How can I preventing sparks from a plasma tube arcing onto electromagnet
What you are asking for makes no sense.

If you get any arcing outside the plasma tube, fix that first.

If this "arc" you talk about is the one existing in the plasma in the tube, then it's not clear what problem you are trying to address.  The arc is on the other side of some glass.  I don't see how you expect this to hurt what is connected to the coils, since the arc is not connected to the coils.

Since the plasma inside the tube becomes a conductor, it will have a magnetic field around it circularly.  Your coils are aligned such that they will pick up or cause magnetic fields parallel to the current in the plasma.  It's not clear what you think the purpose of this is.

If you want the coils to interact with the current in the plasma, then the magnetic field needs to loop around the plasma tube.  That means the electric current needs to loop around that.  In other words, you need to wrap the wire around a toroidal core, then have the plasma tube go thru the center of the toroid.