Fluctuations and correlations of the formative and statistical time delay in neon

Abstract

In this paper the fluctuations and correlations of the formative t f and statistical time delay t s in neon studied by electrical breakdown time delay measurements are presented. The Gaussian distribution for the formative time delay, as well as Gaussian, Gauss-exponential and exponential distribution for the statistical time delay were obtained experimentally. By fitting their dependencies on the afterglow period by simple analytical models, the correlations of the formative and statistical time delay were found. Linear correlation coefficient is ρ ≈ 1 at high electron yields and ρ ≈ 0 at low electron yields. Thus, the formative and statistical time delay are correlated at high electron yields during charged particle decay and therefore not independent.

Empirical Modeling of Electron Transport in Fe/Ti Layered Double Hydroxide Using Exponential, Gaussian and Mixed Gauss–Exponential Distribution

“…The probability of transfer of an e – to CB from VB in the energy interval Δ E would therefore be and the probability of nontransfer would be . 22−26 The electron jump has been considered only when at least one e – shifts from VB to CB in the j th energy gap such that j = 1,2,..., m . According to the law of total probability, the distribution of number of e – in the CB could be represented aswhere P C represents the nonoverlapping energy gap and also the sum of the probabilities of the presence of e – s in the CB within the g energy gaps.…”

“…The energy E = ε delivered to the system is supposed to be divided into “ m ” nonoverlapping equal subintervals, where m is considered to be a positive integer, then each corresponding subinterval Δ E (=ε/ m ) could be assumed to be an infinitesimally small energy level. The probability of transfer of an e – to CB from VB in the energy interval Δ E would therefore be and the probability of nontransfer would be . − The electron jump has been considered only when at least one e – shifts from VB to CB in the j th energy gap such that j = 1,2,..., m . According to the law of total probability, the distribution of number of e – in the CB could be represented as where P C represents the nonoverlapping energy gap and also the sum of the probabilities of the presence of e – s in the CB within the g energy gaps.…”

Processes responsible for electrical breakdown initiation in commercial indicator gas tube

“…This model the statistical and the formative time delays treated as sum of two independent random variables, with exponential (statistical time delay) and Gaussian (formative time delay) distribution. In contrary, in the reference [12] the authors claim in the ca-se of the small relaxation time (relaxation time τ represent time between two successive measurement, then is no voltage on the electrode of the gas tube), the mutual dependence of the statistical and the formation time delay, as well as, that for different relaxation times, total time delay has Gaussian, Gaussexponential and exponential log-normal shape. However the great number of papers indicated that formative time delay has not statistical behavior, and can be treated as constant value.…”

Breakdown in low pressure Ne gas: mechanisms and statistical analysis of time delay

“…One of models in this area was the convolution time delay model [6], which treated the statistical and formative time delays as two independent processes. In contrary, in paper [10] authors assumed dependences of the statistical and formative time delay for small relaxation times. They show that the time delay distributions can be described with the Gaussian, Gauss-exponential and exponential lognormal distributions.…”