let’s see.. search terms could be,
coaxial signal propagation speed; coaxial eddy currents; coaxial velocity factor
much of the discussion is around radio frequency propagation, but the same reasoning should apply to the rising edge of the pulse, here.
the inter-layer coupling capacitance and inductance yields velocity factor,
http://en.wikipedia.org/wiki/Wave_propagation_speed#Calculating_velocity_factor
which depends on respective conductor diameters and dielectric constant of the insulator.
eddy currents are responsible for the skin effect
http://en.wikipedia.org/wiki/Eddy_current#Strength_of_eddy_currents
skin depth depends on the frequency. we’re rather wide-band, here, with the rising edge in ~25 ns, and the pulse lasting microseconds. if 25 ns is 1/2 wave, then f=20 MHz; whereas the bulk of the current is delivered as though it is, say, a ~500 kHz pulse, and skin depth increases through the pulse, as δ = sqrt( (2 ρ) / (ω μ) ).
http://en.wikipedia.org/wiki/Skin_effect
em-field calculations for single and multi-layer coax
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=119816
and there is a book on signal propagation black magic
http://tinyurl.com/33nrh8p