We present high-resolution, polarimetric imaging of the radio hot spots of Cygnus A at 7 mm with the Very Large Array and derive limits to hot spot emission at 12 μm with the Infrared Space Observatory (ISO). The 7 mm images reveal the hot spot structure in total and polarized intensity in unprecedented detail, including images of the projected magnetic field morphology and the spectral index distribution between 7 mm and 3.6 cm at 025 resolution. The magnetic field distribution is consistent with Laing cells, involving a frozen-in field plus simple kinematic dynamo effects due to bulk fluid motions. The spectral index distribution suggests that distributed particle acceleration occurs in the hot spots. The ISO limits at 12 μm require an exponential cutoff in the hot spot spectra at ≈1013 Hz. Such a cutoff is predicted by standard shock acceleration theory for relativistic electrons. The exponential cutoff observed by ISO and the high-resolution images at 7 mm are used to set a lower limit to the streaming velocity of the relativistic electrons, of 0.4c. We also find that the nuclear spectrum of Cygnus A has a peak flux density at about 30 GHz. The origin of this peak is likely to be synchrotron self-absorption in the dominant nuclear component, implying a size of 0.15 mas (= 0.15 pc), with a magnetic field strength of 0.16 G and a pressure in relativistic particles and fields of 10-3 dyn cm-2. The nuclear flux density is 1.6 ± 0.16 Jy at 7 mm, and the nucleus was not seen to vary on a timescale of 1.3 yr to ≤10%. We also have possible detections at 12 μm of three of the galaxies in the Cygnus A cluster within ±3' of Cygnus A.
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