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

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SUMMARY

The discussion centers on the Abraham-Lorentz equation, which describes radiative friction for a particle in an electromagnetic field. The equation is expressed as ma(t)=q(E+vxB) + m(tau)a’(t). The user reports obtaining non-physical runaway solutions when solving this equation numerically, despite expecting a spiral motion due to radiation force. The issue is identified as stemming from the equation's derivation, which is specifically applicable to periodic motion, indicating that non-periodic functions lead to these non-causal solutions.

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  • Understanding of the Abraham-Lorentz equation
  • Familiarity with electromagnetic fields and forces
  • Knowledge of numerical methods for solving differential equations
  • Concept of periodic versus non-periodic motion in physics
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gennryAlbius
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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
 

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