Symmetry filtering and dimensionless response of axial magnet displacement in a levitated dipole field

In a levitated dipole, the primary confining field source is a magnet under active control, so its position fluctuations simultaneously modify the free boundary, the plasma profiles, and the fusion power density. Taking the inner dipole coil radius R D as the characteristic scale, we introduce the dimensionless axial displacement ξ = Δ z D / R D as a physical interface linking levitation control to the plasma response. Under quasi-static, topologically continuous, and near-midplane-symmetric conditions, an analytic expansion shows that local profiles and power densities respond at O ( ξ ) , whereas spatial symmetry filters the dominant antisymmetric component upon volume integration. Consequently, the global fusion-to-radiation power ratio retains only a residual of O ( η ξ ) + O ( ξ 2 ) , where η characterizes the finite up–down asymmetry. This mechanism is verified on the CAT-1 device through free-boundary equilibrium sequences and projections of five fusion reaction systems (D–D, D–T, D– 3 He, T–T, T– 3 He). At typical displacement amplitudes, the rms variation of the local power density reaches 13%–30%, but volume integration cancels more than 98% of the first-order contribution, keeping the same-frequency fluctuation of the global power ratio below 0.1%. Different reaction systems share the same geometric filter and differ only in the residual coefficients set by their respective temperature sensitivities. The second-order nonlinearity produces frequency-doubled components and, under multi-frequency drives, sum- and difference-frequency lines. These results quantify the order separation between local and volume-integrated responses, measure the associated cancellation, and verify the residual response across five reaction channels. Therefore, position tolerances must separately constrain local power-density limits and global power fluctuations as two independent indicators.