Continuum sensitivity and design optimization of superconducting systems under critical current densities with magnetic field dependence

This paper presents an approach for deriving the continuum sensitivity of superconducting systems operating at critical current densities and an optimization method based on the continuum sensitivity. In the sensitivity problem, the superconducting systems is represented by a variational state equation, wherein the magnetic permeability depends on the magnetic field, which is transformed from a state equation with a field-dependent source. The design sensitivity is derived using the material derivative concept of continuum mechanics and the adjoint variable method. The adjoint system has a material property represented as a symmetric tensor that contains the sensitivity of the current density with respect to the magnetic field. The design sensitivity is represented in the analytical form of a surface integral on the interface between the superconducting material and its surroundings, which depends on the sensitivity of the current density. The optimization scheme is constructed based on the continuum design sensitivity. In the design optimization, the level set method is used to express the shape variation of the superconducting materials. The numerical example of infinite solenoids demonstrates that the design sensitivity provides an accurate design solution considering the critical current condition. In addition, the design example of a magnetic resonance imaging solenoid shows that the derived design sensitivity has the inherent ability for attaining the compact design by treating the input current of a superconducting system as a critical condition.

A3COSMOS: the dust attenuation of star-forming galaxies at z = 2.5–4.0 from the COSMOS-ALMA archive

ABSTRACT We present an analysis of the dust attenuation of star-forming galaxies at z = 2.5–4.0 through the relationship between the UV spectral slope (β), stellar mass (M*), and the infrared excess (IRX = LIR/LUV) based on far-infrared continuum observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA). Our study exploits the full ALMA archive over the COSMOS field processed by the A3COSMOS team, which includes an unprecedented sample of ∼1500 galaxies at z ∼ 3 as primary or secondary targets in ALMA band 6 or 7 observations with a median continuum sensitivity of 126 $\rm {\mu Jy\, beam}^{-1}$ (1σ). The detection rate is highly mass dependent, decreasing drastically below log (M*/M⊙) = 10.5. The detected galaxies show that the IRX–β relationship of massive (log M*/M⊙ > 10) main-sequence galaxies at z = 2.5–4.0 is consistent with that of local galaxies, while starbursts are generally offset by $\sim 0.5\, {\rm dex}$ to larger IRX values. At the low-mass end, we derive upper limits on the infrared luminosities through stacking of the ALMA data. The combined IRX–M* relation at $\rm {log\, ({\it M}_{\ast }/\mathrm{M}_{\odot })\gt 9}$ exhibits a significantly steeper slope than reported in previous studies at similar redshifts, implying little dust obscuration at log M*/M⊙ < 10. However, our results are consistent with earlier measurements at z ∼ 5.5, indicating a potential redshift evolution between z ∼ 2 and z ∼ 6. Deeper observations targeting low-mass galaxies will be required to confirm this finding.