Solving Cyclotron Resonance: Azbel-Kaner Method

In summary, The Azbel-Kaner cyclotron resonance involves placing a B field parallel to the sample surface to induce cyclotron motion, while an oscillating electric field is used to induce resonance. The resonance occurs when the frequency of the electric field is equal to a multiple of the cyclotron frequency. To determine when the resonances occur, one can scan a frequency range and look for discrete steps in resonance frequencies. This can be done with the help of equipment specifically designed for this purpose.
  • #1
thuytran
2
0
Hi, I am a new member. May you help me with this problem?
In Azbel-Kaner cyclotron resonance, a B field is placed parallel to the sample surface to make cyclotron motion, an oscillation electric field is place to induce resonance.

There is a link about this:
http://books.google.com.tw/books?id...n resonance+de Haas van alphen effect&f=false

The resonance occurs when ω=n.ω' where ω'=eB/m' (cyclotron frequency_unknown value, we want to determine this) and ω is the frequency of Electric field E (known value). But I don't know how can we know when the resonances occur? ω=ω' or ω=2ω', ...

Thank you a lot!
 
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  • #2
You can scan some frequency range, and you will see discrete steps between the resonance frequencies. If you see resonance at 2.6 GHz, 3.9 GHz, 5.2GHz, ..., (arbitrary example) you can guess that the resonance frequency is 1.3 GHz.
 
  • #3
Thanks a lot for your reply!
I am curious about how we know that the resonance occur when we scan the frequency of the E field. In experiment, I think there must have an equipment so that we can know at which value of the frequency range have resonance. But I don't know what is the equipment in this case? Could you help me, please?
 

FAQ: Solving Cyclotron Resonance: Azbel-Kaner Method

1. What is Cyclotron Resonance?

Cyclotron resonance is a phenomenon in which charged particles, such as electrons, are accelerated by a magnetic field at a specific frequency. This frequency is determined by the strength of the magnetic field and the mass of the particle.

2. What is the Azbel-Kaner Method?

The Azbel-Kaner Method is a mathematical approach used to solve for the resonant frequency of cyclotron resonance. It involves using a variational principle to determine the optimal frequency for the charged particles to resonate.

3. Why is it important to solve for Cyclotron Resonance?

Solving for cyclotron resonance is important in understanding the behavior of charged particles in a magnetic field. It has applications in various fields such as particle accelerators, plasma physics, and magnetic resonance imaging (MRI).

4. What are the challenges in solving for Cyclotron Resonance?

One of the main challenges in solving for cyclotron resonance is accurately determining the strength of the magnetic field and the mass of the particles. Additionally, the mathematical calculations involved can be complex and require advanced knowledge in physics and mathematics.

5. How is the Azbel-Kaner Method different from other methods of solving Cyclotron Resonance?

The Azbel-Kaner Method is a variational approach, which means it involves finding the optimal solution by minimizing a functional. Other methods, such as the perturbation theory or numerical methods, may use different techniques to solve for cyclotron resonance.

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