Linear Accelerator Length Contraction

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SUMMARY

The discussion centers on the effect of relativistic length contraction on electron bunches in a linear accelerator. It highlights that at speeds approaching the speed of light, the lengths of tubular electrodes remain nearly constant due to the increase in particle mass rather than a decrease in length. The gap between electron bunches does not contract because it is not a rigid object; instead, it expands in the instantaneous rest frame of the bunch during acceleration. This understanding clarifies the behavior of particle bunches in high-energy physics environments.

PREREQUISITES
  • Understanding of relativistic physics principles
  • Familiarity with linear accelerator (linac) operation
  • Knowledge of electron dynamics at high velocities
  • Basic grasp of the concept of rest frames in relativity
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  • Study the principles of relativistic length contraction in detail
  • Explore the mechanics of linear accelerators and their design
  • Investigate the relationship between energy, mass, and velocity in particle physics
  • Learn about the concept of rest frames and their implications in relativistic scenarios
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Physicists, engineers working with particle accelerators, and students studying advanced concepts in relativity and high-energy physics will benefit from this discussion.

Orthoceras
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TL;DR
Effect of relativistic length contraction on the electron bunches in a linear accelerator?
I am trying to understand the effect of relativistic length contraction on the electron bunches in a linear accelerator. Figure B is for nonrelativistic speeds, successive cylinder lengths are progressively longer. However, wikipedia says "At speeds near the speed of light, the incremental velocity increase will be small, with the energy appearing as an increase in the mass of the particles. In portions of the accelerator where this occurs, the tubular electrode lengths will be almost constant", so it should figure D or E. I expect length contraction to occur, therefore D. However, I don't see why the the gap between bunches does not contract.

Which option is right?

linac5.png

Red: electron bunches; grey: cylinders
 
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Orthoceras said:
Summary:: Effect of relativistic length contraction on the electron bunches in a linear accelerator?

However, I don't see why the the gap between bunches does not contract.
This has to do with how the acceleration is performed. The gap is not a rigid object (not that rigid objects exist in relativity) that maintains the same rest length. The setup is such that the distance between bunches in the instantaneous rest frame of a bunch increases during the process.
 
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