Principle and Working of Cyclotron

Summary

The Cyclotron, invented by E.O. Lawrence and M.S. Livingstone in 1934, is a device that accelerates charged particles using an oscillating electric field within a magnetic field. This technology enables the production of high-energy particles for nuclear reactions. The device consists of two half-cylinder 'dees' connected to an alternating voltage source, creating an electric field that propels particles in a circular path, increasing their velocity with each orbit. As the particles gain energy, their radius expands until they are ejected through a window, ready for high-energy collisions with a target.

Takeaways

• ⚛️ Cyclotron is a device developed by E.O. Lawrence and M.S. Livingstone in 1934 to accelerate charged particles like protons and deuterons.
• 🔋 The device accelerates particles using an oscillating electric field, allowing them to cross the same field repeatedly with the aid of a strong magnetic field.
• 🌀 Two hollow half cylinders called dees, made of high conductive metals, are placed face-to-face with a small gap and connected to an alternating voltage source.
• ⚡ An electric field is created between the dees by oscillating polarity, with D1 being positive when D2 is negative, and vice versa.
• 🧲 Electromagnets are placed above and below the dees to create a perpendicular magnetic field to the direction of the electric field.
• 🚀 A positively charged particle is accelerated by the electric field, gaining speed until it enters a dee where the electric field is zero but the magnetic field guides it in a circular path.
• 🔄 The particle moves in a circular path with a radius determined by r=mv/qB, making semi-circles and being accelerated each time it exits a dee and encounters the electric field again.
• 📈 With each oscillation and acceleration, the velocity of the charged particle increases, causing it to move in larger circular paths within the dees.
• 🌌 The process continues until the particle reaches a high enough velocity and energy, at which point it is ejected through a window to hit a target.
• 🎯 The cyclotron is used in nuclear physics for bombarding nuclei with high-energy particles, resulting in nuclear reactions.

Q & A

What is a cyclotron?

A cyclotron is a device used to accelerate charged particles, such as protons and deuterons, to high energies using an oscillating electric field and a strong magnetic field.

Who developed the cyclotron and when?

The cyclotron was developed by E.O. Lawrence and M.S. Livingstone in 1934.

What are the primary components of a cyclotron?

The primary components of a cyclotron include two hollow half cylinders called dees, an alternating voltage source (oscillator), and electromagnets placed above and below the dees.

How do the dees in a cyclotron function?

The dees create an oscillating electric field between them by connecting to an alternating voltage source. One dee becomes positively charged while the other becomes negatively charged, and this polarity alternates, creating an electric field that accelerates charged particles.

What role do the electromagnets play in a cyclotron?

The electromagnets create a magnetic field perpendicular to the electric field generated by the dees. This magnetic field forces the charged particles to move in a circular path within the dees.

Why is the entire arrangement of the cyclotron sealed in a vacuum box?

The arrangement is sealed in a vacuum box to eliminate air resistance and other particles that could interfere with the acceleration and path of the charged particles.

What happens to a charged particle when it first enters the cyclotron?

When a positively charged particle enters the cyclotron, it is accelerated by the electric field between the dees. Once inside a dee, the electric field is zero, but the magnetic field causes the particle to move in a circular path.

How does the charged particle gain speed in a cyclotron?

The charged particle gains speed each time it crosses the gap between the dees. The electric field in the gap accelerates the particle, increasing its velocity each time it exits and re-enters the dees.

What determines the radius of the particle's circular path in a cyclotron?

The radius of the particle's circular path is determined by the particle's velocity and the strength of the magnetic field, according to the formula r = mv/qB.

What happens when the particle reaches the edge of the cyclotron?

When the particle reaches the edge of the cyclotron and can no longer increase its radius, it is ejected through an exit window. At this point, the particle has gained high energy and can be directed at a target for experiments or practical applications.

Outlines

00:00

🔬 Cyclotron Operation and Particle Acceleration

The script describes the cyclotron, a device invented by E.O. Lawrence and M.S. Livingstone in 1934, designed to accelerate charged particles like protons and deuterons. The process involves using an oscillating electric field within a vacuum chamber to repeatedly accelerate particles across a gap between two conductive half-cylinders, known as dees. A strong magnetic field is used to keep the particles in a circular path, with the radius of the path determined by the equation r=mv/qB. The magnetic field is perpendicular to the electric field, and the particles are accelerated as they cross the electric field between the dees. The acceleration continues until the particles reach a high enough velocity and radius to be ejected through a window, where they can be used to bombard atomic nuclei in nuclear physics experiments.

05:01

🚀 Incremental Velocity Increase in Cyclotron

This paragraph explains the continuous acceleration process of charged particles within a cyclotron. As the particles move from one Dee to the other, the alternating electric field causes the particles to accelerate incrementally, increasing their velocity with each half-circle traversed. The magnetic field's role is to maintain the particle's velocity constant while directing it to move in a larger semi-circular path due to the increased velocity. The process repeats, with the electric field accelerating the particle to even higher velocities (v1, v2, v3, etc.) until the particle reaches the maximum radius it can occupy within the cyclotron. At this point, the particle is ejected with high energy to collide with a target, which is crucial for high-energy physics research.

Keywords

💡Cyclotron

A cyclotron is a device developed by E.O. Lawrence and M.S. Livingstone in 1934. It is used to accelerate charged particles, such as protons and deuterons, to high energies. In the script, the cyclotron is described as being used in nuclear physics to bombard nuclei and cause nuclear reactions.

💡Charged Particles

Charged particles, like protons and deuterons, are particles with an electric charge. In the context of the cyclotron, these particles are accelerated to high energies to initiate nuclear reactions when they bombard nuclei. The script specifically mentions the acceleration and bombardment processes involving these particles.

💡Oscillating Electric Field

An oscillating electric field is a field that changes its direction and magnitude periodically. In the cyclotron, this field is used to repeatedly accelerate the charged particles by making them cross the same electric field multiple times. This concept is crucial for understanding how the cyclotron increases the energy of the particles.

💡Magnetic Field

A magnetic field is a field that exerts a force on moving charged particles, causing them to move in circular or helical paths. In the cyclotron, a magnetic field is created perpendicular to the electric field, guiding the charged particles in a circular path and providing the centripetal force necessary for their acceleration.

💡Dees

Dees are hollow half-cylindrical electrodes made of conductive metals, placed face-to-face with a small gap between them. They are connected to an alternating voltage source, creating an oscillating electric field between them. The charged particles move through the dees, experiencing acceleration each time they cross the gap.

💡Alternating Voltage Source

An alternating voltage source is a power supply that changes its voltage polarity periodically. In the cyclotron, it is connected to the dees, causing the electric field between them to oscillate. This oscillation is essential for repeatedly accelerating the charged particles as they pass between the dees.

💡Centripetal Force

Centripetal force is the force that keeps a moving object in a circular path, directed towards the center of the circle. In the cyclotron, the magnetic field provides the centripetal force necessary to keep the charged particles moving in circular paths as they gain energy and velocity.

💡Semi-circle Path

In the cyclotron, charged particles move in semi-circular paths within the dees. Each semi-circle corresponds to one-half of the circular motion induced by the magnetic field. The script details how the particles traverse these semi-circular paths, gaining energy with each pass through the electric field.

💡Acceleration

Acceleration is the process of increasing the velocity of an object. In the cyclotron, charged particles are accelerated each time they cross the gap between the dees due to the oscillating electric field. This repeated acceleration increases the particles' energy and velocity.

💡Nuclear Reactions

Nuclear reactions involve the interaction of atomic nuclei, leading to the release or absorption of energy. In the context of the cyclotron, accelerated charged particles are used to bombard nuclei, causing nuclear reactions. The script emphasizes the use of high-energy particles for such bombardment to achieve nuclear reactions.

Highlights

Cyclotron was developed by E.O. Lawrence and M.S. Livingstone in 1934.

It is a device used to accelerate charged particles like protons and deuterons.

The acceleration results in the production of high-energy charged particles.

Energized particles are used in nuclear physics to bombard nuclei and cause reactions.

A positively charged particle is accelerated using an oscillating electric field.

A strong magnetic field is used to make the particle cross the electric field repeatedly.

The device consists of two hollow half-cylinders known as dees made of high conductive metals.

Dees are connected to an alternating voltage source, an oscillator, for polarity change.

An electromagnet arrangement creates a magnetic field perpendicular to the electric field.

The entire Cyclotron setup is sealed in a vacuum box.

The charged particle experiences a force due to the electric field, causing acceleration.

Inside the container, the electric field is zero, and the magnetic field provides centripetal force.

The particle moves in a circular path with a radius determined by its velocity, mass, charge, and magnetic field strength.

With each cycle, the particle's velocity increases, enlarging its circular path.

The particle's velocity increase leads to an increase in the radius of its circular motion.

When the particle reaches the maximum radius, it is ejected through a window.

The high-velocity particle has high energy, suitable for impacting a target in experiments.

Transcripts

Cyclotron is a device

developed by E.O. Lawrence and M.S. Livingstone in 1934

It is used to accelerate charged particles

like protons and deuterons

This results in the production of high energy charged particle.

In nuclear physics

such energized particles are used to bombard nuclei causing nuclear reactions.

A positively charged particle can be accelerated to high energy

with the help of an oscillating electric field,

by making it cross the same electric field

time and again with the use of a strong magnetic field.

Two hollow half cylinders

made of high conductive metals

known as dees are so placed,

that the straight edge will be face-to-face

with a small gap between them.

Now these two Dees are connected to two terminals

of an alternating voltage source

an oscillator

It would help in changing polarity.

If one D1 is in the positive potential

than D2 will be in exact opposite negative potential at same time.

In this way they would be oscillating

and an electric field would be created between them.

One electromagnet is kept below the two Dees

and one E.M is kept above the Dees.

Bottom E.M will have north pole above

and top E.M will have south pole below.

This would create a magnetic field

perpendicular to the direction of the electric field.

This entire arrangement is sealed in a vacuum box.

The two Dees create an electric field .

The direction of Electric field is horizontal.

The direction of magnetic field vertical.

When we place a positively charged particle

which may be a proton

or a combination of proton and neutron both.

Since D1 is positive D2 is negative

there is an electric field between them.

A force acts upon the charged particle

and its direction would be the direction of E.

Because of this force the charged particle gets acceleration

and because of acceleration

the speed increases till it enters the D.

Since D is an enclosed container

and so the value of electric field is zero.

So force becomes zero and acceleration becomes zero.

So inside the container there is no electric field

But there is magnetic field

and its direction is north.

The charged particle now moves perpendicular to the direction of the magnetic field.

It experiences a force

in a direction perpendicular to the plane

containing V and B.

This force provides the centripetal force

and makes the charged particle move along a circular path of radius

r=mv/qB

The particle makes a semi circle and comes to the gap

the time taken is t/2

If the time taken to complete one circle is T

T then the time taken to complete semi circle would be T/2

As soon the pareticle comes to end

it is influenced by electric field

When the particle was born its velocity was Zero

when it enters the Dee its velocity is v

and it is constant

because the magnetic field cannot change the velocity.

The oscillator will change the polarity.

When it comes out of Dee it again comes under the influence of electric field.

The electric field accelerates the charged particle to v1.

When it enters D2

the velocity would remain constant

Now D2 becomes + and D1 becomes –

When it comes out of Dee it again comes under the influence of electric field.

The electric field accelerates the charged particle.

The particle would now move from D2 to D1

because its velocity would increase to v2

When it enters D1 again

the velocity would remain constant

because the magnetic field cannot change the velocity

but the particle would make a greater semi circle

because it is coming inside the Dee

with a greater velocity

When it comes out of Dee it comes under the influence of electric field.

Once again the electric field accelerates the charged particle.

and now the velocity becomes v3.

In this way the particle moves in a circular path

and with each circle the velocity of the charged particle increases

If the velocity of a charged particle increases

the radius of the charged particle would also increase.

Finally when the particle has no more space to grow in radius.

It is thrown out through a window.

With such a high velocity the particle has high energy

and it hits the target.