The magnetic design of a ten-period (each period 14 mm) prototype superconducting undulator is reported using RADIA. The results of modelling the magnetic flux density are presented in an analytical formula. The dependence of the field integrals and phase error on the current density and undulator gap has been calculated, and temperature curves are determined for the models and are compared with earlier reported Moser-Rossmanith fits.
In this paper, we study the magnetic field measurement of U20 undulator. The U20 is a prototype hybrid structure of NdFeB magnets and cobalt steel poles. The hybrid device is made up of 25 periods with a period length of 20-mm each and is designed to deliver magnetic flux density (in rms) from 2400G to 500G in the 10–20-mm gap range. The validity of the theoretical and analytical formulas is analyzed through the measured field and phase integrals.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.