Fermilab, Batavia, Illinois, USA
A Muon Collider promises unique opportunities both as an energy frontier machine and as a factory for detailed study of the Higgs boson and other particles. However, in order to achieve a competitive level of luminosity a number of demanding requirements to the collider optics should be satisfied arising from short muon lifetime and relatively large values of the transverse emittance and momentum spread in muon beams that can realistically be obtained with ionization cooling. Basic solutions which make possible to achieve these goals with Nb3Sn magnet parameters are presented.
Fermilab, Batavia, Illinois, USA
Direct space-charge force shifts the incoherent tunes down from the coherent ones switching off Landau damping of coherent oscillations at high beam intensity. To restore it the nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a "nonlinear integrable optics" insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II parameters the required nonlinear tuneshift can be created without destroying the dynamic aperture.
WEA4CO04
Fermilab, Batavia, Illinois, USA
The particle losses at injection in the FNAL Booster are one of the major factors limiting the machine performance. The losses are caused by motion non-linearity due to direct space charge and due to non-linearity introduced by large values of chromaticity sextupoles required to suppress transverse instabilities. The report aims to address the former - the suppression of incoherent space charge effects by reducing deviations from the perfect periodicity of linear optics functions. It should be achieved by high accuracy optics measurements with subsequent optics correction and by removing known sources of optics perturbations. The study shows significant impact on half-integer stop band with subsequent reduction of particle loss. We use realistic Booster lattice model to understand the present limitations, and investigate the possible improvements which would allow high intensity operation with PIP-II parameters.
Fermilab, Batavia, Illinois, USA
CERN, Geneva, Switzerland
Since a few years MAD-X allows to simulate beam dynamics with frozen space charge à la Basseti-Erskine. The limitation of simulation with a fixed distribution is somewhat overcome by an adaptive approach that consists of updating the emittances once per turn and by recalculating the Twiss parameters after certain intervals, typically every 1,000 turns to avoid an excessive slowdown of the simulations. The technique has been benchmarked for the PS machines over 800, 000 turns. MADX-SC code developments are being discussed that include the re-introduction of acceleration into MAD-X and more advanced beam σ calculations that will avoid code interruptions for the Twiss parameters calculation.
Fermilab, Batavia, Illinois, USA
H2 gas-filled channel for 6D ionization cooling of muons is described which consists of periodically inclined solenoids of alternating polarity with 325MHz RF cavities inside them. To provide sufficient longitudinal cooling LiH wedge absorbers are placed at the minima of transverse beta-function between the solenoids. An important feature of such channel (called Helical FOFO snake) is that it can cool simultaneously muons of both signs. Theoretical considerations as well as results of simulations with G4beamline are presented.
Fermilab, Batavia, Illinois, USA
In a strongly nonlinear system the particle distribution in the phase space may develop long tails which contribution to the covariance (σ) matrix should be suppressed for a correct estimate of the beam emittance. A method is offered based on Gaussian approximation of the original particle distribution in the phase space (Klimontovich distribution) which leads to an equation for the σ matrix which provides efficient suppression of the tails and cannot be obtained by introducing weights. This equation is easily solved by iterations in the multi-dimensional case. It is also shown how the eigen-emittances and coupled optics functions can be retrieved from the σ matrix in a strongly coupled system.