Although high energy cosmic rays are generally assumed to arrive at the earth randomly, some evidence for non-randomness has been reported by several groups. This thesis presents a search for non-random time series ( clustered events ) in the arrival times of air showers.
Extensive air showers with mean energy 1.1 * 10^15 eV and with accompanying muon(s), have been collected by the air shower array with the underground muon detectors at Mitsuishi, Japan. The array locates near sea level. The data collected during the period from Jan. 1989 to Oct. 1996 corresponding to 2427 days, were used for the analysis. First, air showers were reconstructed in those data. The direction, shower size and the number of muons per shower were estimated for each event. Then, existence of non-random time series of cosmic rays were examined in the 3,651,358 air showers.
A new cluster method was used to analyze the arrival time intervals of the air showers, which is particularly sensitive to search for clustered events with long durations. As a result of the analysis, five occasions of rate elevation phenomena( Clustered event ) were found with an expected probability $\leq 0.05 $ ( varying from 0.18 * 10^-2 to 4.0 * 10^-2 ) from a random distribution of the air showers in the sample. These phenomena are characterized by an elevated event rate with a duration of the order of minutes to hours, having arrival time intervals less than of the order of one to several minutes. Size and zenith angles of the air showers in the clustered events have no significant difference from the normal air showers. The arrival directions of clustered events are grouped in two regions on the galactic plane within the latitude +- 25 degrees( the longitude l=60 degrees - 90 degrees, l=150 degrees - 180 degrees), corresponding to a chance probability of 1.6 % from a uniform distribution. This inclination of the arrival directions can suggest that their origins are in the nearby Galactic arms.
The result of this thesis supports the existence of non-random phenomena in the arrival time of primary cosmic rays, whose existence has been controversial in the past measurements. In addition, the origin of the clustered events may be explained as the air showers initiated by many secondary particles from some heavier primary particles, namely dusts, which come from Galactic Arms.