LinAc standing wave I have a question regarding Linear Accelerators (Linacs):
Originally, traveling HF waves were used to accelerate electrons inside a Linac. You can see a sketch in the following picture. The further the electron beam is accelerated, the longer are the chambers, because the electrons move faster. This sounds reasonable.

However, this results in a very long geometry for the accelerator, so for medical applications, we usually end up using a standing wave accelerator. I was told that for this one we can use chambers of equal length. But I do not understand why this would be possible. The electrons still accelerate, how is it possible that the chambers remain the same size?
 A: Electrons have fairly small mass $m_e = 9.11 \times 10^{-31}\,\mathrm{kg} = 0.511\,\mathrm{MeV}/c^2$. Even modest energy beams (a few 10s of MeV) are many times that mass meaning that the electron's speed in the lab frame does not change appreciable when you add more energy (this is a consequence of special relativity).
The speed of a particle is
$$ v = c \sqrt{ 1 - \left( \frac{mc^2}{E} \right)} \,, $$
where $E$ is the total energy (kinetic plus mass) of the particle $E = T + mc^2$.
Beam energies are kinetic energies, but when the beam energy is, say, $20\,\mathrm{MeV}$ (nuclear, particle and accelerator physicists routinely drop the $/c^2$ because they work in natural units where $c=1$) the velocity increases little as you increase to a beam energy of $21\,\mathrm{MeV}$. Above about $50\,\mathrm{MeV}$ you can simply ignore the change of the beams speed.
The CEBAF accelerator takes advantage of this effect to accelerate beam components that have cycle from 0 to 4 full times around the machine in the same cavities at the same time.
