The theory of a circular thermal ionizer is considered. Although originally these papers were first published a long time ago, the sensitivity characteristics of the thermal ionization ion source for uranium samples which utilizes this theory are still a record.

Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
Contact: L. N. Gall, lngall@narod.ru

The paper specifies in precise mathematical terms the problem of optimal adjusting of the beam of charged particles (ion source) and the analyzing system. A special class of 3D electrostatic fields of an additive type with a plane of symmetry is considered which can implement achromatic conveying and 2^nd order focusing for planar beams.

¹Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
²Saint-Petersburg State Polytechnical University, RF
Contact: L. N. Gall, lngall@narod.ru

In this article the new (at that point in time — 1989) class of electrostatic fields in which is carried out the time space focusing control in the direction of ions separation by times of flight is determined and its characteristics are analyzed. The global approach to the synthesis of potentials with ideal time space focusing control, which one was afterwards with great success used by Yu.K. Golikov during synthesis of concrete configurations for multiturn time-of-flight mass-analyzers, is described. The field, having been examined in this work as a basic example, became wildly known because of using it afterwards in the new class of mass-spectrometer devices — electrostatic traps with Fourier analysis (trade mark "ORBITRAP").

¹Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
²Saint-Petersburg State Polytechnical University, RF
Contact: L. N. Gall, lngall@narod.ru

In this article the authors study the three-dimensional Laplace equation. Using innovative techniques such as circular variables and additively multiplicative separation of variables, they are able to find new and unusual physically solutions.

¹Saint-Petersburg State Polytechnical University, RF
²Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
Contact: I. A. Averin, agreer@bk.ru

Elements of the theory of axisymmetric ion trap with quadratic dependence on one coordinate are given. Ion dynamics in the trap is investigated and classified for different ion motion modes.

Saint-Petersburg State Polytechnical University, RF
Contact: K. V. Solovyev, k-solovyev@mail.ru

In the article an analytical representation of the fields for electric spectrographs expressed in an uniform generalized form is developed. The potentials of such fields are of Laplace’s type and presented as φ(x, y, z) = P(x, y, z)lnR(x, y, z) + Q(x, y, z), where P, Q, R — are uniform functions in Euler’s sense with an integer multiplicity. It is built an accurate algorithm to synthesize such potential structures exploiting a complex Donkin’s potential of null multiplicity. In these constructions one can use any function of complex variables. Some surfaces of equal potential of these fields are demonstrated and analyze. The different variants to use in electron spectroscopy are discussed.

Saint-Petersburg State Polytechnic University, Saint-Petersburg, RF
Contact: N. K. Krasnova, n.k.krasnova@mail.ru

Effect of the uniform magnetic field on the resolution power of a quadrupole mass analyzer are discussed in the article. A fragment of the magnetic field as a magnetic lensis located at the different points of the channel of the quadrupole mass analyzer. The cases of axial and transverse fields are considered.

¹Saint-Petersburg State Polytechnic University, RF
²"Scientific instruments", Saint-Petersburg, RF
Contact: N. K. Krasnova, n.k.krasnova@mail.ru

Application of the averaging method to modeling of static perturbations of the Orbitrap mass analyzer allows to explore influence of inaccuracies of manufacturing and voltages on the frequency of axial oscillations of ions and mass resolution. It is shown that shift of the electrodes relative to each other leads only to perturbations of higher order of smallness, while the inaccuracy of electrode shape and presence of the slot for ion injection are the key factors determining the resolution of the analyzer. Examples of mutual compensation are presented for various deviations from the ideal field.

¹ThermoFisher Scientific, Bremen, Germany
²Institute of General Physics of Russian Academy of Sciences, Moscow, RF
Contact: А. А. Makarov, alexander.makarov@thermofisher.com

We reviewed the focusing properties of simple time-of-flight mass spectrometer, which ion-optical path does not contain the ions reflector. High values of resolution and sensitivity are achieved due to the fact that the electrostatic ions package accelerator is designed as a system of external to the ion flow electrodes forming an inhomogeneous electrostatic field, which along with the acceleration, performs concurrent high-performance time-of-flight and spatial focusing of ion packages directly to the input plane of the ions detector.

¹RSE Institute of Nuclear Physics RK Ministry of Industry and New Technologies, Kazakhstan
²Almaty University of Energy and Communications, Kazakhstan
Contact: E. M. Yakushev, evgeniy.yakushev@inbox.ru

The analytical expressions for the two-dimensional electrostatic field potential of five electrodes gridless mirror. Analyzed different methods for calculation of the trajectories of charged particles in this mirrors. The behavior of beams and found instrument characteristics of time-of-flight mass spectrometer on based the proposed mirror.

¹Aktobe Regional State University named after K. Zhubanov, Kazakhstan
²Military Institute of Air Defense them named after T.J. Begeldinov, Aktobe, Kazakhstan
³Alma-Ata University of Energy and Communication, Almaty, Kazakhstan
⁴West-Kazakhstan State Medical University named after M. Ospanov, Aktobe, Kazakhstan
Contact: I. F. Spivak-Lavrov, spivakif@rambler.ru

Method of calculation electrostatic fields with axial and transaxial symmetry based on the decomposition potential into two terms. The main component is a harmonic function of two variables and z, satisfying the given boundary conditions . Harmonic component of the potential is analytically using methods TFCV. The second term is the solution of the inhomogeneous equation with homogeneous Dirichlet boundary conditions and can be found numerically with the required accuracy.

Aktobe Regional State University named after K. Zhubanov, Kazakhstan
Contact: I. F. Spivak-Lavrov, spivakif@rambler.ru

The analytical technique for three dimensional electrostatic fields of complex-shape electrode system and space charge of electron beams is presented in the paper. The singularity analysis of integral representations for the potential and field gradients is provides. The practical problem solution for an electron gun of power sheet-beam klystron is discussed.

Institute of Computational Technologies, Siberian Branch of RAS, Novosibirsk, RF
Contact: V. Ya. Ivanov, vivanov.48@mail.ru

The paper considers the Maxwell's corrections as applied to high frequency electric fields used for "Archimedean" conveying of charged particles. It is shown that there are the exact analytical solutions of the Maxwell's equations which can be used for the Archimedean conveying of charged particles. The said electromagnetic fields implement the analytically ideal Archimedean conveying of charged particles even when the Maxwell's terms are essential in the output electromagnetic field and these terms influence strongly the movement of the charged particles.

Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
Contact: A. S. Berdnikov, asberd@yandex.ru

Ion monotrap with superposition linear high frequency and static homogeneous electric fields have been designed. The ion optical system includes planar discrete electrodes. For study ion optical properties of the monotrap the concept of pseudo potential and ion trajectory simulation have been applied. The several properties of ion motion allow use monotrap as a measuring cell of the Fourier transform mass spectrometer.

Ryazan State Radio Engineering University, RF
Contact: V. V. Zhuravlev, vladimir.rgrtu@mail.ru

Structural singularities of charged particle beam in electrostatic field from the point of view of catastrophe theory and wave front features are studied. Caustic type near focal plane in accordance with the order of focusing has been established. Classification of singularities in terms of catastrophe theory is given.

Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
Contact: A. P. Shcherbakov, anpshch@yandex.ru

Superconducting systems which present any polygon in the cross-section may replace heavy metal magnetic systems especially in and around therapy by beams of protons with energy of the order of 100 MeV. It is shown that fringe fields of such a superconducting systems considerably differ from fringe fields of conventional metal magnetic systems.

Saint-Petersburg State Polytechnic University, RF
Contact: A. A. Matyshev, a2m2001@mail.ru

Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Much more important role Bessel functions with pure imaginary index play in mathematical physics as solutions to Laplace's equation by method of variable separation in cylindrical coordinates. Also it was shown recently that such functions appear as solutions to Lame's equations which are used to characterize the displacement fields in semiconductor nanostructures. But there is no concrete algorithm that computes Bessel functions with pure imaginary order despite the fact that they were discovered long ago. In this paper an algorithm which can be used for the computation of the normal and modified Bessel functions with pure imaginary index is proposed. The developed algorithm is very fast to compute and for small arguments converges after a few iterations.

St. Petersburg State Polytechnic University, RF (Matyshev A.A.)
New Mexico State University, Department of Physics, USA (Fohtung E.B.)
Contact: A. A. Matyshev, a2m2001@mail.ru

One of the important tasks while creating biosensor and microfluidic devices is to control the quality of sensitive layer fixation needed to achieve the required functional characteristics. Among the methods of non-destructive testing of the surface properties of materials are favorably allocated optical spectrophotometry as simple, reliable and the most accessible for the research laboratory. We consider a spectrophotometric method for control of coupling of film micron sizes with an optically transparent substrate. The proposed approach is demonstrated by the example of control fixation polyacrylamide gel on the surface of a plate of polymethylmethacrylate, which has previously been subjected to chemical (or physical) treatment and silanization.

¹Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics, RF
²Institute for Analytical Instrumentation of RAS, Saint-Petersburg, RF
Contact: Y. S. Posmitnaya, posmitnaya@rambler.ru