RE: NEC-LIST: E-M demos/simulations/animations

Hi all,

The discussion about dipole radiation and charge oscillations is very
interesting and challenging, but I guess it could be continued
endlessly.

Each model is a simplification and has its advantages, disadvantages
and limits. It is often not the only possible one and should never
claim to be an "absolute truth", but it should be without
contradictions as far as possible. It is useful to visualize abstract
relations and draw conclusions but always keeping in mind that going
too much into details may stretch a simple model too much and bring
contradictions to light. This holds particularly, if idealizations
(e.g. perfect conductivity) are applied.

In this sense now let me reply to Ed Millers comments:

> -----Original Message-----
> From: EDMUND K MILLER [mailto:EKMILLER_at_prodigy.net]
> Sent: Thursday, April 20, 2000 4:08 PM
> To: nec-list_at_ece.ubc.ca
> Subject: Re: NEC-LIST: E-M demos/simulations/animations
>
>
> I'm not sure that I understand your comment about the acceleration,
> but I don't think that I've ever said that "one electron travels from
> end ...." The external E-field seems to be terminated along the wire
> by a continuous succession of excess negative or positive charge, but
> where the terminating charges don't move far their rest positions.
> Our picture of equivalent current and charge needs never to deal with
> physical electrons in a real metal; once perfect conductivity is
> assumed, infinite mobility follows and these charges response
> instantaneously to the external fields.

1.) O.k., Maxwell's equations do not deal directly with physical
electrons. They form a classical field theory based on a continuum
model and space charge densities. All wavelengths must be large
compared to atomic dimensions. BUT: They may deal with point charges
and Hertzian dipoles (--> Green's functions), the latter one just
being oscillating point charges and the current distribution on a
metallization is given by means of summing up (integrating) these
charges oscillating with different amplitudes. (Just to be complete:
We are operating in frequency domain and thus differentiating
w.r.t. time means multiplying with j*omega). There is no reason to
not identify those point charges with physical electrons. Please
remember that charges are the only sources in Maxwell's equations with
physical meaning. Currents are a consequence of charge motion and
determined by the continuity equation.

2.) The conductivity in a metal is given by: conductivity =
Q*mobility*(electron density). Mobility is very low (30 cm**2/Vs),
much lower than in most semi-conductors (3000 cm**cm/Vs) This means,
the good conductivity is mainly caused by high density of free
electrons. If we assume perfect conductivity, then infinite electron
density follows (not infinite mobility!).

> I'm sorry to disagree with this picture of oscillating charge once
> again. The standing wave on a simple dipole is really comprised of
> two counter-propagating waves moving at constant speed. The apparent
> oscillation is a result of summing the two waves mathematically. If
> the charges actually oscillated all along the wire, then it would seem
> that the radiated power would grow in proportion to the length. This
> occurs for a spatially uniform current, but not for a sinusoidal
> current whose power grows asymptotically as log(kL).

3.) I strongly disagree: Propagating waves are mathematical solutions
of Maxwell's equations, but the same holds for eigensolutions or
modes, if suitable boundary conditions apply. If you measure the field
of a standing wave, the sensor registrates time-varying (oscillating)
fields with different amplitude at each point, not propagating
waves. This is the physical reality of a resonating structure. Of
course, you can split up this mode in two counter-propagating waves
moving at constant speed.

4.) As already mentioned, the charges do not oscillate with equal
amplitude along the wire and are related to the currents just by the
continuity relation. There is no contradiction to radiated power by
these equivalent currents.

Regards,

Achim Dreher

_________________________________________________________
Dr.-Ing. Achim Dreher Tel.: +49-8153-28-2314
Deutsches Zentrum fuer Fax: +49-8153-28-1135
Luft- und Raumfahrt e. V. E-Mail: achim.dreher_at_dlr.de
Oberpfaffenhofen

D-82234 WessFrom davem_at_fs3.ece.ubc.ca Mon May 1 09:10:49 MET 2000
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Date: Fri, 28 Apr 2000 11:10:56 +0200
From: Jos R Bergervoet <Jos.Bergervoet_at_philips.com>
Subject: Re: NEC-LIST: coax line with strip center conductor ?
Sender: davem_at_ece.ubc.ca
To: mjschmit_at_bellatlantic.net
Cc: nec-list_at_ee.ubc.ca
Message-id: <200005010638.XAA17836_at_fs3.ece.ubc.ca>
Organization: Philips Research Laboratories
Status: RO

mjschmit_at_bellatlantic.net wrote:
>
> Dear Jos,
>
> I found two more expressions for the impedance of coax lines with
> center strip :
> ..

Hello Max,

If we plot them against b/d, together with the exact equation:

  Zline = Z0 Sqrt[mur/epsr] * EllipticK[1-m] / (4 EllipticK[m])
      m = 4 / (b/d+d/b)^2

then we obtain, for mur=epsr=1, the figure at:

  http://home.iae.nl/users/bergervo/gouy/tube_strip.gif

You can see that for a value of b/d near 0.75, both approximations are
about 5 percent wrong. But if you would cleverly interpolate between
them, you might come close to the exact result. Of course that would
be "black art" (unlike the conformal mappings, which are crystal clear
:-)

-- Jos
Received on Thu Apr 27 2000 - 07:11:46 EDT