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Simulation Aspects of
the Classical Hydrogen Atom Problem
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Several examples are shown below of simulation
work involving a nonrelativistic classical electron particle
orbiting an infinitely massive classical proton, under a
variety of conditions. The underlying physics is briefly
described here, but for a full understanding of what is
happening, please see the recent article that has been submitted
for publication in the "Journal of Scientific Computing.
(This material was also presented by Prof. Dan Cole and
Yi Zou at a special international workshop on stochastic
electrodynamics, at Boston University, on June 4, 2001.
To view the actual report,
Click
Here or go to Prof. Dan Cole's publications page.
All the orbits shown here start with the
electron in a circular orbit with radius 0.5 Angstroms.
All of the following simulations are currently
being drafted and will be availible in the near future.
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View Orbit: Case
1
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Case 1: Here, one sees a
particle following a circular motion around a center.
This simulation contains no radiation reaction.
Consequently, the circular motion continues indefinitely.
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View Orbit: Case
2
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Case 2: The only force acting
is the Coulombic interaction between the proton
and electron. However, as opposed to Case 1, here
classical radiation reaction is assumed to exist.
As the electron orbits the proton, electromagnetic
radiation is radiated off, resulting in the electron's
orbit decaying as shown. This example exhibits the
classical problem recognized around 1900 of the
collapse that must occur if atoms were composed
of classical electrons and classical protons, and
no other effects existed to compensate the radiation
that must be emitted.
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View Orbit: Case 3
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Case 3: In this example,
in addition to the conditions in Case 2, circularly
polarized plane waves act on the electron, with
an angular frequency equal to the nonperturbed circular
orbit of 0.5 Angstroms. As can be seen, the orbit
still decays, but is retarded in its decay somewhat.
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View Orbit: Case 4
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Case 4: Now the amplitude
of the circularly polarized plane wave is made equal
and opposite to the reaction reaction force. Now,
the orbit does not decrease. The applied circularly
polarized plane waves exactly compensates the effect
of the radiation reaction.
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View Orbit: Case 5
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Cases 5 through 7: Here,
the amplitude of the applied circularly polarized
plane waves are increased in amplitude, by a factor
of about 3 from case 4 to case 5, then by a factor
of 10 beyond that in case 6, and by another factor
of 10 beyond that in case 7. As can be seen, the
electron spirals in and out, but still, the overall
orbit does not decay. What is exhibited here is
a very interesting example of a highly nonlinear
electrodynamic problem. For more details on this
behavior, please contact the authors for the preprints
mentioned earlier.
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View Orbit: Case 6
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View Orbit: Case 7
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