WALÉN TEST AND DE HOFFMANN-TELLER FRAME OF INTERPLANETARY LARGE-AMPLITUDE ALFVÉN WAVES

In this study, three methods of analysis are compared to test the Walen relation. Method 1 requires a good de Hoffmann-Teller (HT) frame. Method 2 uses three components separately to find the frame that is slightly modified from Method 1. This method is intended to improve the accuracy of the HT frame and able to demonstrate the anisotropic property of the fluctuations. The better the relation is, the closer the slope of a regression fitting the data of plasma versus Alfven velocities is to 1. However, this criterion is based on an average HT frame, and the fitted slope does not always work for the Walen test because the HT frame can change so fast in the high-speed streams. We propose Method 3 to check the Walen relation using a sequence of data generated by taking the difference of two consecutive values of plasma and Alfven velocities, respectively. The difference data are independent of the HT frame. We suggest that the ratio of the variances between plasma and Alfven velocities is a better parameter to qualify the Walen relation. Four cases in two solar wind streams are studied using these three methods. Our results show that when the solar wind HT frame remains stable, all three methods can predict Alfvenic fluctuations well, but Method 3 can better predict the Walen relation when solar wind contains structures with several small streams. A simulated case also demonstrates that Method 3 is better and more robust than Methods 1 and 2. These results are important for a better understanding of Alfvenic fluctuations and turbulence in the solar wind.