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Suppress the common Fourier mode factor and define the transverse and full divergences of the fluid Lagrangian displacement byThe perturbed magnetic field is $\mathbf{Q}=({\mathbf{B}}_0\cdot \nabla )\mathbf{\xi }-(\mathbf{\xi }\cdot \nabla ){\mathbf{B}}_0-{\mathbf{B}}_{0}D$. Its components areThus the magnetic part of the energy integrand isUse $p_0^{\prime }=-B_0{B}_0^{\prime }/(4\pi )$ from force balance. The pressure-gradient cross term isThe current term has the azimuthal cross-product component ${\xi }_z^{\ast }{Q}_r-{\xi }_r^{\ast }{Q}_z$, givingEvery term involving $B_0^{\prime }$ cancels in the sum, including the possibly complex ${\xi }_z^{\ast }{\xi }_r$ terms. The magnetohydrodynamic energy principle therefore reduces exactly toFor physical $p_0\ge 0$ and positive adiabatic index $\gamma$, every surviving term is nonnegative. On the admissible displacement domain for the supplied functional, squared ideal-mode frequencies cannot be negative. This is the positive ideal energy of a theta pinch, proving absence of exponentially growing ideal modes. The qualification is stable or marginal, not strictly positive energy for every motion: at $k=0$, suitable incompressible displacements can have zero energy. As usual, the energy principle presumes regularity and boundary conditions eliminating unwanted surface terms; additional external systems are not part of the given functional.