THE PROJECT ADDRESSES THE KEY ISSUES IN THE ASTROPHYSICS OF PULSARS - FROM THE KINETIC EFFECTS RESPONSIBLE FOR THE PRODUCTION OF BROADBAND EMISSION BOTH INSIDE THE PULSAR MAGNETOSPHERE AND IN THE WIND AND TO LARGE SCALE STRUCTURES AND MORPHOLOGY OF RELATIVISTIC FLUID FLOWS. FIRST WE WILL ADDRESS THE LONG-STANDING PROBLEM OF COHERENT EMISSION GENERATION IN RADIO PULSARS. USING RECENTLY THEORETICAL ADVANCES IN OUR UNDERSTANDING OF PARTICLE FLOWS INSIDE THE PULSAR MAGNETOSPHERE AS WELL AS NUMERICAL ADVANCES IN PLASMA MODELING USING PIC SIMULATIONS WE WILL DEVELOP A MODEL OF PLASMA INSTABILITIES AT THE SO-CALLED ANOMALOUS CYCLOTRON RESONANCE WHEREBY ONE-DIMENSIONAL PLASMA IS UNSTABLE TO THE GENERATION OF HIGH BRIGHTNESS EMISSION VIA A CHERENKOV-TYPE EMISSION PROCESS (MODIFIED BY THE PRESENCE OF THE MAGNETIC FIELD). COHERENT EMISSION OF RADIO WAVES EXCITES CYCLOTRON MOTION AND LEADS TO THE PRODUCTION OF THE UV-X-RAY SPECTRAL PEAK. IN TURN INVERSE COMPTON SCATTERING OF THE CYCLOTRON PHOTONS LEADS TO VERY HIGH ENERGY GAMMA-RAY EMISSION. THUS A WHOLE RANGE OF PULSARS' NON-THERMAL EMISSION FROM COHERENT RADIO WAVES TO VERY HIGH ENERGY GAMMA-RAYS - NEARLY TWENTY DECADES IN ENERGY - MAY BE A MANIFESTATION OF INTER-DEPENDENT RADIATION PROCESSES. TO TEST THE MODEL WILL PERFORM DATA ANALYSIS OF THE PULSARS' VERY HIGH ENERGY EMISSION TARGETING THE POSSIBLE OCCURRENCES OF POWER LAW TAILS ABOVE 10 GEV. SECOND WE WILL INVESTIGATE USING THEORETICAL APPROACH AND NUMERICAL SIMULATIONS A MODEL THAT THE PARTICLES PRODUCING CRAB FLARES AND POSSIBLY MOST OF CRAB PULSAR WIND NEBULAS HIGH ENERGY EMISSION ARE ACCELERATED VIA RECONNECTION EVENTS. WE WILL DEVELOP A MODEL OF EXPLOSIVE MERGER OF MAGNETIC FLUX TUBES IN HIGHLY MAGNETIZED FORCE-FREE PLASMA. DURING THE MERGER PARTICLES ARE EFFICIENTLY ACCELERATED PRODUCING NON-THERMAL POWER-LAW TAILS. THE MODEL HAS ALL THE INGREDIENTS NEEDED FOR CRAB FLARES: EXPLOSIVE DYNAMICS ON LIGHT TRAVEL TIME (STARTING FROM QUASI-STABLE SMOOTH INITIAL CONDITION) DEVELOPMENT OF HIGH ELECTRIC FIELD REGIONS IN A MACROSCOPICALLY LARGE VOLUME AND EFFICIENT PARTICLE ACCELERATION. FINALLY USING ANALYTICAL APPROACH AND 3D RELATIVISTIC MHD SIMULATIONS WE WILL STUDY BOW-SHOCK PULSAR WIND NEBULAE CONCENTRATING ON VARIOUS MAGNETIC STRUCTURES WITHIN THE TAILS OF PWNE. DEPENDING ON THE ORIENTATION OF THE PULSARS VELOCITY ROTATION AXIS AND THE LINE OF SIGHT ONE CAN IDENTIFY THREE DIFFERENT TYPES OF GEOMETRIES: (I) RIFLE BULLETS (II) FRISBEES AND (III) CARTWHEELS. WE EXPECT DIFFERENT LONG-TERM DYNAMICS AND DIFFERENT OBSERVATIONAL PROPERTIES IN THESE CASES DRIVEN MOSTLY BY THE LONG-TERM BEHAVIOR OF MAGNETIC FIELDS. THE RESULTS OF MODELING WILL BE COMPARED WITH RADIO H-ALPHA AND HIGH ENERGY X-RAY OBSERVATIONS OF BOW SHOCK PWNE. THIS MULTIDISCIPLINARY PROPOSAL COMBINES RESEARCH IN BROAD AREAS OF HIGH ENERGY ASTROPHYSICS AND PLASMA PHYSICS. THE PROPOSAL WILL COMBINE ANALYTICAL AND NUMERICAL WORK (BOTH FLUID-TYPE AND PARTICLE-IN-CELL SIMULATIONS). THE RESULTS OF THE INVESTIGATION WILL BOTH ADVANCE OUR UNDERSTANDING OF ASTROPHYSICALLY-RELEVANT BASIC PLASMA PROCESSES DYNAMICS AND EMISSION PROPERTIES OF RELATIVISTIC PLASMA PHYSICS OF PULSARS AND THEIR WINDS AND BY EXTENSION WILL CONTRIBUTE TO UNDERSTANDING OTHER ASTROPHYSICAL SOURCES OF HIGH ENERGY EMISSION