

The MagnetosphereThe Ring Current

• There also is a contribution from the gyrational motion of the ring current particles about the magnetic field.

• Each particle has a magnetic moment where is now the energy of each particle.

• This produces a field at the center of the Earth

• Since the contribution from the gyrational motion is opposite to that from the gradient drift motion and since depends only on the particle energy

zE

eLB

Wˆ

3

zE

zE

gyro eRB

We

LRB ˆ

4ˆ

4 30

03

0

B

zE

RCRC e

RB

WB ˆ

2 30

0

221 muW

The MagnetosphereThe Ring Current

• The total energy in the Earth’s dipole magnetic field ( ) above the surface of the Earth is

• Therefore

• This is called the Dessler-Parker-Sckopke relationship• The change in the magnetic field at the Earth is used a measure of the

amount of energy in the ring current. The parameter which gives the change in B is the DST 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 2.8X1015J.

032 2xdB

32

03

4EEmag RBW

zmag

RC

E

eW

W

B

Bˆ

3

2

The MagnetosphereThe Plasmasphere and Alfven Layers

• Assume that the Earth’s magnetic field is a dipole

where rRE is the equatorial distance and B0 is the equatorial field strength of the Earth’s field.

• Assume equatorial mirroring particles (ie. 900 pitch angle)

• Plasma in the equatorial plane drifts toward the Sun. This corresponds to motion in a dawn-dusk electric field

• To this “cross magnetosphere” electric field we must add the effects of the Earth’s rotation– The corotation electric field causes particles to rotate eastward with the Earth

where is the angular velocity of the Earth ( h) and is eastward.

– The corotation potential becomes

3

30

r

RBB E

E

EBW BE

sin0rEconvection

er

B

BE

corotation ˆ)(

2

E 242 e

2

30

r

RB

dr

d Ecorotation E

The MagnetosphereThe Plasmasphere and Alfven Layers

• The corotation potential becomes• We can write all of the drifts of equatorial

particles in the following form

where

r

RB Ecorotation

E

30

2B

Bu eff

D

r

RB

qr

RBrE EE

effE

30

3

30

0 sin

The MagnetosphereThe Plasmasphere and Alfven Layers

• For zero energy particles ( )

• 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.

• 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 ionsophere.

0

r

RBrE EE

eff

30

0 sin

eff

The MagnetosphereThe Plasmasphere and Alfven Layers

• For hot particles the effective potential becomes

where we have assumed that the azimuthal motion of the particles is greater than rotation.

– 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 (farther) to the Earth at dawn (dusk) than are

positive (negative) particles. • The surface inside of which particles can’t penetrate is the Alfven

Layer.

3

30

0 sinqr

RBE Ehot

eff

•These images of the Earth’s plasmasphere was taken by the EUV camera on the Image spacecraft on May 24, 2000.•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 emission at high latitudes is from aurora and is thought to be caused by 53.9nm emission from atomic oxygen.

Northward IMF

The MagnetosphereField Aligned Currents

• There is one more major set of currents in 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 2 currents at lower latitudes flow into the ionosphere on the dusk side and out on the dawn side.