Polarimetric Neutron Magnetic Field Tomography: a non-Abelian ray transform

Naeem Desai (The University of Manchester)

ATB Frank Adams 1,

We consider the problem to determine a magnetic field from Polarimetric Neutron Magnetic Field Tomography (PNMFT) data. We see that this is an example of a non-Abelian ray transform and the problem has a unique solution for smooth magnetic fields. We go on to show that the linearised problem about a zero magnetic field reduces to a plane Radon transform and suggest a Modified Newton Kantarovich type algorithm for the numerical solution of the nonlinear problem. Furthermore we deduce the range for which the Modified Newton Kantarovich type algorithm works and show an example where it fails to reconstruct simulated PNMFT data.

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