Control under Structural Non-Stabilizability in Turbulent Plasmas

The control of plasma turbulence is conventionally formulated as a stabilization problem, despite the persistent failure of complete stabilization in practice. This work shows that stabilization-based control objectives are not merely unrealizable but undefined under the structural dynamics of transport-dominated plasma systems. By isolating quadratic energy growth, antisymmetric transport, and non-commuting constraint projections as minimal features, we prove that stabilizable invariant targets do not exist. Persistent alignment with non-expanding directions is structurally precluded, independent of control implementation. We demonstrate that the only admissible control objectives are time-extended quantities characterizing temporal organization, such as residence times, recurrence statistics, and recovery durations. A control methodology is developed that biases temporal organization rather than enforcing convergence. The framework provides a logically coherent foundation for plasma control under unavoidable instability and clarifies the operational meaning of controllability in fusion-relevant systems.