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Cyclotron

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A modern Cyclotron for radiation therapy

In technology, a cyclotron is a type of  particle accelerator . In physics, cyclotron

frequency is the frequency of a charged particle moving perpendicularly to the directionof a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction.

Since that motion is always circular, the cyclotron frequency is well defined.[1][2]

Cyclotrons accelerate charged particles using a high-frequency, alternating voltage ( potential difference). A perpendicular magnetic field causes the particles to spiral almost

in a circle so that they re-encounter the accelerating voltage many times.

The first cyclotron was manufactured by Ernest Lawrence, of the University of California, Berkeley who started operating it in 1932,[1] though others had been workingalong similar lines at the time.[citation needed ] The first European cyclotron was founded in

Leningrad in the physics department of the Radium Institute (Head Vitali Khlopin). In

1932 George Gamow and Lev Mysovskii presented a draft for consideration by the

Scientific Council of the Radium Institute, and the approval of it, under the guidance anddirect participation of the Igor Kurchatov and Lev Mysovskii cyclotron was installed and

running by 1937 [3][4].

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TRIUMF, Canada's national laboratory for nuclear and particle physics, houses the

worlds largest cyclotron. The 18m diameter, 4000 tonne main magnet produces a field of 

0.46 T while a 23 MHz 94 kV electric field is used to accelerate the 200 μA beam.TRIUMF is run by a consortium of fifteen Canadian universities and is located at the

University of British Columbia, Vancouver, Canada.

Contents

[hide]

• 1 How the cyclotron works

• 2 Uses of the cyclotron

• 3 Problems solved by the cyclotron

• 4 Advantages of the cyclotron

• 5 Limitations of the cyclotron

• 6 Mathematics of the cyclotron

o 6.1 Non-relativistico 6.2 Relativistic

• 7 Related technologies

• 8 See also• 9 References

• 10 External links

[edit] How the cyclotron works

Diagram of cyclotron operation from Lawrence's 1934 patent.

Beam of electrons moving in a circle. Lighting is caused by excitation of gas atoms in a

 bulb.

The electrodes shown at the right would be in the vacuum chamber , which is flat, in anarrow gap between the two poles of a large magnet.

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In the cyclotron, a high-frequency alternating voltage applied across the "D" electrodes

(also called "dees") alternately attracts and repels charged particles. The particles,

injected near the center of the magnetic field, accelerate only when passing through thegap between the electrodes. The perpendicular magnetic field (passing vertically through

the "D" electrodes), combined with the increasing energy of the particles forces the

 particles to travel in a spiral path.

With no change in energy the charged particles in a magnetic field will follow a circular  path. In the cyclotron, energy is applied to the particles as they cross the gap between the

dees and so they are accelerated (at the typical sub-relativistic speeds used) and will

increase in mass as they approach the speed of light. Either of these effects (increasedvelocity or increased mass) will increase the radius of the circle and so the path will be a

spiral.

(The particles move in a spiral, because a current of electrons or ions, flowing

 perpendicular to a magnetic field, experiences a perpendicular  force. The charged

 particles move freely in a vacuum, so the particles follow a spiral path.)

The radius will increase until the particles hit a target at the perimeter of the vacuum

chamber. Various materials may be used for the target, and the collisions will create

secondary particles which may be guided outside of the cyclotron and into instrumentsfor analysis. The results will enable the calculation of various properties, such as the

mean spacing between atoms and the creation of various collision products. Subsequent

chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target.

[edit] Uses of the cyclotron

For several decades, cyclotrons were the best source of high-energy beams for nuclear 

 physics experiments; several cyclotrons are still in use for this type of research.

Cyclotrons can be used to treat cancer . Ion beams from cyclotrons can be used, as in

 proton therapy, to penetrate the body and kill tumors by radiation damage, while

minimizing damage to healthy tissue along their path.

Cyclotron beams can be used to bombard other atoms to produce short-lived  positron-emitting isotopes suitable for PET imaging.

[edit] Problems solved by the cyclotron

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60-inch cyclotron, circa 1939, showing a beam of accelerated ions (likely protons or 

deuterons) escaping the accelerator and ionizing the surrounding air causing a blue glow.

The cyclotron was an improvement over the linear accelerators that were available when

it was invented. A linear accelerator (also called a linac) accelerates particles in a straightline through an evacuated tube (or series of such tubes placed end to end). A set of 

electrodes shaped like flat donuts are arranged inside the length of the tube(s). These are

driven by high-power radio waves that continuously switch between positive andnegative voltage, causing particles traveling along the center of the tube to accelerate. In

the 1920s, it was not possible to get high frequency radio waves at high power, so either 

the accelerating electrodes had to be far apart to accommodate the low frequency or more

stages were required to compensate for the low power at each stage. Either way, higher-energy particles required longer accelerators than scientists could afford.

Modern linacs use high power Klystrons and other devices able to impart much more

 power at higher frequencies. But before these devices existed, cyclotrons were cheaper than linacs.

Cyclotrons accelerate particles in a spiral path. Therefore, a compact accelerator can

contain much more distance than a linear accelerator, with more opportunities to

accelerate the particles.

[edit] Advantages of the cyclotron

• Cyclotrons have a single electrical driver, which saves both money and power,

since more expense may be allocated to increasing efficiency.

• Cyclotrons produce a continuous stream of particles at the target, so the average power is relatively high.

• The compactness of the device reduces other costs, such as its foundations,

radiation shielding, and the enclosing building.

[edit] Limitations of the cyclotron

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The magnet portion of a 27" cyclotron. The gray object is the upper pole piece, routing

the magnetic field in two loops through a similar part below. The white canisters heldconductive coils to generate the magnetic field. The D electrodes are contained in a

vacuum chamber that was inserted in the central field gap.

The spiral  path of the cyclotron beam can only "sync up" with klystron-type (constant

frequency) voltage sources if the accelerated particles are approximately obeying Newton's Laws of Motion. If the particles become fast enough that relativistic effects

 become important, the beam gets out of phase with the oscillating electric field, and

cannot receive any additional acceleration. The cyclotron is therefore only capable of accelerating particles up to a few percent of the speed of light. To accommodate

increased mass the magnetic field may be modified by appropriately shaping the pole

 pieces as in the isochronous cyclotrons, operating in a pulsed mode and changing thefrequency applied to the dees as in the synchrocyclotrons, either of which is limited by

the diminishing cost effectiveness of making larger machines. Cost limitations have beenovercome by employing the more complex synchrotron or  linear accelerator , both of 

which have the advantage of scalability, offering more power within an improved coststructure as the machines are made larger.

[edit] Mathematics of the cyclotron

[edit] Non-relativistic

The centripetal force is provided by the transverse magnetic field B, and the force on a

 particle travelling in a magnetic field (which causes it to be angularly displaced, i.e.

spiral) is equal to Bqv. So,

(Where m is the mass of the particle, q is its charge, B the magnetic field strength, v is its

velocity and r is the radius of its path.)

The speed at which the particles enter the cyclotron due to a potential difference, V.

Therefore,

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v/r is equal to angular velocity, ω, so

And since the angular frequency is

ω = 2π f  

Therefore,

The frequency of the driving voltage is simply the inverse of this frequency so that the

 particle crosses between the dees at the same point in the voltage cycle.

A pair of "dee" electrodes with loops of coolant pipes on their surface at the Lawrence

Hall of Science. The particle exit point may be seen at the top of the upper dee, where thetarget would be positioned

This shows that for a particle of constant mass, the frequency does not depend upon the

radius of the particle's orbit. As the beam spirals out, its frequency does not decrease, and

it must continue to accelerate, as it is travelling more distance in the same time. As particles approach the speed of light, they acquire additional mass, requiring

modifications to the frequency, or the magnetic field during the acceleration. This is

accomplished in the synchrocyclotron.

[edit] Relativistic

The radius of curvature for a particle moving relativistically in a static magnetic field is

wherethe Lorentz factor  

 Note that in high-energy experiments energy, E, and momentum, p, are used rather than

velocity, and both measured in units of energy. In that case one should use the

substitution,

where this is in Natural units 

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The relativistic cyclotron frequency is

,

where

 f c is the classical frequency, given above, of a charged particle with velocity

v circling in a magnetic field.

The rest mass of an electron is 511 keV/c2, so the frequency correction is 1% for a

magnetic vacuum tube with a 5.11 keV/c2 direct current accelerating voltage. The protonmass is nearly two thousand times the electron mass, so the 1% correction energy is about

9 MeV, which is sufficient to induce nuclear reactions.

An alternative to the synchrocyclotron is the isochronous cyclotron, which has a

magnetic field that increases with radius, rather than with time. The de-focusing effect of this radial field gradient is compensated by ridges on the magnet faces which vary the

field azimuthally as well. This allows particles to be accelerated continuously, on every

 period of the radio frequency (RF), rather than in bursts as in most other accelerator types. This principle that alternating field gradients have a net focusing effect is called

strong focusing. It was obscurely known theoretically long before it was put into practice.

[edit] Related technologies

• The spiraling of electrons in a cylindrical vacuum chamber within a transversemagnetic field is also employed in the magnetron, a device for producing high

frequency radio waves (microwaves).

•

The Synchrotron moves the particles through a path of constant radius, allowing itto be made as a pipe and so of much larger radius than is practical with thecyclotron and synchrocyclotron. The larger radius allows the use of numerous

magnets, each of which imparts angular momentum and so allows particles of 

higher velocity (mass) to be kept within the bounds of the evacuated pipe. Themagnetic field strength of each of the bending magnets is increased as the

 particles gain energy in order to keep the bending angle constant.

[edit] See also

• Beamline

• Cyclotron radiation• Synchrotron light

• Bremsstrahlung radiation

• Electron cyclotron resonance

• Gyrotron

• Ion cyclotron resonance

• Linear accelerator 

• Particle accelerator 

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• Storage ring

• Synchrocyclotron

• Synchrotron

• TRIUMF - largest cyclotron in the world

• Radiation reaction

[edit] References

1. ^ a b Physics by M. Alonso & E. Finn, Addison Wesley 1996.2. ^ http://www.wolframalpha.com/input/?i=cyclotron+frequency 

3. ^ Radium Institute named Vitaly Khlopin 

4. ^ Radium Institute named Vitaly Khlopin. Chronology 

[edit] External links

•

Advanced Cyclotron Systems Inc Commercial manufacturer of high outputmedical cycltorons.

• TRIUMF -- The University of British Columbia, Vancouver, Canada & NationalResearch Council of Canada\Conseil national de recherches Canada

• U.S. Patent 1,948,384 -- Method and apparatus for the acceleration of ions 

• Indiana University Cyclotron Facility MPRI treats first patient using roboticgantry system.

• "The 88-Inch Cyclotron at LBNL"

• "The NSCL at Michigan State University" Home of coupled K500 and K1200

cyclotrons; the K500, being the first superconducting cyclotron and the K1200currently the most powerful in the world.

•

Rutgers Cyclotron and "Building a Cyclotron on a Shoestring" Tim Koeth, now agraduate student at Rutgers University, built a 12-inch 1 MeV cyclotron as anundergraduate project, which is now used for a senior-level undergraduate and a

graduate lab course.

• "Resonance Spectral Analysis with a Homebuilt Cyclotron" an experiment done by Fred M. Niell, III his senior year of high school (1994–95) with which he won

the overall grand prize in the ISEF.

• Relativistic accelerator physics PDF

• Wired news article about a neighborhood cyclotron in Anchorage, Alaska 

• web site of company IBA

• The Cyclotron Kids A pair of high school students building their own 2.3 MeV

cyclotron for experimentation.