{'fraction_non_alphanumeric': 0.017970401691331923, 'fraction_numerical': 0.0, 'mean_word_length': 5.912408759124087, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Lagrangian formulation for inverse source problems: minimum energy and reactive power constraints

With the practical interest provided by the antenna synthesis problem and with the expectation of illuminating, from a new perspective, fundamental antenna limits connected to the reactive energy, we investigate the inverse source problem of deducing an unknown source from knowledge of its external field by means of a new Lagrangian formulation that encompasses different solution constraints, including important reactive power constraints. We arrive at a new minimum energy solution with the additional, antenna-motivated constraint of having a zero reactive power. Numerical results (shown at the conference), corresponding to a dipolar source, illustrate interesting properties of the solutions (such as their obeying a certain homogeneous wave equation) and of their fields and energy, and elucidate fundamental questions on antenna limits.