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Electromagnetic Fields in Particle Accelerators
Kevin Mattalo
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Table of ContentsElectromagnetism
y Definitions of Basic Electricity and Magnetism Conceptsy Electric Fieldsy The Relationship Between Electric and Magnetic Fieldsy Maxwells Equations
Electromagnetic Fields in Particle Accelerators
y What is a Particle Accelerator?y The Function of Electromagnetic Fields in Particle Accelerators
i) Types of Acceleratorsii) Particle Accelerationiii) Particle direction and containment
y How the use of Electromagnetic Fields in Particle Acceleratorshas Affected Society and theEnvironment
y Potential Technological Advancements
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Electromagnetism
Definitions of Basic Electricity and Magnetism Concepts
This chart quickly overviews basic electrical and magnetic concepts that are used in defining electric
fields, magnetic fields and electromagnetic fields.
Concept Unit of Measurement Definition
Electric current (ampere) The amount of charge passing apoint in a circuit per second
Electric charge (Coulomb) A physical property of objects
that causes it to interact with the
electric field
Field lines None The shape of the electric fieldwhen in the presence of an
electric charge
Electric field (Newtons per Coulomb) The magnitude of force
generated by an electric charge
Magnetic field (Gauss) The magnitude of a magnetic
fieldper
Electric Fields
In 600 B.C.E, along the coast ofGreece in Miletus, there existed a mathematician and
philosopher by the name ofThales. As Thales rested in his study he polished an orb of amber in his hand
with a clean piece of fur. Once it was unblemished he would place it next to his parchment hoping it
would stay clean for some time. To his surprise, the amber orb quickly became dirty and no matter how
muchhe polished it or moved its location it would always become blackened. Thales was amused and
decided to analyze the amber more closely. After rubbing it again with clean fur Thales again placed the
amber next to his parchment and something became immediately apparent. Thales saw that the Amber
was not becoming dirty from the environment but rather the amber itself was attracting dust towards it.
What Thales uncovered was what we now know as the electrostatic force.Thales was a peculiarity ofhis
time; he respected nature and found great solace in logic and analyzing the physical world without
resorting to myth
ological explanations. It is th
is temperament and state of mind th
at ledTh
ales touncover a hidden truth about nature and begin the development of science itself. From Thales to today,
our perspective on electric fieldshas changed considerably. From what was just an oddity is now
understood to be a fundamental property of the world around us leading to profound implications.
Electric fields exist all around us from the light in your eyes to your ability to stand on the
surface of the Earth without falling through. They are an integral part of why we exist in a society that is
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technologically advanced and evolving. To explain the idea ofelectric fields, Ill introduce the idea of a
point charge.
A point charge is a particle that is indivisible, has no dimensions but has a non-zero electric
charge; this is directly related to the commonly known particle the electron.
Point Charge with a non-zero electric field Two point charges distorting an electric field
surrounding it
Th
e essential idea beh
ind th
e electric fieldis th
at it is an invisible medium th
at permeatesthrough space and time and it communicates electric force to other objects. It exists everywhere, and
through everything, even in the vacuum of space and within the densest regions of the Earth. The
electric fieldonly becomes noticeable when in the presence ofelectrically chargedparticles. Take for
instance now the space you are in, around you everything is neutrally charged as it is natural for all
things to become so but the electric fieldstill exists. Now if we imagine this electric field as an
undisturbed region almost like a regular Cartesian grid then the presence of a point charge distorts the
electric field around it warping it in such a way that the charged objects nearby feel thisforce and
interact with it via itsfield lines(directions of the electric field).
Non-interacting electric field electric fieldin the presence of a point
charge charge (displaying field lines)
It is apparent now what Thales was observing withhis amber and fur. His fur electrically
chargedthe amber causing it to therefore disturb the electric field. This change in the electric fieldwas
felt by the dirt and they were consequently attracted. This is only one aspect of the electric fieldsince
charged objects can either bepositivelyor negatively charged. To further address this point Ill introduce
an equation describing the electric force between twopoint charges.
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From this equation describing the force between the twopoint charges we can derive why two
positive or negative point charges repel and why a negative and positive point charge attracts each
other. If we firstly state that when the electric force calculated is negative they attract, and when it is
positive they repel then the interactions can be easily shown in this chart:
Value of Value of Value of Interaction Type+ + + Repulsion- - +(two negatives give a
positive)
Repulsion
+ - - Attraction
A positive charge interacting with an electric field A negative charge interacting with an electric field
The Relationship between Electric and Magnetic Fields
During 1800s the development of Physics was progressing at a rapid rate and many ideas were
converging into more complete explanations. In particular the notions ofelectric and magnetic fields
were seen to be intricately related but no ph
ysical description sufficed th
is relationsh
ip. One of th
epeculiarities observed in this relationship was that moving electric fields produced magnetic fields and
moving magnetic fields produced electric fields. An example of this can be observed if one brings a
compass atop a mountain during a lightning storm. The needle within the compass aligns itself
accordingly to magnetic north at the base of the mountain but when you reach the top, the needle
becomes disoriented and spins frantically. This occurs because the electric currentflowing through the
clouds at high altitudes produces magnetic fields that coil around the electric currentthus interacting
with the needle and repositioning it.
The following diagram displays a current
flowing through a conductor (the blue rod) in
an upwards direction. The red arrows coiling
around the conductor display that a
movement of charge i.e. a current, produces
a magnetic field This is the samephenomenon experienced by the needle. A
current (the lightning bolt) produces a
magnetic field that interacts with the iron
needle in the compass.
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This chart expands upon the similarities between magnetic and electricfields:
Characteristics Magnetic Fields Electric Fields
Field Lines Yes Yes
Negative and Positive Charges Yes Yes
Force is proportional to
Yes Yes
Produce Magnetic Fields In
Motion
No Yes
Produce Electric Fields In Motion Yes No
Upon further analysis, James Clerk Maxwell, a Scottish-born physicist, was the person that
would unite electric and magnetic fields into the electromagnetic field. His set of four equations with
contributions from Gauss, Faraday and Ampere describe precisely how electromagnetism works and
provide the key link to show how electromagnetism was always in our sighti.e. light itself is an
electromagnetic wave. Light is the combination of two components namely electric and magnetic waves
which are perpendicular to each other and thus produce the electromagnetic spectrum. It was this
realization that affirmed the duality between electricity and magnetism and allowed for major
technological developments including electrical motors, telecommunications, computer networking, and
efficient energy transformations in power plants by electrical generators.
Electrical motor Telecommunications Computing and energy transformations
is the electric fieldcomponent and is themagnetic field
component of the
electromagnetic wave
(light)
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Maxwells Equations
These equations thoroughly describe the relationship between electricity and magnetism:
Equation 1:
The equation states that the electric charge of an object is proportional to its electric field.
Equation 2:
The equation states that if one has a magnet which can only be dipolar, then the net magnetic field
flowing through it is 0 since positive magnetism flows inwards and negative magnetism flows outwards.
Equation 3:
The equation states that if you have a closedelectric currentflowing, then it is proportional to the
negative rate of change with respect to time of the magnetic fieldthrough the area enclosed by the
circuit. Thus when a magnetic fieldchanges it produces an electric current.
Equation 4:
xx The equation states that the magnetic field around an electrical circuitis proportional to the electric
currentflowing through the circuit. This is clearly demonstrated by observing how a speaker works.
Within a speaker there is a magnet within a coiled electric current. This electric currentis an alternating
currentand therefore changes the direction of the magnetic field produced from forward to backwards.
There is a proportionality between these fields and thus allows the magnet to vibrate and produce
sound waves
An alternatingelectric
currentflows through the
voice coil generating a
changing magnetic field
which moves the magnets
and vibrates the speaker
cone generating sound
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Electromagnetic Fields in Particle Accelerators
What is a Particle Accelerator?
Imagine the vastness of the universe in space, how fragile the Earth is as it rests gently in the
blackness like a moat of dust. This characteristic of emptiness and also expansiveness is not a quality of
the Earth but even of the MilkyWay galaxy, an island of stars, one of billions. Now as we move to the
other end of the spectrum, imagine the deepness of the things around you, the atoms and molecules
that compose the paper you are reading and the brain that is percieving these words, everything is one
and the same at this level, this the quantum universe. The world we live in and percieve is only one
aspect of natures intricacy, all of the objects that we manipulate and conjure are only a figment in the
grandness of the universe itself. In this quantum universe there exist what are commonly called
particles. Similar to the explanation of thepoint charge in the previous chapter, aparticle is a point-like
object withhas numerous properties including electric charge and mass. At the level of theparticles,
physicists can peek at the fundamental nature of nature and the most common approach to do so is by
usingparticle accelerators.
Particle accelerators are devices used by scientists to accelerate charged particles by using
electromagnetic fields. These accelerated particles form a beam and are brought incredibly close to the
speed of light. Eventually they collide with another beam ofparticles within a detectorthus producing a
lot of energy which in turn become newparticles by use of Einsteins mass-energy equivalence:
The creation of new particles allows us to better understand the constituents of matter and how
the unvierse forms at the macroscopic level. Although much of this research appears very esoteric ithas
had a tremendous effect on society. The first commercially used product that relied considerably on the
use ofa particle acceleratorwas the Cathode Ray Tube television. This television used an electron
acceleratorto give them enough energy so when they were fired at the screen they produced flashes of
light, or the images you percieve. This is the essential idea of aparticle accelerator, the physics and
societal implications will be discussed thoroughly in the next few chapters.
This is an example of a
particle collision event at the
Relativistic Heavy Ion Collider
(RHIC) at Brookhaven
National Laboratories. Each
line seen in this photo is a
particle created from the
energy of multiple collisions
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The Function of Electromagnetic Fields in Particle Accelerators
Electromagnetic fields carry out two primary functions in the workings of aparticle accelerator.
The first of these functions is to accelerate theparticles, and the second is to contain and direct the
particles for collision in a detector. The particularparticleacceleratorbeing discussed here is the Large
Hadron Collider(LHC) at the European Organization for Nuclear Research(CERN).
Types of Accelerators
Here is a short chart listing and describing the various forms ofaccelerators used at CERN:
Accelerator Description
Linear Accelerator Accelerates particles in a straight line
Synchrotron Accelerator Accelerates particles in a circle
This is a diagram of a linear accelerator This is a diagram of a sychnrotron accelerator
Particle Acceleration
In order to describe howparticles accelerate in the LHC we must introduce a very basic idea.
This idea is known as the Lorentz force law; it states that a charged particle in the presence of an
external electric or magnetic field will experience a force. This force is described by the following
equation:
Here is a traditional
Cathode Ray Tube
television. As you can see
an accelerator on the left
fires electrons which are
deflected by a magnetic
fieldtowards th
e screen
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According to Newton, if a force is being applied on an object then it accelerates at a constant
rate, thus we infer that particles can accelerate in the presence of external magnetic or electric fields.
Well now examine the process of accelerating a proton from its rest state to collision state inside of the
LHC. Notice that the size of each accelerator increases along the protons journey; this is because as
something travels closer to the speed of light it gains kinetic energy and mass according to Einsteins
mass-energy equivalence. Since the protons contain more mass, more energy is required to accelerate
(Newtons force law) them, hence the larger accelerators.
Step 1: Linear Acceleration LINAC2:
The protons journey begins inside of a compressed tank filled with research grade molecular
hydrogen. The gas is guided to a vacuum chamber at the entrance of the LINAC2linear accelerator
where it is broken down into individual atoms and ionized by stripping the electrons from the protons
throughelectric currents. These electric currents increase the energy of the electrons so much that they
cannot maintain a stable bound state around the nucleus and ultimately become free electrons.What is
left is an ionized nucleus and in the case ofhydrogen, a proton. A proton is apositivelychargedparticleand can therefore, according to Lorentzs force law, experience acceleration from an external magnetic
or electric field.
This diagram illustrates the
Lorentz force lawor how
magnetic and electric fieldscan apply forces on charged
particles
Hydrogen
atom is
ionized by
electricity
Molecular
hydrogen
What remains
is a positively
charged
proton
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The LINAC2 accelerates the protons by use ofelectromagnetic waves.The LINAC2 contains
resonance cavities which pulse microwave radiation towards the protons, these protons interact with
the electric fieldin the electromagnetic wave and are pushed forward. The force produced by the
electric fieldin the microwave radiation accelerates the protons forward and as they approach the end
of the LINAC2 they have a velocity of 0.314( is the speed of light in a vacuum).
Step 2, 3, and 4: Proton Synchrotron Booster (PSB)/Proton Synchrotron (PS)/LHC:
The protons now enter the Proton Synchrotron Booster; the acceleration experienced by the
particles at this stage is of the same form throughout the rest of the accelerator complex and thus Ill
explain it in one section. The particles within the PSB accelerate in a circular formation with the aid of a
resonant electromagnetic pulse. Each time the proton beam rotates, a microwave is emitted thus
transferring energy to the protons. The energy in the microwave increases through each rotation since
more force is necessary to accelerate th
e protons.Th
is is analogous to someone being push
ed on aswing. There exists a resonant frequency in which you push the person to maximize the transfer of
energy which is what the resonant electromagnetic pulse does. This process occurs in the PSstage and in
the LHCstage. Once LHCacceleration has finished the total velocity of theproton beams are
approximately 0.999999.
Resonance cavities
in the linear
accelerator
The largest ring is the LHCand along
the circle there are 100s of
electromagnets which emit
electromagnetic microwaves that
accelerate the protons
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Particle Direction and Containment
Throughout this entire process the protons gain an incredible amount of energy and velocity
and it is quite difficult to contain and direct the flow of protons through the collider complex. The LHC
makes use of a novel development in magnetism which is used continually from the LINAC2 accelerator
to the LHC.This development is known as superconductivityand it is achieved when superconductingmagnets, in this case they are niobium-titanium magnets, are cooled to a critical temperature with liquid
helium. At this temperature the superconducting magnet has zero electrical resistance and can
efficiently control the beams of particles.
There are two purposes for the magnets at the LHC that is to direct the beams and focus them.
The superconducting magnets that bend the beams create magnetic field lines that are inside of the
acceleratorby virtue of an electrical currentflowing through the magnets. The magnetic field lines curve
in a circular direction to contain them inside of the synchrotron accelerator. In the linear accelerator the
superconducting magnets generate a magnetic fieldin a straight line allowing the protons to maintain a
linear acceleration. The protons interact with this magnetic field because as stated in Maxwells
Equations: moving electric charges produce magnetic fields and vice versa. Thus, the magnetic field
generated by the moving beam of protons interacts with the superconducting magnets and they follow
the path of the accelerator.
Another property of the superconducting magnets is to focus the proton beams by squashing
them together. This is achieved by a method known as Quadruple Magnetic Quenching. Two pairs of
opposite polarity superconducting magnets focus around the pathway of the proton beams and each
time they pass the magnets they are forced together by the magnetic fieldthat focuses on a small point.
Since theproton charges interact with the focused magnetic fieldthey are subsequently focused. This
focusing process contains the protons inside of the accelerator and also maximizes the rate of proton
collisions by increasing the concentration of particles in a given area.
The bottom magnet is a superconductor
and it traps the top magnet into a
magnetic suspension
The red regions are areas ofhigh intensity
magnetic fields. Along this curve, charged
particles interact with the magnetic fieldand
bend around the curve
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How the use of Electromagnetic Fields in Particle Acceleratorshas Affected Society and the
Environment
Electromagnetic Fieldshave made significant contributions to the state of society and the environment
in the last century particularly in the development of telecommunications, transportation infrastructure
and medical particle therapies.
Telecommunications
The introduction of telecommunications in the late 20th century has significantly changed the
way humans interact and the progression of society in general. By researching how to accelerate particle
beams efficiently by use of radio/micro electromagnetic radiation we have been able to develop the cell
phone which processes audio signals into digital signals (micro/radio waves) and decrease the delay in
human communication. The computer is also the product ofelectromagnetic research inparticle
accelerators and is used for communication and networking. Because of this the society we live in has
developed into a fast-paced network that relies greatly on the expense of social media and advertising.
The environment has been affected from these developments due to the rapid expansion of
world-economies. The growth of these economies is particularly accredited to the introduction of
telecommunications. This novelty has allowed for businesses to become more productive due to faster
communication and tasking. This has lead to the construction of large private sectors that are the
foundation of a countrys wealth. Because of this increase in wealth, particularly in eastern countries,
we are using more energy on average to function and maintain infrastructure. It is immediately obvious
that this need for energy results in a higher demand for fossil fuels and subsequently the release of fossil
fuels into the environment. Statistically, geologists have found massive explosions in fossil fuel output
and inflations in CO2 percentage in the atmosphere in correlation with the development of
telecommunications.
This diagram describes the quenching affect
generated by bar magnets. The effect is the exact
same with the use ofsuperconducting magnets
including the set up of the magnets. Thus the beams
of protons are focused into a dense region due to the
tight magnetic field.
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The graph on the left shows the amount of atmospheric CO2 and the one on the right shows the growth of one of the
most prominent forms of telecommunication the personal computer.
Transportation Infrastructure
The last century was notable for the global-expansion of automobiles and commercial aircrafts.
These inventions persist in our lives and are integral components ofhow our species lives and in
particular how our societies function. Beyond the benefits of economic productivity due to faster and
more efficient travel, society itself is currently being assailed by the progression of global climate
change.
Due to this, societies search for more efficient and socially comfortable forms of transportation
are being researched and are in development phases. The research on electromagnetic fields atparticle
acceleratorshas been at the forefront of developing said technologies and in particular, the application
ofsuperconductors in transportation. The MagLev trains make use ofsuperconductivityas a means of
providing fast and efficient transportation but they are still being tested and modified. The potential of
the MagLev trains to reduce societies dependence on fossil fuels and the affect they have on the
environment is promising. The MagLev is a high-speed (501 km/h), high-capacity and aerodynamic train
that is extraordinarily efficient primarily due to the use of the magnetic superconductors that CERN has
researched considerably. This researchhas lead to the discovery ofhigh-temperaturesuperconductors
that can work without extreme cooling. Since each MagLev has a high-capacity it reduces the amount of
vehicles operating and decreases the amount of domestic flights. With respect to society, this reduces
our dependence on fossil fuels and ensures longevity and grounds for futurehuman development in the
case that we run out of fossil fuels.
The chart displays that the
global centigrade has
increased by about 1 degree
since 1980 which is a
significant amount for a short
period.
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Medical Particle Therapies and Medical Imaging
Our society in general is subjected to various changes in the environment that varies
substantially from previous generations. Because of this humans in the last few decades have become
susceptible to disease and in particular cancer. Oncology researchhas broadened because of this and
recently, answers to create a harmless and potent cancer treatment therapy have developed. The
solution to this problem was discovered unconventionally in research that is done at experiments likethe LHC. What was considered and is now in practical application is the use of proton therapies to target
tumors without damaging unaffected tissue. This contains numerous benefits for society in particular
the extension of life expectancy and the further understanding of cancer itself. Approximately one-third
ofhumans will be diagnosed with a form of cancer and it the odds of surviving decrease dramatically
depending on the stage you are in. Therefore the development of Medical Imaging (i.e. MRIs), which rely
heavily on the principles ofelectromagnetism, can lead to earlier detection and the creation of a
healthier society. Recently, every major medical center in the world has begun using accelerators
producing x-rays, protons, neutrons or heavy ions for the diagnosis and treatment of disease. It is
estimated that there are over 7,000 operating medical linear accelerators around the world that have
treated over 30,000,000 patients. These developments in medicinehave not only been used for
treatment but for th
e understanding of th
e diseases th
emselves.Th
ish
as lead to major advancements indisease control and elimination thus reducing the potential for species loss and the preservation of the
environment.
The interaction among these magnetic
fields allow the MagLev to be suspended
thus decreasing friction and increasing
efficiency
The green bar is the CO2
emissions per seat on a MagLev
train. It is very efficient
compared to a car and airplane
but travels faster than both.
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PotentialTechnological Advancements
Humanity itselfhas created a necessity to develop a more efficient and renewable energy
system that satisfies the demands of growing global-economies. Our use of fossil fuels is growing
steadily every decade and the expansion of infrastructure to third-world countries is also increasing the
usage of non-renewable energy as a means to run a society. Numerous alternatives are being applied in
todays society including wind energy, bio-fuels, solar energy and fission. Each of these, although they
are renewable are very inefficient andhavent been able to meet the energy needs of the global
population. Fission also suffers from various other faults including the volatility of fissile materials in
natural disasters and the limited supply of fissile materials themselves. Recently, research atparticle
accelerators and the study of electromagnetic fields as a way of accelerating and controlling particle
beams has opened new potential in fusion energy. Fusion is the process of combining two light atomic
nuclei (i.e. hydrogen isotopes: deuterium and tritium) to form a heavier element (helium) and resultant
energy. The fusion event efficiently generates energy and relies on the availability of deuterium and
tritium which are two of the most abundant resources on Earth. The primary fault in fusion energy is
meeting a net output of energy, currently the energy needed to create fusion is less than the energy
outputted by it.
Future innovations in fusion energy by research being conducted in electromagnetic fields in
particle accelerators include the global effort to develop a fully functioning and useful fusion reactor.
The current project in development and noted for completion by 2019 is the International
Thermonuclear Experimental Reactor or ITER. ITER is a Tokomak designed fusion reactor that is
The diagram displays X-
ray therapy on the left
and proton therapy on
the right. Notice that the
proton therapy is
significantly more
concentrated on the
tumor where as the X-
rays disperse and harm
unaffected tissue
This diagram shows a
deuterium (2H) and tritium
(3H) atom fusing to form
Helium (4He) and a free
neutron (n) which is
absorbed by an outer
ceramic plate inside of the
fusion reactor and
converted to energy
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expected to generate 5000% energy return from the energy that was inputted. The ITER Tokomak design
needs to have an efficient system to develop magnetic confinement of the plasma (ionized gas) as this is
a critical component to attain fusion. For this reason there has been frequent correspondence between
ITER and CERN including application of the LHCs use ofsuperconducting magnets to confine the plasma.
This has been a falling point from previous Tokomak fusion reactors i.e. they couldnt efficiently
confine to plasma to ach
ieve maximum energy output.Th
e magnets confine th
e plasma th
rough
a veryinteresting process. Surrounding the Tokomak, which is shaped like a donut or a torus, are super-cooled
superconducting magnets. An electric current flows through the superconductors with zero resistance
and generates a magnetic fieldthat around the outside of the Tokomak. An electric currentis produced
inside of the torus like jelly through the insides of a hole-centered donut.
This technology as stated is directly attributed to the major advancements ofsuperconductor
applications in society and the research conducted atparticle accelerators like the LHC. The growth in
global demand for energy is inevitable and the only reasonable solution lies in the power of fusion. It is
th
rough
our understanding of concepts in electromagnetism andh
ow to confine plasmas th
at willbenefit society in its search for a reliable and efficient energy source for the future.
This diagram shows how the
Tokomak design creates magnetic
confinement. Magnetic fields
move around th
eT
okomak andan electric currentis produced
confining the plasma. The result is
a plasma current that is contained
and can safely each 150,000,000
degrees celsius
Here is a picture of
confined plasma fusing
inside of a Tokomak