In this report we suggest some approaches to very intricate problem of the halo formation process. It is known that this process leads to the formation of a sufficiently compact core and a spreading cloud -halo, which surrounds the core. Our approach to this problem is based on two main objects: initial distribution functions and matrix formalism for Lie algebraic tools for time evolution of particle beam. Usage of the matrix formalism allows to investigate the influence of different forms of starting model distributions. All calculations are based on symbolic representation of necessary mapping generated by space charge forces and external control fields. This allows us to formulate the basic requirements which are necessary for halo formation, that gives us a possibility to control this process.

There are briefly considered physical and medical aspects contemporary development of Boron Neutron Capture Therapy (BNCT) system. Choice of accelerator for neutron produce is discussed. Three of accelerator types are compared: electrostatic accelerator, compact cyclotron and RFQ with working frequency of P-diapason. A few factors determine choice: providing required neutron flux, compactness of accelerator and whole BNCT system, economical power consumption. Our choice is radio-frequency quadrupole. Two of RFQ variants are considered: compact RFQ and universal one, which has possibility to accelerate two of types particles (proton and deuteron) and to use two of types targets (Lithium and Beryllium) for neutron production.

1. Введение. Обе части работы посвящены проблемам управления и оптимизации динамики пучков (ансамблей) траекторий. Задачи управления и оценки состоя

An optimized magnetic specification has been searched for a PM quadrupole constructed for the DC-140 cyclotron in JINR, Dubna. The field inhomogeneity should be reduced to come closer to an ideal distribution. The quad parameters should be determined with very high mechanical and magnetic precision in order to reach the specified gradient. Results of the analytic study based on a 2D model gave initial values for the PM blocks dimensions and orientations. To ensure stringent performance criteria, parametrized 2D and 3D models of the quad were built. These models were used to optimize the magnet configuration, analyze its sensitivity to various errors and derive parameter tolerances. Additional adjustment to suitable field quality is foreseen using results of a trajectory analysis and acceptance inspection. The design parameters for the best suited magnet configuration are presented and the performance criteria are defined. However, an electromagnetic analysis of the selected configuration has revealed that the relative field error adopted previously as the optimization criterion gives low accuracy estimate. Alternative estimations are proposed utilizing the field gradient error as the basic criterion to satisfy the constraint on the field inhomogeneity.

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