How is a travelling wave used to generate potential difference in a linear particle accelerator?

The Question

In a linear particle accelerator, particles travel down a vacuum tube under the influence of a travelling wave which appears at electrode gaps.

How does a travelling wave switch the polarity of the plates in an accelerator in phase with the motion of the particle being accelerated?

Secondly, how does this method allow for the use of lower voltages in the accelerator?

Ideas and Suggestions

According to explanations such as this one: https://www.youtube.com/watch?v=ZF6iKUb0UBE , there is a switch in polarity at the moment that the particle passes through the plate.

This is supposedly done using a high frequency a.c. voltage and a travelling wave.

My idea was that this might be achieved by fixing the energy at which the particle is injected and predicting its motion, hence changing the frequency of the polarity shift.

"As the velocity of the particles increases, the lengths of the cavities must also increase along the accelerator."

This suggests that the motion of the particles is predicted and therefore the shifts of polarity are applied at a fixed frequency but at different points.

@Jon Custer argues that it might simply be that only those particles that are at the right place and at the right time get accelerated (indeed, the rest would simply be lost).

This seems odd considering the fact that the arrangement of magnets in most colliders is made to minimise loss of particles even at a greater cost. Is this the case?

Can anyone confirm which of these is the best explanation?

• Should you not be trying to answer these questions yourself? So what are your ideas? – Farcher Apr 22 '17 at 13:09
• @Farcher please see my ideas above – GJZ Apr 22 '17 at 13:14
• This article describes the two types of linear accelerator. britannica.com/technology/particle-accelerator/… – Farcher Apr 22 '17 at 13:29
• Or one could say that only those particles at the right place and time will get accelerated by the traveling wave. Hence the invention of beam bunching to get more particles in the right place at the right time. – Jon Custer Apr 22 '17 at 13:29
• To first order, magnets are for transverse stability. RF is applied in the longitudinal direction. – mng Apr 24 '17 at 2:32