The working principle of Cyclotron and basic design.

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Before you understand the basic working principle of Cyclotron you need to understand the force exerted on a charged particle moving in a magnetic field and the motion of the charged particle in the magnetic field.

Force exerted on a charged particle moving in a magnetic field

If a current-carrying conductor of length L meters with I ampere current is brought vertically into a magnetic field of flux density B Weber per square meter, the force would rather be the magnetic force acting on the conductor

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Assume now that a total of N free electrons move in the conductor with a length of L meters, which causes the current I amps.

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Where e is the electric charge of an electron and corresponds to 1.6 × 10-19 coulombs. Now we get from equations (1) and (2)

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Here, the number N of electrons at the origin of the current I is Ampere, and it is assumed that they pass through a length of L meters in the time t, and therefore a drift velocity of the electrons would be

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From Equation (3) and (4) we obtain

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It is the force acting on a number N of electrons in the magnetic field so that the force exerted on a single electron in that magnetic field can be

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Movement of charged particles in a magnetic field

When a charged particle moves in a magnetic field, there are two extreme conditions. The particle moves either in the direction of the magnetic field or perpendicular to the magnetic field. As the particle moves along the axis of the direction of the magnetic field, a magnetic force acts on it.

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Therefore, no force will act on the particle so that the velocity of the particle does not change and therefore moves in a straight line at a constant velocity.

If the charged particle moves perpendicular to the magnetic field, the velocity of the particle does not change. This is because the force acting on the particle is perpendicular to the movement of the particle so that the force does no work on the particle and therefore does not change the velocity of the particle.

However, this force acting on the particle perpendicular to its movement and the direction of movement of the particle changes continuously. As a result, the particle moves on a circular path of constant radius and constant velocity in the field. If the radius of the circular motion is R meters, then

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Now,

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The movement radius is therefore dependent on the movement speed. The angular velocity and the period are constant.

The basic principle of the cyclotron

This concept of charged particle motion in a magnetic field has been used successfully in a device called a cyclotron. Conceptually, this device is very simple but has enormous applications in engineering, physics, and medicine. It is a charged particle accelerator. The movement of the charged particle under a perpendicular magnetic field is applied only in the device called a cyclotron.

Construction of Cyclotron

1. Large electromagnet to create a uniform magnetic field between its two opposite magnetic poles facing each other.

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2. Two flat hollow half-cylinders of highly conductive metals. These components of the cyclotron are called Dees.

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3. A high-frequency AC power source.

construction details

The Dees are placed face to face between the electromagnetic poles. Circles are placed so that the ruler is face to face with a small gap in between. In addition, the magnetic flux of the electromagnet cuts this Dees exactly vertical.

These two dees are now connected to both terminals of an AC voltage source so that at a positive potential, the other is simultaneously at the opposite negative potential. When the source changes, the potential of the dees changes according to the frequency of the source.

Well, when a charged particle is projected from a point near the center of one of the dees at a certain velocity V1.

Since the movement of the particle is now perpendicular to the externally applied magnetic field. The velocity does not change, but the charged particle follows a circular radius orbit.

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Here m gram mass and q Coulomb is the charge of the projected particle and B Weber / Meter2 is the flux density of the applied from the outside perpendicular magnetic field.

After passing through p radians or 180o with the radius R1, the charged particle arrives at the edge of the Dee. Now, the period and the frequency of the applied voltage source are set with the period of the circular motion

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That the polarity of the other Dee is opposite to the charge of the particle. Due to the attraction of the Dee in front of the moving particle and also the Dee repulsion in which the particle is now located, the particle receives additional kinetic energy. working principle of Cyclotron

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Where ? 1 is the velocity of the particle at the previous Dee and ? 2 is the velocity of the particle at the next Dee. Now the particle moves at this greater speed with the radius of R2 meters.

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Due to the constant vertical magnetic field, the working principle of Cyclotron

the particle will make another half-cycle with this new R2-meter radius and reach the edge of the current Dee.

With respect to this edge, the dee-forward again resists the polarity of the backside and the particle crosses the gap between Dees with a kinetic energy gain qV, resulting in a velocity and radius gain of the particle being charged circularly mobile. working principle of Cyclotron

In this way, the charged particle follows a path in spiral motion at an ever-faster rate. As a result, the charged particle gets the required high speed before leaving the cyclotron gun head.

The frequency of the voltage source says f.

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Here, 2π is constant, m, q, and B are known so that we can calculate and therefore the frequency of the voltage source would be

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Cyclotron application (working principle of Cyclotron)

There are mainly two types of cyclotron applications. We are in the sink of various physical experiments when very fast photons are needed. High-speed photons are also used to irradiate tissues.

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