  A model of a multilayer device with non-trivial geometrical structure and
nonlinear dependencies of thermodynamic material properties at cryogenic
temperatures is suggested. A considered device, called cryogenic cell, is
intended for use in multicharged ion sources for pulse injection of gaseous
species into ionization space of ion sources. The main requirement for the
cryogenic cell operation is the permanent opening and closing for gaseous
species injection in a millisecond range, while cell closing is provided by
freezing of the gaseous specie at the outer surface of the cell and the cell
opening - by the corresponding pulse heating of the cell surface up to definite
temperature. The thermal behaviour of the device in a millisecond time range is
simulated. The algorithm for solving the non-stationary heat conduction problem
with a time-dependent periodical heating source is suggested. The algorithm is
based on finite difference explicit-implicit method. The OpenCL realization of
the algorithm is discussed. The optimal particular choice of the parameters to
provide the required pulse temperature regime of the designed cryogenic cell
for the chosen working gas is presented. Based on these results further
optimization can be formulated.
