Investigation of the Influence of Overvoltage, Auxiliary Glow Current and Relaxation Time on the Electrical Breakdown Time Delay Distributions in Neon

Abstract

Results of the statistical analysis of the electrical breakdown time delay for neon-filled tube at 13.3 mbar are presented in this paper. Experimental distributions of the breakdown time delay were established on the basis of 200 successive and independent measurements, for different overvoltages, relaxation times and auxiliary glows. Obtained experimental distributions deviate from usual exponential distribution. Breakdown time delay distributions are numerically generated, using Monte-Carlo method, as the compositions of the two independent random variables with an exponential and a Gaussian distribution. Theoretical breakdown time delay distribution is obtained from the convolution of the exponential and Gaussian distribution. Performed analysis shows that the crucial parameter that determines the complex structure of time delay is the overvoltage and if it is of the order of few percentage, then distribution of time delay must be treated as an convolution of two random variables.

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

“…An attempt to separate the formative and statistical time delay in neon and krypton was made in [6][7][8][9][10], on the basis of the time delay measurements, numerical simulation and by irradiation. It was assumed [6][7][8][9] that the statistical and formative time delay are independent variables and the breakdown time delay is obtained as their convolution.…”

A Note on the Breakdown Time Delay Distribution: The Analytical Properties

“…In this section, we provide a program for computing the percentage points z p associated with the cdf (3) of Z. The percentage points are obtained numerically by solving the equation F (z p ) = 1 − p, where F (·) is given by (3). Evidently, this involves computation of the complementary error function and routines for this are widely available.…”

“…The electrical breakdown time delay (t D ) is defined as the sum of the breakdown statistical time delay (t S ) and the discharge formative time (t F ). The recent paper by Maluckov et al (2005) provided a statistical analysis of t D by taking t S and t F to be exponential and Gaussian random variables distributed independently of each other. It appears though that the analysis was performed completely by numerical means and that no algebraic expressions were derived for the distribution of t D or its properties.…”

“…We also provide a simple 9-line program for computing the percentile points of t D (and hence the confidence intervals for t D ). In Maluckov et al (2005), t D was defined as the sum of an exponential random variable (with support over the positive real line) to a Gaussian random variable (with support over the entire real line). Because of this mismatch, we re-define t D by Z = X + Y where X is a Gaussian random variable and Y is a Laplace random variable independent of X (note that Laplace is the two-sided version of the exponential random variable).…”

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Following up from the recent work of Maluckov et al (2005), we derive explicit expressions for the probability density function, cumulative distribution function and the means of the electrical breakdown time delay (tD). We also provide a 9-line computer program for computing the associated percentile points (and hence the associated confidence intervals).

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