Find first and second harmonics of the electron cyclotron frequency.

In summary, the expressions for the first and second harmonics of the electron cyclotron frequency are given by v1 = (eB) / (mec) and v2 = [2 + 1/(2∏)] [ (eB) / (mec) ], respectively. The emission frequency and gyration frequency are the same thing. The interval between the first and second harmonics is equal to one gyration frequency. It is important to remember to practice and not doubt your answers in science. Good luck with your course!
  • #1
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Homework Statement



Give expressions for the first and second harmonics of the electron cyclotron frequency.

Homework Equations



Gyration frequency is ωB = (eB) / (mec)

Interval between cyclotron lines is Δv = (eB) / (2∏mec)

The Attempt at a Solution



I think that (although my equations use ω and v) they are both talking about the same thing, eg that emission frequency v is identical in value to gyration frequency ωB. Is that correct?

If am right here, I can just say that:

fundamental frequency v1 = (eB) / (mec)

second harmonic frequency v2 = v1 + Δv

so v2 = [ (eB) / (mec) ] + [(eB) / (2∏mec)]

v2 = [1 + 1/(2∏)] [ (eB) / (mec) ]

This is probably a really simple question but I am struggling with this course and doubting my answers to everything!
 
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  • #2




You are correct in your understanding that the emission frequency and gyration frequency are the same thing. However, there is a slight error in your calculation for the second harmonic frequency. It should be v2 = [2 + 1/(2∏)] [ (eB) / (mec) ] instead of [1 + 1/(2∏)] [ (eB) / (mec) ]. This is because the interval between the first and second harmonics is equal to one gyration frequency, not half a gyration frequency. So the second harmonic frequency should be two times the fundamental frequency plus one gyration frequency.

I hope this helps and don't doubt your answers! Science can be challenging but keep practicing and you will get better. Best of luck with your course.
 

1. What is the electron cyclotron frequency?

The electron cyclotron frequency is the frequency at which an electron in a magnetic field will gyrate or spiral around the magnetic field lines. It is given by the equation f = eB/m, where e is the charge of the electron, B is the strength of the magnetic field, and m is the mass of the electron.

2. What is the significance of finding the first and second harmonics of the electron cyclotron frequency?

The first and second harmonics of the electron cyclotron frequency are important in plasma physics and astrophysics. They determine the frequency at which particles can absorb and emit energy, and play a crucial role in plasma heating and particle acceleration processes.

3. How are the first and second harmonics of the electron cyclotron frequency calculated?

The first and second harmonics can be calculated by multiplying the fundamental frequency (electron cyclotron frequency) by 2 and 4, respectively. This is because the harmonics are integer multiples of the fundamental frequency.

4. Can the first and second harmonics of the electron cyclotron frequency be observed in experiments?

Yes, the first and second harmonics of the electron cyclotron frequency can be observed in experiments by measuring the absorption or emission of electromagnetic radiation at these frequencies. This is commonly done in plasma physics experiments and astrophysical observations.

5. How do the first and second harmonics of the electron cyclotron frequency affect particle motion in a magnetic field?

The first harmonic determines the maximum energy that a particle can gain from absorbing electromagnetic radiation, while the second harmonic can lead to resonant particle acceleration. Both harmonics play a crucial role in determining the dynamics of charged particles in a magnetic field.

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