Cyclotron

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 Although the cyclotron may have been outdated with the introduction of new ideas and inventions, it was still used to produce particle beams in physics.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.

Particle Therapy is a specific example that displays the usage of the cyclotron in our society

Connectedness

1. 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.

1. 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.