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

[gennryAlbius]

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?

 

[Dale]

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