25 September 1995 Theory of group applied to calculate field of multielectrode systems with symmetrical geometry of electrodes
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Abstract
If electrodes of ion optical system possess definite geometrical symmetry then the potential p of the system field can be written in the form of the sum of functions p(alpha ). These functions fall into one of the irresolvable representations of the group for symmetry of field- forming surfaces of the system. Each of the functions p(alpha ) possesses a definite symmetry in relation to the transform of the group and is the solution for a respective boundary value problem. Due to symmetry these new boundary value problems for p(alpha ) are usually simpler than the original problem for the potential p. In more detail is dealt the case, when the ion optical system's field-forming surfaces have the group symmetry Cnv. It is group symmetry of the body with n planes of symmetry penetrating through the axis of symmetry in n-order. For n equals 2,3,4,... it furns quadrapole, hexapole, octapole,... systems respectively. Proposed method allows to receive confined analytical formulas for electrostatic potential of different multipole systems with reference to the width of the clearance between the lamellar electrodes. In so doing, Dirihle's boundary value problem for multi-bound space may be reduced to the solution of Neyman's, Dirihle-Neyman's or Dirihle's boundary value problem for the function p(alpha ), but in a single-bound space what is bound are the two symmetry planes and the part of surface in the original electrode system. We have defined the conditions when such a solution is possible.
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Igor Felixovich Spivak-Lavrov, Igor Felixovich Spivak-Lavrov, } "Theory of group applied to calculate field of multielectrode systems with symmetrical geometry of electrodes", Proc. SPIE 2522, Electron-Beam Sources and Charged-Particle Optics, (25 September 1995); doi: 10.1117/12.221571; https://doi.org/10.1117/12.221571
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