NEC-LIST: Plane wave question

I've run into an interesting result from both NEC-2 and NEC-4. The
problem consists of determining the current induced in a vertical wire
connected to perfect ground as a result of an impinging plane wave. I
get two answers for induced current, differing by a factor of two,
depending on whether this wave is generated by a plane wave excitation
source or by driving a distant vertical wire with a conventional voltage
source to produce an apparently same magnitude field at the test
antenna. The difference occurs only when a ground plane is present.

The test file and its output are at the end of this message. Please
refer to them for illumination of the following comments.

For both tests, the test antenna is a one meter high, one mm diameter
vertical wire, connected to perfect ground. Frequency is 10 MHz.

For the first test, the test antenna is at the origin and plane wave
excitation is applied. Plane wave amplitude is 1 V/m, which is fixed for
NEC-2 and the default for NEC-4. The output shows a current at the base
of the test antenna of 2.6297E-04 A.

For the second test, the test antenna is moved 1 km from the origin, and
an excitation antenna (tag 2) is placed at the origin. The excitation
antenna is also 1 m high, and has a 302,875 volt source at its base. The
field reported by an RP 1 card shows that the resulting field strength
is 1 V/m at a distance of 1 km from the origin, a value which is
consistent with theory. But with apparently the same 1 V/m amplitude
field, the current at the base of the test antenna is only 2.6297E-04 A,
exactly half what it was when excited with the plane wave source.

I've run a number of tests which convince me that no serious numerical
errors are occurring. For example, single and double precision programs
give essentially the same results, and moving the excitation antenna has
the expected effect on the induced current. Both NEC-2 and NEC-4 give
the same results. Average gain is very close to what it should be when
using the excitation antenna. A free space but otherwise essentially
identical model produces the same induced current for both types of
excitation, but the 2:1 current ratio remains when the wires are
disconnected from but still over a ground plane. So the presence of a
ground plane seems to be the causative factor.

Can someone explain why the two excitation methods produce currents
which differ by a factor of two, but only when over a ground plane? And
what should the induced base current be for a 1 V/m field when a ground
plane is present?

Roy Lewallen

   -------- Input file (complete) -------

CM Short vertical over perfect ground with
CM two kinds of excitation:
CM 1. Plane wave
CM 2. Field from another vertical one km distant
CE
GW 1,10,0.,0.,0.,0.,0.,1.,.0005
GE 1
FR 0,1,0,0,10.
GN 1
EX 1,1,1,0,90.,0.,0.,0.,0.,0.
XQ
NX
CE
GW 1,10,1000.,0.,0.,1000.,0.,1.,.0005
GW 2,10,0.,0.,0.,0.,0.,1.,.0005
GE 1
FR 0,1,0,0,10.
GN 1
EX 0,2,1,0,302875.,0.
RP 1,1,1,1000,0.,0.,0.,0.,1000.
EN

   ------- Output file (edited, with comments) ----------

[First setup - plane wave excitation. Test antenna is tag 1.]

                                         - - - EXCITATION - - -

     PLANE WAVE THETA= 90.00 DEG, PHI= 0.00 DEG, ETA= 0.00
DEG, TYPE -LINEAR= AXIAL RATIO= 0.000

                              - - - CURRENTS AND LOCATION - - -

                                  DISTANCES IN WAVELENGTHS

   SEG. TAG COORD. OF SEG. CENTER SEG. - - - CURRENT
(AMPS) - - -
   NO. NO. X Y Z LENGTH REAL IMAG.
      MAG. PHASE
      1 1 0.0000 0.0000 0.0017 0.00334 -1.6583E-07
-5.2595E-04 5.2595E-04 -90.018

. . .

[Second run: Two wires. The test wire is tag 1, placed 1000 m from the
origin. The second wire, at the origin, has a 302,875 volt source at its
base to produce 1 V/m at a distance of 1 km.]

                              - - - CURRENTS AND LOCATION - - -

                                  DISTANCES IN WAVELENGTHS

   SEG. TAG COORD. OF SEG. CENTER SEG. - - - CURRENT
(AMPS) - - -
   NO. NO. X Y Z LENGTH REAL IMAG.
      MAG. PHASE
      1 1 33.3556 0.0000 0.0017 0.00334 2.0632E-04
-1.6305E-04 2.6297E-04 -38.317

. . .

                             - - - RADIATED FIELDS NEAR GROUND - - -

         - - - LOCATION - - - - - E(THETA) - - - -
E(PHI) - - - - E(RADIAL) - -
        RHO PHI Z MAG PHASE MAG
   PHASE MAG PHASE
      METERS DEGREES METERS VOLTS/M DEGREES VOLTS/M
  DEGREES VOLTS/M DEGREES

      1000.00 0.00 0.00 1.0000E+00 51.98 0.0000E+00
     0.00 0.0000E+00 0.00

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