Multiturn charge-exchange injection is the primary method of creating high-intensity hadron beams in circular accelerators, and phase space painting during injection enables tailoring of the accumulated phase space distribution. A technique we call eigenpainting allows injection of particles into a single mode of a coupled ring, providing full four-dimensional control of the phase space distribution. Under ideal conditions, uniform eigenpainting generates a linear-force equilibrium distribution in the transverse plane, with zero volume in four-dimensional transverse phase space, even including space charge. We have implemented eigenpainting for the first time in the spallation neutron source accumulator ring. Injecting $8.8\mathrm{\mu }\mathrm{C}$ of an 800 MeV beam, we obtain a final ratio of intrinsic transverse emittances of $\approx 2.4$. We analyze the effect of space charge on the final distribution through comparison of the reconstructed phase space to particle-in-cell simulations.

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• Beam injection, extraction & transport
• Space charge in beams