Tom Donaly wrote:

Jim Kelley wrote:

Tom Donaly wrote:

Next, Cecil, you're going to be talking about a "current gradient"
and a "scalar current field." Here's a question for you, Cecil, and
Richard Harrison, and Yuri, too: how do you take the gradient of
the current at a point on a transmission line, and, if were possible
to do so, what is the physical significance of the result?
73,
Tom Donaly, KA6RUH



The standing wave current profile along, for example, a quarter wave
radiator is a cosine function. The gradient then would be the
derivative of the cosine function which is a -sine function.

73, ac6xg


Jim,
current, in a wire, is the total current density integrated across
a cross section of the wire. It's a vector, as is the current density.
Now tell me, how do you take the gradient of a vector? David K. Cheng,
in his book Field and Wave Electromagnetics, defines the gradient
operation this way: "We define the vector that represents both the
magnitude and the direction of the maximum space rate of increase
of a scalar as the gradient of that scalar." He wrote "scalar,"
not "vector," Jim. You and the rest of the boys are acting as if
current had magnitude but no direction, whereas it has both.
73,
Tom Donaly, KA6RUH

Not sure why you don't like gradients, Tom. I'm sure Mr. Cheng is
undoubtedly correct, but I'm just as sure he didn't intend that sentence
as any sort of definition of the term "gradient". That's something you
have apparently read into it. The gradient in our case (since you
proposed the question) would be expressed as the superposition of
forward and reverse currents, with magnitude and phase (or direction if
you prefer) written as a function of either position or angle *along*
the radiator. It's nothing fancy. Honest. It's simply the rate of
change of current as a function of position. The gradient across the
radiator at any given point along the radiator could then be determined
using some additional parameters - if someone were really that
interested in it (which I'm not).

73, ac6xg