## Type of accelerator (Ring type)

Ring type accelerator solved the difficulties by linear type.

1. the particle circulate inside the accelerator, so, it can be accelerate infinite time in principle.
2. The space require is smaller compare with similar energy output Linac.

However, there is a draw back is, for charged particle running in a circular path, it will radiate energy by EM wave due to the centripetal acceleration, thus, even it is just running in constant speed, it will radiate and energy lost. this is called synchrotron radiation.

There are mainly 2 types of ring accelerators, 1) cyclotron, 2) synchrotron.

Cyclotron

cyclotron is the simplest type, it has 2 D shape cavities and the 2 D shape formed a circle. the 2 D shape cavities is under a magnetic field to blend the particle. and the 2 Ds have different electric potential. when a particle pass from 1 D to the others, due to the potential different, it will be accelerate.

as you can imagine, the potential of the Ds has to be oscillating so that the particle is accelerated when passing each gap between the 2Ds. That frequency is called cyclotron frequency. and it also reflects the particle circulating frequency. surprisingly, the cyclotron frequency only depends on the magnetic field strength, the charge and the mass of the particle.

$\omega = 2\pi f = \frac { B q} {m}$

which means, no matter the particle position, it moves in same frequency. Thus, the outer particle move faster then the inner one.

now a day, cyclotron may not just contains 2 D cavities but any $\frac { 2 \pi }{n}$ cavities. where n is number of cavities. thus, 2Ds is also called π – cavity.

The typical speed it can reach is about 10% of speed of light.

The only draw back is, the energy it can reach is limited, if using fixed B field or E field, due to relativistic effect. (i.e. the cyclotron frequency also depend on the speed ) the particle cannot match the frequency and accelerated, after it goes to relativistic speed.

another factor is the B field strength is limited, even using super conductive magnetic. and the limit of B field, limited the max output.

particle is released at the center of the B-field and go outward as it acquire speed. Thus, the limitation of radius also limited the max speed. and also, a large radius means a large B field area, which raise a problem on uniform on the B-field.

So, there are another type of cyclotron, which changing the B field or E field to cope with the changing frequency. such cyclotron is called Synchrocyclotron. but due to the velocity dependent of the frequency, only certain speed of particle can be accelerate, thus, the intensity of the beam is smaller then cyclotron.

Synchrotron

synchrotron can reach a great energy and accelerate particle very close to speed of light.

it uses a lot beam focusing devices and accelerating devices to accelerate the beam in a very large radius. each device is well tuned, and all devices are well synchronized for different particle. Thus it is a very delicates and sophisticated machine.

1. particle can have every high energy
2. high intensity of beam
3. it can have some section only for linear motion with accelerate.
4. it is not limited by the B field. since the narrow of the beam, a higher forcing B field can be applied.

The only factor reduced the power output is the synchrotron radiation. that’s why they build a bigger and bigger one, since the large radius can reduce the radiation lost.

## type of accelarator I (Linac)

The machine used in nuclear physics is call Accelerator. Because it accelerate, speed up the particle.

There are basically 2 types, one is called Linear Accelerator (Linac) , another type is called Circular Accelerator.

in fact, there are many other type of accelerator, as long as they can accelerate particle, by definition, it can be called as accelerator. for example, The vacuum tube in old day TV is an electron accelerator! However, most other type of accelerators can only speed up particle at low speed, not comparable to speed of light. So, in modern nuclear physics, we don`t use them. Nevertheless, the mechanism of them may be reviewed and other type of accelerator may be invented in future, who know!

so, far, all Accelerator can only handle charged particle.

Linac

The particle being accelerated in Linac is moving in a straight line. that is why the name Linear. Linac constitutes of  many sectors, each sector is a mini accelerator, which speed up the particle by adding energy into it.

The simplest type of Linac is 2 parallel plate with a hole at the middle, and has the electric potential different V. when an electron passed through it, it will gain eV of energy and then speed up. so, if there is n sector, and each sector are identical, the final energy is neV. This LINEAR behavior also address the name.

Working Principle

Now, imagine you have many plates, when the particle passed plate 1, a voltage applied on plate 2 to speed up the particle. after the particle passed plate 2, you have to turn off the voltage and apply the voltage on plate 3, and the process go on. thus, the voltage on each plate is oscillating, which is the working frequency of Linac. Moreover, when the particle speed up, the time for it with in each section will be smaller and smaller, thus, the working frequency has to be increase and matching the particle speed. the other way around it, building each sector in different length, but this method will set a definite frequency of the Linac and the output energy.

The advantage of Linac is that :

1. it can produced continuous beam
2. less energy lost during acceleration. where all charged particle will radiate energy while accelerating.