INITIAL ESTIMATE OF FRINGE FIELD EFFECTS IN HL-LHC USING FREQUENCY MAP ANALYSIS

Abstract

The planned High Luminosity upgrade to the LHC will re- quire stronger focusing of the beam in the interaction regions. To achieve this, the inner triplet quadrupoles will be replaced with new magnets having larger gradient and aperture. In this new focusing regime the quadrupole fringe fields are expected to have a greater effect on the beam dynamics, due to their large aperture, as compared to the nominal LHC. In this preliminary study, simplified models are used in a tracking code to assess the impact of the fringe fields on the dynamics using frequency map analysis. INTRODUCTION The High Luminosity upgrade to the Large Hadron Col- lider (HL-LHC) aims for an increase in luminosity by an order of magnitude. This will be achieved by decreasing the � function (and hence the beamsize) at the interaction points. The inner triplet (IT) quadrupoles are to be replaced with stronger magnets to achieve greater focusing, but they will also require a large physical aperture to accommodate the beam which will have a largefunction at these points (1). The large aperture and increased strength of these magnets means the fringe field may have an detrimental effect on the dynamic aperture of the HL-LHC lattice. An initial estimate of the impact of the fringe fields could be determined by Frequency Map Analysis (FMA) (2). This paper introduces a technique used to calculate a semi-analytical description of the fringe fields, and describes how the HL-LHC lattice was modified to include the fringe fields whilst keeping the linear dynamics as close as possible to the nominal lattice. The results of a preliminary FMA are presented, and we make an initial assessment of the possible impact of the fringe fields on the dynamic aperture. Further work required to fully assess the impact of the inner triplet fringe fields is discussed.