Linear Accelerator Length Contraction

The length contraction effect also decreases the gap, but not enough to counteract the increase due to the acceleration. This results in a smaller contraction effect than expected, and thus, a different outcome from what would be predicted in the nonrelativistic case. Therefore, the option that is right is figure D or E, where the tubular electrode lengths are almost constant due to the small incremental velocity increase near the speed of light.
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Orthoceras
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TL;DR Summary
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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FAQ: Linear Accelerator Length Contraction

What is linear accelerator length contraction?

Linear accelerator length contraction is a phenomenon in which the length of an object appears to decrease when it is moving at high speeds. This is due to the effects of special relativity, which states that as an object's velocity increases, its length in the direction of motion will appear to decrease to an observer.

How does linear accelerator length contraction occur?

Linear accelerator length contraction occurs due to the effects of time dilation, which is another aspect of special relativity. As an object's velocity increases, time appears to slow down for that object. This means that the distance between two points on the object will also appear to decrease, leading to the phenomenon of length contraction.

What is the formula for calculating linear accelerator length contraction?

The formula for calculating linear accelerator length contraction is L = L0 * √(1 - v2/c2), where L is the contracted length, L0 is the rest length of the object, v is the velocity of the object, and c is the speed of light.

Does linear accelerator length contraction affect all objects?

Linear accelerator length contraction only affects objects that are moving at high speeds, close to the speed of light. For everyday objects moving at slower speeds, the effects of length contraction are negligible and cannot be observed.

What are some real-world applications of linear accelerator length contraction?

Linear accelerator length contraction has been observed and confirmed in various experiments, including the famous Muon experiment. It is also a crucial factor in the design and functioning of particle accelerators, such as the Large Hadron Collider, which rely on the principles of special relativity to accelerate particles to high speeds.

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