For your set up it's important to consider how the frequency of the driver compares to the Alfven frequency of the plasma. Magnetically confined plasma equilibrate on time scales comparable to the Alfven frequency.
If you drive the AC at a frequency slower than the Alfven frequency, then the Z-pinch evolution can be modeled a progression through a series of quasi-equilibria. As Astronuc hinted at when the current cycles through zero you will completely lose confinement. Your plasma will likely quench. And it's best to think of the next current cycle as a distinct Z-pinch. People have studied similar pulsed configurations as a means of operating a "steady state" fusion power plant.
On the other hand it's not exactly clear what will happen if your operate the current at a frequency that exceeds the Alfven frequency. You might be able to achieve macroscopic force balance in some average sense, but the plasma particles will no longer be confined to magnetic field lines. This will greatly reduce the particle and energy confinement. It is counterproductive and not ideal for a fusion reactor.
If you're interested in plasma physics/nuclear fusion you need to move beyond a physical mode based on the interaction of individual particles. An important aspect of plasma physics is the collective behavior that arises from the interaction many particles. In your white paper you make multiple erroneous statements that mostly stem from an over reliance on the individual particle mode. For instance there is no longitudinal force in a Z-pinch (you call in a current force), in steady-state the pinch force is balance by the plasma pressure not the coulomb force, and at no point is the pinch force overcome the coulomb barrier. If you're interested I can recommend several textbooks. Chen's book "Introduction to Plasma Physics and Controlled Fusion" is a standard introductory textbook.