Magnetic property of a staggered-array undulator using a bulk high-temperature superconductor

Abstract

The magnetic field of a staggered-array undulator using a bulk high-temperature superconductor is calculated by analytical and numerical methods. Analytical formulas for the undulator field and the solenoid field required to generate the undulator field are derived from a simple two-dimensional model. The analytical calculation shows the degree of dependence of these fields on the undulator parameters, the generation of a high undulator field proportional to the critical current density of the bulk superconductor, and the good tunability of the undulator field over a wide range of values. The numerical calculation is performed in a three-dimensional geometry by two methods: the center field and energy minimization methods. The latter treats the current distribution inside the bulk, whereas the former neglects it as a natural extension of the analytical model. The calculation also reveals the dependence of the fields on the undulator parameters arising from the current distribution. From the comparison with experimental results, we find that the latter method reproduces the experimental results well, which indicates the importance of the current distribution inside the bulk. Therefore, we derive a semiempirical formula for the required solenoid field by modifying the analytical formula using the numerical results so as to include the effect of the current distribution. The semiempirical formula reproduces the numerical result with an error of 3%. Finally, we estimate the magnetic performance of the undulator as an example of using the formulas and values presented in this paper. The estimation shows that an undulator field twice as large as that of the present in-vacuum undulator but with an equal period and gap can be obtained at a temperature of approximately 20-40 K, and that deflection parameters (K values) of 1 and 2 can be achieved with periods of 5 and 10 mm at approximately 4-20 K.

Superconducting undulators: permanent magnets after all

“…The first practical prototype of a bulk HTS staggered array undulator was reported by Kinjo et al in 2013 [17] showing a field B 0 of 0.85 T in a 2 T solenoid for a periodicity of 10 mm and a 4 mm gap. By numerical and analytical methods, theoretically possible B 0 fields of up to 7 T were predicted for a critical current density J c of the HTS bulk of 20 kA cm −2 [18]. Also Chen et al considered and worked on that concept [19,20].…”

Current status and future perspectives of accelerator-based x-ray light sources

“…Although the magnetization system of the latter is more complicated than that of the former, the achievable performance is much higher. It has been reported that the latter scheme can generate a magnetic field twice as high as that is available in conventional IVUs at a moderate cryogenic temperature above 20 K [150], which makes the design of the cooling system and the operation in the storage ring much more feasible than the conventional SCUs based on low temperature SC wires. It should be noted, however, that there are a number of issues to be overcome before this concept can be put into practical use, especially in SR facilities.…”

Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods

“…However, other numerical methods, including those combined with FEM, have also shown excellent performance in modelling the critical state [37,40,46,50,52]. So far, the numerical analysis of magnetization currents in the BHTSU has been carried out with the 3D H-formulation [81,82], the MEM method [83], the RAA-combined T-Ω formulation [45,46,84], and the recently proposed backward computation method [52]. In particular, the backward computation method has shown excellent performance in simulating the magnetization currents in a periodical BHTSU model with 1.8 million DOFs within 1.4 h [52].…”