author = "Franco, Adriane Marques de Souza and Fr{\"a}nz, M. and Echer, 
                         Ezequiel and Bolzan, M. J. A. and Zhang, T. L.",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Max Planck 
                         Institute for Solar System Research} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)} and {Universidade Federal de 
                         Jata{\'{\i}}} and {Space Research Institute of the Austrian 
                         Academy of Sciences}",
                title = "The correlation length of ULF waves around Venus: VEX 
              journal = "Planetary and Space Science",
                 year = "2020",
               volume = "180",
                pages = "e104761",
                month = "jan.",
             keywords = "Venus induced magnetosphere, ULF waves, Correlation length.",
             abstract = "A study of the correlation length of ultra-low frequency (ULF) 
                         waves around Venus was developed using electron density and 
                         magnetic field data obtained from the Analyzer of Space Plasmas 
                         and Energetic Atoms (ASPERA-4) and magnetometer (MAG), 
                         respectively, on board of the mission Venus Express (VEX). The 
                         analysis was conducted using the whole interval of the mission 
                         (2006-2014). The correlation scales have been calculated by the 
                         correlation length parameter that is a characteristic distance 
                         over which fluctuations in a variable are correlated. We limited 
                         the study to the frequency range from 8 to 50 mHz because previous 
                         studies have shown that ULF waves produced in the foreshock have 
                         the highest power in this range. In this study the correlation 
                         length was calculated by an exponential fit employed to the 
                         auto-correlation curve. The auto-correlation function was 
                         calculated lagged by a time between 0 and 60 s and sliding a 
                         window with 120s across the data. This analysis has been also 
                         extended to correlation length determinations in spatial scale. In 
                         order to obtain the correlation length in a spatial domain, the 
                         temporal correlation length must be multiplied by the solar wind 
                         velocity. Here, the ASPERA-4/IMA (Ion Mass Analyzer) velocity data 
                         was used. It was found that the dominant correlation length in 
                         temporal scale varies from 9 to 14 s in electron density and 
                         between 7.5 and 11 s in the magnetic field. In spatial scale, 
                         correlation length varies between 2.8 x 10(3) and 5 x 10(3) km in 
                         electron density data, and between 1.7 x 10(3) -4X10(3) km for the 
                         total magnetic field data value in this frequency window. 
                         Fluctuations in the magnetosheath and in the MPB may be correlated 
                         with fluctuations at the ionosphere, since correlation lengths in 
                         those regions are larger than the size of these regions, 
                         indicating that local resonant effect of wave trains at the 
                         ionopause may enhance the atmospheric ion escape at Venus. Our 
                         results also show that pickup heavy ions can interact with 
                         discontinuities in the magnetosheath of Venus and can destroy ULF 
                         wave trains during periods of low solar wind pressure. The results 
                         obtained here are compared with a similar previous analysis in the 
                         Mars environment.",
                  doi = "10.1016/j.pss.2019.104761",
                  url = "",
                 issn = "0032-0633",
             language = "en",
           targetfile = "franco_correlation.pdf",
        urlaccessdate = "2021, Feb. 27"