Analysis on matrix gradient coil modeling

The current distribution of the matrix gradient coil can be optimized via matrix gradient coil modeling to reduce the Lorentz force on individual coil elements. Two different modeling approaches are adopted, and their respective characteristics are summarized.

The magnetic field at each coil element is calculated. Then, the Lorentz force, torque, and deformation of the energized coil element in the magnetic field are derived. Two modeling approaches for matrix gradient coil, namely, optimizing coil element current (OCEC) modeling and optimizing coil element Lorentz force (OCEF) modeling, are proposed to reduce the Lorentz force on individual coil elements. The characteristics of different modeling approaches are compared by analyzing the influence of the weighting factor on the performance of the coil system. The current, Lorentz force, torque, and deformation results calculated via different modeling approaches are also compared.

Coil element magnetic fields are much weaker than the main magnetic field, and their effect can be ignored. Matrix gradient coil modeling with different regularization terms can help to decrease the current and Lorentz force of coil elements. The performance of the coil system calculated via different modeling approaches is similar when suitable weighting factors are adopted. The two modeling approaches, OCEC and OCEF, can better reduce the maximum current and Lorentz force on individual coil elements compared with the traditional modeling approach.

Different modeling approaches can help to optimize the current distribution of coil elements and satisfy various requirements while maintaining the performance of the coil system.