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.

According to https://www.britannica.com/technology/particle-accelerator/Constant-voltage-accelerators#ref365053

"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?

  • $\begingroup$ Should you not be trying to answer these questions yourself? So what are your ideas? $\endgroup$ – Farcher Apr 22 '17 at 13:09
  • $\begingroup$ @Farcher please see my ideas above $\endgroup$ – GJZ Apr 22 '17 at 13:14
  • $\begingroup$ This article describes the two types of linear accelerator. britannica.com/technology/particle-accelerator/… $\endgroup$ – Farcher Apr 22 '17 at 13:29
  • 1
    $\begingroup$ 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. $\endgroup$ – Jon Custer Apr 22 '17 at 13:29
  • $\begingroup$ To first order, magnets are for transverse stability. RF is applied in the longitudinal direction. $\endgroup$ – mng Apr 24 '17 at 2:32

There is a huge zoology of accelerating structures and without restricting the analysis to some of them it is pretty hard to answer.

Linacs may or may not use travelling waves. When travelling waves are used they can be forward or backward travelling, this indicates the group velocity (eg. the direction of the power flow), while the phase velocity has always to be matched to the particle velocities. The EM field between the various cells is always coupled to some extent in order to maintain the relative phases stable.

If the beam is not relativistic, meaning that its velocity changes with the energy, the structures have to change shape/size along linac to remain in phase.

Finally a fast variable energy RF linac can be extremely challenging. Indeed it is common to have focusing magnets along the linac to keep the beam within the aperture. When reducing the energy, by either reducing the input power or by switching off some sections, one still needs to make sure that the beam can go through the focusing system either by having a very large acceptance (hard) or by adjusting it all the time (slow).


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