Beam power absolute measurements using the calorimetric method

Abstract

Mathematical models for three types of beam power calorimeters that do not require calibration are considered. These types are: adiabatic, with a calibrated heat sink, and based on water-flow cooling. For the adiabatic type a transient solution of the corresponding heat transfer equation is presented and its features are considered. Two definitions of the response time are proposed. The question of determining its sensitivity is considered. Based on these definitions, a solution to the problem of the receiving plate material optimal choice in terms of the ratio of sensitivity and response time is proposed. For the type with a calibrated heat sink a simple lumped parameters model is considered. Based of this model estimations of the calorimeter sensitivity and response time were made. For the water-flow type some analytical results following from equations describing its operation within the framework of a quasi-one-dimensional thermal model are presented. A consistent simplification of these equations is considered, which made it possible to obtain simple relationships for assessing the sensitivity, response time, and heating temperature of the receiving plate. A thermal energy balance equation for the stationary mode of operation is obtained. Within the framework of the proposed approach, a rough estimate of the lower boundary of the response time of the water-flow calorimeter was obtained. Wherever possible, comparisons have been made with published experimental and theoretical results. The results obtained can be used for development and design of calorimetric diagnostics systems of fast neutral particle beams.