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Purpose: Dosimetry of ionizing radiation in the presence of strong magnetic fields is gaining increased relevance in light of advances for MRI-guided radiation therapy. While the impact of strong magnetic fields on the overall response of ionization chambers has been simulated and measured before, this work investigates the local impact of the magnetic field on dose response in an ion chamber. High-resolution 1D and 2D response maps have been created for two small clinical thimble ionization chambers, the PinPoint chambers 31006 and 31014 (Physikalisch Technische Werkstaetten Freiburg, Germany)., Methods: Working on the Imaging and Medical Beam Line of the Australian Synchrotron an intense kilovoltage radiation beam with very low divergence, collimated to 0.1 mm was used to scan the chambers by moving them on a 2D motion platform. Measured current and beam position were correlated to create the response maps. Small neodymium magnets were used to create a field of about 0.25 T. Chamber axis, magnetic field, and beam direction were perpendicular to each other. Measurements were performed with both orientations of the magnetic field as well as without it. Chamber biases of 5 and 250 V in both polarities were used., Results: The local distribution of the response of small thimble-type ionization chambers was found to be impacted by a magnetic field. Depending on the orientation of the magnetic field, the chamber response near the stem was either enhanced or reduced with the response near the tip behaving the opposite way. Local changes were in the order of up to 40% compared to measurements without the magnetic field present. Bending of the central electrode was observed for the chamber with the steel electrode. The size of the volume of reduced collection near the guard electrode was impacted by the magnetic field. As the here investigated beam and field parameters differ from those of clinical systems, quantitatively different results would be expected for the latter. However, the gyroradii encountered here were similar to those of a 6-7 MV MRI linac with a 1.5 T magnet., Conclusions: Magnetic fields impact the performance of ionization chambers also on a local level. For practical measurements this might mean a change in the effective point of measurement, in addition to any global corrections. Further knowledge about the local response will help in selecting or constructing optimized chambers for use in magnetic fields., (© 2019 The Authors. Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.)