Comparison of two methods for magnetic field synthesis on a solenoid’s axis

Abstract

Magnetic field synthesis problems have been discussed at length in scientific literature but they still remain as a topic of research in electrical engineering, physics and medical applications. In these disciplines, there is often a need to design an electromagnetic arrangement which can generate a magnetic field of required distribution. Such an arrangement can also work as an active shield. The aim of an active shield is to generate a specified magnetic field which counteracts the external magnetic fields in a protected region. The idea of active shielding is to construct a suitable arrangement of coils, excited with currents that generate an opposite magnetic field sufficient to cancel out the unwanted external fields. The opposite field must have the same frequency and amplitude as the external field. If the incident field presents a wide bandwidth, the final aim is to generate an opposite field in the same frequency range or at least in a range as large as possible. Two independent methods of magnetic fields synthesis, i.e. iteratively regularized Gauss-Newton method and Genetic Algorithm coupled with Bezier curves-based method, are discussed and compared in this paper.

Genetic algorithm coupled with Bézier curves applied to the magnetic field on a solenoid axis synthesis

“…1. A definition sketch for a solenoid of unknown shape r = f (z') and solenoid's thickness t By using the formula for the magnetic field intensity on the circular loop axis, it can be shown that the magnetic field intensity vector on the solenoid axis has a simple form (only z-component exists) [1]:…”

“…The Fredholm equation of the first kind belongs to the class of ill-posed inverse problems as defined by Hadamard. In order to solve (3) well known iteratively regularized Gauss-Newton can be applied [1]. However, such a deterministic approach is possible, when during optimization process t parameter has an assumed constant value.…”

“…A certain application of such an electromagnetic system can be a compensation of external magnetic fields in order to protect sensitive electronic apparatus from harmful electromagnetic interferences. This technique is called active shielding [1,2]. Usually, sources of a magnetic field are set of coils and various types of solenoids.…”

“…Similar magnetic field synthesis problems have been considered in the past as well but objective functions and design variables have been defined in a different way. For example, in [1] the optimization has been performed for assumed constant solenoid's thickness values, while in [2] the magnetic field has been synthesized in the axisymmetric three-dimensional finite region. This paper is a continuation of [1,2,[4][5] and discusses a problem of designing the shape of a solenoid which produces a uniform magnetic field on its axis.…”

“…For example, in [1] the optimization has been performed for assumed constant solenoid's thickness values, while in [2] the magnetic field has been synthesized in the axisymmetric three-dimensional finite region. This paper is a continuation of [1,2,[4][5] and discusses a problem of designing the shape of a solenoid which produces a uniform magnetic field on its axis. The method of finding the optimal shape is based on a genetic algorithm (GA) coupled with Bézier curves [6][7][8].…”