“…Though it is time consuming, but due to its probabilistic nature, it is an excellent technique for studying the energy degradation of particles, provided sufficient sample size is taken. Hence, Monte Carlo methods have been widely used in problems dealing with energetic particle degradation in gases and in applications to the planetary atmospheres [e.g., Cicerone and Bowhill , 1971; Ashihara , 1978; Green et al , 1977, 1985; Singhal et al , 1980; Singhal and Green , 1981; Singhal and Bhardwaj , 1991; Bhardwaj and Singhal , 1993; Michael and Bhardwaj , 2000; Bhardwaj and Michael , 1999a, 1999b; Shematovich et al , 2008].…”