A new numerical technique to design satellite energetic electron detectors

Energetic charged particles trapped in the magnetosphere are routinely detected by satellite instruments. However, it is generally difficult to extract quantitative energy and angular information from such measurements because the interaction of energetic electrons with matter is rather complex. Beam calibrations and Monte-Carlo (MC) simulations are often used to evaluate a flight instrument once it is built. However, rules of thumb and past experience are common tools to design the instrument in the first place. Hence, we have developed a simple numerical procedure, based on analytical probabilities, suitable for instrumental design and evaluation. In addition to the geometrical response, the contributions of surface backscattering, edge penetration, and bremsstrahlung radiation are estimated. The new results are benchmarked against MC calculations for a simple test case. Complicated effects, such as the contribution of the satellite to the instrumental response, can be estimated with the new formalism.