Cosmic Rays: Invisible Particles from Outer Space

Raymond Jimenez, Leonard Tampkins, Daniel BladoYoung Engineering and Science Scholars 2008

(Dated: July 10, 2008)

We provide a short introduction of what cosmic rays are. We also discuss how they are detected,and how they behave in the presence of homogenous magnetic fields.

1. INTRODUCTION

Cosmic rays are highly energized particles (90% areprotons, but there are alpha and beta particles as well)from space that collide with the Earth’s atmosphere. Acommon misconception is that cosmic rays are actualrays; in reality, this phenomenon occurs as a slew of singleparticles. Most of them can penetrate through Earth’smagnetic field to the atmosphere, where they interactand scatter, as we will later show. What makes this phe-nomenon so fascinating is that these particles are con-stantly barraging and entering the atmosphere, thoughmany people do not even realize it. What is more, cos-mic rays travel incredibly long distances; not only dothey come from the sun, but other celestial bodies aswell. Research on cosmic rays has its benefits. It is pos-sible to gain insight into the intricate workings of the vastuniverse, and developments for protection from the sideeffects of cosmic rays on living creatures can be made.������� ����� ������� ���������� ������������ ��!�"#$ % ��� �����&'��� ����� ��!�"((�)*� $+, $+-$+.$+/$+�$+ $+0$+#,$+#-$+#0$+#1$+#2$+#.$+#/$+#�+3$$+$456789:;< =>?8@?AB?C9CDE?FDG9B85A=8H@?EA5@8=HEIF8?A J5ABE?CKL

FIG. 1:

2. WHAT ARE COSMIC RAYS?

It is necessary to establish a clear foundational under-standing of basic particle physics in order to comprehendthe characterization, behavior, and detection of cosmicrays. The Standard Model is a theory which explains thefundamental particles and their interactions. Three typesof fundamental particles exist: i) quarks (which make upprotons and neutrons) ii) leptons (such as the well knownelectron) and iii) force carrier particles (like the photon).Quarks exist only in groups of two (known as mesons) orthree (known as baryons). In particular, there are twomesons that are associated with cosmic rays—kaons andpions. Leptons, the second classification, can exist alone.Other leptons are muons, a charged particle whose massis much greater than that of the electron, and neutrinos,hard-to-find neutral particles with very little mass. Thethird classification, force carrier particles, is involved ininteractions between particles. These particles, however,are not crucial to a basic understanding of cosmic rays,so they will not be thoroughly discussed. Of these, it hasbeen established through observation that some are morestable than others, and that the more unstable particleswill decay into the more stable ones. For example, theheavy muon, once produced, quickly decays into neutri-nos and the more stable electron.

Cosmic rays are charged particles. Once they en-counter the atmosphere, the particle breaks down andsets a chain reaction of several decays. For instance, aproduced gamma ray can break down into an electronand positron, which can emit more gamma rays, which inturn decays into more electrons and positrons. The mainconstituent of cosmic rays, the proton, strikes the atmo-sphere and almost immediately breaks down into unsta-ble pions and kaons, which in turn decay further intothe more stable electrons, muons, and neutrinos. Theresult is a cascade of various types of particles known asa cosmic shower.

Out of all these numerous traveling particles, only cer-tain types actually reach the surface of the earth. Theoriginal proton, for example, never actually reaches thesurface, and thankfully so: if it did, its immensely power-ful collisions would damage living creatures. Those thatdo reach the earth, such as electrons and muons, are notas damaging. .

Cosmic rays are strange forms of matter, as theygenerally travel velocities near the speed of light andthey are extremely tiny. Because of these factors theparticles emitted by the cosmic rays display unusual

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FIG. 2: A cosmic ray shower

behaviors, which create a variety of problems forclassical mechanics. One easily observable problem isthe fact that scientist are even able to detect cosmicray particles on the earth. In reality, most particlesshould decay before they reach the surface of the earth,but they don’t. Using Albert Einstein’s Theory ofSpecial Relativity this problem can easily be solved,for as an object moves faster time flows faster incomparison to the time of a stationary observer. Onecan use the muon to help explain this problem and itssolution. A muon travels approximately 2.997 ∗ 108

meters per second. A muon must be able to travelat least 50 km from the atmosphere to the surface;however, because the average lifetime of a muon isonly 2.197 ∗ 10−6 seconds, a muon should decay aftertraveling at most 658.638 meters. Although this eventseems contradictory, because the muon should decaybefore it reaches the surface, it can in fact be explainedby time dilation. Time dilation shows that whentraveling near the speed of light, an observer sees thatthe muon actually decays slower than if it was stationary.

c = speed of light = 2.97 ∗ 108m/sv = speed of muon = .99999c

t = decay time of muon = 2.197 ∗ 10−6st′ = relativistic muon decay time = t√

1− v2

c2

t′ = 4.192 ∗ 10−4s

After calculating the time dilation one finds that an av-erage muon decays in approximately 4.912 ∗ 10−4 sec-onds from the perspective of an Earth observer; thus,the muon can actually travel 1.474 ∗ 104 meters beforedecaying. This allows for the muon to be detected onthe surface of the earth.

3. HOW DO COSMIC RAYS BEHAVE?

Since cosmic rays are usually charged particles, theyare affected by the Lorentz force. The Lorentz force,written

F = q(E + v ×B)

dictates a single particle’s behavior in relation to electricand magnetic fields, where F is force on the particle,q is its charge, v is its velocity, E is the electric field,and B is the magnetic field. For the moment, we ignorethe electric field component and focus on the behaviorof a particle only in a magnetic field; the equation thensimplifies to F = qv × B. We can then use Newton’ssecond law, F = ma to calculate the acceleration of theparticle; summing this acceleration over time gives us theparticle’s velocity and trajectory.

The Earth has a magnetic field, so we can use thisequation to see how much of the cosmic rays get de-flected due to Earth’s magnetosphere. We need to makea number of assumption in order to simplify the calcula-tions: we assume that the Earth’s magnetic field is ho-mogeneous and perpendicular to the direction of the cos-mic ray’s travel, and that there are no other forces thanthe Lorentz force acting upon the cosmic ray. For thesecalculations, we used a proton (the most common “cos-mic ray”) with an energy of 300 MeV and assumed thatEarth’s magnetic field is a homogenous 6.0 ∗ 10−5 Tesla(0.6 Gauss). This is a very generous assumption: thevalue of the magnetic field comes from an average of val-ues on the Earth’s surface; since field drops off as thecube of distance, the field in outer space is much, muchsmaller.

FIG. 3: A particle flies into the magnetospehere and feels aforce

We start with the Lorentz force equation:

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FIG. 4: The orbit of a deflected, trapped particle, and theright hand rule/cross product that leads to it.

FLorentz = qv ×B

Since the Lorentz force is always perpendicular to thevelocity of the particle, it will lead to circular motion:constant acceleration perpendicular to the velocity leadsto a circular orbit. Therefore, we set it equal to the cen-tripetal force required to bend the particle into a circularorbit:

Fcentripetal = v2tangential

r|Fcentripetal| = |FLorentz|mv2

tangential

r = q(vBsin(θ))vtangential = v

r = v2mqvB = vm

qB

We can find the proton’s velocity, given its kinetic en-ergy:

v =

√c2(

1− m0c2

KE +m0c2

)(1)

(relativistic effects apply to protons above 50MeV or so).We then plug our values in to find the radius of the orbit(and deflection) that the proton would take in Earth’smagnetic field. The number turns out to be large, 25, 674meters. If the proton traveled toward the Earth fromouter space, it would experience an extremely small fielduntil it came into close proximity. This bending radiusindicates that if the proton experienced a homogenous .6Gauss field, it would turn around in a 25km radius. Sincethe field is decidedly not homogenous, it would likely turnin much greater than 25km and would not be deflected.

Protons are quite heavy, and when in cosmic rays, aretravelling quite fast. Suprisingly, the Earth’s magne-tosphere blocks nearly none of the cosmic proton flux;the protons are simply traveling too fast and the Earth’smagnetic field is too low. A generalized form of the equa-tions above were plotted; they show that in order for aproton to be deflected just by the Earth’s magnetic field,it would need to be traveling extremely slowly and havea near thermal speed.

0

10000

20000

30000

40000

50000

60000

1e-

006

0.0

001

0.0

1 1

100

100

00

1e+

006

1e+

008

1e+

010

Ben

ding

rad

ius

(m)

Proton energy (ev)

Deflection radius as a function of energy

r(x)

FIG. 5: Bending radius at high energies

0 0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8

1e-

006

1e-

005

0.0

001

0.0

01

0.0

1

0.1 1

Ben

ding

rad

ius

(m)

Proton energy (ev)

Deflection radius as a function of energy

r(x)

FIG. 6: Bending radius at low energies

4. HOW DO WE DETECT COSMIC RAYS?

Since cosmic rays are made up of extremely small par-ticles nearly traveling at light speed, it is impossible todetect these particles by the naked eye. Moreover, thetraditional methods of observing sub-atomic particles,such as electrode microscopes, are totally useless becauseof the intense speed of the particles. Generally, althoughsome particles that result from cosmic showers react withthe surrounding environment, such interactions are dif-ficult to trace; thus, they pass through most matter un-detected and without any visible changes or alterationsto the subsequent matter. Hence in order to observe andanalyze these particles one must be able to observe theinteractions between the particle and matter. There arevarious methods to observe such interactions; however,for one to view these interactions certain conditions mustbe met, such as the ability of the device to display ion-ization caused by the particles. Scientists have developedmany devices that display these interactions which gener-ally alter a certain type of matter so that the interactions(seen as tracks or trails in the matter) can be observed.Such devices include the cloud chamber, bubble chamber,wire chamber, spark chamber, and drift chamber.

The most simplistic of these chambers is the cloudchamber, which detects fundamental particles and parti-cles of ionizing radiation. However, its overall function issimilar to the other chambers. In short, the cloud cham-ber is filled with super cooled water or alcohol vapor.

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FIG. 7: A simple cloud chamber

FIG. 8: Muon tracks in a cloud chamber

Because the mixture inside the chamber is at the thresh-old of condensation a fine mist can be seen throughoutthe chamber. Particles are detected in this mist becausetheir charges ionize the mist with which it comes intocontact. Thus, the mist enables for an observation of theparticles path.

Much analysis can be done based on the shape, speed,and size of the formed ion trails. For example, a trailthat seems to fork into two trails depicts the decay ofone particle into two. Likewise, one can also observe hownegatively charged particles curve in opposite directionsupon encountering a magnetic or electric field.

We observed particle tracks ourselves at the Caltechcloud chamber; while the chamber needed maintenance(notably, it had puddles of condensation at the bottom),the tracks were clearly visible. We saw alpha particles,muons as a result of cosmic showers, and electrons. A Vshaped trail can be particle decay, annihilation, or parti-cle creation by the fusion of matter and antimatter. Themajority of trails observed in a cloud chamber are skinnywhite lines. These trails can be created from a varietyof charged particles such as positrons. Spiral trails arecreated by low energy Beta particles such as electrons or

muons. Specifically, electron trails are more exaggeratedand random, compared to muon trails. Since an elec-trons mass is relatively small compared to atomic nuclei,electrons are bounced around by the various nuclei inthe alcohol vapor. Larger particles, like muons, containa much greater mass thus remain virtually undisturbedupon contact with the nuclei

5. CONCLUSION

We now know that cosmic rays are 90% protons, andthat they are easily detected on the Earth’s surface. Weknow what sort of particles arise from cosmic ray showers(mostly muons and electrons), and we know how thesehighly energetic, charged particles behave in a magneticfield (and how they are sometimes trapped by the Earth’sown magnetic field).

Cosmic rays are all around us, shooting through ourbodies even now as we are writing this. Careful study ofcosmic rays have a number of useful applications—cosmicray astronomy and spectroscopy can discover the secretsof the universe. This introduction to cosmic rays is justthe tip of the iceberg.

6. ACKNOWLEDGEMENTS

We would like to thank to Juan Pedro Ochoa, our ad-visor, as well as the physics teaching staff for teaching usthe necessary concepts to understand this material. Wewould also like to thank the YESS program.

7. BIBLIOGRAPHY

Bernlohr, Konrad. 1999 January 1. Cosmic-ray airshowers. <http://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html>. Accessed 2008 July 09.

Haxton, Wick. 2007 September 1. Cosmic Rays.<http://www.int.washington.edu/PHYS554/2005/chapter8−07.pdf>. Accessed 2008 July 09.

Nave, C.R. 2005 January 1. HyperPhysics.<http://hyperphysics.phy-astr.gsu.edu/>. Accessed2008 July 10.

Particle Data Group. 2000 January 1. The ParticleAdventure. <http://www.particleadventure.org>. Ac-cessed 2008 July 06.