It may be very helpful for you to review freshman E&M.I don't know why you feel it appropriate to adopt such a tone with me. I'm starting to suspect that you are less interested in learning the correct answers, and more interested in advancing some sort of kook science agenda.
Gauss's law applies to electrostatics, not moving charge.
Gauss's law is absolutely universal. In fact, it's one of Maxwell's equations.
Apply Gauss's law to a current carrying wire. The integral of E over the cylindrical volume is zero, is it not? That means there's no net charge enclosed, as is true in an electrically neutral conductor. Yet the measured E field is in the direction of the current travel is it not?
Yes, but the integral of the field, as you point out, is zero, thus Gauss's law is satisfied. I'm not sure why you bring this up in any case, as there is no gravitational analogue (any mass current will have a net gravitational charge, as there are no antigravity charges).
E is in the direction of the current density. The wire has a net E field,
No, it doesn't. You correctly stated above that the integral is zero.
but net zero charge. Where would this net E field come from if the total electrostatic charge of the wire is zero? Why does it exist only when the charge is moving?
That's just wrong. Moving current in a wire does not create the electric field; rather, the electric field causes the current to flow.
Gauss's law looks at E perpindicular to the surface. The wire, or ion beam has an equal, but opposite E on both ends of the cylinder so it cancels in the integral. The E field that is responsible for the charge movement (whether it causes the charge to move or it is a result of it) exists in addition to the E of the charge and does not affect Gauss's law. You said it does. Please demonstrate.
My apologies. Your comment about Gauss's law being invalid in the presence of moving charge had me suspect. If I take a tennis ball put lots of charge on it and throw it will a stationary observer see only the static field of a collection of charge pass by? Will the charged tennis ball have any additional inertia due to the charge? Assume the charge has zero mass.
More importantly:
If I take a plastic torus that has charge fixed on the surface and spin it about its center axis will I see an E field due to this current/charge movement? (will it be in the direction of the current/ moving charge?) If so, this E field exists as a result of charge movement and no E field caused the charge to move,as no E field was ever applied, it was purely mechanical rotation. Will I see a magnetic field corresponding to this ring of current (revolving ring of charge)despite no applied electric field?
So I ask again, does moving charge create an additional E field?