DETERMINATION OF THE ION-OPTICAL PROPERTIES OF AN ELECTROSTATIC QUADRUPOLE LENS AS PART OF A COMPACT NUCLEAR MICROPROBE

The definition of the space of trajectory phase moments is introduced. The nonlinear differential equations of motion of a charged particle in the field of an electrostatic quadrupole lens in trajectory phase coordinates are transformed into a system of four linear ordinary differential equations in the third-order trajectory phase momentum space with 28 unknowns. The missing equations are obtained by applying a formal procedure of immersion of the original equations in the space of trajectory phase moments. The solution of the obtained complete system of equations is sought in the form of a matrizant, i.e., the matrix of phase moment transformation along the motion of a charged particle, which determines the ion-optical properties of an electrostatic quadrupole lens.