Logbook,
How did you 'see' this transient? It must have been with a scope. Did you use a clamp-on probe or did you use a shunt and measure the voltage across it?
"The large voltage spike created when the coil is energised
gets through to the current probe output and causes the problem. A better current probe that is shielded against the electric field is needed."
Was the probe located right next to the coil or something? I can't imagine this being an issue with your measurement unless it was right next to the coil. Also, what kind of voltage spike are you seeing in relation to that voltage applied?
What is the voltage of the coil? What is its normal function (contactor, actuator, valve, etc)?
"I have been looking at solenoid coils recently and you do see a massive inrush current when the voltage is first applied. This transient rapidly dies and you then get the ramping up of current required by E= L*di/dt. After that the current may start increasing faster than a ramp due to saturation of the core, or it may start slowing down due to the current limiting effect of the winding resistance."
Why is there a voltage spike? If there is, then by the resistive properties you could argue there is a corresponding current spike. However, the inductive properties would limit the current rise. And on and on.
The inductance will limit the current rise no matter what, we all agree on that. However, the current amplitude is what is being debated. It will be interesting to hear how you made your measurement for sure.