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A machine that accelerates charged particles or ions to higher energies is called a Cyclotron. The cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.
- As the electric and magnetic fields are perpendicular to each other, they are called crossed fields.
- A magnetic field keeps these particles on a spiral path, and a strong electric field accelerates them.
- Both magnetic and electric fields play equal roles in increasing the energy of charged particles.
- A cyclotron accelerates charged particles along a spiral path outwards from the center of a flat cylindrical vacuum chamber.
- A static magnetic field and a rapidly varying electric field hold the particles to a spiral trajectory.
- A Cyclotron in nuclear physics experiments is used to accelerate charged particles to bombard atomic nuclei.
- Cyclotrons are also used for radiation therapy for the treatment of cancer.
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Keywords: Cyclotron, energy, oscillator, force, velocity, frequency, Accelerator, static magnetic field, alternating electric field, energy
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Definition of Cyclotron
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A cyclotron is a type of particle accelerator, used to accelerate charged particles or ions to high energy along a spiral path under the actions of a static magnetic field and alternating electric field.
- It was invented by an American physicist, Ernest O Lawrence in 1929- 1930 and patented in 1932. Lawrence received the Nobel Prize in Physics in 1939 for his invention.
- The cyclotron was the first "cyclical" accelerator. Before the invention of cyclotron, the primary accelerators were electrostatic accelerators, such as the Van de Graaff generator and Cockcroft–Walton accelerator.
- A linear accelerator, also called linacs is also a type of particle accelerator. The basic difference between a linear accelerator and a cyclotron is that the linear accelerator accelerates particles in a straight line, while a cyclotron accelerates particles along an outward spiral path.
- Cyclotron uses the fact that the frequency of revolution of a charged particle in a magnetic field is independent of its energy and speed.
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Working Principle of Cyclotron
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- Cyclotron works under the principle that charged particles moving normally to magnetic fields experience Lorentz force due to which the particle moves in a circular path.
- The charged particle move most of the time inside two semicircular disc-like metal containers called dees as they look like the letter D. These dees are put face to face with a little gap between them.
- Inside the dees, the charged particle is shielded and is not acted on by the electric field. However, the magnetic field acts on the particle and makes it go around in a circular path inside a dee.
- Every time the particle moves from one particle to another it is acted upon by the electric field.
- The sign of the electric field is changed alternately in tune with the circular motion of the particle to ensure that the particle is always accelerated by the electric field.
- Each time the charged particle enters the gap, the electric field increases the energy of the particle.
- As energy increases, the radius of the circular path increases. So the path of the charged particle is spiral.
- The whole assembly is evacuated to minimize the collision between ions and the air molecules. A high-frequency alternating voltage between the dees.
Diagram of Cyclotron
Time Period of Cyclotron
When the charged particle is released at the center, they move in a semicircular path in one of the dees and arrive in the gap between the dees in a time interval T/2; Where T is the period of revolution, and is given by
\(T={2\pi m \over qB}\)
Where,
- m is the mass of the charged particle
- q is the magnitude of the charge of the particle
- B is the magnitude of the magnetic field
Frequency of Cyclotron
Cyclotron frequency, also known as magnetic resonance frequency is the frequency with which a charged particle oscillates in between the dees of the cyclotron. It is equal to the frequency of a high-frequency oscillator connected across the dees of the cyclotron. The expression for cyclotron frequency is given by
\(f={1\over T} =\frac{qB}{2 \pi m}\)
Cyclotron Energy
The magnetic force acting on the charged particle moving with velocity v at a right angle to the magnetic field B is given by
\(F=qvBsin90=qvB\)
The magnetic force provides the charged particle necessary Centripetal Force to move in a circular path of radius r. Therefore,
\(qvB={mv^2\over r }\Rightarrow v ={qBr\over m}\)
Energy gained by the charged particle in a cyclotron is given by
\(E = {1 \over2} mv^2\)
On Substituting the value v on the above equation, we get
\(E = {1 \over2} m ({qBr\over m})^2\)
Therefore the output energy of the particle is given by the following expression
\(E=\frac{q^2B^2r^2}{2m}\)
Read More: Derivation of Lorentz transformation
Types of Cyclotron
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The various types of cyclotrons are:
- Classical cyclotron: These are the earliest and simplest cyclotron that have uniform magnetic fields and a constant accelerating frequency. The output energy of this type of cyclotron is small compared to the particle's rest energy.
- Synchrocyclotron: In a synchrocyclotron, the driving RF electric field is varied to compensate for relativistic effects as the particle's velocity approaches the speed of light. Lawrence 184-inch Cyclotron is the first Synchrocyclotron.
- Isochronous cyclotron: In isochronous cyclotrons, the magnetic field is adjusted to compensate for the particle's relativistic speed change as the cyclotron frequency changes.
- Separated sector cyclotron: Separated sector cyclotrons have magnets in separate sections separated by gaps without fields.
- Superconducting cyclotron: A cyclotron uses a superconducting magnet to bend particle orbits into spirals.
Some other examples of cyclotrons are TRIUMF cyclotron, Gentrace Cyclotron, Tabletop Cyclotron, Rutgers Cyclotron, PSI cyclotron etc.
Uses of Cyclotron
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- Research purpose: Cyclotrons are the best source of high-energy beams and are still used to create beams for research where the primary consideration is not achieving the maximum possible energy for research purposes for nuclear physics experiments.
- Medicinal value and therapeutic value: Production of short-lived isotopes has several medical uses that include PET scans, CT scans, and other diagnostic and therapeutic purposes. The facility is also the site for research into the development of new compounds – called radiopharmaceuticals that help to improve the detection, diagnosis, and treatment of diseases such as Alzheimer’s, Parkinson’s, and multiple sclerosis.
Particle therapy that involves the usage of beams from cyclotrons is used to treat cancer.
Limitations of Cyclotron
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The following are the limitations of a cyclotron:
- Cyclotron cannot accelerate uncharged particles like neutron.
- Cyclotron cannot accelerate electrons because they have small mass. Electron moving at a very high speed when they gain small energy in the cyclotron. Oscillating electric field makes them to go quickly out of the phase because of their very high speed.
Things to Remember
- A cyclotron is used to accelerate charged particles or ions to high energy.
- The first-ever cyclotron was invented by Earnest O Lawrence at the University of California which had a diameter of 69 cm and produced a maximum of 4.8 MeV.
- TRIUMF is the largest cyclotron constructed with a diameter of 18 m and maximum energy of 520 MeV.
- A cyclotron is an accelerator that produces radioactive isotopes that have therapeutic and medicinal values.
- In 1950 the cyclotron was superseded by the synchrotron which is another type of particle accelerator that uses magnets to bend particles into a circular trajectory. The particle path in a synchrotron has a fixed radius, unlike a cyclotron.
- Particle therapy uses ion beams emitted from cyclotrons that are used to penetrate the body and kill tumors by radiation damage.
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Sample Questions
Ques. When the frequency of the radiofrequency of the field is doubled, what effect does it have on the radius of a charged particle in a cyclotron? (5 Marks)
Ans. Under the influence of a magnetic field, a charge in a cyclotron will move in a circular path.
If the time to complete one orbit of radius R is T, T= 2 π R/v…………………(1)
Where v is the linear speed of charge q.
If the charge q is moving in a magnetic field B, and speed v then,
q X B X v= \( \frac{mv^2}{r}\)……………………(2)
On simplification of equation 2 we get, \( \frac{r}{v}\)= \( \frac{m}{qB}\)……………………..(3)
From equation 1 and 3 we get, T=\( \frac{2\pi m}{qB}\) ……………………..(4)
Hence the period is independent of radius. If the varying voltage is applied at an angular frequency of qB/ m between the dees, the charge will spiral outward by increasing its speed and a corresponding increase in orbit radius R so the ratio R/v is constant.
If the frequency has doubled the charge will be accelerated at alternate cycles with no change in orbit radius.
Ques. A cyclotron's oscillating frequency is 10 MHz. For accelerating protons, what should the operating magnetic field be? What is the kinetic energy of the proton produced by the accelerator if the radius of the dees is 60 cm?( e= 1.60 X 10 -16 C , mp =1.67 X 10 -27kg, 1 Mev= 1.6 X10 -13 J ) (3 Marks)
Ans. The oscillator frequency should be the same as the proton cyclotron frequency.
We know that, B = 2 mv/ q
=6.3X 1.67 X 10 -27 X 10 7 / ( 1.6 X 10 -19 )
= 0.66 T.
Final velocity of protons is v = r X 2 v
=0.6 m X 6.3 X 10 7 =3. 78 X 10 7 m / s.
E= 1/2 mv 2
=1.67 X 10 -27 X 14.3 X 10 14/ ( 2 X 1.6 X 10 -13 )
= 7 MeV.
Ques. A cyclotron has an applied voltage of 20-kilo volt. After 50 cycles the proton stops rotating. Find out the energy of the particle? (3 Marks)
Ans. In a cyclotron, a proton is accelerated twice in each cycle.
Gain in kinetic energy k per cycle = 2 q V
Where q is the charge on proton V is the potential difference.
Gain in kinetic energy per cycle = 2 X 1.602 X 10 -19 X 20000= 6.4 X 10 -15 J
= 6.4 X 50 X 10 -15 J
= 3.2 X 10 -13 J
Ques. Who and when was the cyclotron invented? What are its limitations? (3 Marks)
Ans. The cyclotron was invented by Earnest O Lawrence in 1930 and patented in 1932.
The limitations of cyclotron are as follows:
- Neutral particles (e.g. neutrons) fail to interact with electric or magnetic fields. As a result, they cannot be accelerated by cyclotrons.
- Electrons have a very small mass so their speed increases very rapidly and soon the resonance between the high voltage and the particle becomes lost.
- Cyclotrons can accelerate particles to speeds much less than the speed of light but cannot accelerate electrons.
Ques. What is the major advantage of synchrocyclotron over cyclotron? (3 Marks)
Ans. Synchrocyclotrons are cyclic machines that have a much lower time-averaged output flux. The kinetic energy of 1 GeV can be achieved. The fundamental benefit is that in a synchrocyclotron, the rf frequency may be changed to keep particle synchronization in the reasonable range.Cyclotrons were a major hit until they became superseded in 1950.
Ques. A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns carrying a current of 5 A. What is the magnitude of the magnetic field inside the solenoid? (3 Marks)
Ans. The number of turns per unit length is,
n= \(\frac{500}{0.5}\) = 1000 turns/m.
The length= 0.5m , radius is 0.01m. Thus l/a = 50 i.e, l>a . hence we use the long solenoid formula
B=μ?In
= 4πX 10 -7X 10 3 X 5 =6.28 X 10 -3 T
Ques. Consider a 1A current flowing through a tightly wound 100 turn coil with a radius of 10 cm. What is the strength of the magnetic field at the coil's centre? (3 marks)
Ans. We can assume that each circular element has the same radius R = 10 cm= 0.1m as the coil is tightly wrapped.
The number of turns N =100, the magnitude of the magnetic field is
B = \(\frac{\mu_o ln}{2R}\)
= \(\frac{4\pi \times 10^7 \times 10^2 \times 1}{2 \times 10^{-1}}\)
= 2 X 10 -4
= 6.28 X 10 -4 T.
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