A LOW GRADIENT TRIPLET QUADRUPOLE LAYOUT COMPATIBLE WITH NbTi MAGNET TECHNOLOGY AND β * = 0.25m *
The paper presents a triplet layout option with long (about 100m total triplet length), low gradient (45T/m to 70T/m) quadrupole magnets. Assuming a maximum magnet diameter of 200mm, the peak coil field at the magnet coils still remains below 7T which is still compatible with conventional NbTi magnet technology. The peak beta function inside the triplet magnets reaches 22km and the configuration therefore requires an additional chromaticity correction scheme similar to a dipole first layout option. However, at the same time, the presented solution provides an interesting alternative to a high gradient triplet layout which requires the new Nb3Sn magnet technology.
ADVANCES IN MATCHING WITH MAD-X
A new algorithm and mode has been developed for the matching in MAD-X [1]. The new algorithm, called JACOBIAN, is able to solve a generalized matching problem with an arbitrary number of variables and constraints. It aims at solving the corresponding least square problem. The new mode, called USE MACRO, allows the user to construct his own macros and expressions for the definition of the constraints in a matching problem. The new algorithm combined with the macro constructs was successfully used for finding optic transitions and a non-linear chromaticity correction. This new approach can be seen as a major upgrade of the matching capabilities of MAD-X taking advantage of various modules like twiss, ptc, track, survey, aperture, etc.
Luminosity optimization near the beam-beam limit by increasing bunch length or crossing angle
We discuss the choice of bunch length and crossing angle near the beam-beam limit in a storage-ring collider. First, we derive expressions for the tune shifts of either bunched or continuous round beams which are induced by a single collision with arbitrary crossing angle and bunch length, and for the associated luminosities. Then, considering two collision points with alternating planes of crossing, we demonstrate that, if the total beam-beam tune shift is held constant, the collider luminosity increases as a function of bunch length and crossing angle. This implies a corresponding increase in the bunch intensity. As an illustration, we present numerical examples for an LHC upgrade and for the VLHC.