UDC 519.633.6, 519.688 Model with One Spatial Variable for Design of a Technical Device A. S. Ayriyan Laboratory of Information Technologies Joint Institute for Nuclear Research Joliot-Curie, 6, 141980 Dubna, Moscow Region, Russia Model with one spatial cylindrical variable for optimization of a technical device is presented. <...> Device is in the form of a multilayer cylindrical sample with a pulse source operating at cryogenic temperatures. <...> The results of numerical experiments are shown. <...> Key words and phrases: heat equation, partial differential equation, finite-difference scheme, mathematical modeling. 1. <...> Introduction The main goal of this work is to implement a model of thermal processes for a given object (Fig. 1) for systematic studies in order to find optimal materials and composition of the technical device. <...> The object subject to the investigation is a cryogenic cell pulse (in the millisecond range) feeding the working gases into the working space of charged ion source [1]. <...> Thermal processes occur at periodic passage electric current through conductive layer. <...> Full period of the process is requested to be 10 ms: the heating period is 1 ms (current on, the object surface should be heated up to 60 K), for 9 ms it is cooling (current off, the surface should be cooled down to 4.2 K ∼ 10 K). 3 2 1 r 0 4 cm 5 cm z Figure 1. <...> The slice of the object: 0 – cooler (r∗ r∗ 0 = 0.12), 1 – electrical insulator (r∗ 2 = 0.13), 3 – external insulator (rmax = 0.1301), 4 – liquid helium temperature terminal with T = 4.2 K Due to the cylindrical symmetry of the object, the heat conductivity inside it can be simulated by a model with two spatial cylindrical variables r and z (instead of three) and time variable. <...> Possibility of using model with one spatial cylindrical variable r was proposed and discussed in [3], it is shown that thermal flow in the z direction can be neglected for beginning part of thermal process. <...> Author thanks J´ an Pribiˇ RFBR grants 11-01-00278. s and Hovik Grigorian for useful advices. <...> Main Equations and Boundary Conditions <...>