Cyclotron: Difference between revisions

Revision as of 23:48, 5 December 2015

Work of Adway Dhillon (adhillon6)

Short Description of Topic

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.

PRINCIPLE:
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:
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:
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).
This gives us the following expression:
[math]\displaystyle{ Bqv = mv^2/r }[/math]

Here: m and q are the mass and the charge of the ion respectively.

Therefore: [math]\displaystyle{ r = mv/Bq }[/math]

MAXIMUM ENERGY OF POSITIVE ION:
Let [math]\displaystyle{ v_0, r_o }[/math] = maximum velocity and maximum radius of the circular path followed by the positive ion in the cyclotron.

Then: [math]\displaystyle{ mv_0^2/r_0 = Bqv_0 or v_0 = Bqr_0/m }[/math]

Therefore: [math]\displaystyle{ Max K.E. = 1/2 mv_0^2 = 1/2 m(Bqr_0/m)^2 = B^2q^2r_0^2/2m }[/math]

CYCLOTRON FREQUENCY:
If T is the time period of oscillating electric field then: [math]\displaystyle{ T = 2t = 2pim/Bq }[/math]

The cyclotron frequency is given by

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\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.

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.

Is there an interesting industrial application?

History

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.

"Latest Experiment at Large Hadron Collider Reports First Results." MIT News. N.p., n.d. Web. 05 Dec. 2015.

"Large Hadron Collider Starts Doing Science Again." Scientific American. N.p., n.d. Web. 05 Dec. 2015.

@@ Line 1: / Line 1: @@
-Created by Raymond Han(rhan36)
+Work of Adway Dhillon (adhillon6)
-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.
+Short Description of Topic
-[[File:Lawrence1.jpg|thumb|400px]]
 ==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.
+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.
-[[File:cyclotron1.png|thumb|285px|basic diagram of a Cyclotron with 'dees']]
+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 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:
+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>
-<math>\frac{mv^2}{r} = Bqv</math>
+<math>Bqv = mv^2/r</math>
+Here: m and q are the mass and the charge of the ion respectively. <br>
+Therefore:      <math>r = mv/Bq</math>
+MAXIMUM ENERGY OF POSITIVE ION:<br>
+Let <math>v_0, r_o</math> = maximum velocity and maximum radius of the circular path followed by the positive ion in the cyclotron.
-The speed at which the particles enter the cyclotron due to a potential difference, V, is:
+Then: <math>mv_0^2/r_0 = Bqv_0    or    v_0 = Bqr_0/m</math>
-<math>v = \sqrt{\frac{2Vq}{m}}</math>
-Since v/r is equal to angular velocity, w, so
+Therefore: <math>Max K.E. = 1/2 mv_0^2 = 1/2 m(Bqr_0/m)^2 = B^2q^2r_0^2/2m</math>
-<math>\omega = \frac{Bq}{m}</math>
-Angular frequency is
-<math>\omega = {2\pi} f_c </math>
-This all equals the speed at which the particles enter initially :
-<math>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.
+CYCLOTRON FREQUENCY:<br>
+If T is the time period of oscillating electric field then:
+<math>T = 2t = 2pim/Bq</math>
-==Applications of cyclotron==
+The cyclotron frequency is given by
-===Cancer===
-For several decades, cyclotrons have seen the most usage in the broad topic of nuclear physics. 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.
+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.
-[[File:particle_therapy1.jpg|200px|thumb|proton beam therapy combats brain tumor]]
+===A Computational Model===
-===NASA===
+Go to the following link to have a look at the picture: http://i64.tinypic.com/mil0sz.jpg
-In order to find safer and less expensive means of space travel NASA has proposed the idea of launching payloads in to orbit using a two mile long railgun.  The process would prove much safer for astronauts by taking out the highly explosive rocket fuel currently used to propel them into orbit, and for the same reason it would be a faction of the cost since the energy required would be significantly less.  Another bonus is the flexibility that would be allowed.  As opposed to current rockets which could never be launched on consecutive days, a railgun would allow another launch as soon as there was enough potential in the batteries.
+==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?
-Like most Tech students I am interested in all of the newest technologies and their variety of applications.  Both the implications on the military side and space travel side are fascinating and could easily influence our lives and certainly the lives of future generations.
+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.
 #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 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.
 #Is there an interesting industrial application?
-The idea of commercial space travel could be greatly helped out by the advent of a railgun which would launch customers in to orbit for much cheaper than is now imaginable.
 ==History==
-[[File:USS Zumwalt (DDG-1000) at night.jpg|250px|thumb|USS Zumwalt (DDG-1000) at night, future versions could feature railguns|alt=USS Zumwalt (DDG-1000) at night.jpg]]
-The physics behind a railgun and the Lorentz Force has been known many years since Oliver Heaviside discovered in it 1889, five years before Hendrik Lorentz derived it.  In 1919 frenchman Louis Octave Fauchon-Villeplee filed the first U.S. Patent for a rail gun type device calling it an "Electric Apparatus for Propelling Projectiles." However only in recent decades has it been a practical option for much of anything due to the large amounts of potential and current it requires to produce a meaningful force.  The United States Navy for example started heavily researching the capabilities of the railgun due to their new Zumwalt-class Destroyer which can produce 78 megawatts of power when it only needs 20 megawatts to operate, leaving 58 for the requirements of the railgun.
+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.
+== 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==
-http://www.onr.navy.mil/media-center/fact-sheets/electromagnetic-railgun.aspx
+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.popsci.com/technology/article/2010-11/nasa-engineers-propose-combining-rail-gun-and-scramjet-fire-spacecraft-orbit
+"Latest Experiment at Large Hadron Collider Reports First Results." MIT News. N.p., n.d. Web. 05 Dec. 2015.
-http://www.popsci.com/article/technology/navy-wants-fire-its-ridiculously-strong-railgun-ocean
+"Large Hadron Collider Starts Doing Science Again." Scientific American. N.p., n.d. Web. 05 Dec. 2015.
-http://www.google.com/patents/US1421435?dq=Fauchon-Villeplee
 [[Category:Which Category did you place this in?]]

Cyclotron: Difference between revisions

Revision as of 23:48, 5 December 2015

Contents

The Main Idea

A Mathematical Model

A Computational Model

Examples

Connectedness

History

See also

Further reading

External links

References

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