Cyclotron: Difference between revisions

Latest revision as of 00:15, 6 December 2015

Created by Raymond Han(rhan36)

First invented and created in 1932 by inventor Ernest O. Lawrence, the cyclotron was considered to be an invention that would produce images of charged particles accelerating outwards from the center to form about a spiral path. The cyclotron was also known to be one of the earliest types of particle accelerators before the introduction of the synchrotron. Although the cyclotron may have been outdated with the introduction of new ideas and inventions, it was still used to produce particle beams in physics. The functionality of the cyclotron is best described as moving charges and bending these moving particles into a semicircular path that come from a magnetic force. We begin to understand the importance of the cyclotron when we define what magnetic force means on a moving charge. The magnetic force provides the centripetal force, any motion in a curved path that represents an accelerated motion, and requires force directed toward the center of the path, to bend the moving charge into a circle of radius (X). Since we have begun to have a better understanding of the importance of the cyclotron, Lawrence has allowed us calculate the frequency of the acceleration of moving charges.

The Main Idea

The idea that a magnetic field perpendicular to the plane of motion will create a particle along a curved path was the first notion for the creation of the cyclotron. Lawrence wanted to measure the acceleration that the particle will have about a curved path and the relation that an increase in radius of a path will have on the velocity/acceleration of the moving charge. Using two hollowed sheet metals, otherwise known as 'dees', the cyclotron accelerates a beam of charges onto them. The 'dees' applies a static magnetic field, B, as the beam is applied to them. Doing so, the magnetic field is bent about the circular shape of the 'dees' in accordance to the Lorentz force.

basic diagram of a Cyclotron with 'dees'

A Mathematical Model

The centripetal force is simplified by the transverse magnetic field B. The cyclotron can only accelerate to speeds slower than the speed of light. Thus, for non relativistic particles, the centripetal force to keep them aligned on the curved path is: [math]\displaystyle{ \frac{mv^2}{r} = Bqv }[/math]

The speed at which the particles enter the cyclotron due to a potential difference, V, is: [math]\displaystyle{ v = \sqrt{\frac{2Vq}{m}} }[/math]

Since v/r is equal to angular velocity, w, so [math]\displaystyle{ \omega = \frac{Bq}{m} }[/math]

Angular frequency is [math]\displaystyle{ \omega = {2\pi} f_c }[/math]

This all equals the speed at which the particles enter initially : [math]\displaystyle{ f_c = \frac{Bq}{2\pi m} }[/math]

This is all to say that the particle of constant mass does not depend upon the radius of the orbit. Deriving the equations for angular frequency to see the speed at which the particles enter, the particles require additional mass and requires change in frequency or magnetic field to derive the acceleration.

Applications of cyclotron

Cancer

For several decades, cyclotrons have seen the most usage in the broad topic of nuclear physics. Nuclear physics involves investigation of the building blocks and interactions of atomic nuclei.Primarily, cyclotrons are efficient in treating cancer since we can focus on particles that are cancerous within the body. This is also known as particle therapy where the ion beams can use protons to penetrate the body and kill any tumors. More and more, cyclotrons are being incorporated into hospitals to combat cancer because of this particle therapy. Claimed to be more effective than radiotherapy and with less side effects, particle therapy has increasingly combated early stages of cancer. The reason this is used to combat cancer is because the treatment can precisely target where in the body the energy is deposited. Being able to pin point a desired spot can at times destroy both healthy and cancerous cells in a specific area. However, the ability to kill cancer with radiation damage has allowed to produce short-lived-emitting isotopes for PET imaging. PET( Positron emission tomography) is a technique that produces a 3-D image of the body. With the system detecting gamma rays emitted by a tracer, the computer can construct images of the body and display images of active molecules in the body.

Connectedness

How is this topic connected to something that you are interested in?

This is relevant to my major and the reason why engineers are needed in this world. Understanding how much the cyclotron requires to be operated and how much more it can be improved upon is something engineers should be focused on. Engineers are needed to design, analyze, and produce new products/ideas for the society to be more efficient.

How is it connected to your major?

As a Mechanical engineer, our goal is to design and produce more efficient and sustainable ideas for the future. Working with ideas and products that are always being replaced by new inventions such as the synchotron, mechanical engineers need to process desired needs that are realistic under constraints such as environment, social, and personal health. Solving problems and being able to interpret data from the cyclotron involving cancerous tumors will solve many engineering problems for BME, Biology, and chemistry majors. Also, it links to my major because using my knowledge and engineering these products to be more modern and applicable is something I should always be practicing no matter what it is.

History

Ion Beam Therapy about to be used at the Hospital in Heidelberg, Germany

The idea was first published and developed by Lawrence and Livingston at UC Berkeley. Using the design, Lawrence's first accelerator was built in 1931 and was able to accelerate beam of hydrogen ions. After a year, Lawrence was able to advance the energy to almost 2 times as strong. Thus, with this change the cyclotron became the most effective and preferred choice across the world for many years. This was until the synchotron was introduced and was more efficient.

References

http://www.accelerators-for-society.org/about-accelerators/index.php?id=21#cyclotron

http://www.newworldencyclopedia.org/entry/Cyclotron

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/cyclot.html

I placed this under "Real life applications of Electromagnetic Principles". However, while I was working on this assignment, another student was trying to edit my wiki page. Thus, I am sending proof and evidence that I was editing and claimed it first.

@@ Line 1: / Line 1: @@
-Work of Adway Dhillon (adhillon6)
+Created by Raymond Han(rhan36)
-Short Description of Topic
+First invented and created in 1932 by inventor Ernest O. Lawrence, the cyclotron was considered to be an invention that would produce images of charged particles accelerating outwards from the center to form about a spiral path. The cyclotron was also known to be one of the earliest types of particle accelerators before the introduction of the synchrotron. Although the cyclotron may have been outdated with the introduction of new ideas and inventions, it was still used to produce particle beams in physics. The functionality of the cyclotron is best described as moving charges and bending these moving particles into a semicircular path that come from a magnetic force. We begin to understand the importance of the cyclotron when we define what magnetic force means on a moving charge. The magnetic force provides the centripetal force, any motion in a curved path that represents an accelerated motion, and requires force directed toward the center of the path, to bend the moving charge into a circle of radius (X). Since we have begun to have a better understanding of the importance of the cyclotron, Lawrence has allowed us calculate the frequency of the acceleration of moving charges.
+[[File:Lawrence1.jpg|thumb|400px]]
 ==The Main Idea==
-This page is about an apparatus called the Cyclotron. This device is used to accelerate charged particles (like protons, neutrons, alpha particles, etc.) and ions to high energies. It uses a combination of strong magnetic and electric fields to accelerate the charged particles. The two fields (electric and magnetic) are perpendicular to each other, hence very aptly name "crossed fields". When the charged particle is accelerated by the cyclotron, the frequency of tis revolution in the two semi-secular plates (also called the "Ds") is independent of its energy. This is an important fact in the working of the device, as we will subsequently study in this lesson.
+The idea that a magnetic field perpendicular to the plane of motion will create a particle along a curved path was the first notion for the creation of the cyclotron. Lawrence wanted to measure the acceleration that the particle will have about a curved path and the relation that an increase in radius of a path will have on the velocity/acceleration of the moving charge. Using two hollowed sheet metals, otherwise known as 'dees', the cyclotron accelerates a beam of charges onto them. The 'dees' applies a static magnetic field, B, as the beam is applied to them. Doing so, the magnetic field is bent about the circular shape of the 'dees' in accordance to the Lorentz force.
+[[File:cyclotron1.png|thumb|285px|basic diagram of a Cyclotron with 'dees'|alt=cyclotron1.png]]
-PRINCIPLE:<br>
-The working of the cyclotron is based on the fact that a positively charged particle can be accelerated to a sufficiently high energy with the help of smaller values of oscillating electric field by making it cross the same electric field time and again, with the help of a stringer magnetic field.
-CONSTRUCTION:<br>
-A cyclotron device consists of two D-shaped hollow evacuated metal chambers (say D1 and D2) called the dees. These dees are placed horizontally with their diametric edges parallel and slightly separated from each other. The dees are connected to a high frequency oscillator which can produce a potential difference of the order of 10^4 volts at a frequency of about 10^7 hertz. The two dees are enclosed in an evacuated steel box and are well insulated from it. The box is placed inn a string magnetic field produced by two pole pieces of an electromagnets N,S. The magnetic field is perpendicular to the plane of the dees. At the centre of the device, P is a place of ionic source or positively charged (Check the diagram).
-WORKING AND THEORY:<br>
-The positive ion to be accelerated is produced at P. Suppose, at that instant D1 is at negative potential and D2 is at positive potential. Therefore, the ion will be accelerated towards D1. On reaching inside D1, the ion will be in a field free space (as the two dees are hollow and metallic). Hence it moves with a constant speed in D1, say v. But due to a perpendicular magnetic field of strength B, the ion will describe a circular path of radius r (say) in D1.
-Now in case the time taken by the positive ion to describe a semicircular path is equal to the time during which half cycle of the electric oscillator is completed, then as the ion arrives in the gap between the two dees, the polarity of the two dees is reversed, i.e. D1 becomes positive and D2 becomes negative. Then, the positive ion is accelerated towards D2 and it enters D2 with a greater speed, which remains constant in D2. The ion will describe a semicircular path of greater radius due to a perpendicular magnetic field and again will arrive in the gap between the two dees exactly at the instant, the polarity of the two dees is reversed. Thus, the positive ion will go on accelerating every time it comes into the gap between the dees and will go on describing a circular path of greater and greater radius with greater and greater speed and finally acquires a sufficiently high energy. The accelerated ops can be removed out of the dees from the window W, by applying at the elected field across the deflecting plates E and F (check the diagram).
 ===A Mathematical Model===
-The charged particle describes a circular path of radius r (say) in D1, due to the perpendicular magnetic field B. Hence, the magnetic force experienced by the particle is balanced by the centripetal force on the particle due to its circular motion (in a circle of radius r). <br>This gives us the following expression:<br>
+The centripetal force is simplified by the transverse magnetic field B. The cyclotron can only accelerate to speeds slower than the speed of light. Thus, for non relativistic particles, the centripetal force to keep them aligned on the curved path is:
-<math>Bqv = mv^2/r</math>
+<math>\frac{mv^2}{r} = Bqv</math>
-Here: m and q are the mass and the charge of the ion respectively. <br>
+The speed at which the particles enter the cyclotron due to a potential difference, V, is:
+<math>v = \sqrt{\frac{2Vq}{m}}</math>
-Therefore:      <math>r = mv/Bq</math>
+Since v/r is equal to angular velocity, w, so
+<math>\omega = \frac{Bq}{m}</math>
-MAXIMUM ENERGY OF POSITIVE ION:<br>
+Angular frequency is
-Let <math>v_0, r_o</math> = maximum velocity and maximum radius of the circular path followed by the positive ion in the cyclotron.
+<math>\omega = {2\pi} f_c </math>
-Then: <math>mv_0^2/r_0 = Bqv_0    or    v_0 = Bqr_0/m</math>
+This all equals the speed at which the particles enter initially :
+<math>f_c = \frac{Bq}{2\pi m}</math>
-Therefore: <math>Max K.E. = 1/2 mv_0^2 = 1/2 m(Bqr_0/m)^2 = B^2q^2r_0^2/2m</math>
+This is all to say that the particle of constant mass does not depend upon the radius of the orbit. Deriving the equations for angular frequency to see the speed at which the particles enter, the particles require additional mass and requires change in frequency or magnetic field to derive the acceleration.
+==Applications of cyclotron==
+===Cancer===
-CYCLOTRON FREQUENCY:<br>
+For several decades, cyclotrons have seen the most usage in the broad topic of nuclear physics. Nuclear physics involves investigation of the building blocks and interactions of atomic nuclei.Primarily, cyclotrons are efficient in treating cancer since we can focus on particles that are cancerous within the body. This is also known as particle therapy where the ion beams can use protons to penetrate the body and kill any tumors. More and more, cyclotrons are being incorporated into hospitals to combat cancer because of this particle therapy.
-If T is the time period of oscillating electric field then:
+Claimed to be more effective than radiotherapy and with less side effects, particle therapy has increasingly combated early stages of cancer. The reason this is used to combat cancer is because the treatment can precisely target where in the body the energy is deposited. Being able to pin point a desired spot can at times destroy both healthy and cancerous cells in a specific area. However, the ability to kill cancer with radiation damage has allowed to produce short-lived-emitting isotopes for PET imaging. PET( Positron emission tomography) is a technique that produces a 3-D image of the body. With the system detecting gamma rays emitted by a tracer, the computer can construct images of the body and display images of active molecules in the body.
-<math>T = 2t = 2pim/Bq</math>
-The cyclotron frequency is given by
+[[File:particle_therapy1.jpg|200px|thumb|Particle Therapy is a specific example that displays the usage of the cyclotron in our society|alt=particle_therapy1.jpg]]
-What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
-===A Computational Model===
-Go to the following link to have a look at the picture: http://i64.tinypic.com/mil0sz.jpg
-==Examples==
-The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider, and its functioning is based on the same principle as a simple cyclotron. It is the largest, most complex experimental facility ever built, and the largest single machine in the world. It was built by the European Organization for Nuclear Research (CERN). The LHC's aim is to allow physicists to test the predictions of different theories of particle physics, high-energy physics and in particular, to further test the properties of the Higgs Boson.
 ==Connectedness==
 #How is this topic connected to something that you are interested in?
-I have been closely monitoring and following the developments at the Large Hadron Collider at CERN. The device's functioning and the underlying principle it works on got me interested in this field. This led me to study more on cyclotrons and particle accelerators.
+This is relevant to my major and the reason why engineers are needed in this world. Understanding how much the cyclotron requires to be operated and how much more it can be improved upon is something engineers should be focused on. Engineers are needed to design, analyze, and produce new products/ideas for the society to be more efficient.
 #How is it connected to your major?
-As a Computer Engineering major there are many connections with electromagnetics in my major. Specifically there will be many connections with the hardware and software components of any railgun which is what I am specifically interested in.
+As a Mechanical engineer, our goal is to design and produce more efficient and sustainable ideas for the future. Working with ideas and products that are always being replaced by new inventions such as the synchotron, mechanical engineers need to process desired needs that are realistic under constraints such as environment, social, and personal health. Solving problems and being able to interpret data from the cyclotron involving cancerous tumors will solve many engineering problems for BME, Biology, and chemistry majors. Also, it links to my major because using my knowledge and engineering these products to be more modern and applicable is something I should always be practicing no matter what it is.
-#Is there an interesting industrial application?
 ==History==
+[[File:PR-ParticleTherapy.jpg|250px|thumb|Ion Beam Therapy about to be used at the Hospital in Heidelberg, Germany|alt=PR-ParticleTherapy.jpg]]
-The cyclotron was first developed by Lawrence and Livingston at the University of California, Berkeley. Lawrence, having worked extensively on electromagnets before, was behind much of the theoretical work. On the other hand, Livingstone was responsible for translating that to a tangible device. When the device was created, it was the strongest particle accelerator of its kind. This was true till another accelerator was constructed in Leningrad, at the Radium Institute.
+The idea was first published and developed by Lawrence and Livingston at UC Berkeley. Using the design, Lawrence's first accelerator was built in 1931 and was able to accelerate beam of hydrogen ions. After a year, Lawrence was able to advance the energy to almost 2 times as strong. Thus, with this change the cyclotron became the most effective and preferred choice across the world for many years. This was until the synchotron was introduced and was more efficient.
-== See also ==
-Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?
-===Further reading===
-Books, Articles or other print media on this topic
-===External links===
-[http://www.wsj.com/articles/physicists-restart-souped-up-hadron-collider-1437948498/]
-[http://www.theguardian.com/science/cern/]
-[http://www.express.co.uk/news/world/565315/Scientists-at-Large-Hadron-Collider-hope-to-make-contact-with-PARALLEL-UNIVERSE-in-days/\
 ==References==
-Baldwin, Paul. "Scientists at Large Hadron Collider Hope to Make Contact with PARALLEL UNIVERSE in Days." N.p., n.d. Web. 05 Dec. 2015.
+http://www.accelerators-for-society.org/about-accelerators/index.php?id=21#cyclotron
-"Latest Experiment at Large Hadron Collider Reports First Results." MIT News. N.p., n.d. Web. 05 Dec. 2015.
+http://www.newworldencyclopedia.org/entry/Cyclotron
-"Large Hadron Collider Starts Doing Science Again." Scientific American. N.p., n.d. Web. 05 Dec. 2015.
+http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/cyclot.html
 [[Category:Which Category did you place this in?]]
+I placed this under "Real life applications of Electromagnetic Principles". However, while I was working on this assignment, another student was trying to edit my wiki page. Thus, I am sending proof and evidence that I was editing and claimed it first.