SOLAR WIND TURBULENCE CONSISTS OF FLUCTUATIONS THAT SPAN A VAST RANGE OF SPATIAL SCALES. ON LENGTH-SCALES LARGER THAN THE ION GYRORADIUS THE TURBULENCE CONSISTS OF A DOMINANT INCOMPRESSIBLE ALFV NICALLY POLARIZED COMPONENT AND A MINORITY COMPRESSIVE POPULATION [KLEIN ET AL. 2012] WHOSE SPECTRUM TRACKS THAT OF THE ALFV NIC FLUCTUATIONS [CHEN ET AL. 2011]. ACCORDING TO LINEAR THEORY THE COMPRESSIVE FLUCTUATIONS SHOULD BE STRONGLY DAMPED: THUS THEIR PRESENCE ON ALL INERTIAL-RANGE SCALES IS SOMEWHAT SURPRISING. THIS PROJECT WILL STUDY THE COMPRESSIVE COMPONENT OF THE SOLAR WIND CLOSE TO THE SUN OBSERVED BY NASA'S PARKER SOLAR PROBE (PSP) AND CAN BE SUBDIVIDED INTO THREE MAIN PARTS. THE FIRST TASK WILL BE TO MEASURE AND THEORETICALLY MODEL THE STATISTICAL PROPERTIES OF THE COMPRESSIVE COMPONENT INCLUDING ITS INTERMITTENCY FOLLOWING ON FROM EARLIER MODELS OF ALFV NIC-ONLY INTERMITTENT TURBULENCE [MALLET ET AL. 2015 2017]. THIS WILL ALREADY BE A SIGNIFICANT ADVANCE IN OUR UNDERSTANDING OF COLLISION LESS PLASMA TURBULENCE A FUNDAMENTAL PHYSICAL PROCESS IN THE HELIOSPHERE AND IN MANY OTHER ASTROPHYSICAL SETTINGS. RECENTLY A MECHANISM HAS BEEN PROPOSED TO EXPLAIN THE LACK OF DAMPING THE STOCHASTIC PLASMA ECHO [SCHEKOCHIHIN ET AL. 2016]: IN A STRONGLY TURBULENT PLASMA LINEAR DAMPING OF THE COMPRESSIVE MODES MAY BE SUPPRESSED BY NONLINEAR INTERACTIONS WITH THE TURBULENT FLUCTUATIONS. THIS HAS BEEN OBSERVED IN NUMERICAL SIMULATIONS [MEYRAND ET AL. 2019] BUT NOT YET IN REAL TURBULENCE. THE OTHER PARTS OF THE PROJECT INVOLVE LOOKING FOR OBSERVATIONAL SIGNATURES OF THE STOCHASTIC ECHO AS WELL AS THEORETICAL WORK. THE SECOND PART INVOLVES THE MODE STRUCTURE OF THE COMPRESSIVE FLUCTUATIONS. ALTHOUGH THE SOLAR WIND IS NEARLY COLLISION LESS THE COMPRESSIVE FLUCTUATIONS HAVE POLARIZATION MORE SIMILAR TO THE MHD (COLLISIONAL) SLOW MODE THAN TO THE COLLISION LESS MODE [VERSCHAREN ET AL. 2017]. THIS COULD BE DUE TO THE STOCHASTIC ECHO SUPPRESSING THE DAMPING WITH THE SIDE EFFECT THAT THE POLARIZATION ADJUSTS. WE WILL STUDY THIS PROBLEM THEORETICALLY SOLVING THE COUPLED EQUATIONS FOR THE POLARIZATION IN THE PRESENCE OF THE STOCHASTIC ECHO AND TESTING THE MODEL USING MEASUREMENTS OF THE TURBULENCE FROM PSP. THIS MEASUREMENT ONLY REQUIRES KNOWLEDGE OF THE PLASMA DENSITY VELOCITY AND TEMPERATURE AND THE MAGNETIC FIELD ON INERTIAL RANGE TIMESCALES. THE FINAL PART OF THE PROJECT STUDIES FINE STRUCTURE IN THE ION VELOCITY DISTRIBUTION FUNCTION (VDF). SCHEKOCHIHIN ET AL. 2016 USED A SPECTRAL (HERMITE-MOMENT) REPRESENTATION OF THE PERTURBED VDF SHOWING THAT WHILE A LINEARLY DAMPING MODE HAS A SHALLOW SPECTRUM THE STOCHASTIC ECHO RESULTS IN A STEEP SPECTRUM. THE FORMALISM USED RELIES ON THE ASSUMPTION THAT THE BACKGROUND VDF IS MAXWELLIAN - NOT THE CASE IN THE SOLAR WIND. THUS THE THEORY NEEDS TO BE EXTENDED TO MORE REALISTIC VDFS DEVELOPING PREDICTIONS FOR THE SCALING PROPERTIES OF THEIR FLUCTUATIONS AND FINALLY COMPARED WITH REAL DATA FROM PSP. OUR PROPOSED PROJECT WILL CHARACTERIZE AND EXPLAIN THE COMPRESSIVE COMPONENT OF THE SOLAR WIND TURBULENCE AN IMPORTANT PHYSICAL PROCESS WHICH AFFECTS THE THERMODYNAMIC BACKGROUND UPON WHICH ALL OTHER HELIOSPHERIC PHYSICS OCCURS. LOOKING FOR THE STOCHASTIC ECHO IN THESE COMPRESSIVE INERTIAL-RANGE FLUCTUATIONS IS VERY OBSERVATIONALLY ACCESSIBLE SINCE IT ONLY REQUIRES MEASUREMENTS OF THE ION VDF ON LONG INERTIAL-RANGE TIMESCALES (BETWEEN 10S AND 1000S). FINALLY IT IS WORTH POINTING OUT THAT THE STOCHASTIC ECHO MAY OCCUR MUCH MORE GENERALLY THAN IN THIS SITUATION FOR EXAMPLE IN THE SMALL-SCALE DISSIPATION RANGE TURBULENCE IN THE SOLAR WIND AS WELL AS IN FUSION AND ASTROPHYSICAL PLASMAS. THUS OBSERVATIONAL ATION WOULD DRAMATICALLY ALTER OUR PICTURE OF THE PHYSICAL PROCESS OF TURBULENT HEATING IN MANY OTHER PLASMAS THROUGHOUT THE UNIVERSE.