Background
In modern measurement science, the kilogram is defined through the fixed numerical value of Planck's constant. Today, the primary method for realizing the kilogram is the Kibble balance, in which the gravitational force acting on a test mass is balanced against a magnetic force generated from quantum-traceable electrical quantities. To be able to accurately convert from force to mass, precise knowledge of the local gravitational acceleration is required, which varies over time due to environmental and geophysical influences. Consequently, continuous gravity monitoring is essential for maintaining the accuracy of high-precision mass measurements based on a Kibble balance.

As part of the forthcoming kilogram realization experiment at RISE (Establishing traceability from the Kibble balance | RISE), one promising approach for monitoring temporal gravity variations is a superconducting gravimeter based on a magnetically levitated test mass. In such a system, small gravity-induced displacements of the mass produce corresponding changes in the magnetic field. These changes can be detected with exceptional high sensitivity using a SQUID (Superconducting Quantum Interference Device). The development of such an instrument would not only support the accuracy and long-term stability of the RISE kilogram realization but could also provide a versatile platform for quantum-based ultra-precise gravity measurements in geophysics, environmental monitoring, inertial navigation and other areas.

Description
The proposed Master's thesis would act as a comprehensive technical pre-study for a potential upcoming project aimed at developing a SQUID-based differential gravimeter. The main focus of the thesis would be the modelling and analysis of the magnetic physics package using COMSOL Multiphysics, with particular emphasis on identifying and investigating important design challenges such as geometrical tolerances, parasitic magnetic forces, magnetic cross-coupling and screening effects. The mechanical dynamics of the system would also be investigated analytically and analysed in conjunction with the finite-element simulations performed in COMSOL.

The end product would be a quantitative analysis of the magnetic physics package, providing an improved understanding of the expected behaviour and limitations of the proposed system. The study would identify important design parameters and trade-offs, evaluate the sensitivity of the system to realistic operating conditions and non-idealities, and provide design recommendations for a future experimental prototype. The resulting models would furthermore provide a foundation for continued simulation and optimisation during a subsequent experimental development project.

Main Tasks

• Develop and validate a COMSOL model of a single superconducting test mass with levitation and sensing coils, including magnetic field distribution, levitation force and equilibrium position.

• Extend the model to a differential two-mass configuration and quantify magnetic cross-coupling and parasitic forces between the two test-mass systems.

• Investigate and optimise test-mass and coil geometries, including dimensions, positioning, separation and coil-to-mass distances.

• Investigate the sensitivity of the system to realistic geometrical tolerances, misalignments and asymmetries between the two test-mass systems.

• Investigate the effects of superconducting housing and magnetic screening on the magnetic field distribution, levitation forces and cross-coupling.

• Evaluate the validity of the ideal Meissner approximation and investigate possible non-ideal effects associated with the type-II superconducting behaviour of the test masses.

• Develop an analytical model of the test-mass dynamics and combine it with the finite-element results to describe the response of the levitated system.

• Investigate the system over realistic displacement and operating ranges, including its response to slowly varying gravitational signals such as solid-Earth tides.

• Combine the results into a quantitative assessment of the magnetic physics package and provide design recommendations for a future experimental prototype.

Student profile
The project is suitable for an MSc student in Engineering Physics or a closely related field, with a strong interest in electromagnetism, superconductivity, numerical modelling and precision measurement. The student should be comfortable working independently with mathematical and computational physics and be motivated to combine analytical modelling with numerical simulations.

The applicant must be enrolled in an MSc-level programme at a Swedish university and eligible to undertake a 30-credit Master's thesis within their programme. A solid background in electromagnetic field theory and analytical mechanics is required, while previous experience with COMSOL Multiphysics, FEM methods, circuit theory, superconductivity, or SQUIDs is advantageous but not mandatory. Good proficiency in written and spoken English is required.

Conditions
Location: RISE office in Borås (Brinellgatan 4, Borås) at the national metrology institute

Working conditions: on-site or hybrid

Estimated start: January 2027

Estimated duration: 20 weeks

Credits: 30 ECTS credits (hp)

Compensation: After project completion and approval 39 990 sek

RISE supervisors: Joakim Hagel (joakim.hagel@ri.se), Maria Ekström (maria.ekstrom@ri.se).

Welcome with your application!
The application must contain:

- 1-2 page CV with clear details on the candidate's qualifications with respect to the described project

- Full transcript of academic records

Contact person: Joakim Hagel (joakim.hagel@ri.se)

Deadline: September 30, 2026 (applications will be evaluated continuously during the application period).