Electromagnetic Fields in Particle Accelerators

8/6/2019 Electromagnetic Fields in Particle Accelerators

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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


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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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

Electromagnetic Fields in Particle Accelerators

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