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We describe an open structure of permanently magnetized material for interventional magnetic resonance imaging of the brain. We transformed the ideal magnet, contained between two coaxial cones, into a practical device by a series of geometrical steps that minimize field perturbations. By taking advantage of the quasi-linear demagnetization characteristics of rare-earth materials, we could analyze the structure with an exact mathematical model. The magnet, built of material of remanence 1.38 T, generates a field of 0.45 T within its central gap 30 cm wide. Our numerical computations show a remarkable 0.25% field uniformity in the imaging region. The large opening makes the conical magnet suitable for interventional and surgical imaging.