Quadropole Formalism: Necessary Condition?

  • Thread starter mersecske
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In summary, the necessary condition for using the formalism is v << c. Higher moments have a decreasing contribution at 1/c^2, making them negligible for v << c. The quadrupole moment must also assume that the radiation is traveling radially and that the space intervals can be replaced by the radius. Terms with r^-2 and non-dominant r^-1 terms can be ignored in the slow motion approximation. Additionally, r must be much larger than the source size, d, and the wavelength, lambda. For v << c, the system must have a quadrupole moment in order to radiate. However, for large velocities, the quadrupole formalism is not reliable. It is possible to radiate
  • #1
mersecske
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v << c is the only necessary condition to use the formalism?
 
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  • #2
Contributions from higher moments fall off at 1/c2 so for the v << c range you can forget them.

If you mean the quadrupole moment.
 
  • #3
You also have to assume that the radiation being generated is pretty much traveling radially so that the space intervals in the retarded potential can simple be replaced by the radius and the quadrupole tensor can be defined in the normal way under the quadrupole approximation. Also, you ignore any r^-2 terms and the r^-1 terms that are not dominant in the slow motion approximation you mentioned.
 
  • #4
You also need r>>d, where d is the size of the source,
and r>>lambda.
v<<c is also equivalent to lambda>>d.
 
  • #5
For v << c the system must have quadrupole to radiate.
For large velocities the quadrupole formalism is not good,
but this statement is still true?
Or it is possible to radiate without quadrupole moment?
 

1. What is the Quadropole Formalism?

The Quadropole Formalism is a mathematical framework used to describe the behavior of systems with four poles, or four separate points of interaction. It is commonly used in physics and engineering to analyze and predict the behavior of complex systems.

2. What are the necessary conditions for a system to be described by the Quadropole Formalism?

The necessary conditions for a system to be described by the Quadropole Formalism are that the system must have four poles, and the interactions between these poles must be linear. Additionally, the system must be in a steady state or have a period of time where it can be considered in equilibrium.

3. How is the Quadropole Formalism used in practical applications?

The Quadropole Formalism is commonly used in fields such as electrical engineering, acoustics, and optics to analyze the behavior of complex systems. It is also used in some areas of physics and chemistry to study the interactions between molecules and their surroundings.

4. What are some advantages of using the Quadropole Formalism?

One advantage of using the Quadropole Formalism is that it allows for a simplified representation of complex systems, making it easier to analyze and understand their behavior. Additionally, it can be used to predict the response of a system to different inputs, making it a valuable tool for engineers and scientists.

5. Are there any limitations to the Quadropole Formalism?

Yes, there are some limitations to the Quadropole Formalism. It is only applicable to systems with four poles and linear interactions, so it cannot be used to describe all types of systems. Additionally, it assumes that the system is in a steady state or equilibrium, which may not always be the case in real-world scenarios.

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