Localization of Electrical Insulation Failures in Superconducting Collared Coils by Analysis of the Distortion of a Pulsed Magnetic Field

The localization of possible electrical faults in superconducting accelerator magnets may, in most cases, be a complex, expensive and time-consuming process. In particular, inter-turn short circuits and failures of the ground insulation are well detectable when the magnet is collared, but often disappear after disassembly for repair due to the release of the pre-stress in the coils. The fault localization method presented in this paper is based on the measurement and analysis of the magnetic field generated inside the magnet aperture by a high voltage pulse. The presence of the fault modifies the distribution of the current in the coils and produces a distortion of the magnetic field. The described method aims at locating both the longitudinal and azimuthal position of the fault-affected area. The test method, the transient case FEM models and the implemented experimental set-up are presented and discussed for the LHC dipole models

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation