Radiation Friction: Solving Abraham-Lorentz Eq for Non-Physical Solutions

In summary, the conversation discusses the Abraham-Lorentz equation, which describes radiative friction for a particle moving in an electromagnetic field. The speaker mentions solving the equation numerically and getting non-physical solutions, which they believe should result in the particle's movement decaying due to the radiation force. The speaker then questions what they may be doing wrong and is advised to look at the derivation, which may only apply to periodic motion and not non-periodic functions. There may be known solutions for non-periodic functions that result in runaway or non-causal solutions.
  • #1
gennryAlbius
1
0
There is a well-known Abraham-Lorentz equation describing radiative friction. Suppose a particle moves in an electromagnetic field.
ma(t)=q(E+vxB) + m(tau)a’(t)

By solving this equation numerically, I get non-physical solutions(runaway solutions) Although, it would seem that an electron in an electromagnetic field should move in a spiral, and due to the presence of a radiation force, its movement should decay (I should get such a result). What am I doing wrong?
 
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  • #2
I am not completely certain, but I believe that if you look at the derivation you will see that it is specifically for periodic motion. I believe that for certain non-periodic functions the runaway and non-causal solutions are known
 

1. What is radiation friction?

Radiation friction is a phenomenon in which a charged particle moving through a medium experiences a force due to the emission of electromagnetic radiation. This force is caused by the interaction between the particle's electric charge and the electric and magnetic fields of the medium.

2. What is the Abraham-Lorentz equation?

The Abraham-Lorentz equation is a mathematical formula used to calculate the radiation friction force on a charged particle. It takes into account the particle's charge, mass, velocity, and the properties of the medium it is moving through.

3. Why is it important to solve the Abraham-Lorentz equation for non-physical solutions?

Non-physical solutions of the Abraham-Lorentz equation can provide valuable insights into the behavior of charged particles in different environments. These solutions can also help in the development of new technologies, such as high-energy particle accelerators and advanced propulsion systems.

4. How is the Abraham-Lorentz equation solved for non-physical solutions?

The Abraham-Lorentz equation can be solved using various mathematical techniques, such as perturbation theory, numerical methods, and analytical approximations. These methods allow for the identification of non-physical solutions and their implications.

5. What are some potential applications of understanding non-physical solutions of the Abraham-Lorentz equation?

Understanding non-physical solutions of the Abraham-Lorentz equation can have a wide range of applications in fields such as astrophysics, plasma physics, and materials science. It can also aid in the development of more accurate models for predicting the behavior of charged particles in different environments.

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