Re: How is the speed of a particle in a particle accelerator determined?

In most particle accelerators, the "speed" isn't measured as much as the energy of the particle. No particle with mass can go faster than the speed of light in a vacuum, and even small particle accelerators are able to get electrons or protons very close to light speed. After that, you can continue to add energy, but it doesn't increase the speed much. You'd be looking at the difference between 99.9% and 99.99% of light speed.

Given that, the most common way to measure the energy of a high-energy charged particle is to send it through a magnetic field. (The particles have to have an electric charge in order for us to accelerate them.) A charged particle passing through a uniform magnetic field will be bent around in a perfect circle. The radius of the circle depends on the strength of the magnetic field and the energy of the particle.

For very high-energy particles, this radius can be as much as several miles in the kinds of magnetic fields we can easily make. So, we usually send them through a small region of field which just deflects the particles, and we can measure the angle of deflection. The higher the energy, the less the beam is bent by the magnetic field.

In practice, at a linear accelerator such as the one at Stanford, there is a detector sitting at some angle from the straight beam, and they turn up the magnetic field until the beam is bent enough to hit the detector. From the strength of the field needed to bend the beam that far, they can calculate the energy in the beam.

In circular accelerators, like at Fermi National Laboratory, you don't have to "measure" the energy, because the whole accelerator is bent in a circle, and only particles of a particular energy can make it around without banging into the walls. In this case, there are electric and magnetic fields turning the beam all along the accelerator. As they put more energy into the beam, they have to continually increase the strength of the fields in order to bend the beam along the correct path. So, in order to keep the beam going at all, they have to know just what the beam energy is at all times. The whole system is computer controlled so that the bending fields are kept in sync with the acceleration process. Otherwise, if at any moment the field strength and particle energy aren't matched just right, the beam doesn't make the curve and hits the wall of the beam pipe.

That's the basic idea. There are, as you might imagine, many variations on this theme. Hope this answered your question.

Jay