# Converting Linear Accelerator To Circular One

1. Nov 10, 2012

### Mohamed Nedal

Hi guys ,

Suppose there is a circular accelerator has the same inner structure of a linear accelerator in terms of the rings of acceleration ...

The angular frequency of accelerated particles is : ω = qB/m = 2πf , and this is also the supplied current frequency ...

The question is , The above formula of ω works in this case ?

Sincerely , ...

2. Nov 10, 2012

### ZapperZ

Staff Emeritus
Just for future references, "accelerator" topics do not belong in High Energy/Nuclear Physics. While accelerators ARE used in those fields, the area of accelerator physics deals mainly with classical E&M, and thus, belong in the Classical Physics forum, which is where this thread will be moved to.

Zz.

3. Nov 10, 2012

### Staff: Mentor

For slow particles, that is fine. For relativistic particles, you need an additional factor of γ: $\omega = \frac{qB}{\gamma m}$
Current where?

4. Nov 10, 2012

### Mohamed Nedal

Okay , I'll be careful in the next time

5. Nov 10, 2012

### Mohamed Nedal

The current that supplied to the accelerator

6. Nov 10, 2012

### Simon Bridge

Re: Angular Frequency Of Circular Accelerator

Not sure what you are imagining here:
I think of a linear accelerator like that (link) ... so the picture I get is somehow putting the rings in a circle. But this uses electric fields so...
... I'm not sure where the B comes in to it.

7. Nov 11, 2012

### greswd

just curious, is the decrease in angular frequency due to time dilation or an increase in mass?

8. Nov 11, 2012

### Staff: Mentor

That is extremely vague.

The connection to the electrical grid? That can be any frequency (or even DC), it does not matter as long as you know it in advance.

The electricity for dipole magnets? That depends on the energy of the particles in the ring. In storage rings, it is constant. If the energy of the particles increases, the current has to increase in most setups, too.
The electricity for kicker magnets? Varies with the beam and the setup.
The electricity for other magnets? Depends on the magnets.

The electricity for radio-frequency cavities? Those cavities need radio frequency as input, where the frequency depends on the cavity geometry.

@greswd: It comes from the modified reaction of particles to forces: $F_T=\gamma m a_T$. The mass of particles is constant, "relativistic mass" is something you find in outdated text books only.

9. Nov 11, 2012

### Mohamed Nedal

yes I mean the current ( electricity ) that I apply on the accelerator .

According to what I understand , The angular frequency of moving particles is equal to the angular frequency of the current which is applied on the accelerator , is equal to : ω = q*B/m = 2*π*f , where ( f ) is the frequency of the current , right ?

If it was right , It is for one particle , So for all particles .. should I multiply with ( N ) the total number of particles ?

10. Nov 11, 2012

### ZapperZ

Staff Emeritus
You do know that circular accelerators do not move electrons the way you are describing here's don't you?

Zz.

11. Nov 12, 2012

### Mohamed Nedal

yes I know how cyclotron , synchrotron , betatron .. etc. works

I suppose another design for circular accelerator

12. Nov 12, 2012

### ZapperZ

Staff Emeritus
I don't think you do, and you're making very little sense in this thread, but OK.

Zz.

13. Nov 12, 2012

### Staff: Mentor

As mentioned before, that is not a useful description.

In that case, you should describe it first.

I agree with ZapperZ.