Effective Polytropic Index of Small-Scale and Force-Free Magnetic Flux Ropes in the Solar Wind

The effective polytropic index, alpha eff, of small-scale magnetic flux ropes in the solar wind is investigated using the Wind observations near 1 AU. A total of 59 flux ropes were selected with a good estimation on alpha eff and divided into two categories, namely, CAT1 for flux ropes accompanied with torsional Alfven waves and CAT2 for those without. These 59 flux ropes were satisfied the constant-alpha, force-free flux rope model. It is found that the alpha eff index ranges between 1.05 and 2.34, with a mean of 1.68 +/- 0.43, for CAT1, while it ranges between 0.71 and 2.42, with a mean of 1.52 +/- 0.44, for CAT2. Apparently, the mean alpha eff of CAT1 flux ropes is closer to the adiabatic condition (alpha eff = 5/3), as compared to CAT2 ones. No clear correlation of the alpha eff index with the solar wind speed and flux rope size is found for these 59 flux ropes. For each flux rope category, the flux ropes are further distinguished by the presence of counterstreaming suprathermal electrons (CSEs) inside it. For both CAT1 and CAT2 flux ropes, it seems that the median and mean of alpha eff are alpha eff index spreads over a wide range of values, it is suggested that various polytropic processes may happen within the flux ropes during their propagation in the solar wind.