ASEN 5335 Aerospace Environment -- Geomagnetism 1 Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail:

ASEN 5335 Aerospace Environment -- Geomagnetism 1

Aerospace EnvironmentASEN-5335

• Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee)

• Contact info: e-mail: [email protected] (preferred)

phone: 2-3514, or 5-0523, fax: 2-6444,

website: http://lasp.colorado.edu/~lix

• Instructor’s office hours: 9:00-11:00 am Wed at ECOT 534; before and after class Tue and Thu.

• TA’s office hours: 3:15-5:15 pm Wed at ECAE 166

• Read Chapter 4 and class notes

• HW3 due 2/27

mailto:[email protected]

http://lasp.colorado.edu/~lix


Solar wind speed and IMF 1995-1999

Descending phase

Solar Minimum

Ascending phase


Geomagnetism

Dipole Magnetic Field

Geomagnetic Coordinates

B-L Coordinate system

L-Shells

Paleomagnetism

External CurrentSystems

Sq and L

Disturbance Variations

Kp, Ap, Dst


GEOMAGNETISM

It is generally believed that the Earth’s magnetic field is generated by movements of a conducting “liquid” core.

The self-sustaining “dynamo” converts the mechanical motions of the core materials into electric currents.

We are almost certain that these motions are induced and controlled by convection and rotation (Coriolis force).


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).



Measurements from 400 km altitude



• 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].


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

B 1

o

J0

B

V

B 0

2V0


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

Va Pnmm0

n

n1

cos

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

= 0 for m > n


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


“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°


We will now examine a few simple approximations to the earth's magnetic field and the magnetic coordinate systems that result.

SIMPLE DIPOLE Approximation

Referring back to the expression on p. 12, neglecting externalsources, we have

For a single magnetic dipole at the earth's center, oriented along the geographic axis,

n = 1 m = 0 and

Va Pnmm0

n

n1

cos

ar

n1

gnm cos m hn

m sin m

P10

cos cos

V ag10 a

r2

cos

Note that the r-dependence of higher and higher order dipoles goes as r-n


The field components are:

X = = (northward)

Y = 0 (eastward)

Z = = (radially downward)

V ag10 a

r2

cos

1

r

V

g10 a

r3

sin

Vr

2g10 a

r3

cos

= colatitude(southward positive)

northward component ofmagnetic field at equatorat r = a, X 0.31 G

1 = 10-5 G = 10-9 T (Tesla or Wbm-2)


Total field magnitude:

=

A "dip angle", I , is also defined:

=

I is positive for downward pointing field

(simple dipole field)

X2 Y 2 Z 2

g10 a

r3

13cos2 1/2

tan I

Z

X2 Y 22cot

I tan 1

2 cot


TILTED DIPOLE Approximation

As the next best approximation, let n = 1 , m = 1

We find that

and

where = longitude (positive eastward).

P11

cos sin

V aa

r2

g10 cos g1

1 cosh11sin sin


Physically, the two additional terms could be generated by two additional orthogonal dipoles placed at the center of theearth but with their axes in the plane of the equator.

Their effect is to incline the total dipole term to the geographic pole by an amount

In other words, the potential function could be produced by a single dipole inclined at an angle to the geographic pole and with an equatorial field strength

This "tilted dipole" is tipped 11.5° towards 70°W longitude and has an equatorial field strength of .312G.

tan 1 g1

1 2 h11 2

g10 2

1/2

g10 2 g1

1 2 h11 2

1/2


It is often more convenient to order data, formulate models, etc., in a magnetic coordinate system. We will now re-write the tilted dipole in that coordinate system rather than the geographic coordinate system.

DIPOLECOORDINATE SYSTEM

Dipole Equator

Dipole latitude

Dipole Axis

(79N, 70W)

(79S, 70E)

Rotation axis

sin sin sino cos coso cos o

sin cos sin o

cos= geographic latitude

= geographic longitude = 79°N, 290°E

o,o


The above formulation representing dipole coordinates (sometimes called geomagnetic coordinates) is now more or less the same as that on p. 20 & 21.

We will now write several relations in terms of dipole latitude , (instead of geographic colatitude, ) and dipole

longitude .

Dipole longitude is reckoned from the American half of the great circle which passes through (both) the geomagnetic and geographic poles; that is, the zero-degree magnetic meridian closely coincides with the 291°E geographic longitude meridian. Therefore,

in our previous notation = "dipole moment"

= 8.05 ± .02 1025 G-cm3

V M sin

r2

M g1o

a3


From the above expression we can derive the following:

H 1

r

V

M cos

r3

Z Vr

2M sin

r3

tan I Z

H 2tan

B H 2 Z 2 M

r3 13sin2 1/2

These look very much like the simple dipole approximation in geographic coordinates.


Aerospace EnvironmentASEN-5335

• Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee)

• Contact info: e-mail: [email protected] (preferred)

phone: 2-3514, or 5-0523, fax: 2-6444,

website: http://lasp.colorado.edu/~lix

• Instructor’s office hours: 9:00-11:00 am Wed at ECOT 534; before and after class Tue and Thu.

• TA’s office hours: 3:15-5:15 pm Wed at ECAE 166

• Read Chapter 4 and class notes

• HW3 due 2/27

• Quiz-4 on March 4, Tue, close book.

mailto:[email protected]



A field line is defined by , so

and we may integrate to get

This is the equation for a field line.

If = 0 (dipole equator), r = ro ; ro

is thus the radial distance to the equatorial field line over the equator, and its greatest distance from earth.

dr

Z

rdH

rddr

H

Z

1

2 tan

r ro cos2

B

rdH

dr, Z

ro

d


The point (magnetic or dipole latitude) where the line of force meets the surface is given by

Note also that the declination, D, which is the angle between H and geographic north, is

tanD = Y/X

X = H cosD

Y = H sinD

a

rocos

2

cos a

ro

1/2


The B-L Coordinate System "L-shells"

Let us take our previous equation for a dipolar field line

and re-cast it so the radius of the earth (a) is the unit of distance. Then R = r/a and

where R and Ro are now measured in earth radii. The latitude where the field line intersects the earth's surface (R = 1) is given by

r ro cos2

R Ro cos2

cos Ro 1/2


Now we will discuss an analagous L-parameter (or L-shell) nomenclature for non-dipole field lines, often used for radiation belt and magnetospheric studies.

We will understand its origin better when we study radiation belts; basically, the L-shell is the surface traced out by the guiding center of a trapped particle as it drifts in longitude about the earth while oscillating between mirror points.

For a dipole field the L-value is the distance, in earth radii, of a particular field line from the center of the earth (L = Ro on the previous page), and the L-shell is the "shell" traced out by rotating the corresponding field line around the earth.

Curves of constant B and constant L are shown in the figure on the next page. Note that on this scale, the L-values correspond very nearly to dipole field lines.


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.


By analogy with our previous formula for calculating the dipole latitude of intersection of a field line with the earth's surface, we can determine an invariant latitude in terms of L-value:

where = invariant latitude

Here L is the actual L-value (i.e., not that associated with a dipole field).

Where does this L map to at high altitude, such as at the equatorial plane depend on the geomagnetic activity. As an approximation, this L usefully serves to identify field lines even though they may not be strictly dipolar.

cos L 1/2


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


Change in equatorial field

strength over the past 150 years


Sept-aurora

External Current Systems


External Current Systems and Ionosphere


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

SqSqo Sq

p

Solar Quiet Current systems

10,000 Abetweencurrentdensitycontours


Geographic Distribution of Magnetic Observatories


A Magnetogram


Local time

northward eastward vertical

Sq groundmagneticperturbations


Note:

• According to Ampere's law, a current will induce a magnetic field, and conversely a time-changing magnetic field will induce a current to flow in a conductor.

• Currents flowing in the ionosphere induce a magnetic field variation in the ground .... this is the "external" source we referred to before.

• But, some of this changing magnetic flux links the conducting earth, causing currents to flow there.

• These, in turn, induce a changing magnetic field on the ground which is also measured by ground magnetometers. These induced earth currents contribute about 25-30% of the total measured Sq field.

• The above mutual feedback is very much like "mutual inductance"


An interesting phenomenon, the equatorial electrojet, which is stronger than the sum of the two Sq, occurs at the magnetic equator:

eastward electric field induced by dynamo action

looking down

magnetic equator

E

N

B

E

J

1E

2Ez

Jz2E 1Ez“Pedersenconductivity”

“Hallconductivity”


Pedersen and Hall conductivity

Pederson conductivity creates electric currents that are perpendicular to the magnetic field and parallel to the electric field, Hall currents are perpendicular both to the electric and magnetic fields


(3) is an intense eastward current (the equatorial electrojet) driven by the vertical polarization field.

(2) compensating vertical

field to maintain = 0. (no vertical currents due to insulating boundaries)

(The above scenario only occurs within a few degrees of the equator, otherwise the polarization charges can leak away.)

2E

Ez

Jz

100 km

- - - - - -

+ + + + + +

150 km

region ofconductivity

looking eastward

B

2Ez

J

1E

2Ez

Jz2E 1Ez

(1) Charge separation due to (downward Hall current, upward e-)

Note:

EZ 2

1

E J 1 2

2

1

E 3E= Cowlingconductivity


Another quiet current system, the lunar daily variation, L, similarly exists because of lunar tidal winds in the ionospheric E-region. These are gravitational tides, as opposed to solar-driven (thermally-driven) atmospheric tidal oscillations. The L variation is about 10-15% of the Sq variation.

L-variation

fg fc

fg r-2

M


Ionospheric currents inferred from the observed L variation. Current between adjacent contours is 1,000A, and each dot indicates a vortex center with the total current in thousands of Amperes.


= 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).


(Temerin and Li , JGR, 2002)

Prediction efficiency=91%

Linear correlation coeff.=0.95


Real Time Forecast of The Dst Index



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


AE is the "envelope" of deviations (of H from its quiet value) from a selection of high-latitude stations -- it is the difference between the curves AU and AL ("upper" and "lower") drawn through the max and min excursions of the deviations.

Auroral Electrojet Index (AE)


Density Variation from Orbital Drag of a High-Latitude Low-Perigee (~150 km) Satellite vs. AE and Kp





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,localized hot spots can occur and cause 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


geomagnetic field variations at Ottawa magneticobservatory

pipe-to-soil potential difference on a pipeline inCanada

During the magnetic storm the pipe-to-soil potential difference went outside the safe region. That can increase the possibility of corrosion.

Documents

ASEN 5335 Aerospace Environment -- Geomagnetism 1 Aerospace Environment ASEN-5335 Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: