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
 

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

What is the Abraham-Lorentz equation and its significance in radiation friction?

The Abraham-Lorentz equation describes the motion of a charged particle under the influence of its own electromagnetic radiation. It accounts for the radiation reaction force, which is the recoil force experienced by the particle as it emits radiation. This equation is significant because it helps in understanding how radiation affects the dynamics of charged particles, which is crucial in fields like accelerator physics and astrophysics.

Why do non-physical solutions arise in the Abraham-Lorentz equation?

Non-physical solutions, such as pre-acceleration and runaway solutions, arise due to the third-order time derivative present in the Abraham-Lorentz equation. These terms can lead to solutions where the particle accelerates before any external force is applied (pre-acceleration) or accelerates indefinitely without bound (runaway solutions), both of which are not physically realistic.

How can one identify non-physical solutions in the context of the Abraham-Lorentz equation?

Non-physical solutions can be identified by examining the behavior of the solutions over time. If a solution shows pre-acceleration or runaway behavior, it is considered non-physical. Mathematically, this often involves looking at the characteristics of the differential equation and its solutions, such as the presence of exponentially growing terms that indicate runaway solutions.

What methods are used to eliminate or mitigate non-physical solutions in radiation friction problems?

Several methods can be used to address non-physical solutions, including:1. Applying boundary conditions that exclude non-physical behavior.2. Using approximations or modifications to the equation, such as the Landau-Lifshitz formulation, which provides a more physically realistic description by avoiding the problematic third-order derivative.3. Employing numerical techniques that carefully handle the stability and behavior of solutions.

What are the practical implications of solving the Abraham-Lorentz equation accurately?

Accurately solving the Abraham-Lorentz equation has important implications in various scientific and technological fields. For example, in accelerator physics, it helps in designing particle accelerators by predicting the behavior of charged particles. In astrophysics, it aids in understanding the dynamics of particles in strong electromagnetic fields, such as those near pulsars or black holes. Additionally, it can impact the development of radiation therapies in medical physics and the design of electronic components subjected to high radiation environments.

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