Direct measurements of cosmic-ray energy: The kinematical method revisited

At an energy scale of 1015–1016 eV, a direct measurement of the energy carried by charged cosmic radiation is a real challenge for balloon-borne and space based instruments. As a consequence of the very small fluxes, a large collecting power is required which is difficult to accommodate with weight-limited instruments equipped with calorimeters. A different approach has been proposed that might allow for a sizeable reduction of the instrument mass. It is based on a kinematical technique, whereby the energy of the cosmic-ray is estimated on the basis of the measured angular distribution of the secondaries resulting from its interaction in a target. In this paper, we review the basic principles of the method and study the properties of different energy estimators by means of a full simulation of the interaction of the incident particle in a conceptual instrument. We also discuss the intrinsic limitations of the method and investigate its possible application to direct measurements of the cosmic-ray spectrum in the region of the ‘knee’.