Physics 6 Tutorial 4 - Cosmic Rays

 

Contents

Cosmic Rays
Discovery
Nature of Cosmic Rays

Sources of Cosmic Rays

Interaction of Cosmic Rays

Magnetic Fields

Path through the Magnetosphere

Exposure to Cosmic Rays

 

Cosmic Rays

Cosmic rays are not well understood, but are thought to be fragments of atoms that originate from space beyond the Solar System.  They travel at close to the speed of light.  They are NOT photons of electromagnetic radiation.  They have been known to damage electrical and electronic equipment.  They have the following properties:

Some cosmic rays have huge amounts of kinetic energy due to relativistic effects as they approach the speed of light and the energy is much higher than is possible with photons.

 

Question 1

From where does a photon get its energy?

Answer

 

The maximum energy of an ultra high energy gamma ray photon is reckoned to be 1.0 × 1019 eV.

 

Question 2

What is this energy in joules?

Answer

 

Contrast this with the Oh-My-God particle (yes, it was called that) that was recorded in 1991.  It had an energy of 3 × 1020 eV equivalent to 48 J.   This high energy was due to the very high relativistic kinetic energy due to the speed which was exceptionally close to the speed of light.  Its Lorentz factor was about 3.2 × 1011.  It would take a photon racing it about 200 000 years to get a 1 cm lead on it.  Its energy was about 40 × 106 times higher than the energy of the highest energy accelerated protons.

 

A simple kinetic energy calculation will show you that 48 J is equivalent to a 5 kg dumbbell hitting you at a speed of about 4 m s-1.  It would thump you hard.

 

 

Discovery

The first observation was made by Charles-Augustin de Coulomb in the 1780s.  He had a charged sphere that was insulated from the ground by air, which was considered to be an insulator.  The charge on the sphere was spontaneously lost and there was no explanation for it.  Later discoveries suggested that air could be ionised by charged particles or X-rays and become conducting as a result.

 

Later experiments showed the loss of charge even if the charged spheres were kept behind thick lead walls that would stop X-rays and any charged particles from radioactive sources.

 

In 1909, Victor Hess (1883 - 1964) demonstrated the existence of intense radiation at a height of 5 km above the ground by using very sensitive electrometers.  The radiation at 5300 m was about 4 time as intense than the radiation experienced at 1 km above the ground, and this led him to believe that this radiation came from space.  Similar findings were made by Werner Kohlhörster in 1913.   Hess' results were confirmed by Robert Millikan (Millikan's Experiment) in 1925.  Millikan first used the expression "Cosmic Rays".

 

Work to discover the interaction with particles in atmosphere was carried out in 1937.  This led to the discovery of the first anti-particle, the positron.  Also a range of short-lived particles such as pions and muons were discovered.  These were the result of interactions between the cosmic rays and molecules in the atmosphere.  Physicists still did not know the precise nature of the cosmic ray.  It was only recently that the nature of cosmic rays was finally worked out, almost a century after physicists started to study them.

 

Nature of Cosmic Rays

Cosmic rays are misnamed.  They are not electromagnetic radiation at all.  They gain their huge energies by travelling at close to the speed of light, and their Lorentz factors are very high. 

 

The majority (90 %) are protons.  9 % are helium nuclei (alpha particles).  The remaining 1 % include electrons and other nuclei of elements.  Some of these are radioactive, and the half lives of the radionuclides and their products can be used to date the particles.  One example is iron-60, a radioisotope of iron.

 

Question 3

What kind of radiation would iron-60 emit?  Explain your answer.

Answer

 

Iron 60 has a half-life of 2.6 × 106 years.  It decays to Cobalt-60.  Look at Nuclear Physics 5 to revise exponential decay.

 

Studies of the iron-60 and its decay products suggested that the source of iron-60 cosmic rays was about 3000 light-years, about the distance to a spiral arm of the galaxy.

 

Sources of Cosmic Rays

It is thought that cosmic rays have their source in the explosion of supernovae.  When a giant star collapses in itself, vast amounts of energy are released in the shock wave that bounces back as a result of the collapse (see Astrophysics 6).  Often gamma rays accompany the cosmic rays, as a result of neutral pions, which are antiparticles to themselves, annihilating.  The pions arise to collisions of protons that are caught up in the intense magnetic fields produced by the shockwave of a supernova.

 

 

Interaction of Cosmic Rays with the Earth's Atmosphere

When a cosmic ray particle enters the atmosphere, it will interact with molecules in the atmosphere to produce a shower of a range of different particles including:

As the neutral pions annihilate themselves almost immediately (8 × 10-17 s) there are gamma rays that then interact with each other close to the nuclei of air molecules to produce electrons and positrons in pair production events.  The electrons may pass through the electron shells of other atoms to produce bremsestrahlung (braking radiation) events to produce further gamma photons, which may go on to be involved in pair production.  See Particles 6 for annihilation and pair production.

 

Remember that pair production only happens when there is interaction between gamma photons in the presence of a nucleus.

Where there is no nucleus present, the gamma photons simply superpose and carry on as before.

 

Charged pions have a longer lifetime, about 26 × 10-9 s, while kaons have a lifetime of about 12 × 10-9 s.  Muons have a life time of 2.2 × 10-6 s, which gives them time to reach the Earth's surface, before they decay to electrons.   See Particles Tutorials 7 to 11 by clicking HERE.

 

The diagram shows a shower of particles produced by the interaction of a cosmic ray particle with molecules in the atmosphere:

 

If a high speed electron interacts with a nitrogen atom by electron collision, the electron can be captured by the nucleus to turn a proton into a neutron, emitting an electron neutrino:

 

 

This is the source of Carbon-14 in the atmosphere.

 

The table below shows typical cosmic ray fluxes.  The extreme energy events are rare.

 

Particle Energy /eV

Flux / m-2 s-1

1 × 109

10 000

1 × 1012

1

1 × 1016

1 × 10-7

(A few times a year)

1 × 1020

1 × 10-15

(Once a century)

 

It is thought that cosmic rays are instrumental in setting of lightning strikes.  Air loses its insulating properties at an electric field strength of about 3 × 106 V m-1.  However such a field strength has never been detected even in the most violent thunderstorm.  Therefore there needs to be another explanation and this puzzled meteorologists for many years.

 

 

It is thought now that lightning is set off by cosmic ray particles.  As we have seen above, the interaction of the cosmic ray particles with molecules in the atmosphere causes intense local ionisation, which makes the air conductive.  Electrons then tend to pool, leading to localised intense electric fields.  The lightning stroke propagates in a series of small steps (called a stepped leader) until it reaches close the ground.  The electric field is then intense enough to attract ions from nearby objects to complete a conducting path.  Then the main stroke occurs, allowing a current of about 25000 A to flow.  The intense heating effect on the air causes a loud bang, if you are close to the strike.  The subsequent rumble is because the source of the sound wave is not a point source, but along a long and irregular front.  The low frequency sound is because the higher frequency sounds from the distant sources are absorbed by the atmosphere.  In the picture above, you can see the step-wise propagation of the earth strike.

  

 

Interaction with Magnetic Fields

Cosmic ray particles are mostly hydrogen and helium nuclei.  They are positively charged.  Therefore they will interact with magnetic fields of any planet.  The Earth's magnetic field will protect us from them.

 

Consider two cosmic rays.  Ray 1 strikes the Earth's magnetic field at point 1 at 90o.  Ray 2 strikes the Earth above the North Pole.

 

We will look at the behaviour of Cosmic Ray 1.  To understand how a positively charged particle interacts with a magnetic field, you need to review Magnetic Fields 3.

 

We find that in a magnetic field, the force acts on a stream of electrons always at 90o to the direction of the movement.  Therefore the path is circular.

 

 

The magnetic force always acts on the charged particles at 90o, and that gives us the condition for circular motion. 

 

 

We can combine the relationship a = v2/r with Newton II to give us:

 

Therefore:        

                                                           

 

The v on the left cancels to get rid of the v2 term on the right:

 


 

 

This rearranges to give us:

 

 

Question 4

A cosmic ray particle consists of a helium nucleus.  It is travelling at a speed of 0.98 c.  It then enters the Earth's magnetic field where it is parallel to the surface.

(a)  Show that the Lorentz factor of the helium nucleus at this speed is about 5.

(b)  Calculate the relativistic mass of the helium nucleus.

(c)  Calculate the radius of the circular path, assuming that the helium nucleus has not collided with any molecules in the atmosphere.

 

Mass of a helium nucleus at rest = 6.64 × 10-27 kg;

Speed of light = 3.00 × 108 m s-1;

Magnetic field of the Earth = 43.5 × 10-6 T.

Answer

 

We assumed that the cosmic ray particle struck the magnetic field at a perfect right angle and tracked a perfectly circular path.  This would be rare.    The side view of the path would look like this:

 

 

 

The majority of particles, though, would strike at an angle other than 90 degrees, so there would be a component of velocity along the magnetic field.  So let us think about the particle hitting the magnetic field with a velocity v at an angle of q The magnetic field is horizontal and has a flux density of B.

 

The velocity vector can be split into its vertical component and its horizontal.  As with all motion in two directions, we treat the two components separately.  So for the horizontal component:

 

vH = v cos q

 

Since the horizontal motion is parallel to the magnetic field, the force acting on it is zero.  Therefore there is no horizontal force acting on it.  Newton I applies, so the horizontal velocity remains the same.

 

The vertical component will be affected by the magnetic field.  The vertical component is:

vV = v sin q

 

So we can write:

 

Therefore we can rewrite this for the radius:

 

Therefore the radius of the circular path is smaller than if the particle struck the field at right angles.

 

Question 5

A cosmic ray particle is identical to the one in Question 4, but strikes the Earth's magnetic field at an angle of 60o  to the horizontal.  Calculate the radius of the circular path made by the particle now.

Answer

 

Because there is horizontal motion, the path of the particle is helical (like the coil of a spring), not circular.  This is shown side-on in the diagram:

 

 

 

If viewed end-on, the cross section of the path is circular

 

The pitch, d, of the coil can be worked out simply by multiplying the magnitude of the horizontal velocity by the time, T, it takes the particle to complete one revolution of the circular cross section.   Therefore:

 

d = vHT

 

The time taken to complete one revolution is the circumference of the circle divided by magnitude of the vertical velocity:

It doesn't take a genius to write:

 

This tells us that the rate of rotation is NOT affected, as the radius and the magnitude of the vertical velocity are both changed by the same amount

 

Question 6

Use your answers to Question 5 to:

(a) work out the time taken for the particle to make one revolution;

(b) to calculate the pitch of the coiled path.

Answer

 

The path of the cosmic ray follows the field lines of the Earth's magnetic field.  It is guided towards the North Pole, where it will interact with molecules high in the atmosphere.  If the particles produced by the interaction are charged, they too will spiral with the magnetic field.  If they are uncharged, they will go off in random directions.

 

 

Path through the Magnetosphere

We treated the Earth's magnetic field as uniform in the argument above.  The Earth's magnetic field (the magnetosphere) extends to about 90 000 km from the Earth.  At its limit, the magnetic field strength has a low value, much lower than the figure given in Question 4.  The radius of the curved path traced by a lower energy cosmic ray will be large at the limit of the magnetosphere, but will decrease as the magnetic field strength gets bigger.  The idea is shown in the picture below:

 

Image of Antartica - Wikimedia Commons

 

So the cosmic ray particle spirals as shown.

 

Very high energy cosmic ray particles would not be affected by the Earth's magnetic field to the extent shown in this diagram.  The path would be slightly curved, but would strike the atmosphere and interact with molecules, or even strike the ground.

 

The interactions produce high energy particles, such as muons and pions, which in turn form ions.  These should, in theory, produce visible photons that could be seen near the poles in the form of the aurora borealis (and the aurora australis).  In practice, the effect is weak.  The effect is more marked due to the Solar Wind, which we will consider in the next tutorial.

 

 

Exposure to Cosmic Rays

The magnetosphere protects us from many cosmic rays, although some cosmic ray particles get through.  The dose received on the ground is quoted about 3.0 × 10-8 Sv per hour.  This is increased to about 5 × 10-6  Sv h-1 when flying at 10 000 m in a commercial aeroplane.  Even so, a passenger flying across the Atlantic will receive of dose of 3.2 × 10-5 Sv, about the dose that you would get from an X-ray at the dentist.

 

Cosmonauts travelling to Mars will not have the protection afforded by magnetosphere, so will receive significantly more exposure to cosmic rays.  Additionally Mars has no magnetic field.  It is possible that such cosmonauts could be exposed to significant damage to the DNA. 

 

Cosmic ray particles can also cause damage to electronic components, which is not desirable on a long distance spaceflight.