Sets of weak sequential continuity for polynomials
Abstract Let P : E → K be an N-homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set Cp = {x ∈ E : P is weakly sequentially continuous at x}.
Bounded weak continuity of homogeneous polynomials at the origin
Abstract. Given a Banach space E we study Pw0(nE), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of Pw0(nE) with P(nE), of Pw0(nE) with Pw(nE) and of P(nE) with Pw(nE) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.
Reduction of Surface Flashover of the Beam Screen of the LHC Injection Kickers
The LHC injection kicker magnets include beam screens to shield the ferrite yokes against wake fields resulting from the high intensity beam. The screening is provided by conductors lodged in the inner wall of a ceramic support tube. Operation with increasingly higher bunch intensity, and narrow bunches, now requires improved ferrite screening. This will be implemented by additional conductors; however the good high-voltage behaviour of the kicker magnets must not be compromised by the supplementary screening. Extensive studies and optimisations have been carried out, to better satisfy the often conflicting requirements for low beam coupling impedance, fast magnetic field rise-time, high vacuum and good high voltage behaviour. A new configuration is proposed which reduces significantly the electric field associated with the screen conductors and the secondary electron yield of the surface of the ceramic tube. Results of high voltage test results are also presented.