Q:

Measuring a magnetic pulse using a coil, and circuit adjustments

I have the following circuit, 

I am using it to create a pulsed magnetic field, in the coil. I am trying to measure and verify the magnetic field in the coil. I am testing it with 40 V to drive the coil at the moment, which should provide 20 A of current to the coil and produce a 12.5 mT field within it. There are additional unwanted oscillations that are making things less straight forward for me.
First I would like to verify the current going through the coil, so I included R8, to measure the voltage across it, to work out the pulsed current in the circuit.
The model result comes out a lot smoother, which is expected, as it is more ideal.

There is a lot more ringing/oscillations in my built circuit, but it comes out at just over 200 mV which indicates approximately 20 A of current.
I am curious about the large spike and oscillations, what might be causing this and how I might reduce these. Below I mention additional inductance that appears to be cause by the resistors R4 and R7, so this is a likely contributing factor.
Next I want to measure the magnetic field using a coil. Based on the design of the coil in the circuit, for 20 A of current it should theoretically produce a 12.5 mT B field.
Using a single turn loop, with an area of 1.29e-4 m^2 placed at the centre of the coil, the voltage should theoretically be V = -1.6125e-6/dt
based on V = -N dBA/dt
My plot of the loop voltage is 

It spikes when the current goes on and off. However there is a lot of oscillation

If I use the first peak of the voltage, taking its time, the formula suggests a output voltage of 47 V needed for the 12.5 mT I expect, not the ~250 mV I am getting. So I have made a mistake somewhere or am missing something in my assumptions. The formula I am using I have typically seen for an oscillating field, but I thought it is applicable here also.
I would like to know where I am going wrong with my assumptions with the measurement coil, either theoretical or with my set up.

I noticed that the oscillations reduce further away from the initial spike if I touch the casing of R4 (and to some degree R3), which suggests they are adding an additional inductance to my circuit which is being reduced by the capacitance of my body as I touch it, and I have missed in the model.
Also looking at my pulse signal to switch on/off M1, it is not quite a square pulse when it is connected to the circuit.

This graph shows what happens to my function generator signal as from what it is set to do, when connected to the circuit with V3 OFF, and with V3 ON. It kind of gets up to 6 V which is about where M2 should switch on and goes down before going up again.
Note that M2 in the model is not the same MOSFET as in my circuit, it is actually a IRFP260NPNF MOSFET, I am unable to model the exact one in the circuit simulation (still learning).
I am hoping for suggestions as to how I might improve my circuit and reduce unwanted oscillations, and to improve the method I am using to measure the magnetic field, and how I might be going wrong.

A:

When you have a fast rise time in current or voltage, the inductance of all current loops and load capacitance are both important and often overlooked. Also the ratio of that reactive impedance to resistive at its resonant frequency determines the dampening factor or its inverse gain ratio, Q .  In this case I see 25MHz with high Q >10.
Model errors
There will always be some capacitance in every part connected to or near the ground or supply.  This includes the FET and your scope probe and finger.
This is when you need to add stray inductance and FET  capacitance to your schematic model. (See specs for Ciss and Coss) . For instance a 1cm wire or resistor to the gate can be 10nH and the Ciss is 5150 pF which resonates near the 25 MHz of your gate Vgs pulse.  This has a resonant impedance around 1.5 Ohms so 0.1 Ohms results in a Q >10, so increase R3 to at least the Rg of the FET = 1.5 Ohm for a more critically damped response.
Then all coils have interwinding capacitance, so all Inductors have a unique Self Resonant Frequency (SRF)  parallel for L and in series for Capacitors with some inductance and often referred as Series Resonant Frequency, because microwave Caps also have a PRF (parallel mode).
Probe effects
Even a scope probe with low 60 pF/m coax will resonate with your probe ground wire inductance, ESL of ~10nH/cm so that inductance must be kept short as well.
Then there are stray effects which are much smaller in your layout such as coupling capacitance, Cs, to ground effects and series inductance to load, ESL.  All 10:1 probes are notorious for >20MHz resonance with long ground clips on a pulse wave.
Finger results
Since the FET inverts and your finger has high capacitance over a resistor area and your body conducts and radiates this putting your finger on the gate R3 tends to couple to the radiated resonant output field and cancel. It also reduces the rise time of the gate signal.
Putting your finger on R4 acts as a bypass cap to the stray inductance of that circuit which is part of the same current loop as the ground signal. So that too bypasses some current bandwidth thru your finger instead of the inductive resistor path. R4= 1 Ohm is equivalent to about 10nF at 25MHz which is what you might get by pressing hard on a resistor.
Calibrating your fingers on an RLC meter is a good way to understanding how to tune you circuit.  
Anecdote
When I was young, there were several times when I wished I could ship my finger along with my final instrument design ... ;) 
That is until I mastered EMC by a thorough understanding of RF loops, stray capacitance and slot/strip antennae.  Then you can estimate the radiated noise and susceptibility issues with resonance just by looking at the geometry of the layout and the bandwidth of the signal.  Estimating tracks by RLC and Z. (Hint: get an RLC Nomograph and Saturn PCB analyzer software.)  Examine the effects of ESD @ 0 to 300MHz which depends on the gap of the avalanche effect. (arc in air)

