A detailed study on the range fluctuations of 10^{11}eV to 10^{18}eV muons in water and the fluctuations of the Cherenkov light yields due to the accompanied cascade showers initiated by muons. Part1: High Energy Muons

The validity of our Monte Carlo simulation procedure (the time sequential procedure) had been verified by the corresponding analytical procedure which is independent of our method methodologically. Also, the results obtained by our procedure are compared with those obtained by the different Monte Carlo simulation procedure (the v_{cut} procedure) which has been exclusively utilized by different authors and the agreement between ours and theirs are found to be good. By utilizing our Monte Carlo procedure, the validity of which is guaranteed in two different procedures, we investigate not only the fluctuation of high energy muons themselves but also the fluctuation of the various quantities related to the energy losses by the muons, which are difficult to obtain by the v_{cut} procedure. Namely, we obtain the fluctuation on energy losses of muons in the present paper(Part1). In a subsequent paper (Part2), based on the idea developed in Part1, we will examine the correlation between the primary energies of muons and their energy deposits and the correlation between the energy deposits of the muons concerned and their Cherenkov light yields in the KM3 detector in detail.