Identification of magnetic fields by charged projectiles data

The problem of direct measurement of magnetic fields is in several cases not trivial when the region of interest is not directly accessible, or when conventional probes could be of disturbance. There are several "indirect" schemes, based on different physical effects, Proposed as alter-native to direct probing. We discuss here a novel technique for the identification of 1-D and 2-D magnetic fields, based on the analysis of trajectories of charged projectiles crossing the region under analysis. The magnetic field map is obtained through an inverse formulation of the motion problem of charged particles in the field. The inverse problem is solved by minimization procedures that identify the coefficients of suitable representations for the field In this way we are able to identify typical magnetic field configurations with great accuracy even in presence of noisy data. We give an overview on the method for the 1-D and 2-D cases, with reference to the field representation and the used optimization algorithms; moreover, the robustness of the technique in presence of noisy data is assessed via a numerical analysis.