Transit time of particle in a particle accelerator question

In summary: I think it would be a pretty nifty way to measure the mass of an electron, especially in a CRT.Do you want to know the mass of the electron, or the angular frequency of the electron?I'm more interested in the angular frequency, at least for now.
  • #1
bitrex
193
0
I have a question about the behavior of a charged particle being accelerated in an electric field. I know that it is possible to find the approximate final velocity of the particle (assuming it doesn't reach too great a fraction of the speed of light) simply by an energy balance, [tex]1/2mv^2 = qV[/tex]. However, I'm interested in learning how to find the "time in flight" of an electron in the same potential field, and I don't think I can use the above equation to find it out because I need the average velocity, not the final velocity. Particularly I'm interested in the case of knowing the flight time of an electron in a small electrostatically-deflected CRT. I know there should be a straightforward way to do this, but I'm blocking on it. Thanks for any ideas.
 
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  • #2
Do you want to know the TOF during the acceleration of the electron up to speed, or the time spent being electrostatically deflected?
 
  • #3
I'm interested in figuring out the TOF from the cathode to the CRT screen, assuming the electrons in the beam aren't being deflected sideways by the electrostatic deflection plates, for now. So yes, the first one. :biggrin:
 
  • #4
Here is a description of both TV and oscilloscope cathode ray tubes. As I recall, the accelerating voltages range from about 5,000 volts to 15,000 volts.
http://en.wikipedia.org/wiki/Cathode_ray_tube
The acceleration occurs in the first few cm, and the electron drifts the rest of the way at constant velocity. Your foumula, 1/2 mv2 = qV is adequate.
 
  • #5
Thanks, Bob. I wasn't sure if the electron was quickly accelerated to its final velocity, or whether it underwent a constant acceleration all the way down the barrel. I was reading about a neat experimental way to determine the mass of a charged particle (in this case an electron) by putting the CRT in a longitudinal magnetic field and giving the electron a sideways deflection as it leaves the gun. The magnetic field causes the particle to rotate (I guess because the magnetic field is always providing a force tangential to the particle's velocity component that's perpendicular to the longitudinal field) with an angular frequency of [tex]w = \frac{q}{m}B[/tex]. Like a cyclotron essentially. So if you can get the electron to complete one complete rotation, and you know the travel time down the tube, you know the angular frequency, and if you know the magnetic field strength you can calculate the mass of the electron.
 

1. What is a particle accelerator and how does it work?

A particle accelerator is a machine that uses electric fields to accelerate particles to high speeds, close to the speed of light. It works by sending particles through a series of tubes, called accelerators, and increasing their speed with each stage until they reach the desired energy level.

2. What is the transit time of a particle in a particle accelerator?

The transit time of a particle in a particle accelerator refers to the time it takes for a particle to travel from the starting point to the end point of the accelerator. This time can vary depending on the length and design of the accelerator, as well as the energy level of the particles being accelerated.

3. How is the transit time of a particle measured in a particle accelerator?

The transit time of a particle in a particle accelerator can be measured using specialized equipment such as a time-of-flight detector. This detector measures the time it takes for a particle to travel a known distance and uses this information to calculate the particle's transit time.

4. Why is the transit time of a particle important in particle accelerator experiments?

The transit time of a particle is important in particle accelerator experiments because it affects the accuracy of the data collected. By measuring the transit time, scientists can determine the speed and energy of the particles, which can provide valuable insights into the behavior of matter at high speeds and energies.

5. What are some factors that can affect the transit time of a particle in a particle accelerator?

The transit time of a particle in a particle accelerator can be affected by various factors such as the length and design of the accelerator, the energy level of the particles, and external influences such as magnetic fields. Additionally, the type and properties of the particles being accelerated can also play a role in their transit time.

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