Using the integral equations method to model a 2G racetrack coil with anisotropic critical current dependence

Abstract

Second-generation (2G) superconducting wires have already proved their potential in several applications. These materials have a highly nonlinear behavior that turns an optimized engineering project into a challenge. Between several numerical techniques that can be used to perform this task, the integral equations (IE) method stands out for avoiding mesh problems by representing the 2G wire cross-sectional area by a line. While most applications need to be represented in a 3D geometry, the IE is limited to longitudinal or axisymmetric models. This work demonstrates that a complex 3D geometry can be modeled by several coupled simulations using the IE method. In order to prove this statement, the proposed technique was used to simulate a 2G racetrack coil considering the self-field magnitude (B) and incidence angle (θ) on the tape. The J c characteristic was modeled in terms of parallel and normal to the tape plane magnetic field components (J c (B P , B ⊥ )) obtained from a V-I(B, θ) characterization of a tape segment. This result was implemented using commercial software with both A-V (vector magnetic potential and scalar voltage potential) and IE coupled simulations solved by finite elements. This solution bypasses the meshing problem due to the tapes slim geometry, considering each turn a single 1D model, all magnetically interacting in two 2D models. The simulations results are in good agreement to what was both expected and observed in the literature. The simulation is compared to the measured V-I characteristic for a single pancake racetrack coil built with same geometry as its simulation models, and a theoretical study demonstrates the possibilities of the proposed tool for analyzing a racetrack coil current density and electric field behavior in each of its turns.

How to Choose the Superconducting Material Law for the Modelling of 2G-HTS Coils

“…This is because strong changes in the critical current density of the SCS4050 tape have been observed only for parallel components of the magnetic field (θ=0,boldB=By) greater than 50 mT [20], which is a condition seen only for about the first three-to-seven innermost and outermost turns of the HTS coil at moderate-to-high applied transport currents, Itr⊂(0.5Ic0,Ic0) (see Figure 3). Then, by observing the full penetration condition (i.e., Itr=Ic0 at ωt=5π/2 in Figure 1), it is possible to see that with exemption of the CM model, the critical current density of the superconducting coil changes across the width and thickness of each of the REBCO turns, which is a phenomenon that was experimentally observed in [13,31]. However, in order to be able to properly see how the Jc changes across the different turns of the HTS coil for the different material law models, in the following section we aim to present a more quantitative approach to the above-mentioned observations, which ultimately will be connected to the macroscopic quantities that can be experimentally measured.…”

“…In this sense, the simulation of the electromagnetic behaviour of 2G-HTS coils presents serious challenges, especially in conditions where one needs to consider the in-field dependence of the critical current, Ic, this in terms of the direction and intensity of the magnetic field per coil-turn, as pointed out in early experiments measuring the magnetic field distribution and AC loss of HTS thin films in superconducting coils [25,26]. Nonetheless, regardless of the 2G-HTS tape being used, certain consensus has been reached in terms of describing the current-voltage characteristics of all type-II superconductors as a power law, V(I/Ic)n, with n≫1, which from the computational point of view renders the well-known form of the material law for the electric field, also called the E-J power law, boldE(J)=E0·boldJ/Jc·(|J|/Jc)n−1, which in a local but macroscopical approach allows solution of the Maxwell equations inside the superconducting domains within diverse mathematical formulations, for a large range of experimental measurements [16,23,27,28,29,30,31,32,33,34,35,36,37,38]. Here, Jc is the critical current density of the 2G-HTS tape defined within the standard electric field criterion E0 = 1 …”

Simulations of REBCO tape jointless double crossed loop coils with an integral equations method

“…Therefore, (4) becomes (5): There are different ways to write the field-dependent critical current density [18][19][20][21] and for this work we choose to use the Kim-like elliptical dependence [18] (6). The set of parameters that compose this function was obtained by a V-I characterization process of a superpower SCS4050 REBCO tape segment, as explained in a previous work [22]. The sample was subjected to different magnetic fields in different incidence angles for each measurement.…”

“…During the iterative solution process, each 1D simulation imports the external magnetic field calculated on the 2D simulation. Then, the field-dependent K z 's are calculated and sent back to the 2D simulation to recalculate the magnetic field distribution, and so on until convergence for each time step [22,23].…”

Local electromagnetic properties and hysteresis losses in uniformly and non-uniformly wound superconducting racetrack coils

“…Attaining a clear understanding of the physical and designing parameters that might render to the minimization of AC losses in these systems is, by default, one of the most important subjects in the physics and engineering of applied superconductivity. [6][7][8][9][10][11][12] However, despite many experimental and theoretical studies have been performed on the AC losses of HTS racetrack coils, [13][14][15][16][17] these always assume that the coil is perfectly wound, neglecting thence any influence of a possible misalignment between the coil turns (tapes), a situation that is likely to happen either during the coil manufacturing, their assembling in practical applications, or even due to possible axial alterations caused by extrinsic magnetic, thermal, or mechanical pressure over the coil turns. In fact, despite than in the last two decades the applied superconductivity field has experienced a significant increase in the physical understanding of the local electromagnetic properties of type II superconductors, including the second generation of high temperature superconducting (2G-HTS) tapes, it is the high aspect ratio of the 2G-HTS tapes what from the computational perspective is still imposing significant challenges to understand their performance in practical superconducting machines.…”