Minimum Volume of a Hom., Bare Cylindrical Reactor

[Uranium]

Just trying to do a problem to find the minimum volume for a homogeneous, bare cylindrical reactor, and my main question is if the radial and axial bucklings are equal to one another at min. V or if there is some other condition that would be helpful. Thanks.

 

[Astronuc]

Is there a constraint on geometry, e.g., height H = diameter D = 2R?

What does one know about the relationship between k and k_∞, and between B_z and B_r?

V = πR²H

 

[Uranium]

There is not a constraint on the geometry. The volume is supposed to be a function of material buckling.

One doesn't know anything about k-eff or k-inf, but I am thinking we might know the relationship between Bz and Br. I'm just trying to figure out if my assumption that Vmin occurs when (Bz)^2 = (Br)^2 =((Bm)^2)/2 is a reasonable one. I haven't been able to find anything regarding the relationship in the text though.