Deconvolution of the Energetic-Particle Count Rates of Voyager 1 and Voyager 2 to Identify the Causes of Dropouts and Enhancements and to Characterize the Structure of the Heliopause

The Voyager spacecraft are the only spacecraft to make direct measurements of the heliopause, where the solar wind and the interstellar wind are in equilibrium. Therefore, analyzing these Voyager measurements is important to our understanding of this region. Of special interest in this research are anomalies in the energetic-particle count rates measured by the Low-Energy Telescopes (LETs) of Voyager 1 (V1) and Voyager 2 (V2) around the heliopause; V1 observed two dropouts just before its crossing of the heliopause in August 2012, and V2 observed two enhancements just after its crossing of the heliopause in November 2018. We analyze these signals by deconvolution to identify the physical causes of these anomalies, which are hypothesized to be either A) magnetic flux tubes between the heliosheath and the very local interstellar medium (VLISM) or B) the motion of the heliopause itself. Prior to deconvolution, the signals are processed by 1) nonlinear least squares polynomial curve fitting to decrease the effect of low-period noise and, for the dropouts only, 2) reflection about a horizontal axis to better condition the deconvolution since this operation is not well behaved at the extremities of signals. An additional processing operation that is being explored for use in this analysis is differentiation. To deconvolve the Voyager signals, we use a nonnegative least squares (NNLS), total variation diminishing (TVD) solver. Preliminary results of the time delays between the V1 signals during its first dropout agree with those from visual inspection. Further analysis based on the computed time delays, the sightlines of the LETs of V1 and V2, the measured magnetic field directions, and the width of the intensity transitions will result in 1) identification of the physical causes of the measured anomalies in energetic-particle count rates, 2) the radial velocity of the plasma around the Voyagers as they crossed the heliopause, and 3) the widths of the structures that caused the anomalies. In summary, this study contributes to our understanding of the structure of the heliopause and demonstrates for the first time in the field of space plasma physics the successful application of deconvolution to time delay estimation.