Accelerating electrons and positrons

[Jeff97]

Homework Statement

This is not for homework I have just defaulted here as it could be seen as "homework"

Relevant Equations

N/A

I've been looking int Large Electron-Positron collider at CERN (an experiment which ended in the year 2000), groups of electron and positrons were accelerated along a circular tunnel so that they collided. Electromagnets were used to keep the particles moving in a circle.

could someone tell me how the strength and direction of the magnetic field would need to be adjusted to:

One: keep a particle traveling in a circle while it is increasing its speed

Two: bend the paths of both positrons and electrons which are traveling in opposite directions in the same tunnel.

Thanks

 

[etotheipi]

One: keep a particle traveling in a circle while it is increasing its speed

Try starting with this. Consider a particle of charge $q$ undergoing circular motion within a magnetic field of magnitude $B$. How might we relate $v$ and $B$? As a hint, the force due to the magnetic field is $\vec{F} = q\vec{v}\times \vec{B}$.

 

[berkeman]

Are you familiar with the Lorentz force? The more familiar you are with that concept, the easier it will be to answer your questions about this.

Also, have you looked at the CERN website to see if they have some good basic explanations for how that accelerator works? (I have not looked yet, but it seems like they should have something...).

https://en.wikipedia.org/wiki/Lorentz_force

 

[Jeff97]

In simple terms for question one. As the energy of the circulating particles increases, the strength of the magnetic field guiding them is increased, which thus keeps the particles on the same path(circular). As fo part two I think this makes sense, an electric field that accelerates an electron will decelerate a positron moving in the same direction as the electron. But if the positron is traveling through the field in the opposite direction, it will feel an opposite force and will be accelerated. Similarly, an electron moving through a magnetic field will be bent in one direction—left, say—while a positron moving the same way will be bent in the opposite direction—to the right. If, however, the position moves through the magnetic field in the opposite direction to the electron, its path will still bend to the right, but along the same curve taken by the leftward-bending electron. Taken together, these effects mean that an antielectron can travel around a circular ring guided by the same magnets and accelerated by the same electric fields that affect an electron traveling the opposite way.

Is this correct? in term of my questions.

 

[Jeff97]

In simple terms for question one. As the energy of the circulating particles increases, the strength of the magnetic field guiding them is increased, which thus keeps the particles on the same path(circular). As fo part two I think this makes sense, an electric field that accelerates an electron will decelerate a positron moving in the same direction as the electron. But if the positron is traveling through the field in the opposite direction, it will feel an opposite force and will be accelerated. Similarly, an electron moving through a magnetic field will be bent in one direction—left, say—while a positron moving the same way will be bent in the opposite direction—to the right. If, however, the position moves through the magnetic field in the opposite direction to the electron, its path will still bend to the right, but along the same curve taken by the leftward-bending electron. Taken together, these effects mean that an antielectron can travel around a circular ring guided by the same magnets and accelerated by the same electric fields that affect an electron traveling the opposite way.

Is this correct? in term of my questions.

@berkman

 

[berkeman]

@berkman

I used to work for an Engineering Manager whose last name is Berkman. Should I ping him with an e-mail?

Taken together, these effects mean that an antielectron can travel around a circular ring guided by the same magnets and accelerated by the same electric fields that affect an electron traveling the opposite way.

Most of what you posted was close to correct (with a few small wording issues, but mostly technically correct). Please keep in mind that I'm not an accelerator designer or physicist, though.

I think the main problem that bothered me in your post is that a DC E-field is not used for accelerating charged particles in an accelerator, AFAIK (as opposed to the 1-way trip from electron gun to CRT phosphor screen in old-style CRT displays). You can use a DC B-field to help guide the charged particles (although you may need to increase its strength as the energy of the particles increases). I've seen AC E-fields used as part of accelerating charged particles.

https://www.sciencedirect.com/topics/medicine-and-dentistry/electron-accelerator

https://en.wikipedia.org/wiki/Particle_accelerator

https://en.wikipedia.org/wiki/Free-electron_laser

https://en.wikipedia.org/wiki/Synchrotron

Paging @ZapperZ to please help you out with your basic understanding...

 

[Jeff97]

I used to work for an Engineering Manager whose last name is Berkman. Should I ping him with an e-mail?

Most of what you posted was close to correct (with a few small wording issues, but mostly technically correct). Please keep in mind that I'm not an accelerator designer or physicist, though.

I think the main problem that bothered me in your post is that a DC E-field is not used for accelerating charged particles in an accelerator, AFAIK (as opposed to the 1-way trip from electron gun to CRT phosphor screen in old-style CRT displays). You can use a DC B-field to help guide the charged particles (although you may need to increase its strength as the energy of the particles increases). I've seen AC E-fields used as part of accelerating charged particles.

https://www.sciencedirect.com/topics/medicine-and-dentistry/electron-accelerator

https://en.wikipedia.org/wiki/Particle_accelerator

https://en.wikipedia.org/wiki/Free-electron_laser

https://en.wikipedia.org/wiki/Synchrotron

Paging @ZapperZ to please help you out with your basic understanding...

Ok, I apologize for the incorrect naming, haha. I'll be waiting for Zapper response thanks for your help!

 

[ZapperZ]

In simple terms for question one. As the energy of the circulating particles increases, the strength of the magnetic field guiding them is increased, which thus keeps the particles on the same path(circular). As fo part two I think this makes sense, an electric field that accelerates an electron will decelerate a positron moving in the same direction as the electron. But if the positron is traveling through the field in the opposite direction, it will feel an opposite force and will be accelerated. Similarly, an electron moving through a magnetic field will be bent in one direction—left, say—while a positron moving the same way will be bent in the opposite direction—to the right. If, however, the position moves through the magnetic field in the opposite direction to the electron, its path will still bend to the right, but along the same curve taken by the leftward-bending electron. Taken together, these effects mean that an antielectron can travel around a circular ring guided by the same magnets and accelerated by the same electric fields that affect an electron traveling the opposite way.

Is this correct? in term of my questions.

Someone who knows exactly the configuration of LEP ring can correct me here if I'm wrong. I can only respond to this based on the "generic" setup of a typical circular particle collider.

First of all, by the time these particles are injected into the main ring, they are already at their optimum energy. I think this was true at the Tevatron ring.

Secondly, each particle (in your case, the electron and the positron) are in separate beam pipes. They do not share the same beam pipe. So the RF that accelerates or maintains the speed of each type of particle are not "shared". The beams only cross with each other at various points along the ring where the detectors are located. These are points where collisions take place. Significantly many more particles pass through without colliding and continue on in the ring to the next crossing points. The LHC, for example, has several.

The bending magnets are set so that they will correctly bend the amount needed to keep the particle at the center of the beam pipe. Luckily, the same magnetic field will cause e and p moving in opposite direction to be bent in the same direction.

Zz.

 

[JonasKK]

Hi!
You've already received the correct answers above, but I just wanted to correct the statement regarding the injection energy into colliders made by @ZapperZ above: For LEP, and most other high-energy colliders, the injected particles have a lower energy than the final energy.

For LEP, the electrons and positions was injected at 22 GeV, and then ramped to 94.5 GeV [1] (the most common operation energy in '98).

The Tevatron received protons and anti-protons from the Fermilab Main-Injector at 150 GeV and accelerated them to 980 GeV [2]. On Fig. 6 you'll find a plot of the proton and antiproton intensities and energies during one fill of the Tevatron in 2011.

LHC receives protons from the Super Protron Synchrotron at 450 GeV, and then increases the energy to 6.5 TeV [3].

The PEP-II and (Super)KEKB colliders were/are some of the few examples of machines applying the top-up injection (top-off in American ;-) ), where the particles are injected at the full energy [4]. The idea behind top-up injection is that you can keep the beam current high (and therefore the luminosity high) all the time, providing stable conditions for the measurements. CESR and BEP-II are other examples of a colliders with top-up operation (the former is now turned into a light source "CHESS") [5,6]. Most modern synchrotron light sources employ the top-up injection scheme in order to keep the photon flux to the experiments high and stable, while also keeping the heat-load to the accelerator components constant, improving beam stability [7].
Traditional top-up injection relies on injecting new particles into a region of phase-space off-set from the orbit of the stored beam. After injection, the beam must shrink due to synchrotron radiation in order to free up the region of phase-space for the next injection. This, however, shows why top-up is not done for hadron machines; protons, ions etc. emit very little synchrotron radiation at the energies that we can currently reach, meaning that the injected beam does not shrink.

[1] https://jwenning.web.cern.ch/documents/LEPop/pac99-op.pdf
[2] https://iopscience.iop.org/article/10.1088/1748-0221/6/08/T08001/pdf
[3] https://en.wikipedia.org/wiki/Large_Hadron_Collider
[4] https://www.sciencedirect.com/science/article/pii/S0168900217311646
[5] https://cds.cern.ch/record/556568/files/rpph117.pdf
[6] http://english.ihep.cas.cn/doc/1840.html
[7] https://accelconf.web.cern.ch/e08/talks/mozcg01_talk.pdf