Analytical expressions for Barkhausen jump size distributions

Abstract

In previous calculations of Barkhausen jump size distributions, the Langevin equation was used to describe the pinning held h/sub c/. In this paper, h/sub c/ is modeled by discretized random walks which are used to obtain analytical expressions for the Barkhausen jump size distribution, P(/spl tau/). For a bounded random walk which reduces to the Langevin function in the continuum limit, P(/spl tau/) is a sum of exponentials which is compared to functions of the form P(/spl tau/)=/spl tau//sup -/spl alpha//exp(-/spl tau///spl tau/0). The scaling exponent changes from /spl alpha//spl sime/1.5 for small jumps to /spl alpha//spl sime/1.0 for jumps larger than the correlation length. For an unbounded random walk with exponentially distributed distances between steps in h/sub c/, P(/spl tau/) is shown to be proportional to a modified Bessel function which, for long jumps, is asymptotically a pure power law, /spl tau//sup -3/2/. This suggests that the scaling exponent shift and the exponential cutoff are caused by correlations in h/sub c/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>