According to the principle of the "uniform magnetization" and harmonic analytic method, the fields of the ring structure system with multi-segmented and trapezoidal magnet are analysed.

According to the principle of "Uniform magnetization", the field-shape of plane head quadrupole of "coil replacement" and "Quasi coil replacement" is analysed by means of series expansion.

The energy spectrum and the ground state magnetization of electron are calculated and analyzed, and are compared with the situation in uniform magnetic filed.