The TESS spacecraft observed the asynchronous polar CD Ind at a two-minute cadence almost continuously for 28 days in 2018, covering parts of 5 consecutive cycles of the systems 7.3-day beat period. These observations provide the first uninterrupted photometry of a full spin-orbit beat cycle of an asynchronous polar. Twice per beat cycle, the accretion flow switched between magnetic poles on the white dwarf, causing the spin pulse of the white dwarf (WD) to alternate between two waveforms after each pole-switch. An analysis of the waveforms suggests that one accretion region is continuously visible when it is active, while the other region experiences lengthy self-eclipses by the white dwarf. We argue that the previously accepted periods for both the binary orbit and the WD spin have been misidentified, and while the cause of this misidentification is a subtle and easily overlooked effect, it has profound consequences for the interpretation of the systems accretion geometry and doubles the estimated time to resynchronization. Moreover, our timings of the photometric maxima do not agree with the quadratic ephemeris from Myers et al. (2017), and it is possible that the optical spin pulse might be an unreliable indicator of the white dwarfs rotation. Finally, we use Doppler tomography of archival time-resolved spectra from 2006 to study the accretion flow. While the accretion flow showed a wider azimuthal extent than is typical for synchronous polars, it was significantly less extended than in the three other asynchronous polars for which Doppler tomography has been reported.
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