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Register a new userRelation between particle beam eigen-emittances and canonical vorticity flux
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Particle beams provided by accelerators occupy a finite volume of the four dimensional transverse phase space. The latter is spanned by the four degrees of freedom, i.e., horizontal/vertical position and momentum. This volume is referred to as emittance. Horizontal and vertical emittances are obtained through projections onto the two transverse sub-phase spaces. Eigen-emittances are obtained from the latter by removing all horizontal-vertical correlations through an appropriate beam optics section. Canonical vorticity flux is used for instance for modelling dynamics of tubes formed by magnetic field lines and particle currents embedded into plasmas. This report is on the relation of eigen-emittances and canonical vorticity flux. Change of beam eigen-emittances is equivalent to change of beam canonical vorticity flux.
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Particle beam eigen-emittances comprise the lowest set of rms-emittances that can be imposed to a beam through symplectic optical elements. For cases of practical relevance this paper introduces an approximation providing a very simple and powerful relation between transverse eigen-emittance variation and the beam phase integral. This relation enormously facilitates modeling eigen-emittance tailoring scenarios. It reveals that difference of eigen-emittances is given by the beam phase integral or vorticity rather than by angular momentum. Within the approximation any beam is equivalent to two objects rotating at angular velocities of same strength and different sign. A description through circular beam modes has been done already in [A. Burov, S. Nagaitsev, and Y. Derbenev, Circular modes, beam adapters, and their applications in beam optics, Phys. Rev. E 66, 016503 (2002)]. The new relation presented here is a complementary and vivid approach to provide a physical picture of the nature of eigen-emittances for cases of practical interest.
In a strongly nonlinear system the particle distribution in the phase space may develop long tails which contribution to the covariance (sigma) 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 sigma 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 sigma matrix in a strongly coupled system. Finally, the developed algorithm is applied to 6D ionization cooling of muons in HFOFO channel.
The dynamics of wave-particle interactions in magnetized plasmas restricts the wave amplitude to moderate values for particle beam acceleration from rest energy. We analyze how a perturbing invariant robust barrier modifies the phase space of the system and enlarges the wave amplitude interval for particle acceleration. For low values of the wave amplitude, the acceleration becomes effective for particles with initial energy close to the rest energy. For higher values of the wave amplitude, the robust barrier controls chaos in the system and restores the acceleration process. We also determine the best position for the perturbing barrier in phase space in order to increase the final energy of the particles.
A dedicated device to fully determine the four-dimensional beam matrix, called ROSE (ROtating System for Emittance measurements) was successfully commissioned. Results obtained with 83Kr13+ at 1.4 MeV/u are reported in Phys. Rev. Accel. Beams 19, 072802 (2016). Coupled moments were determined with an accuracy of about 10%, which is sufficiently low to reliably determine a lattice which could decouple the beam. However, the remaining uncertainty on the corresponding eigen emittances was still considerable high. The present paper reports on improvement of the evaluation procedure which lowers the inaccuracy of measured eigen emittances significantly to the percent level. The method is based on trimming directly measured data within their intrinsic measurement resolution such that the finally resulting quantity is determined with high precision.
The radiation reaction (beamstrahlung) effect on particle dynamics during interaction of oppositely charged beams is studied. It is shown that the beam focusing can be strongly enhanced due to beamstrahlung. An approximate analytical solution of the motion equation including the radiation reaction force is derived. The disruption parameter is calculated for classical and quantum regime of beamstrahlung. The analytical model is verified by QED-PIC simulations. The model for head-on collision of long beams undergoing a number of betatron oscillation during interaction is also developed. It is demonstrated that the beamstrahlung-enhanced disruption effect can play a significant role in future lepton colliders with high-current particle beams.
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