Physics 6 Tutorial 5 - Solar Wind
The Sun is a middle sized and middle-aged star. It has shone for about 4500 million years and is expected to do so for another 4500 million years. We know that it provides energy to the Earth at a rate of about 500 W m-2. Observations on the star reveal it to be a very dynamic system. The structure of the Sun is shown here:
Image by Kelvinsong - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=23371669
A lot of information has been observed during solar eclipses, as well as viewing of the star through special telescopes. The surface of the Sun, the top part of the photosphere, has a temperature of about 4100 K at its coolest point. The surface is under the atmosphere of the Sun. The particle density of the upper part of the photosphere is about 1023 m-3, about 0.4 % of the atmospheric density at sea-level on Earth.
NEVER attempt to view the Sun with the naked eye.
To do so will cause permanent damage to your eyesight.
The atmosphere of the Sun consists of 4 different layers:
the chromosphere, a layer about 2000 km deep with a temperature of 20 000 K;
the transition region, a layer about 200 km deep where the temperature rises from 20 000 K to about 1 × 106 K;
the corona, a region of very low particle density (about 1015 m-3) and very high temperatures, about 1 - 2 × 106 K;
the heliosphere, a tenuous layer that extends about 50 astronomical units from the Sun. (1 AU = 150 × 106 km)
Why the atmosphere is so much hotter than the surface is not well understood, although physicists are sure that the magnetic field of the sun has some bearing on it.
The Solar Wind
In the late nineteenth and early twentieth centuries astronomers had observed that the Sun was at times a lot more active than normal, giving out intense flares that went deep into space. They associated this activity with the occurrences of intense activity of the Aurora Borealis (Northern Lights) and the Aurora Australis (Southern Lights). These events became known as geomagnetic storms, causing magnetic disturbances on the ground. The most severe of these could also affect telegraph lines, and later on, electricity distribution systems.
Observations of comets revealed that the tails always pointed away from the Sun, regardless of whether the comet was approaching or going away.
The first direct observations were made by the Soviet satellite Luna 1 in 1959.
Nature of the Solar Wind
The solar wind is formed by bulk movement of charged particles, mostly protons and electrons, but also other small atoms. At the very high temperatures, the atoms are stripped of their electrons, and exist as naked nuclei. This state is called a plasma. The particles in the corona move at speeds that are above the solar escape speed, 618 km s-1.
The particles in the fast solar wind travel at about 750 km s-1, while those of the slow solar wind travel at 300 - 500 km s-1. The temperature of the slow solar wind particles is about 106 K, suggesting that they have their source in the corona. The fast solar wind particles have a temperature of about 80 000 K, suggesting an origin in the photosphere.
Physicists cannot at the moment explain fully how the particles are accelerated. Their high speed was originally put down to their high temperatures, although this could not fully account for their speed. It is now thought that they are accelerated by effects of the solar magnetic field. The fastest of the solar winds appear to originate from coronal holes near the magnetic poles where small magnetic fields confine the plasma in magnetic fields and funnel it out into space. As the sun rotates on its axis, the streams of charged particles from these sources are hurled in a helical pattern, rather like water drops from a rotating lawn sprinkler. The idea is shown in this rather simplified diagram:
Energy of the Solar Wind
The energy of the solar wind particles is much lower than those of cosmic ray particles, between 1.5 keV and 10 keV.
A particle has an energy of 3.2 keV. What is this in joules?
This energy is equivalent to the energy carried by a soft (low energy) X-ray photon. Contrast this with the very high energy of cosmic particles.
An alpha particle is travelling at 500 km s-1. Explain whether or not there will be any relativistic effects.
Interaction with Magnetic Fields
The Earth has a magnetic field, which is similar to the field of a bar magnet. The region of the Earth's magnetic field is called the magnetosphere. The boundary of the magnetosphere is called the magnetopause. This is distorted by the solar wind as shown in this diagram:
Image by Alec Baravik (adapted), Wikimedia Commons
The charged particles are deflected by the magnetic field to form a bow shock wave, rather like the way air molecules pile up on the leading surfaces of a supersonic aeroplane. The magnetic field is pulled outwards to form a wake on the right hand side (the night side)
The Earth's magnetic field protects us from these particles, by trapping particles that penetrate the magnetosphere in the magnetic field. The way the charged particles interact with the magnetic field is identical to the way the particles of cosmic rays do, except that the radii of the circular paths are smaller. We will look at this in more detail. The important relationship is:
An alpha particle is travelling at 500 km s-1. Where it interacts with the Earth's magnetic field, the magnetic field strength of the horizontal component is 2.3 × 10-5 T. It strikes the magnetic field at 90o.
(a) Calculate the kinetic energy of the alpha particle. Express your answer in keV as well as J.
(b) Work out the radius of the circular path it forms. Give your answer to an appropriate number of significant figures.
Mass of a helium nucleus = 6.64 × 10-27 kg.
If the angle is not 90o then we have to take into account the angle. The charged particle follows a helical path:
We use exactly the same argument that we used in the previous tutorial, to give:
The vertical velocity component gives the radius of the helical path;
The horizontal velocity component gives the pitch of the helix.
The horizontal component and the vertical component are treated separately.
An alpha particle is travelling at 500 km s-1. Where it interacts with the Earth's magnetic field, the magnetic field strength of the horizontal component is 2.3 × 10-5 T. It strikes the magnetic field at 70o to the horizontal
(a) Work out the radius of the helical path it forms.
(b) Work out the time it takes to make one revolution.
(c) Work out the pitch of the helical path.
Mass of a helium nucleus = 6.64 × 10-27 kg.
The charged particles move down the field lines towards the poles. They interact with particles to form ions. The positive ions attract electrons, and energy is lost in the form of photons. We see this as the glow of an aurora.
The Aurora Borealis (Northern Lights) is seen in northern regions around the north pole. They can be seen occasionally in latitudes as far south as northern England. Charged particles from the solar wind from the Sun is captured by the Earth's magnetic field. The particles are guided along the field lines until they come low enough to collide with molecules in the atmosphere. The collisions cause ionisation. This picture shows the formation of the Aurora Australis (Southern Lights).
When the ions lose their charge, they lose energy by emitting photons of particular energy, which results in different colours being seen. Molecular nitrogen glows purple, while atomic nitrogen glows blue. Ionisation events with oxygen lead to yellow and green lights. UV is also emitted, as well as red light.
Image by Kristian Pikner - Wikimedia Commons
Altitude also affects the colours:
Reds are seen above 240 km;
Greens up to 240 km;
Violet and purple above 100 km;
Blue up to 100 km.
Auroras can be observed on other planets. The planets that have a magnetic field have auroras at the poles, for example, Jupiter.
Image by J T Clarke (University of Michigan), Wikimedia Commons
Planets that have no magnetic fields still have auroras, but these are distributed across the surface of the planet.
Auroras have been observed on a nearby brown dwarf star.
Effects of the Solar Wind
We are protected from high energy particles from the Sun by the Earth's Magnetic field. This is just as well, for the particles could interact with molecules in our bodies to cause genetic damage. During particular intense periods of solar activity, the bow shock wave can be pushed closer to the Earth, and solar wind particles can penetrate to the surface. This can interfere with telecommunications equipment and power networks. Outside the magnetosphere, the particles can cause damage to electronic equipment on satellites and space probes.
Where there is no magnetic field, the particles of the solar wind can strip away the molecules that form an atmosphere by collisions. This is thought to be how Mars has lost most of its atmosphere. A reversal in the Earth's magnetic field (which happens from time to time) will result in a period in which the magnetic field is zero. This will leave us exposed to the solar wind, and some of the atmosphere will be lost.
A wind in the atmosphere is the result of bulk movement of particles. The change in momentum of the particles acting on a surface results in a force. This can be used to propel a ship, or the blades of a wind-turbine. The solar wind can be harnessed in a similar way. A sail 800 m × 800 m is thought to be able to produce a force of about 5 N.
What is the pressure on a sail 800 m × 800 m that produces a force of 5 N?
The idea of using space sails has been considered as a way of propelling probes into interplanetary space. The force may be low, but space is a zero friction environment.
Two sails as described above are used to propel a space probe of total mass 1500 kg.
(a) Calculate the acceleration of the space probe using the two sails.
(b) The probe is initially accelerated by a rocket. If the initial speed of the probe is 5000 m s-1, calculate the speed after 1 day.
While this acceleration is low, probes have all the time in the universe to accelerate.