Thank you for your comments. I think they got me headed in the right direction. After looking up the topics you all suggested here is what I have come up with.
This is only the circuitry required to trigger one coil. I would need to build one of these for each coil I want to use.
My thoughts are: (I am listing these so that you can tell me where I am right or wrong.)
C1 is charged by the voltage from my power source. This charge is released through L1 when a voltage is applied to the gate on T1.
R1 is used to control the rate C1 charges. I want C1 to charge very quickly...so I might not need it.
R2 is used to control the rate C2 discharges. Thereby allowing me to control the amount of time the magnet is on and hopefully not burn up the coil. For my test article I may use a variable resistor to tune the discharge time.
D1 is there to control EMF from the permanent magnet that will be moving near the coil. When the magnet moves near the coil it induces an EMF and the diode allows the current to flow to the other side of the coil. During operation D1 prevents current from flowing "back" through thereby forcing the current through the coil creating a magnetic field. (Am I understanding this correctly?)
T1 is a mosfet (as suggested by zoomkat). In the example I looked at, the transistor had a zener diode it it,hence Z1. I will need to look at the specs of the transistor and determine if one is built in. I am assuming that it is there to allow any undesigned large currents to flow through the diode instead of through the transistor..?
Does that look more reasonable? Any other thoughts?
Thank you again.