talk

I'm preparing a talk for this Friday. Its been a long time coming, but somehow my preparation is not where it should be. Its ok.

I will talk about the physics of electron beams in a synchrotron. The goal is to explain the origin of the equilibrium beam sizes and the beam lifetime. What I'd like to say is that these are two basic things everyone should understand if you want to know where your photon beam comes from. From a web perspective, I think these topics are not well covered. Here is beam emittance on wikipedia. The fact that an equilibrium emittance exists for an electron ring, independent of the initial distribution isn't mentioned. The perspective is entirely from non-radiating (or not much) hadron storage rings.

The first question is how do you store an electron. Basically, you create a 6-D harmonic oscillator. Transversely this comes from quadrupole magnets. Longitudinally, this comes from an RF cavity. Using quadrupoles to create a stable quadradatic potential was not discovered immediately. It is referred to as the concept of Strong Focusing, and was found by Courant and Snyder and by Cristofolis independently. The problem is that a quadrupolar magnet field focuses in one direction, but is defocusing in the perpendicular direction. However, by creating a system of several quadrupoles of alternating polarity, one can create a net focusing effect.

So, we have a stable bucket both transversely and longitudinally. Now what? Throw an electron in there! Next, we observe that the energy loss through radiation depends on the energy in such a way that a higher energy electron loses more, and a lower energy electron loses less. Thus we have a damping effect where the electron will head towards a fixed value. This damping effect also comes into the transverse dimensions, and thus overall a bunch of electrons wants to spiral down to a single point in phase space.

What stops the spiraling process? What comes into play to limit the beam size. First, one may imagine it is the coulomb repulsion. However this turns out to be extremely small for a relativistic beam. Basically, the electric repulsion is cancelled (reduced by gamma squared) by the magnetic attraction.

The effect that does set the beam size is the quantum nature of the radiation. The radiation is emitted in photons, and indeed a rather small number of them. This causes a randomness in the energy change that results in a diffusion process. This diffusion, together with the radiation damping effect mentioned cause the equilibrium beam sizes.

The interaction between the electrons is important however. The typical interactions are quite small, but the less frequent short range scattering causes large energy changes which may result in an electron being lost. This is the source of the beam lifetime (actually there's also a part from scattering off the gas in the chamber.).

That's the basic story I want to get across.