THERMALIZATION OF CHARGED PARTICLE FLOWS IN A WIDE RANGE OF SPACE PLASMA SYSTEMS IS ORGANIZED THROUGH THE PARTICLE INTERACTION WITH COLLISIONLESS SHOCK WAVES. THE ENERGY CONVERSION FROM KINETIC TO THERMAL IS MEDIATED BY COLLECTIVE PROCESSES I.E. DC AND AC ELECTRIC FIELDS GENERATED WITHIN A SHOCK. THE EARTH S BOW SHOCK IS AN EXCELLENT PLASMA LABORATORY FOR INVESTIGATION OF VARIOUS PROCESSES RESPONSIBLE FOR THE CHARGED PARTICLE HEATING AT COLLISIONLESS SHOCKS IN THE UNIVERSE. THE NET HEATING OF PARTICLES WITHIN THE SHOCK IS BELIEVED TO BE SIGNIFICANTLY CONTRIBUTED BY ADIABATIC PROCESSES. HOWEVER RECENT SPACECRAFT OBSERVATIONS INDICATE IMPORTANT PROBLEMS APPEARING IN THE APPLICATION OF THIS BASIC THEORY TO ELECTRON HEATING MEASURED AT THE EARTH S BOW SHOCK. DETAILED ANALYSIS OF SPACECRAFT DATA SHOWED THAT ELECTRONS ARE HEATED ISOTROPICALLY ACROSS A SHOCK WAVE WHEREAS ADIABATIC MECHANISMS SHOULD PROVIDE A STRONG ANISOTROPY. TWO COMPETING INTERPRETATIONS WERE PROVIDED TO EXPLAIN THIS CONTRADICTION: ELECTRIC FIELD FLUCTUATIONS WITHIN THE SHOCK CAN DRIVE AN EFFICIENT ELECTRON PITCH-ANGLE SCATTERING OR ALTERNATIVELY ELECTRON DISTRIBUTION FUNCTION BEHIND THE SHOCK IS SHAPED VIA SIGNIFICANT NON-LOCAL PROCESSES. DETAILED INVESTIGATION OF ELECTRON HEATING WITHIN THE SHOCK IS REQUIRED TO DETERMINE A ROLE OF BOTH PROPOSED MECHANISMS AND TO DEVELOP A NEW MODEL DESCRIBING ISOTROPIC ELECTRON HEATING. THIS OPPORTUNITY BECOMES AVAILABLE WITH THE UNPRECEDENTED HIGH TIME RESOLUTION MULTI-SPACECRAFT MEASUREMENTS OF THE MAGNETOSPHERIC MULTISCALE (MMS) MISSION AT SHOCK WAVES. THUS THE MAIN GOAL OF OUR PROJECT IS TO INVESTIGATE ELECTRON HEATING AND ESTIMATE A ROLE OF ELECTROSTATIC FLUCTUATIONS IN ELECTRON ISOTROPIZATION AT THE EARTH S BOW SHOCK. WE PLAN TO SOLVE THE FOLLOWING SPECIFIC PROBLEMS IN OUR PROJECT: 1) COLLECT THE STATISTICS OF QUASI-PERPENDICULAR BOW SHOCK CROSSINGS BY MMS; 2) COLLECT AND ANALYZE STATISTICS OF MEASUREMENTS OF THE ELECTRON DISTRIBUTION FUNCTION ACROSS THESE SHOCKS; 3) USE THE CROSS-SHOCK ELECTRIC FIELD DISTRIBUTION AND THE WAVE ACTIVITY FOR CALCULATIONS OF THE SCATTERING RATES AND THEIR INCORPORATION INTO THE LIOUVILLE KINETIC EQUATION; 5) NUMERICAL SOLUTION OF THE LIOUVILLE KINETIC EQUATION AND COMPARISON OF THE PREDICTED EVOLUTION WITH ELECTRON DISTRIBUTION FUNCTIONS MEASURED BY MMS. OBSERVATIONAL METHODOLOGY OF THE PROJECT INCLUDES ANALYSIS OF: ELECTRIC FIELD (BOTH DC AND WAVE ACTIVITY) MEASUREMENTS ACROSS THE SHOCKS AND MEASUREMENTS OF THE ELECTRON DISTRIBUTION FUNCTION WITHIN THE SHOCK WITH SUFFICIENTLY HIGH TIME RESOLUTION TO RESOLVE ELECTRON HEATING. THEORETICAL METHODOLOGY OF THE PROJECT INCLUDES: 1) CALCULATION OF THE ELECTRON PITCH-ANGLE SCATTERING AND HEATING RATES DUE TO INTERACTION WITH OBSERVED WAVE ACTIVITY; 2) INCORPORATION OF THE SCATTERING RATES INTO THE LIOUVILLE KINETIC EQUATION AND TRACING OF THE DISTRIBUTION FUNCTION FROM UPSTREAM TO DOWNSTREAM IN THE MACROSCOPIC ELECTROMAGNETIC SHOCK FIELD (AS ADOPTED FROM OBSERVATIONS) . RELEVANCE OF THE PROBLEM TO ONE OR MORE OF THE DECADAL SURVEY GOALS. THIS PROPOSAL WILL PROVIDE A BETTER UNDERSTANDING OF ELECTRON HEATING AT COLLISIONLESS SHOCKS IN THE UNIVERSE AND AT THE EARTH S BOW SHOCK IN PARTICULAR. THIS WORK CONTRIBUTES TO ONE OF THE FOUR SCIENTIFIC OBJECTIVES OF THE HELIOPHYSICS DECADAL SURVEY NAMELY DISCOVERING AND CHARACTERIZING FUNDAMENTAL PROCESSES THAT OCCUR BOTH WITHIN THE HELIOSPHERE AND THROUGHOUT THE UNIVERSE (AND TWO SCIENCE AREAS: PARTICLE ACCELERATION TRANSPORT MODULATION IN THE HELIOSPHERE; HELIOSPHERIC PLASMA PROCESSES TURBULENCE WAVES COMPOSITION).