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Ludger Klinkenbusch, Kiel University, “Advanced Applications of Multipole Analysis in Electromagnetics”, 5 - 9 September 2016

20 hours (5 credits)

Aula Riunioni del Dipartimento di Ingegneria dell'Informazione, via G. Caruso 16, Pisa – Ground Floor

Short Abstract:
Multipole Analysis counts to the classical methods in Electromagnetics, and its outstanding mathematical and physical features are of practical importance for many areas of modern electromagnetic applications and developments. Of course, multipole techniques are not only used for analytically treating simple problems. Rather, they are applied to enhance the features of numerical methods (e.g., for the MultiLevel Fast Multipole Approach - MLFMA), for a very accurate probe-corrected near field antenna measurement, for investigating the general limits and features of radiating structures, or in the context of distinguishing very low quasi-stationary magnetic fields coming from the brain to those coming from external sources (Signal-Space Separation method), to mention just a few. Finally, multipole analysis allows a unique insight into - and thus deepens the understanding of - the mathematical and physical properties of electromagnetic fields.

After a brief introduction and motivation the course summarizes the derivation of the spherical-multipole expansion of the electromagnetic field including a discussion of its physical interpretation and low-frequency interpretation in case of a quasi-stationary magnetic field. In a kaleidoscopic manner then three examples of applications will be demonstrated: The process of radiation including the interpretation of radiated and reactive (non-radiated) energies, the spherical antenna near-field measurement, and the application of a spherical-multipole expansion for the noise reduction in sensoring bio-magnetic fields.

Course Contents in brief:

  • Introduction (6 hrs.)
    • History and classical applications
    • Derivation of the spherical-multipole expansion

    • Physical interpretation as modes

    • Specialization to quasi-stationary magnetic field

  • Radiated fields (5 hrs.)
    • Multipole interpretations of near-fields and far-fields
    • Inseparability of radiated and non-radiating field parts

    • What would be an optimal antenna?

  • Spherical antenna near-field measurement (4 hrs.)
    • Basis outline of a measurement system
    • Summary of the multipole approach

    • Probe-corrected measurement system

  • Noise reduction for bio-magnetic measurements (4 hrs.)
    • Bio-magnetic measurements
    • Example: Magnetoencephalography

    • Distinguishing between internal and external magnetic fields

  • Summary, Conclusion and Outlook (1 hr.)


5 to 9 September, 2016: 9:00-13.00 each day