Jim Kelley wrote:
Dave wrote:
"Art Unwin" wrote in message
...

( I am assuming that skin depthg is not limitless.)
of course it is limitless, it is an exponential function so it never
goes to zero. the so called 'skin depth' is only the point where the
current has dropped to 1/e or about 37% of the surface value, still a
significant current.

The plots at the link Frank provided show current going rather abruptly
to zero - even negative ("contrary"?) in some cases. I wouldn't
presume to know whether it is modeled correctly.


Decrease of RF current with depth below the surface of a conductor is
only a true exponential if the available conductor depth is infinite.
In the modeled situations where there is 'competition' from a skin
effect on the opposite side of the conductor, the solution is a Bessel
function which does pass through zero and reverse direction at certain
depths.

In other words, the model is behaving as expected.

Programs such as NEC and Maxwell are not released until they have gone
through a very detailed process of checking and validation. The first
step is to check against special cases that can be independently solved
by analytical methods (in other words, pure math). The work isn't
complete until all the results agree within close margins, and the
reasons for any differences are fully understood.

By the time we amateurs come to hear about these programs, they have
already been thoroughly validated by developers and professional users.
That doesn't make them immune from further criticism... but only by
people who have done the work to earn that right.


--

73 from Ian GM3SEK
http://www.ifwtech.co.uk/g3sek

On Jan 14, 2:46*am, Ian White GM3SEK wrote:
Jim Kelley wrote:
Dave wrote:
*"Art Unwin" wrote in message
...

( I am assuming that skin depthg is not limitless.)
*of course it is limitless, it is an exponential function so it never
goes to zero. *the so called 'skin depth' is only the point where the
current has dropped to 1/e or about 37% of the surface value, still a
significant current.

The plots at the link Frank provided show current going rather abruptly
to zero - even negative ("contrary"?) in some cases. *I wouldn't
presume to know whether it is modeled correctly.

Decrease of RF current with depth below the surface of a conductor is
only a true exponential if the available conductor depth is infinite.
In the modeled situations where there is 'competition' from a skin
effect on the opposite side of the conductor, the solution is a Bessel
function which does pass through zero and reverse direction at certain
depths.

In other words, the model is behaving as expected.

Programs such as NEC and Maxwell are not released until they have gone
through a very detailed process of checking and validation. The first
step is to check against *special cases that can be independently solved
by analytical methods (in other words, pure math). The work isn't
complete until all the results agree within close margins, and the
reasons for any differences are fully understood.

By the time we amateurs come to hear about these programs, they have
already been thoroughly validated by developers and professional users.
That doesn't make them immune from further criticism... but only by
people who have done the work to earn that right.

--

73 from Ian GM3SEKhttp://www.ifwtech.co.uk/g3sek

So the developers know why the programs in the final analysis
gyrate towards radiators and arrays in equilibrium?
Do you know what that reason is?
Present thinking, I thought, suggest that the skin depth is quite thin
when used
for non destructive testing of materials. Is that also known by the
developers?
If the providing current is on the surface of a radiator then why does
the resulting eddy current
penetrate to the limits? Seems a sort of scrambled assumptions at play
here!

On Jan 14, 10:13*am, Art Unwin wrote:


So the developers know why the programs in the final analysis
* gyrate towards radiators and arrays in equilibrium?

I don't see how they could, being you won't describe how the
word "equilibrium" applies in such a case.

Do you know what that reason is?

Being I have never seen an antenna modeling program gyrate,
whether towards or away from a radiator or array, I sure don't.

Art Unwin wrote:

So the developers know why the programs in the final analysis
gyrate towards radiators and arrays in equilibrium? Do you know what
that reason is? Present thinking, I thought, suggest that the skin
depth is quite thin when used for non destructive testing of materials.
Is that also known by the developers? If the providing current is on
the surface of a radiator then why does the resulting eddy current
penetrate to the limits? Seems a sort of scrambled assumptions at play
here!

Well, at least the last sentence was correct.


--

73 from Ian GM3SEK
http://www.ifwtech.co.uk/g3sek

I don't want to add ammunition to support Art's gibberish, but it's
interesting and not widely known that current *does* flow in the
opposite direction to the main flow, at certain depths in a homogeneous
conductor.

In a solid conductor, the current density does, of course, decrease
exponentially with depth. The depth at which it's decayed to 1/e (about
37%) of the surface density is the "skin depth". This is why a hollow
tube is just as good a conductor as a solid one, providing only that the
tube wall is at least several skin depths thick.

But the *phase* of the current changes with depth, too, quite
dramatically. As you go each skin depth deeper below the surface, the
phase becomes one radian (about 57 degrees) more lagging. So at pi skin
depths below the surface, the current is completely out of phase with
the surface current, i.e., it's flowing in the opposite direction. Of
course, the current density at this point is very small, only 1/e^pi ~
4% of the surface density, so only a small fraction of the total current
flows completely backward. (Good thing!) At two pi skin depths, the
current is again in phase with the surface current, but its magnitude is
only 1/e^(2*pi) ~ 1/500 of the surface density. And so forth.

This isn't of much immediate practical use, and it's certainly not
offered as supporting in any way Art's fanciful theories (whatever they
might be). But it is an interesting fact.

Roy Lewallen, W7EL

On Jan 14, 3:49*pm, Roy Lewallen wrote:
I don't want to add ammunition to support Art's gibberish, but it's
interesting and not widely known that current *does* flow in the
opposite direction to the main flow, at certain depths in a homogeneous
conductor.

In a solid conductor, the current density does, of course, decrease
exponentially with depth. The depth at which it's decayed to 1/e (about
37%) of the surface density is the "skin depth". This is why a hollow
tube is just as good a conductor as a solid one, providing only that the
tube wall is at least several skin depths thick.

But the *phase* of the current changes with depth, too, quite
dramatically. As you go each skin depth deeper below the surface, the
phase becomes one radian (about 57 degrees) more lagging. So at pi skin
depths below the surface, the current is completely out of phase with
the surface current, i.e., it's flowing in the opposite direction. Of
course, the current density at this point is very small, only 1/e^pi ~
4% of the surface density, so only a small fraction of the total current
flows completely backward. (Good thing!) At two pi skin depths, the
current is again in phase with the surface current, but its magnitude is
only 1/e^(2*pi) ~ 1/500 of the surface density. And so forth.

This isn't of much immediate practical use, and it's certainly not
offered as supporting in any way Art's fanciful theories (whatever they
might be). But it is an interesting fact.

Roy Lewallen, W7EL

Exactly.
And every phase change support current /charge flow in the opposite
direction
in accordance with Newtons laws. Use a vector drawing to prove it for
yourself !
Or provide same as proof of my errors.
While you are at it do the same for a full wave radiator which IS in
equilibrium per Maxwells law
when the inner vector is now non existant since radiation occurs on
the surface at all times in accordance with the "tank circuit"
abilities And where the center path is only resistive in the case of a
fractional wave antenna. This is very, very basic physics to which I
know no challedge in the physics world. For you it is no difference
when you were affiliated with QST and supported the
commercial publishing of rediculas specifications to oppose change.
Sooner or later you will again have to change your tune to one that
does not include opposition to the truth.
The book that Richard is quoting is available on the web for $1.99
which will allow you to confront all the authors of their "rediculus"
errors at the same time together with all the Universities that use
the book as part of their physics curriculum
I await your appearance on CNN where it will undoubtably push aside
the viewing of the president

Cecil,
This is how you defrock the self perceived pompous expert. He
ofcourse does make errors which he will not own up to.
Art Unwin......KB9MZ....(xg)

Roy Lewallen wrote:
I don't want to add ammunition to support Art's gibberish, but it's
interesting and not widely known that current *does* flow in the
opposite direction to the main flow, at certain depths in a homogeneous
conductor.

In a solid conductor, the current density does, of course, decrease
exponentially with depth. The depth at which it's decayed to 1/e (about
37%) of the surface density is the "skin depth". This is why a hollow
tube is just as good a conductor as a solid one, providing only that the
tube wall is at least several skin depths thick.

But the *phase* of the current changes with depth, too, quite
dramatically. As you go each skin depth deeper below the surface, the
phase becomes one radian (about 57 degrees) more lagging. So at pi skin
depths below the surface, the current is completely out of phase with
the surface current, i.e., it's flowing in the opposite direction. Of
course, the current density at this point is very small, only 1/e^pi ~
4% of the surface density, so only a small fraction of the total current
flows completely backward. (Good thing!) At two pi skin depths, the
current is again in phase with the surface current, but its magnitude is
only 1/e^(2*pi) ~ 1/500 of the surface density. And so forth.

This isn't of much immediate practical use, and it's certainly not
offered as supporting in any way Art's fanciful theories (whatever they
might be). But it is an interesting fact.


I wonder if one could set up some sort of interesting demonstration of
this. If you could, for instance, have a 1 foot diameter conductor with
skin depth of an inch or so, and some (probably not feasible) way to
indicate current flow. (yes, in order for this to happen it has to be
AC, etc.)

On Jan 14, 4:18*pm, Jim Lux wrote:
Roy Lewallen wrote:
I don't want to add ammunition to support Art's gibberish, but it's
interesting and not widely known that current *does* flow in the
opposite direction to the main flow, at certain depths in a homogeneous
conductor.

In a solid conductor, the current density does, of course, decrease
exponentially with depth. The depth at which it's decayed to 1/e (about
37%) of the surface density is the "skin depth". This is why a hollow
tube is just as good a conductor as a solid one, providing only that the
tube wall is at least several skin depths thick.

But the *phase* of the current changes with depth, too, quite
dramatically. As you go each skin depth deeper below the surface, the
phase becomes one radian (about 57 degrees) more lagging. So at pi skin
depths below the surface, the current is completely out of phase with
the surface current, i.e., it's flowing in the opposite direction. Of
course, the current density at this point is very small, only 1/e^pi ~
4% of the surface density, so only a small fraction of the total current
flows completely backward. (Good thing!) At two pi skin depths, the
current is again in phase with the surface current, but its magnitude is
only 1/e^(2*pi) ~ 1/500 of the surface density. And so forth.

This isn't of much immediate practical use, and it's certainly not
offered as supporting in any way Art's fanciful theories (whatever they
might be). But it is an interesting fact.

I wonder if one could set up some sort of interesting demonstration of
this. *If you could, for instance, have a 1 foot diameter conductor with
skin depth of an inch or so, and some (probably not feasible) way to
indicate current flow. *(yes, in order for this to happen it has to be
AC, etc.)

Why not insert a wafer of the same material parallel to the axis and
apply
a non destuctive test on the material as a whole. When the wafer is
withdrawn
would it not be possible to observe the actual effective skin depth.
Of course, the slot for the wafer must not enter the radial surface
of the
radiator other wise circular flow would be interupted thus destroying
the
datum apearance. Obviously I have not utelised a non destructive test
first hand.
From my point of view as long as there is an eddy current on the
surface to eject a resting particle
there is not the requirement for endles depth and decay would be the
condition of the particle alone
and not that of the conductor. The particle still has nuclear content
when it emerges from the Sun's
arbritary field which is obviously subject to decay
Regards
Art

Ian White GM3SEK wrote:
Jim Kelley wrote:
Dave wrote:
"Art Unwin" wrote in message
...


( I am assuming that skin depthg is not limitless.)
of course it is limitless, it is an exponential function so it never
goes to zero. the so called 'skin depth' is only the point where the
current has dropped to 1/e or about 37% of the surface value, still a
significant current.

The plots at the link Frank provided show current going rather
abruptly to zero - even negative ("contrary"?) in some cases. I
wouldn't presume to know whether it is modeled correctly.


Decrease of RF current with depth below the surface of a conductor is
only a true exponential if the available conductor depth is infinite. In
the modeled situations where there is 'competition' from a skin effect
on the opposite side of the conductor, the solution is a Bessel function
which does pass through zero and reverse direction at certain depths.

In other words, the model is behaving as expected.

Programs such as NEC and Maxwell are not released until they have gone
through a very detailed process of checking and validation. The first
step is to check against special cases that can be independently solved
by analytical methods (in other words, pure math). The work isn't
complete until all the results agree within close margins, and the
reasons for any differences are fully understood.

By the time we amateurs come to hear about these programs, they have
already been thoroughly validated by developers and professional users.
That doesn't make them immune from further criticism... but only by
people who have done the work to earn that right.

Hi Ian,

Please know that my comment was never intended as a slight of anyone's
work. I simply don't presume to know anything about it other than to
observe that the citation appears to contradict the assertion that skin
depth is limitless and exponential in real conductors.

73, ac6xg

Jim Kelley wrote:

Hi Ian,

Please know that my comment was never intended as a slight of anyone's
work. I simply don't presume to know anything about it other than to
observe that the citation appears to contradict the assertion that skin
depth is limitless and exponential in real conductors.

73, ac6xg

that's because the usual discussion of "skin depth" is cribbed from a
physics textbook, where the (not always explicitly said) assumption is
"in an infinite uniform plane of infinite depth with no other magnetic
fields"

In that restricted (but useful) case, you can model the current (for the
purposes of things like resistivity) as if it were uniform from the
surface to the skin depth.

In cases where the thickness of the conductor is "large" relative to the
skin depth, the error in using the rectangular layer of current
assumption is "small".

In cases where this assumption isn't valid (or, if you need higher
precision), then a more complete analytical formulation is needed. If
the conductor happens to be circular, then Bessel functions are surely
involved (differential equations in circular things almost always
involve Bessel functions and/or Hankel transforms). Since most of us
don't do Bessel functions in our heads, we use tables or lookups.

There's two sets of tables and graphs for round conductors: one is for
solid conductors; the other is for tubular conductors. Different
boundary conditions on solving the differential equations, so different
analytical solutions.

A 1998 paper by Gaba and Abou-Dakka gives all the equations and
background, and adds the details needed for stranded wires and cables
made of multiple substances (e.g. ACSR power lines).

There's also some analytical solutions for square and rectangular cross
sections, but they're pretty ugly, compared to the round conductors.

once you start talking multiple materials and dielectrics, it becomes
easier to do FEM (following the dictum of my father's differential
equations professor: useful differential equations should be solved
numerically, because the analytical solution is often harder and more
computation than the numerical one). (another good example of this is
calculating the field between two spherical electrodes)