ch 6 solar wind interactions. earth’s magnetic field

UML_reinisch_85.511_Ch7 1

Ch 6 Solar Wind Interactions.Earth’s Magnetic Field

-4

The solar wind interacts with the planets and comets in the solar syatem.

Most planets have a magnetic field (see Table 7.1). Mercury's and and

Mars's fields are tiny, <2x10 of Earth's field. To first order these fields

are dipole fields. Consult Ch 3.8. Fig. 3.11.


GeomagnetismDipole Magnetic Field

Geomagnetic Coordinates

B-L Coordinate system

L-Shells

Paleomagnetism

External CurrentSystems

Sq and L

Disturbance Variations

Kp, Ap, Dst


GEOMAGNETISM According to Ampere’s Law, magnetic fields are produced by electric currents:

Earth's magnetic field is generated by movements of a conducting "liquid" core, much in the same fashion as a solenoid. The term "dynamo" or “Geodynamo” is used to refer to this process, wherebymechanical motions of the core materials are converted into electrical currents.


The core motions are induced and controlled by convection and rotation (Coriolis force). However, the relative importance of the various possible driving forces for the convection remains unknown:

• heating by decay of radioactive elements

• latent heat release as the core solidifies

• loss of gravitational energy as metals solidify and migrate inward and lighter materials migrate to outer reaches of liquid core.

Venus does not have a significant magnetic field although its coreiron content is thought to be similar to that of the Earth.

Venus's rotation period of 243 Earth days is just too slow to produce the dynamo effect.

Mars may once have had a dynamo field, but now its most prominentmagnetic characteristic centers around the magnetic anomalies inIts Southern Hemisphere (see following slides).


• The main dipole field of the earth is thought to arise from a single main two-dimensional circulation.

• Non-dipole regional anomalies (deviations from the main field) are thought to arise from various eddy motions in the outer layer of the liquid core (below the mantle).

• Anomalies of lesser geographical extent (surface anomalies) are field irregularities caused by deposits of ferromagnetic materials in the crust. [The largest is the Kursk anomaly, 400 km south of Moscow].


Note on ELECTRIC and MAGNETIC DIPOLES

An electrostatic dipole consists of closely-spaced positive and negative point charges, and the resulting electrostatic field is related to the electrostatic potential as follows:

By analogy, if we consider the magnetic field due to a current loop, the mathematical form for the magnetic field looks just like that for the electric field, hence the "magnetic dipole" analogy:

E 0

E

B 0

B V


In the current-free zone

Therefore

Combined with another Maxwell equation:

Yields

Laplace’s Equation

The magnetic field at the surface of the earth is determined mostly by internal currents with some smaller contribution due

to external currents flowing in the ionosphere and magnetosphere

1 0o

B J

B

V

B 0

2V 0


The magnetic scalar potential V can be written as a spherical

harmonic expansion in terms of the Schmidt function, a particular

normalized form of Legendre Polynomial:

internal sources

external sources

r = radial distance = colatitude = east longitudea = radius of earth (geographic polar coordinates)

ar

n1

gnm cosm hn

m sin m

ar

n

Anm cosm Bn

m sin m

V a Pnmm0

n

n1

cos

n = 1 --> dipolen = 2 --> quadrapole

= 0 for m > n


“magnetic elements”

(H, D, Z)(F, I, D)(X, Y, Z)

Standard Components and Conventions Relating to the Terrestrial Magnetic Field


Max

Min.24 G

Surface Magnetic Field Magnitude () IGRF 1980.0

.61 G

.33 G

.67 G


Surface Magnetic Field H-Component () IGRF 1980.0

.13 G

.33 G

.025 G

.40 G

.025 G


Surface Magnetic Field Vertical Component IGRF 1980.0

0.0 G

0.0 G0.0 G

.61 G

.68 G


Surface Magnetic Field Declination IGRF 1980.0

10° 20°0°

0°


Paleomagnetism

Natural remnant magnetism (NRM) of some rocks (and archeological samples) is a measure of the geomagnetic field at the time of their production.

Most reliable -- thermo-remnant magnetization -- locked into sample by cooling after formation at high temperature (i.e., kilns, hearths, lava).

Over the past 500 million years, the field has undergone reversals, the last one occurring about 1 million years ago.

See following figures for some measurements of long-term change in the earth's magnetic field.


Equatorial field intensity in recent millenia, as deduced from measurements on archeological

samples and recent observatory data.

~10 nT/year


3

3

2 23

ˆˆ, 2sin cos

Values for the diple moments M of the different planets are given

in Table 7.1 of Cravens.

ˆ ˆˆ ˆB , 2sin cos 2sin cos

B , 1 3sin 1 3sin 3.68

:

E

MR

R

MR

R

MR B

R

B r λ

r λ r λ

The dipole field

R

20

0

Using the differential arc lengths in spherical coordinates and the

vector components B and B , one gets the equation of a dipole

field line: cos 3.69

where R is the geocentric distance of the

R R

0

field line at the equator

( =0). One usually writes . ER LR


2

2 23 3 3 6

2

3 6

2

Then cos , and

B , 1 3sin 1 3sincos

1 3sinB , 3.71

cos

In the next figure shows:

cos for L=2,3,4,...30

, 0.2,0.5, ... 0.001 Orstedt

E

E

E

E

R LR

M ML

R R L

BL

L

RL

R

B R const


The B-L Coordinate System:Curves of Constant B and L

The curves shown here are the intersection of a magnetic meridianplane with surfaces of constant B and constant L (The difference betweenthe actual field and a dipole field cannot be seen in a figure of this scale.


2

0

On the dayside at the subsolar point, the thermal pressure in the

magnetosheath just outside the magnetopause (MP) must equal the

magnetic pressure in 2

B

7.2 Location of the Magnetopause for Earth

the magnetosphere just inside the MP. We

approximate here by neglecting the IMF in the magnetosheath,

and the thermal pressure in the magnetosphere. Let us further

assume that the upstream solar wind

2SW

2SW

22

SW0

dynamic pressure

(see Section 4.6.6) gets "deshocked" at the bow shock and converted

into thermal pressure p:

0.85 7.1

For equilibrium: ( )

0.852

SW

SW

MPSW

u

p u

p MSheath p Msphere

Bu


22

SW0

MP

3

2 23 3

622

SW0

2

0 S

0.852

For a first cut, we consider a dipole field to find the radius R .

1 3sin where 1 3sin .

Then: 0.85 2

2 0.85

MPSW

EMP E E

MP MP E

E ESW

MP

MP E

E

Bu

M R MB B B

R R R

B Ru

R

R B

R

1 6

2W

6 3 27 20 3SW SW

5 2 9 2SW SW

7.6

7 10 1.67 10 10 /

4 10 /

Cha

2 10 /

7.5 at the

pman-Ferra

sub-

ro 1931

solar point.

SW

p

SW

MP E

u

n m m kg kg m

u m s u N m

R R


Measurements show that 10 , so what is wrong?

Magnetosheath protons and electrons impinging on the "edge" of

Earth's magnetosphere (see Fig. 7.1) are deflected (gyrated) in

opposite direction, for

MP ER R

K 0

ming a . A current

sheet (A/m) has a magnetic field:

1ˆ

2ˆwhere is the normal to the plane of the current

sheet. The current direction is such that it cancels the Earth's dipol

current sheet

K

B K n

n

MP MP

e

field for R > R , and adds to the field for R < R :


1 3

For : 0 ( cancels outside)

.

For : =2

Then 2 7.5 9.5 . Better!

The magnetic field of a c

How big i

urrent s

s the surface current K

hee

?

MP dipole K K dipole

K dipole

MP dipole K dipole

MP E E

R R B B B B B

B B

R R B B B B

R R R

0

3

40

42

3 70

1t K is .

2

1 for = 0; 0.5 10

2 9.5

2 108 10 /

1000 10 4 10

K

Edipole E E

E

E

B K

RK B B B T

R

BK A m

K 100mA/m


External Current Systems Currents flowing in the ionosphere and

magnetosphere also induce magnetic field variations on the ground. These field variations generally fall into the categories of "quiet" and "disturbed". We will discuss the quiet field variations first.

The solar quiet daily variation (Sq) results principally from currents flowing in the electrically-conducting E-layer of the ionosphere.

Sq consists of 2 parts:

due to the dynamo action of tidal winds; and

due to current exhange between the

high-latitude ionosphere and the magnetosphere along field lines (see following figure).

Sqo

Sqp


Sqo

Sqp

dusk

dawn


Sqo

Sq Sqo Sq

p

Solar Quiet Current systems

10,000 Abetweencurrentdensitycontours

UML_reinisch_85.511_Ch7 26 = storm time, time lapsed from SSC

DISTURBANCE VARIATIONS

In addition to Sq and L variations, the geomagnetic field often undergoes irregular or disturbance variations connected with solar disturbances. Severe magnetic disturbances are called magnetic storms.

Storms often begin with a sudden storm commencement (SSC), after which a repeatable pattern of behavior ensues.

However, many storms start gradually (no SSC), and sometimes an impulsive change (sudden impulse or SI) occurs, and no storm ensues.

disturbed value of a magnetic element (X, Y, H, etc.):

disturbedfield X = Xobs - Xq

= Dst() + DS()storm-time variation, theaverage of X around acircle of constant latitude

Disturbance local timeinequality (“snapshot” ofthe X variation with longitude at a particularlatitude)

longitude

t=t’


Typical Magnetic Storm

SSC followed by an "initial" or "positive" phase lasting a few hours. During this phase the geomagnetic field is compressed on the dayside by the solar wind, causing a magnetopause current to flow that is reflected in Dst(H) > 0.

During the main phase Dst(H) < 0 and the field remains depressed for a day or two. The Dst(H) < 0 is due to a "westward ring current" around the earth, reaching its maximum value about 24 hours after SSC.

During recovery phase after ~24 hours, Dst slowly returns to ~0 (time scale ~ 24 hours).


Various indices of activity have been defined to describe the degree of magnetic variability.

For any station, the range (highest and lowest deviation from regular daily variation) of X, Y, Z, H, etc. is measured (after Sq and L are removed); the greatest of these is called the "amplitude" for a given station during a 3-hour period. The average of these values for 12 selected observatories is the ap index.

The Kp index is the quasi-logarithmic equivalent of the ap index. The conversion is as follows:

The daily Ap index, for a given day, is defined as

Ap apn1

8


Long-term records of annual sunspot numbers (yellow) show clearly the ~11 year solar activity cycle

The planetary magnetic activity index Ap (red) shows the occurrenceof days with Ap ≥ 40

Ap and Solar Cycle Variation


Transformer Heating

Saturation of the transformer core produces extra eddy currents in the transformer core and structural supports which heat the transformer. The large thermal mass of a high voltage power transformer means that this heating produces a negligible change in the overall transformer temperature. However,localised hot spots can occur andcause damage to the transformer windings


Time-varying magnetic fields induce time-varying electric currents in conductors.

Variations of the Earth's magnetic field induce electric currents in long conducting pipelines and surrounding soil. These time varying currents, named "telluric currents" in the pipeline industry, create voltage swings in the pipeline-cathodic protection rectifier system and make it difficult to maintain pipe-to-soil potential in the safe region.

During magnetic storms, these variations can be large enough to keep a pipeline in the unprotected region for some time, which can reduce the lifetime of the pipeline.

See example for the 6-7 April 2000 geomagnetic storm on the following page.

How Geomagnetic Variations Affect Pipelines


7.3 Ionospheres THE NEUTRAL ATMOSPHERE

• Temperature and density structure

• Hydrogen escape

• Thermospheric variations and satellite drag

• Mean wind structure


Tropo (Greek: tropos); “change”Lots of weather

Strato(Latin: stratum);Layered

Meso(Greek: messos);Middle

Thermo(Greek: thermes);Heat

Exo(greek: exo);outside


Variation of the density in anatmosphere with constanttemperature (750 K).


Vertical distribution of density and temperature for high solar activity (F10.7 = 250) at noon (1) and midnight (2), and for low solar activity (F10.7 = 75) at noon (3) and midnight (4) according to the COSPAR International Reference Atmosphere (CIRA) 1965.


Atmospheric Compositions Compared

The atmospheresof Earth, Venus andMars contain manyof the same gases,but in very differentabsolute andrelative abundances.Some values arelower limits only, reflecting the pastescape of gas tospace and otherfactors.


MarsVenus

Earth

night

day

VenusAverage Temperature Profiles for Earth, Mars & Venus


At 80-100 km, the time constant for mixing is more efficient than recombination, so mixing due to turbulence and other dynamical processes must be taken into account (i.e., photochemical equilibrium does not hold).

Mixing transports O down to lower (denser) levels where recomb-ination proceeds rapidly (the "sink" for O).

After the O recombines to produce O2, the O2 is transported upward by turbulent diffusion to be photodissociated once again (the "source" for O).

O Concentration


The most variable parts of the solar spectrum are absorbed above about 100 km


Formation of Ionospheres

2 2

2 2

Photo ionization: If ( 10 to 20 )

In the terrestrial ionosphere:

(1)

M M

photoelectron

photoelectron

photoelectron

photoelectron

h I I eV

h M M e E

h N N e E

h O O e E

h O O e E

HW : Show that λ < 100nm.


HYDROSTATIC EQUILIBRIUM If …..n = # molecules per unit volume

m = mass of each particle

nm dh = total mass contained in a cylinder of air (of unit cross-sectional area)

Then, the force due to gravity on the cylindrical mass = g nmdh

and the difference in pressure between the lower and upper faces of the cylinder balances the above force in an equilibrium situation:

dP

nmgdh

P + dP

P

PdP Pnmgdh


Assuming the ideal gas law holds,

Then the previous expression may be written:

where H is called the scale height and

dP

dh nmg

P nkT RT

R R*

m

1

P

dP

dh

1

H

H kT

mg

RT

g

g g(0)RE

2

RE h 2


This is the so-called hydrostatic law or barometric law.

Integrating, where

and z is referred to as the "reduced height" and the subscript zero refers to a reference height at h=0.

Similarly,

For an isothermal atmosphere, then,

P P0e z

z dh

H0

z

T zon n eo T

hH PPeo

h

Hn n eo

hHeo


17 2 13 2

At top of atmosphere .

sec

The photoabsorption cross section 10 10

exp sec ,

where sec

n n

n

z

n

F F

dF n F ds F n dz

cm m

F z F n dz F e

z n

Exponential decrease of photon flux

λ λ n n

n

HW: (2) Show that for an atmosphere τ z =σ n z H secχ,

where H is the neutral scale height.

z

z dz

isothermal


2

The production rate at height z is

( ) .

In an isothermal atmosphere, if we assume equilibrium ,

i.e. , and :

1exp 1 sec ,

2

zn n

e d e

e e m

P z n F z F n z e

L k n

n z n z e

e eproduction P = loss L

is the height of maxi

Chapman 1932

mum production ( 1).

m

n

m

z z

H

z


Absorption of Solar Radiation vs. Height and Species

ch 6 solar wind interactions. earth’s magnetic field

Documents

significant magnetic

magnetic fields

main field

electric field

dynamo field

magnetic dipole analogy

ch7 magnetic elementsh

earths magnetic fielduml