# Magnetic Fields All Around

It’s not often you can see lightning above Glasgow, so this 2006 Flickr photograph is a rare and impressive sight.  But that’s not the point…  A study by researchers in the United Kingdom shows it is not just conditions here on Earth that determine how much thunder and lightning we get.  The Sun’s magnetic field also has a major influence, more than doubling the number of lightning bolts on some days…

Scientists have long wondered about the manner in which lightning bolts are triggered, particularly since the air is known to be a perfectly good insulator of electricity.  Sometimes thunder and lightning fail to materialise, even after the most stifling hot summer days.  Sometimes the sky starts to flash and rumble with no provocation.

# The Sun’s Magnetic Field and Lightning on Earth

By studying lightning data gathered by the UK’s Meteorological Office and plotting it against satellite measurements of the solar magnetic field, Owens and his colleagues at the University of Reading were able to assess what influence the solar magnetic field has on electrical storms here on Earth.

The Sun’s magnetic field causes solar activity, including sunspots on the surface of the Sun, solar flares, and variations in solar wind that carry ionised particles throughout the Solar System.  This solar activity changes the very structure of Earth’s outer atmosphere.  The effects on Earth include auroras at high latitudes and the disruption of radio communications and electric power networks.

# The Earth’s Magnetic Field

In the Solar System, most planets generate magnetic fields through the motion of highly conductive fluids.

### The Earth’s field originates in its core.

Textbooks often depict the Earth as having a simple and symmetrical magnetic field, as if there were a bar magnet placed at the centre of Earth.  But in fact, the field of the Earth’s magnetic dipole is usually skewed, with its poles about 5° out of line.  And it is far from simple…

The geomagnetic field extends from the Earth’s deep interior to the outer regions of its atmosphere and beyond… where it meets the solar wind – a stream of charged particles emanating from the Sun.

At the Earth’s surface, its magnitude ranges from 25 to 65 microtesla.

Unlike a bar magnet, Earth’s magnetic field changes over time because it is generated by a geodynamoIn the case of planet Earth, this is generally accepted to be the motion of molten iron alloys in its outer core.

## The Dynamo Theory

Inside the Earth, the structure is layered.  Scientific understanding is based on observations of topography and bathymetry.  This layering as been inferred using the time of travel of refracted and reflected seismic waves.  Each layer can be identified according to their chemical or rheological properties.

The Earth’s core is a region of iron alloys extending to about 3400 kilometres.  By comparison, the radius of the Earth is 6370 km.

The core is divided into a solid inner core, with a radius of 1220 km, and a liquid outer core.

The motion of the liquid in the outer core is driven by heat flow from the inner core, which is about 6,000 K (5,730 °C; 10,340 °F), to the core-mantle boundary, which is about 3,800 K (3,530 °C; 6,380 °F).

The pattern of flow is organised by the rotation of the Earth and the presence of the solid inner core.

The mechanism by which the Earth generates a magnetic field is known as a dynamo.  It also applies to how the Sun’s magnetic field and that of the other stars arise.

## Magnetic Induction

A Magnetic Field is essentially caused by a feedback loop.  It takes three known laws:

• #### Current loops generate magnetic fields – Ampère’s  Law

$\bigtriangledown \times \boldsymbol H = \boldsymbol J + \frac {\partial \boldsymbol D}{\partial t}$

• #### A changing magnetic field generates an electric field – Faraday’s Law,

$\bigtriangledown \times \boldsymbol E = - \frac {\partial \boldsymbol B}{\partial t}$

• #### The electric and magnetic fields exert a force on the charges that are flowing in currents – Lorentz Force

$\boldsymbol F = q \left ( \boldsymbol E + \boldsymbol v \times \boldsymbol B \right )$

These effects can be combined in a partial differential equation for the magnetic field called the magnetic induction equation:

#### $\frac{\partial \boldsymbol B}{\partial t} = \eta \bigtriangledown ^2 \boldsymbol B + \bigtriangledown \times \left ( \boldsymbol u \times \boldsymbol B \right )$$\frac{\partial \boldsymbol B}{\partial t} = \eta \bigtriangledown ^2 \boldsymbol B + \bigtriangledown \times \left ( \boldsymbol u \times \boldsymbol B \right )$

where

u is the velocity of the fluid,

B is the magnetic B-field,

$\eta = \frac {1}{\sigma \mu}$ is the magnetic diffusivity – a product of the electrical conductivity σ and the permeability μ,

$\frac{\partial \boldsymbol B}{\partial t}$ is the time derivative of the field,

$\bigtriangledown^2$ is the Laplace operator,

$\bigtriangledown \times$ is the curl operator.

### Just Add Convection and the Coriolis Effect…

The motion of fluids at the Earth’s core is sustained by convection – a type of motion driven by buoyancy.  The temperature increases towards the centre of the Earth, and the higher temperature of the fluid lower down makes it buoyant.

The buoyancy is enhanced by chemical separation.  As the core cools, some of the molten iron solidifies and is plated to the inner core.  In the process, lighter elements are left behind in the fluid, making it lighter.  This process is known as compositional convection.  A Coriolis effect caused by the overall planetary rotation, tends to organise the flow into rolls aligned along the north-south polar axis.

The average magnetic field in the Earth’s outer core was calculated as being 50 times stronger than the magnetic field at the surface.

In 2009, independent researcher Dennis Brooks found that Earth’s magnetic field was not produced by an internal dynamo.  Nor is it produced by ocean currents.  The dynamo is outside the planet!  His findings show that Earth’s magnetic field and the planet itself are components of a complex dynamo system, which surrounds the planet.  The planet and its magnetic field are part of the dynamo.  According to this theory, no internal dynamo or ocean current helps in producing or maintaining the magnetic field because other planets with magnetic fields do not have ocean currents or iron cores.

There is yet much to be learned about the geomagnetic field…

# The Wandering Magnetic Field

The North magnetic pole wanders widely.  But it does so sufficiently slowly for ordinary compasses to remain useful for navigation.

At irregular intervals averaging several hundred thousand years, the Earth’s field reverses its polarity and the North and South magnetic poles relatively abruptly switch places.  These reversals of the Earth’s magnetic poles leave a record in rocks.  This is of great value to paleo-magnetists in calculating the geomagnetic fields of the past.

Such information is also helpful in studying the motions of continents and ocean floors in the process of plate tectonics.

The magnetosphere is the region above the ionosphere, which extends several tens of thousands of kilometres into space, protecting the Earth from the charged particles of the solar wind and cosmic rays that would otherwise strip away the upper layers of the atmosphere, including the ozone layer that protects the Earth from harmful ultraviolet radiation.

These kinks are caused by the pull of the Sun’s magnetic field, which fluctuates with sunspot number and the strength of the solar wind.

The Sun is a magnetically active star with a strong, changing magnetic field that varies from year to year and reverses direction about every eleven years around solar maximum.

# The Heliospheric Magnetic Field

All matter in the Sun is in the form of plasma – that is to say, ionised matter particles.

Differential rotation of the Sun’s latitudes causes magnetic field lines to become twisted together over time, producing magnetic field loops to erupt from the Sun’s surface and trigger the formation of dramatic sunspots and solar prominences.

This twisting action creates the solar dynamo and an 11-year solar cycle of magnetic activity, as the Sun’s magnetic field reverses itself about every 11 years.

The heliospheric current sheet rotates along with the Sun with a period of about 25-35 days, depending on the latitude.  During this time, the peaks and troughs of the so-called “ballerina’s skirt” pass through the Earth magnetosphere, interacting with it.

Near the surface of the Sun, the magnetic field produced by the radial electric current in the sheet is of the order of 5 x 10−6 T.

#### At the surface of the Sun, the magnetic field is about 10-4 Teslas.

If the form of the field were a magnetic dipole, the strength would decrease with the cube of the distance, resulting in about 10−11 teslas at the Earth’s orbit.

The heliospheric current sheet results in higher order multipole components, so that the actual magnetic field at the Earth due to the Sun is 100 times greater.

#### Sometimes the heliomagnetic field points away.

The Sun’s magnetic field is bending the Earth’s own magnetic field, thereby increasing our exposure to cosmic rays.

And cosmic rays are thought to increase the number of thunderclouds and trigger lightning bolts in places.

Since the nature of the Sun’s magnetic field is well known, weather scientists could incorporate this information into future meteorological forecasts.

Typically, the solar field shifts every 10 to 15 days, meaning that the Earth’s magnetic field is usually bent in one direction or the other.

# Of Sound and Fury…

Over five years, the United Kingdom experienced 50% more lightning strikes when the Earth’s magnetic field was affected by the Sun.  The new research suggests that the orientation of the Sun’s magnetic field is playing a significant role in the number of strikes.

The Sun’s magnetic field could be loosely compared to that of a bar magnet, on a much smaller scale.  As the Sun spins around, the magnetic field orientation changes.  The Sun’s magnetic field sometimes point towards the Earth, and it points away at other times.

Owens et al. believe that the solar magnetic field, either pulling away or pushing on the Earth’s magnetic field, allows a flow of energetic charged particles (cosmic rays) down our atmosphere at specific locations, and that those particles trigger lightning.

Between 2001 and 2006, the UK’s thunder and lightning rates were up by 40-60% when the Sun’s magnetic field pointed away from Earth.

#### The rates were the highest during summer.

During July, records indicate an almost doubling of the number of lightning strikes compared to when the solar magnetic field was pointing the opposite way.  There was an average of 40 lightning flashes on “away sector” days, but about 90 flashes on “towards sector” days.

The scientists suspect the changes in shape of the Earth’s magnetic field affect the number of energetic charged particles channelled into the Earth’s atmosphere from outer space.  Each time the Earth’s field bends, it exposes different locations to different particle intensities.  For lightning to occur, a thin conducting channel is needed, like a wire, and galactic cosmic rays can provide this thin column of ionisation in the atmosphere.

# Geomagnetic Field Variations at High Latitudes

Equatorial regions generally have stronger and more frequent convection.  As a result, there is more opportunity for solar modulation to act, even if that modulation is generally weaker.

Because geomagnetic variations are more significant at high latitudes, the effect is likely to be greater in higher-latitude countries, such as the United Kingdom.  But other factors are important too.

According to Owens and his colleagues, areas with lower atmospheric ionisation from ground level sources, such as radon – a radioactive noble gas occurring naturally, are more sensitive to cosmic-ray variation.

In future, the researchers hope to find out how the relationship between solar field and lightning holds for other countries, and assess it over time using historical records going back 150 years.

And while they admit that the mechanics of how cosmic rays might trigger lightning is still a theory, Owens and his colleagues believe that their discovery of an association with the movements of the Sun’s magnetic fields, could lead to better predictions of thunder and lightning events.

Ultimately, such findings could be used to improve forecasts, by incorporating information about the solar magnetic field into numerical weather predictions.