Katsufumi Tsuji

Chaos in Cosmic Ray Air Showers

Unexpected chaotic features are found in time series of arrival time intervals of successive air showers with (E > 3 × 1014 eV). Over 99 % of air shower arrival time intervals obey the Poisson distribution law representing stochastic behaviors, but occasionally there are air showers showing real chaotic behaviors as distinguished from both random and colored noises. With two systems of the Kinki university installations, we found 13 cases showing chaotic time series in 3.36 yr with the system-1 and the 1.37 yr with the system-2. Five out of 10 chaotic air showers of the Kinki installation are detected during the same time zone also by the Osaka City university installation which is at 115 km distance from the Kinki one. In a remarkable example of September 19, 1991, the correlation dimension was observed to have dropped from about 4 to the minimum of 1.3 and recovered smoothly in about 38 h. The chaos structure in this case is detected in nearly the same time zone at the Ohya station of the Institute for Cosmic Ray Research, University of Tokyo, which is separated from the Kinki one by 460 km. Formation of chaos structure due to energetic cosmic ray dust particles is suggested. Progress of cosmic ray physics may be expected with the study of air showers marked with chaos.

Observation of time correlation in cosmic air shower network

In order to measure time correlation of primary cosmic rays, a network observation of extensive air showers started in Japan. The network as Large Area Air Shower (LAAS) group consists of nine air-shower-stations (seven institutes and 26.000 km2) using the Global Positioning System (GPS). We propose an analytical procedure to extract time-limited fractal structure from time series of arrival time intervals of successive air showers and present the results of the analysis by using the network data.

Chaos in different far-off cosmic rays: a fractal wave model

The air shower arrival time intervals (ASATIs) were observed for several years at five different far-off stations to study the chaotic feature of the cosmic rays. The total number of chaotic time series of ASATIs is 99 from February 1994 to November 2000. The chaotic ASATIs appear six times simultaneously between two different stations, showing a higher probability of simultaneous chaos detection than the random occurrence as implied by the fractal wave pattern of cosmic ray clouds. The average fractal dimension of the fractional chaotic ASATIs for each station is 3.7 ± 0.1 pm with average duration of 23 h. The distribution of the representative (central) right ascension of air showers among 99 chaotic ASATIs has two peaks around 4 h and 20 h. The time variation of the chaotic feature of the ASATIs for several days shows a quasi-periodic behaviour with the rotation of the earth. These results seem to indicate that the chaotic cosmic rays arrive at the earth, forming wave trains like a fractal pattern which covers an area of the galactic plane surrounding the earth.