Polynomial approximation of the magnetic field for track detector

We offer to your attention a preprint “Polynomial approximation of the magnetic field for track detector” (P1-2023-20) issued by the JINR Publishing Department.
The authors: Rikhvitsky V. S. (MLIT JINR), Belyaev A. V. (VBLHEP JINR) .

The magnetic field of the 1-meter hydrogen bubble chamber at LHE JINR was measured in 1971. In the programs for the geometric reconstruction of physical events, these data were used to calculate the field at arbitrary points in space using linear interpolation methods.

It is convenient to approximate the measured magnetic field by polynomials, which makes it possible to exploit the connections imposed by the magnetic field equations. The method of least squares is used to construct basic polynomials that satisfy the Laplace equation. The proposed method for constructing the basis was implemented and used in a number of programs for processing experimental data obtained on track detectors.

The presented method can be applied not only to bubble chambers, where the field is stationary and close to uniform, but also to other track detectors.