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

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The discussion centers on the Abraham-Lorentz equation, which describes radiative friction for a particle in an electromagnetic field. The user encounters non-physical, runaway solutions when solving the equation numerically, despite expecting a spiral motion with decay due to radiation force. There is uncertainty about the derivation's applicability, particularly regarding its validity for non-periodic functions. The user suggests that the equation's derivation is tailored for periodic motion, which may explain the unexpected results. The conversation highlights the complexities of applying the Abraham-Lorentz equation to different motion types.
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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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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
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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