An Introduction to the Structure of the · PDF fileUCL DEPARTMENT OF SPACE & CLIMATE PHYSICS...

UCL DEPARTMENT OF SPACE & CLIMATE PHYSICS

SPACE PLASMA PHYSICS GROUP

18th September 2012 STFC Summer School

An Introduction to the Structure of

the Magnetosphere

Prof. Chris Owen

Mullard Space Science Laboratory,

University College London

Lecture to the STFC Summer School, Armagh

September 18th 2012




1. Overview

• An introduction to the structures and processes that occur in the vicinity of the magnetized planets.

• Ways to understand plasma behaviour

• Applications – The Solar Wind (brief recap)

– Collisionless Shocks

– Magnetosheath

– Magnetic Reconnection

– The ‘Open’ Magnetosphere

– Magnetic Substorms

• Conclusion




Recap (?): Definition

• A plasma is a quasi-neutral gas consisting

of positively and negatively charged

particles (usually ions and electrons)

which are subject to electric, magnetic and

other forces and which exhibit collective

behaviour (oscillations, instabilities, etc.).

2

1

2

32

1

2 2

1;1

3

4;

oe

o

PeCNoDD

o

o

Dm

neffnNL

ne

kT




The Realm of Plasma Physics




2. Ways to Understand Plasmas

• You will learn more details about these

from the programme for tomorrow:

– Single Particle Dynamics;

– Magnetohydrodynamics (MHD);

– Kinetic Theory;

• I will briefly ‘pre-cap’ some of these only to

the extent necessary to follow this lecture.




2.1 Single Particle Dynamics

• Particle gyromotion

• Particle drifts

• Particle mirroring




Basic Particle Motion in a Magnetic Field

• Gyroradius (Larmor

radius): rL = mv/qB

• Gyro- or cyclotron

frequency:

WL = qB/m

• Pitch angle:

a = tan-1(v/v||)

(0 a 180o) B

• Lorentz Force:

FL = q(E + v B)




B

VF

F

( ) 2 qB B F v F x =

Particle Drifts

• FxB drift • FxB drift




• ExB drift

B

VF

F

( ) 2 qB B F v F x =

Particle Drifts





• Gradient drift

• ExB drift • ExB drift

B

VF

F

( ) 2 qB B F v F x =

Particle Drifts





• Gradient drift • Gradient drift

• ExB drift • ExB drift

B

VF

F

( ) 2 qB B F v F x =

Particle Drifts

• FxB drift

• Curvature drift

• FxB drift

3




Particle Mirroring

•

is conserved.

(as is K.E.)

21

2mv B




Applications - Particle Trapping

c.f. planetary radiation belts.

N.B. Opposing drift of ions and electrons creates a ‘Ring

Current’ around the planet.




Van Allen Radiation Belts




2.2 Magnetohydrodynamics

(MHD) • See lectures tomorrow (Alan Hood and Robert

von FS);

• Plasma is treated as a fluid……

• ….but accounts for additional phenomena due to

electromagnetic influences – modifications to

classical fluid dynamics equations plus Maxwells

equations!

• However, ‘Frozen-in’ magnetic flux is a key

concept.




Frozen-in Magnetic Field

P1 P1

P2

P2

A

B A

B

V1

V2

21

ot

BV B BMHD Induction Equation:




Frozen-in flow Implications

1. Particles remain associated with

the same field line for all time

2. Plasmas on different field lines

do not mix

3. Corollary: ‘Frozen-out’ plasma

Caveats

1. Only an approximation to the

actual flow (but usually a good

one in space plasmas!)

2. Applies when the field seen by a

particle varies slowly in space

and time compared with its

gyrofrequency and gyroperiod




Gyro-periods and -radii: Typical Values

Electrons Protons

We

(rad s-1)

e (s)

Rge (km)

Wp

(rad s-1)

p (s)

Rgp (km)

Solar Wind (B ~5 nT, KE ~10 eV)

1000 0.01 2 0.5 10 100

Magnetosphere (B ~100 nT, KE ~1 KeV)

18000 0.003 1 10 0.5 50

Ionosphere (B ~50,000 nT, KE ~0.1

eV)

9x106 1x10-6 2x10-5 300* 0.02* 0.004*

* Atomic oxygen




Magnetic Flux Tubes




2.3 Kinetic Theory • Particle level descriptions of the plasma are

crucial for understanding advanced topics

(e.g. plasma waves and instabilities)

• Statistical approach – distribution function

f(r, v ,t) = dn(r, v, t)/drdv

• N.B. 6-dimensional phase space

• Macroscopic parameters (density,

temperature etc.) deduced from ‘moments’ of

the distribution function

• Beyond the scope of this short lecture.




3. Space Plasma Applications

• The Solar Wind (again v. brief precap –

see lectures later in week)

• Collisionless Shocks

• Magnetosheath

• Magnetic Reconnection

• The ‘Open’ Magnetosphere

• Magnetic Substorms




3.1 The Solar Wind

• Extension of solar

corona into

interplanetary space

Average properties at Earth:

Density ~ 7cm-3 (~ 4% He2+)

Speed ~ 450 km s-1

Proton Temp. ~ 1.2x105 K

Electron Temp. ~1.4x105 K

B-Field Strength ~ 7 nT

MS ~ MA ~ 2-10

MFP ~ 1 AU




What happens when the solar wind encounters

a planetary magnetic field?

Solar

Wind




Formation of a

Closed

Magnetosphere

Solar

Wind

Bow Shock

Magnetosheath




3.2 Collisionless Shocks/Bow Shock

• Basic Physics

• Shock geometry and structure

• Particle acceleration

• Foreshock

• Magnetosheath




Rankine-Hugoniot (Shock Conservation)

Relations

22

22

[ ]

[ ] 0

02

0

10

2 1

[ ] 0

[ ] 0

UPSTREAM DOWNSTREAM

n

n

o

nn

o

nn n

o o

n

n n

X X X

u

Bu P

Bu

BP Bu u u

B

u B

t t

t t

u B

u.B

B u

Upstream Shock Downstream

UU Ud

Fast (M > 1),

cool, rarefied

plasma

Slow (M < 1),

compressed,

heated plasma




Shock Geometry and Structure i) Quasi-perpendicular Shock


n̂

UU Ud

BU BD





n̂

2.Quasi-parallel Shock

UU Ud

BU BD

BIMF

Magnetosheath

Bow Shock

Q

Q||

Obstacle to

SW flow

VSW

Ion

Foreshock

Electron

Foreshock




E-field

Shock Acceleration • Shock Drift Acceleration

Multiple interaction with a Q

shock can lead to particle drift

in the direction of the

convection electric field ESW –

hence the particle gains

energy.




E-field

• Shock Drift Acceleration

Multiple interaction with a Q

shock can lead to particle drift

in the direction of the

convection electric field ESW –

hence the particle gains

energy.

E-field

VSW

Shock

• Fermi (Diffusive)

Acceleration

Multiple interaction and

reflection at a Q|| shock and at

upstream solar wind

turbulence can lead to particle

acceleration via the Fermi

mechanism – hence the

particle gains energy.

VO

VO + 2nVSW

Shock Acceleration




3.3 The Magnetosheath

• The hot, high-beta plasma region, lying between the

bow shock and the magnetopause is known as the

magnetosheath.

• The magnetosheath is also a region of great wave

activity – plasma is thus also processed through mode

coupling and damping.

• Studies of the high beta, non-linear plasma processes

of the magnetosheath require understanding of the hot

plasma conditions and the complexity/activity of this

environment.




Gasdynamic Magnetosheath Flows

N.B. Structure

is rotationally

symmetric

about the X-

axis in these

plots




Density, Velocity, Temperature




BX = 0 BX ≠ 0

Draped Magnetosheath Field

• Magnetosheath

plasma flow is away

from subsolar point in

all directions around

the magnetosphere;

• Frozen in flow

implies that the

magnetic field

remains connected to

given plasma parcels;

• Thus the field must

drape around the

magnetosphere.




Plasma Depletion Layer

• Draping of B-field over

magnetosphere results in a

field strength maximum just

upstream of the subsolar

magnetopause.

• Plasma is ‘squeezed’ out of

this region along the field

lines by the action of the

mirror force.

• This can create a relative

void of plasma, the PDL, in

this region (particularly for

northward IMF).




Formation of the Magnetosphere 2

Solar

Wind

Bow Shock

Magnetosheath

Magnetopause




• Currents flow over magnetopause surface and act to contain the terrestrial

magnetic field within the cavity (and any IMF outside of it).

• Tail magnetopause currents close via the equatorial cross-tail current

3.4 Chapman-Ferraro

Currents




Chapman-Ferraro Currents - Model

Current flows in narrow sheet ~1 rgi thick, where ions and

electrons turn in opposite directions when they encounter

the terrestrial magnetic field.




• Typical solar system plasmas:

– (eVkeV thermal energies)

– approximation is valid in the usual field gradients

• Frozen-in motion not applicable to high energy

particles (MeV and above);

• If the field gradients become large (i.e. small

scale lengths) then the frozen-in approximation

breaks down, even for low-energy particles.

3.5 The Breakdown of the Frozen-In

Approximation




?

On small scale-lengths, the diffusion term in the induction equation

becomes important – the magnetic field diffuses through the plasma.

Magnetic Reconnection




Magnetic Reconnection – Mixing of

Plasma Populations




• Application of strict frozen-in flow implied that magnetic

field and plasma from different sources could not mix;

• However, the frozen-in flow approximation is not always

valid where gradients are sharp;

• Reconnection allows:

1. Magnetic field regions that were previously

independent to interact;

2. The plasma populating the magnetic fields to intermix;

3. Plasma acceleration as magnetic field energy

released.

Magnetic Reconnection – Key

Points



18th September 2012 STFC Summer School 3.6 Formation of the ‘Open’ Magnetosphere

Solar

Wind

Bow Shock

Magnetosheath

Magnetopause

Interplanetary

Magnetic Field

ESW

JTAIL

JMP




• The global convective motion of field lines that arises as a consequence

of (even relatively localized) magnetic reconnection is often called the

Dungey Cycle

• The main implications:

1. Field lines reconnected at dayside are dragged tailwards at high-

latitudes, return at equatorial latitudes after tail reconnection;

2. Thus solar wind momentum is transferred into the magnetosphere;

3. Open field lines allow plasma to cross the boundary between the

magnetopause and solar wind (in both directions);

4. Plasma on field lines that are reconnected is accelerated and heated as

the field line contract away from the reconnection site;

5. N.B. These processes are modulated by the direction of the

interplanetary magnetic field:

• N. IMF reduced dayside reconnection reduced convection;

• S. IMF enhanced dayside reconnection enhanced convection.

The “Open” Magnetosphere




Plasma Populations in an ‘Open Magnetosphere’




Time-Dependent Convection –

Substorms

• A process in which vast amounts of solar wind

energy (~1016 J) are first stored within the

magnetotail and then explosively released.

• Involves major reconfigurations of entire solar

wind/magnetosphere/ionosphere system

• Growth, expansion and recovery phases.

• Controversial subject.




Substorm Growth Phase




Growth Phase Phenomenology Ground/Ionosphere

• Dawn-dusk E-field

in polar cap

intensifies;

• Polar cap expands

equatorward;

• Fading auroral

features.

Geosynchronous

• B-field becomes

more tail-like

(stretched).

Magnetotail

• Magnetopause

flaring increases;

• Lobe magnetic flux

content increases;

• Plasma sheet thins;

• Tail current sheet

intensifies;

• Slow Reconnection

of closed flux at

NENL.




Substorm Expansion Phase




Current Diversion




Substorm Auroral Activity from Space




Plasmoid

Ejection




Expansion Phase Phenomenology Ground/Ionosphere

• Equatorward

auroral arc brightens;

• W. Electrojet

intensifies;

• High latitude -ve

bays/Mid-latitude +ve

bays;

• Pi2 pulsations;

• Poleward

expansion of pre-

midnight auroral

surge.

Geosynchronous

• Energetic particle

injections;

• B-field rapidly

dipolarizes;

• Substorm current

wedge expands.

Magnetotail

• Fast reconnection

of open flux at NENL;

• Lobe magnetic flux

content decreases;

• Field-aligned

currents/AKR

intensify;

• Plasmoid pinched

off and ejected

downtail;

• TCR perturbations

in lobes.




Recovery Phase Phenomenology

Ground/Ionosphere

• Auroral bulge fades

and contracts.

Geosynchronous

• Current wedge

weakens.

Magnetotail

• NENL retreats

downtail.

• Plasma sheet

thickens.

• Tail currents and

fields ‘relax’.




Conclusion • Briefly reviewed some key concepts in understanding

collisionless space plasmas;

• Introduced a number of applications of these concepts (shocks, magnetosheath, radiation belts);

• Introduced the basic structure and dynamics of a magnetically ‘open’ magnetosphere;

• In this short lecture we have only touched on some of the basics of the subject – inevitably much has been left out;

• In addition, we have concentrated on the terrestrial system here – however, each magnetised obstacle to the solar wind has unique aspects to its interaction with the solar wind.




END

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