Polars (AM Herculis binaries) are a prominent class of bright soft X-ray sources, many of which were discovered with ROSAT. We present a homogenous analysis of all the pointed ROSAT PSPC observations of polars subdivided into two papers that discuss the prototype polar AM Her in detail and summarize the class properties of all other polars. We derive the high-state soft X-ray flux and short-term spectral variability of AM Her using a new detector response matrix and a confirmed flux calibration of the ROSAT PSPC below 0.28 keV. The best-fit mean single-blackbody temperature and integrated bright-phase energy flux of AM Her in its April 1991 high state are 27.2 +/- 1.0 eV and (2.6 +/- 0.6) x 10^-9 erg cm^-2s^-1, respectively. The total blackbody flux of a multi-temperature model that fits both the soft X-ray and the fluctuating far-ultraviolet components is Fbb = (4.5 +/- 1.5) x 10^-9 erg cm^-2s^-1. The total accretion luminosity at a distance of 80 pc, Lbb = (2.1 +/- 0.7) x 10^33 erg s-1, implies an accretion rate of Mdot = (2.4 +/- 0.8) x 10^-10 Msun yr^-1 for an 0.78 Msun white dwarf. The soft X-ray flux displays significant variability on time scales down to 200 ms. Correlated spectral and count-rate variations are seen in flares on time scales down to 1 s, demonstrating the heating and cooling associated with individual accretion events. Our spectral and temporal analysis provides direct evidence for the blobby accretion model and suggests a connection between the soft X-ray and the fluctuating far-ultraviolet components.
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