Bright-rimmed clouds (BRCs) are formed at the periphery of H$~$II regions as the radiation from the central star interacts with dense gas. The ionization and resulting compression of the clouds may lead to cloud disruption causing secondary star formation depending on the stellar and gas parameters. Here we use R-band polarimetry to probe the plane-of-the sky magnetic field in the two near-by BRCs IC,59 and IC,63. Both nebulae are illuminated by $gamma$ Cas with the direction of ionizing radiation being orientated parallel or perpendicular to the local magnetic field, allowing us to probe the importance of magnetic field pressure in the evolution of BRCs. Because of the proximity of the system ($sim$200pc) we have acquired a substantial sample of over 500 polarization measurements for stars background to the nebulae. On large scales, the magnetic field geometries of both clouds are anchored to the ambient magnetic field. For IC 63, the magnetic field is aligned parallel to the head-tail morphology of the main condensation, with convex morphology relative to the direction of the ionizing radiation. We estimate the plane of the sky magnetic field strength in IC,63 to be $sim90mu$G. In IC,59, the projected magnetic field follows the M shape morphology of the cloud. Here, field lines present a concave shape with respect to the direction of the ionizing radiation from $gamma$ Cas. Comparing our observations to published theoretical models we find good general agreement, supporting the importance of magnetic fields in BRC evolution.
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