Undergrad Linear Accelerator Length Contraction

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The discussion focuses on the impact of relativistic length contraction on electron bunches in a linear accelerator. It highlights that while the lengths of the tubular electrodes may appear constant at relativistic speeds, the gaps between electron bunches do not contract due to the nature of acceleration. The gap is not a rigid structure; instead, it changes dynamically in the rest frame of the bunches as they accelerate. This leads to the conclusion that the observed behavior of the gaps differs from the expected contraction. The complexities of relativistic effects in particle accelerators are emphasized in this context.
Orthoceras
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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.
 
MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...

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