This is the model I used for the secondary. The top resistors simulate the loss on the coil. This model differs from a transmission line in that the inductors are coupled to each other as they would be in a real coil. I think this is what keeps the voltage and currents in phase along the coil's length. The inline resistors simulate the DC resistance of the wire. The capacitors simulate the distributed capacitance of the coil. There is a 10.25pF top capacitance to simulate the top terminal. The 1000Meg resistors are to keep the computations stable.

 

This is a frequency sweep with 1 volt p-p input

 

 

The same sweep on a log scale

 

 

These are the voltage and current waveforms along the coil. Not that everything is in phase along the coil!! This matches what I measure in that the top and bottom currents are in phase but the current is lower at the top.

 

This is a chart of the voltages and currents along with the plot
 
Test Point Voltage Current (mA)
Top 194.6 1.359
L7 169.9 2.244
L5 130.6 2.950
L3 80.8 3.419
L1 24.5 3.613

 

This is a model of the voltage distribution using a simple sine function

 

 

This is the current using a cosine function with a multiplication factor

 

 

a:=0.78

 

This function seems to match the model well and simulates the current seen at the top of the coil.