Radiation reaction and radiative losses derived from kinetic power...

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Radiation reaction and radiative losses derived from kinetic power...

Postby DeltaV » Fri Jan 22, 2016 5:51 pm

Radiation reaction and radiative losses derived from the kinetic power of the electric inertial mass of a charge

It is shown that formulas for radiation reaction and radiative losses from a charge can be derived from the kinetic power of its electric inertial mass. The derivation assumes a non-relativistic but otherwise an arbitrary motion of the charge. We exploit the fact that as the charge velocity changes because of a constant acceleration, there are accompanying modifications in its electromagnetic fields which can remain concurrent with the charge motion because the velocity as well as acceleration information enters into the field expression. However, if the acceleration of the charge is varying, information about that being not present in the field expressions, the electromagnetic fields get "out of step" with the actual charge motion. Accordingly we arrive at a radiation reaction formula for an arbitrarily moving charge, obtained hitherto in literature from the self-force, derived in a rather cumbersome way from the detailed mutual interaction between various constituents of a small charged sphere. This way we demonstrate that an irretrievable power loss from a charge occurs only when there is a change in its acceleration and the derived instantaneous power loss is directly proportional to the scalar product of the velocity and the rate of change of the acceleration of the charge.

We have thus derived radiation reaction and the radiative
losses from the kinetic power of the electric inertial
mass of a charged particle. This novel approach allowed
us, in a few simple and easy mathematical steps, to arrive
at radiative power-loss formula, obtained hitherto
in literature from very lengthy and tedious calculations
of the self-force of a charged sphere. It demonstrated
in a succinct manner the basic soundness of the assertion
that the radiation losses result from a non-uniform
acceleration of the charged system. But even more important,
it provides us a totally different physical outlook
on the energy-momentum conservation relation between
electromagnetic and mechanical phenomena in classical

D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Re: Radiation reaction and radiative losses derived from kinetic power...

Postby D Tibbets » Mon Jan 25, 2016 6:42 pm

From the quote, it seems to me that they are just restating the current understanding, at least for the most part. The light electrons undergo the most acceleration, speed change, because their inertia is much smaller than ions. Higher KE and smaller mass leads to the greatest acceleration and thus the highest radiative energy loss -Bremsstruhlung. The electrons inertia or momentum is ~ 1/ 60th that of the deuterium ion. The electron accelerating around a nearby ion emits ~60 times the Bremsstruhlung, as the ion accelerating around the electron. Because of this difference in speed and acceleration effect the ions are generally considered as stationary and the electron as the only moving element. This simplification greatly eases the math and gives a fairly accurate picture.

Since the ion is considered as stationary and fixed in his approximation, it doesn't matter what the mass of the ion is. The amount of charge on the ion is a different matter, the charge , or Z - atomic number(if fully ionized) has a significant effect on the acceleration of the electron. It scales as the Z squared. Boron at +5 results in the electron radiating 25 times more Bremsstruhlung radiation with everything else being equal.

Why does the electrons not radiate away energy when they accelerate (orbit) a nucleus in a neutral atom? Quantum mechanics comes to the rescue. Usually, the amount of radiation is too small to change the electrons orbit sufficiently to change it's orbit to the next allowed orbit, thus it is prohibited. There are conditions though where things change. Einstein won his Nobel prize for describing this (the photoelectric effect).

Dan Tibbets
To error is human... and I'm very human.

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