Energy loss in synchrotron accelerators

In summary, the question is about calculating the energy lost by a single electron on each turn in a perfectly circular accelerator with a circumference of 25 km and beam energy of 50 GeV. The equation for this loss is given by (4pi/3)*(e^2)*(gamma^4)/radius, where gamma is the ratio of beam energy to the rest mass of the electron. The poster is unsure about the value of e^2 and how to calculate gamma, and requests clarification. A link to a helpful page is provided.
  • #1
wakko101
68
0

Homework Statement



For the LEP, we are given that it is a perfectly circular accelerator with circumference 25 km and that the energy of each beam is 50 GeV. Calculate the energy lost in GeV/s by a single electron on each turn.

Homework Equations


The loss is given by (4pi/3)*(e^2)*(gamma^4)/radius, and gamma is the ratio of beam energy to the rest mass of the electron.

The Attempt at a Solution


First of all, I'm not really sure what to do about that e^2...if we are working in gaussian units, does this equal 1? Secondly, if I simply substitute 50 Gev and .501 MeV/c^2 for energy and mass in gamma, and then take it to the fourth power, I get a huge number that couldn't possibly be the energy loss.

Basically, I'm confused by what this equation is really saying, so any clarification would be appreciated.

Cheers,
W. =)
 
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  • #2
You might find this page useful http://hyperphysics.phy-astr.gsu.edu/HBASE/Particles/synchrotron.html"
 
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FAQ: Energy loss in synchrotron accelerators

1. What causes energy loss in synchrotron accelerators?

Energy loss in synchrotron accelerators is primarily caused by synchrotron radiation, which is emitted as high-energy particles are accelerated and bent by magnetic fields within the accelerator. This radiation carries away some of the particle's energy, resulting in a decrease in overall energy.

2. How does energy loss affect the performance of synchrotron accelerators?

Energy loss can significantly impact the performance of synchrotron accelerators. It can lead to a decrease in the maximum energy that can be achieved by the particles, as well as a decrease in the beam intensity and stability. This can result in a lower quality of data produced by experiments conducted at the accelerator.

3. Can energy loss be minimized or controlled in synchrotron accelerators?

While energy loss is an inherent aspect of synchrotron accelerators, there are measures that can be taken to minimize or control it. These include optimizing the magnetic fields within the accelerator, using special materials to reduce the effects of synchrotron radiation, and implementing advanced beam collimation techniques.

4. How is energy loss in synchrotron accelerators measured?

Energy loss in synchrotron accelerators is measured using a variety of instruments, including beam position monitors, beam loss monitors, and beam current monitors. These devices track the trajectory and intensity of the particle beam, allowing scientists to calculate the amount of energy lost.

5. What impact does energy loss have on the design and operation of synchrotron accelerators?

Energy loss is a crucial factor in the design and operation of synchrotron accelerators. It must be carefully considered during the construction and optimization of the accelerator to ensure that it can achieve the desired energy and beam intensity. Additionally, energy loss can also impact the reliability and maintenance requirements of the accelerator, making it a crucial aspect to monitor and control during operation.

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