# Voltage of a quadrupole magnet

I have a simple question and it's my first one in this community. :)

Does the voltage of a quadrupole magnet depend on the power of the electron beam in a synchrotron?

Perhaps someone has a good source I can refer to.

UPDATE 1: I had to write it a bit more exactly: If I change the current of an electron beam, do I have to change the power of the quadrupoles? So theoretically my beam runs on 2000V with a 20Ohm resistance, and I want to focus the beam with a quadrupole, what power (voltage etc.) does the magnet need? Is it twice the size of the current of the beam or whatever, so you understand what I meant.

(If you have a dipole for bending the beam the power of the dipole is important for the angle the beam goes out of the dipole-field.)

I thought there would be a relationship with the beam and the quadrupole as there is a relationship with the dipole.

But thank you (Mark H) for your help. I will refer to the sources you posted.

• The voltage of the magnet is whatever voltage you choose to supply. Can you clarify your question? "Do I need a larger voltage to do x" (normally you would consider the current rather than the voltage through an electromagnet to be the significant parameter... why are you asking about voltage?). The clearer your question (including why you think it would be so), the more likely you will get a pertinent answer. Commented Aug 13, 2015 at 21:42

It depends on how the power is varied in the beam. Increased beam current does not require more current (and thus voltage) in the quadrupoles to focus. Increased beam energy does require more current in the quadrupole magnets.

Higher energy particles have more momentum, and so require stronger fields to bend. A higher current beam just means more particles of the same energy passing through the pipe.

Here are some slides from an introductory class at the U.S. Particle Accelerator School (http://uspas.fnal.gov/): http://uspas.fnal.gov/materials/09VU/Lecture2.pdf

Just in case I read your question wrong: varying the beam in any way does not induce changes in a quad magnet. All magnets on a beam line have their own power supplies that determine the amount of current through them.

## Update from OP's update

Electron and other particle beams are different than electric currents through a wire. It doesn't make sense to refer to a resistance of 20 Ohms. If you shut off the accelerating cavities in a synchrotron, the beam will keep circulating while only losing energy to synchrotron radiation. This is unlike a resistive wire that stops a current as soon as the voltage source is removed.

In addition, the power of a beam and the power running through an electromagnet are only somewhat related. Higher energy beams require electromagnets with more current to keep the beam on the right trajectory.

• Thanks for your help. I think you understood my question. See Update 1.
– Nico
Commented Aug 14, 2015 at 7:28
• You are absolutely right. An electron beam is not comparable to a wire, but you have to generate the beam with an electron gun. So the Volts and Ohms were meant to be values for the gun.
– Nico
Commented Aug 14, 2015 at 14:17