Electromagnetic modeling of REBCO high field coils by the H-formulation

In this paper, we employ the anisotropic bulk approximation to successfully implement the electromagnetic modeling of superconducting coils wound with rare-earth-barium-copper-oxide (REBCO) tapes based on the H-formulation, in which the field-dependent critical current density and highly nonlinear characteristic are considered. The total number of turns in the stacks of REBCO pancake coils is up to several thousand. We validate the anisotropic bulk model by comparing the ac loss of a small four-pancake coil between the bulk model and the original model which takes the actual thickness of the superconducting layer into account. Then, the anisotropic bulk model is used to investigate the self-field problem of the REBCO prototype coils of the National High Magnetic Field Laboratory all-superconducting magnet. The field and current density distributions are obtained, and an obvious shielding effect is observed at the top and bottom of the coils. The ac losses in the first and second cycles are calculated. The former is crucial to the design of the cooling system and the latter relates to the routine consumption of the liquid helium. It is found that the ac loss in the first cycle is 2.6 times as large as that in the second cycle. We also study the ac loss dependences on some key parameters (the critical current, n-value and ramp rate of the applied current). It is found that both in the first and second cycles, the ac loss increases with decreasing critical current. Moreover, the influence of the n-value on the ac loss is negligible. In addition, the ac loss decreases logarithmically with increasing ramp rate. However, the average power loss increases linearly with increasing ramp rate. We also compare some analytical estimates with the simulation result for the ac loss of the dual prototype coils. It is found that the results of Bean's slab model are closer to the simulation result. The presented model is a useful tool to help us understand electromagnetic behavior and ac losses in REBCO high field coils. It also provides a basis to analyze the mechanical characteristics in the coils in the future.