Eur. Phys. J. D 18, 37-49 (2002)
https://doi.org/10.1140/e10053-002-0004-9

Molecular flow and wall collision age distributions

¹ Sektion Physik, Ludwigs-Maximilians-Universität München, 85748 Garching, Germany
² Physikalisches Institut, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
³ Physics Department, University of Liverpool, Liverpool L69 7ZE, UK
⁴ Istituto Nazionale di Fisica Nucleare and Universita', 44100 Ferrara, Italy
⁵ Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
⁶ Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF), 1009 DB Amsterdam, The Netherlands
⁷ Institute of Automation and Electrometry of SB RAS, Russia
⁸ Department of Physics and Astronomy, Vrije Universiteit, 1081 Amsterdam, The Netherlands
⁹ DESY Zeuthen, 15738 Zeuthen, Germany

Corresponding author: ^a steffens@physik.uni-erlangen.de

Received: 9 July 2001
Revised: 18 September 2001
Published online: 15 January 2002

Abstract

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target.