Here is the concept:
To a first approximation, antenna captures the magnetic energy from a
volume of space in proportion to the length of the ferrite rod, and also
in proportion to the area of the ends of the rod (or, in other words, in
proportional to the volume of space between the ends of the rod). This
description works regardless of the diameter of the middle of the rod.
The "regardless" part holds as long as the permeability of the material
is high enough that there is a lower reluctance path through the necked
down middle section is much lower than the reluctance of a constant
diameter cylindrical volume of space between the large ends of the rod.
You can assemble (with epoxy) a stack of ferrite pieces into a long rod
middle section with a modest diameter, and add large diameter end pieces
as flux collectors, using low cost ferrite beads and plates that allow a
big cost savings, compared to buying a big cylindrical rod of the same
length and end diameter.
Here is an example with parts from Digikey:
Middle rod section made of 10 pieces of Steward 28B0591-200, 15mm dia.
35mm long, 5.9mm hole Bead @ $0.77 ea.
These stack into a 15 mm diameter hollow rod, 350 mm long. As best I
can tell, the leading 28 implies type 28 material, which, as best I can
tell from the Steward web site, is 125 permeability RF nickel zinc ferrite.
The large pole pieces on each end is made of a Steward HM1400-300,
35.56mm dia. 2.54mm thick Disk @ $1.09 ea. epoxied into the end of a
Steward 28B2400-000, 60.96mm dia. 12.7mm long 35.56mm hole Bead
$3.36 ea.
Total cost for ferrite pieces, 10*.77 +2*(1.09+3.36)=$16.60
Since the dimension for the disk and end bead are the same, you may need
to trim the disk a bit or expand the hole with silicon carbide sandpaper
for a slip fit. The disk comes with adhesive on one side, but I
wouldn't use that side as the surface glued to the rod. Epoxy is
stronger and thinner. Use a slow cure (20 or 30 minute, not 3 or 5
minute) epoxy for more strength, unfilled for thinner joints. If the
middle pieces have rough ends, polish them down to smooth with a piece
of fine silicon carbide sandpaper laying on a piece of window glass or
other flat surface for low reluctance joints.
By my estimation, the reluctance of the rod is about 1/3rd of the
reluctance of a similar cylinder of space, so the assumption that most
of the flux entering one end will pass through the rod, and not around
it are fairly good.
Wind the middle third or so of the rod with the antenna coil. If
desired, cover the coil with a grounded shield made of thin brass shim
stock, being careful not to let the ends of the 1 turn wrap make contact
as a shorted turn. The number of turns and the gauge of wire depend on
the input impedance of the first stage amplifier and on how much
capacitance you want to use to tune the coil to 60kHz and how narrow
band you want the antenna to be.
If you want to add physical armor and protection from the elements, seal
the whole thing in a piece of 2.5 or 3 inch I.D. PVC pipe or just coat
it all over with epoxy.
Here are the Steward long links to details for these 3 pieces:
http://www.steward.com/web_part_no.... Round and Cylindrical Cores&part=28B0591-200
http://www.steward.com/web_part_no....&progroup=4. Disks and Plates&part=HM1400-300
http://www.steward.com/web_part_no.... Round and Cylindrical Cores&part=28B2400-000
I think this design should provide a big increase in signal energy (say,
40 or more times) compared to the usual 1/4 or 1/2 inch diameter, 5 to
7.5 inch long rod designs.