# Enhancing Precision in SQUID Sensors: Analyzing Washer Geometry Dependence at the Microscale
## 3 Methodology
### Other Parameter Settings
#### 3.3.3 Simulation Target  
To explore the interaction between superconducting washer rings and magnetic fields, we first simulate the Meissner effect to predict the microscale behavior of superconductors under applied magnetic fields, analyzing how washer geometry influences device performance. Additionally, in the operation of DC SQUID devices, the shielding current is crucial. This current circulates within the superconducting loop of the SQUID to maintain the quantization of magnetic flux within the loop. This process is closely related to the Meissner effect, where surface currents automatically counteract the external flux to stabilize the internal flux, thereby effectively shielding against variations in the external magnetic fields. The strength of the shielding current directly impacts the sensitivity and precision of the  
Figure 5: The magnetic field generated by the magnetic dipole on a planar grid covering the area from \(-250\)\(\upmu\)m to \(250\)\(\upmu\)m.  
SQUID. The design of washer inductance directly affects multiple performance metrics of DC SQUID devices, making it crucial for device optimization. Well-designed inductance balances the dynamics of quantum systems and noise. * Meissner Screening. In our simulation model of the superconducting ring, we emulate the influence of an external magnetic field by introducing a circulating current through the central aperture of the ring. Specifically, we designate a circulating current of 1 mA to mimic the effect of an external magnetic field, thus ensnaring an equivalent magnetic flux within the apertures of the superconducting ring. However, it is pertinent to acknowledge that, within these apertures, the boundary effect of the superconductor may induce a stable magnetic flux, consequently fostering the generation of a circulating current in response to this external magnetic field. This methodological approach affords us the opportunity to scrutinize the efficacy of various washer designs in repulsing magnetic fields, thereby facilitating the identification of designs that optimize Meissner screening. * Current distribution. Our analytical endeavor primarily revolves around scrutinizing the distribution of the current and integrated current density across the washer structure to corroborate the presence of circulating currents. Our overarching objective is to delineate the spatial distribution of supercurrents and compute the aggregate circulating current within the washer, thereby furnishing insights into how design modifications engender alterations in current confinement efficiency and overall sensor efficacy. The sheet current, serving as a proxy for thickness-integrated current density, emerges as a pivotal physical quantity indispensable for scrutinizing both the static and dynamic responses to applied magnetic fields and currents, as well as for comprehending the nuances of eddy currents within the film. Concurrently, the stream function, denoted as g, assumes the role of delineating the local magnetization of the film or the area density of magnetic dipole sources. \[\overset{\rightarrow}{J}(x,y)=-\hat{z}\times\overset{\rightarrow}{\
abla}g =\overset{\rightarrow}{\
abla}\times(g\hat{z})=\left(\frac{\partial g}{ \partial y},-\frac{\partial g}{\partial x}\right) \tag{22}\]
* Magnetic flux and self-inductance. The process of computing the magnetic flux and self-inductance of a ring is pivotal for comprehending the behavior of superconductivity in a non-zero magnetic flux state. These parameters serve as cornerstones for quantifying the sensor's response to an external magnetic field and its self-resonant properties. Following the calculations in Section 2, aimed at providing a preliminary assessment of the varying impacts of different ring designs on the final device, our overarching objective is to pinpoint configurations that maximize the sensitivity and dynamic range of the sensor.