Topband: An oddball question about a BOG.

[Mikek]

  I want a BOG that will have a proper pattern over 500kHz to 4Mhz.
  As I understand it,
"loaded Beverages show increased directivity because velocity of 
propagation along the antenna is /*decreased*/."

I assume that is for antennas that are shorter than what is required for 
that frequency.

Info from here, https://www.w8ji.com/slinky_and_loaded_beverages.htm


    Is there any reason I can't load a BOG to make it directive at 500kHz?
My BOG length limit is 250ft.

Assuming the answer is yes.

If I do add the proper inductances along the length of the antenna
  then at 4MHz the pattern suffers. (previously I used nine inductors)
The inductance must be reduced as frequency goes up.

To that end I'm searching for a specific ferrite core geometry, like this,
https://www.dropbox.com/s/2bwsxrc58g51yu8/E%20Core%20Ferrire%20DB.jpg?dl=0
  Note, I dropped this and chipped the important part in the center, but 
before that, it did what I wanted.
  This material was not good at the frequencies I'm interested in.
So I need a material good to at least 4MHs and with an AsubL of 2000 to 
3000, or more, with a similar
geometry. Or any geometry that necks down to a smaller cross section.

Where can I buy such a core?

                 Thanks, Mikek
  PS, if anyone here wants to model a 250ft bogit over that frequency 
range, you would have my undying gratitude.