Accordingly following plasma inductance formula, the inductance is proportional to meters that can be true, BUT I do not understand that the inductance is directly proportional with squared radius and inverse proportional with plasma length.
As more length, less inductance?
It is said that plasma has a little inductance due electron inertia
This formula is obtained by considering the plasma as a cylinder, in the sense that the current is concentrated in a thin layer around the plasma (skin effect). You should note that the equation is very similar to that of a coil. See the Friedman book as reference.
http://books.google.it/books?id=9wqtYiy_gloC&pg=PA673&lpg=PA673&dq=plasma+inductance&source=bl&ots=hddIS_q-xQ&sig=h68-5V73yWi6NLsYpNMSBm3BKIE&hl=en&sa=X&ei=UutEU-rGM-Gp4gTS5ICoCA&ved=0CEoQ6AEwAw#v=onepage&q=plasma%20inductance&f=false
I could not read the book.
Accordingly to high frequency in wires equation in SI is:
L=2e-7*l * ( ln(4l/d)-1) as can you see it is proportional to the length.
Perhaps this formula describes better the plasma inductance as long as electron inertia is the same in a conductor than in a plasma.
The formula in your question is calculated under some assumption, considering the magnetic field in the direction of L and the current rotate around it. The other formula probably is for another geometry, probably with B perpendicular to L and with L>>d. I just noticed the similitude with the coil inductance.
About the book,
it is a google book. Usually are free. Probably you do not have the proper plugins.
I supose N must be 1.
Coil inductance could be obtained better using Nagaoka coefficients (year 1909!) obtained for a wider range of diameter/length ratio
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