IN FLARES ELECTRONS ARE ACCELERATED OUT OF THE AMBIENT ATMOSPHERE TO HIGH ENERGIES (GREATER THAN OR EQUAL TO 20 KEV) THROUGH A PROCESS THAT IS NOT YET WELLUNDERSTOOD. ONCE ACCELERATED THESE ELECTRONS MOVE THROUGH AND HEAT THE ATMOSPHERE. THE LOCATION OF AND RADIATION PRODUCED BY THE HEATED PLASMA DEPEND UPON THE ELECTRON ENERGY DISTRIBUTION. THUS THIS DISTRIBUTION IS KEY TO UNDERSTANDING THE FLARE ACCELERATION PROCESS AS WELL AS THE THERMAL RESPONSE OF THE ATMOSPHERE. FOR THIS REASON MUCH EFFORT HAS FOCUSED ON ACCURATELY DETERMINING THESE DISTRIBUTIONS. THIS PROJECT WILL ENHANCE PREVIOUS WORK TO PROVIDE THE MOST ACCURATE CONSTRAINTS EVER ON ELECTRON ENERGY DISTRIBUTIONS PRODUCED DURING SEVERAL LARGE FLARES. WE DETERMINE DETAILS OF FLARE-ACCELERATED ELECTRON SPECTRA FROM THE X-RAY BREMSSTRAHLUNG PRODUCED AS THEY INTERACT WITH THE AMBIENT PLASMA. THIS IS DONE BY FITTING OBSERVED X-RAY SPECTRA PROVIDED BY RHESSI WITH MODELS OF X-RAY PRODUCTION. IN THIS FITTING SCHEME THE INFERRED ELECTRON SPECTRA DEPEND CRITICALLY UPON THE ASSUMPTIONS IMPLICIT IN THE X-RAY PRODUCTION MODELS SO IT IS CRUCIAL THAT THESE ASSUMPTIONS ARE SOUND AND SELF-CONSISTENT. IN THE ORIGINAL COLD THICK-TARGET MODEL (TTM) NON-THERMAL ELECTRONS ARE BEAMED FROM THE ACCELERATION SITE IN THE CORONA INTO THE DENSER FOOTPOINT. THE ELECTRON DISTRIBUTION IS ESTIMATED FROM THE BREMSSTRAHLUNG CROSS-SECTION AND THE FOOTPOINT DENSITY AND TEMPERATURE. HOWEVER THIS APPROXIMATION HAS BEEN INSUFFICIENT TO EXPLAIN MANY OBSERVATIONS AND MUCH WORK HAS BEEN DONE TO EXTEND THE TTM. FOR EXAMPLE RECENTLY THE EFFECTS OF RETURN CURRENTS (RC) ARE BEING INCLUDED INTO AN EXTENDED TTM. ELECTRONS MOVING IN A LOOP PRODUCE AN ELECTRIC CURRENT THAT MUST BE NEUTRALIZED BY A COUNTER-STREAMING RC. THE RC PRODUCES A POTENTIAL DROP ACTING TO DECELERATE BEAM ELECTRONS. THIS CAN BE DETECTED BY A FLATTENING IN THE X-RAY SPECTRUM AT LOW ENERGIES. SINCE THE RC ARISES IN RESPONSE TO THE BEAM ELECTRONS CHANGES IN THE BEAM DRIVE CHANGES IN THE RC. THIS NON-LINEAR FEEDBACK MUST BE ACCOUNTED FOR TO MOST ACCURATELY DETERMINE THE ACCELERATED ELECTRON SPECTRUM. ALAOUI&HOLMAN (2017) STUDIED 1054 SPECTRA FROM 19 FLARES SHOWING SPECTRAL FLATTENINGS CAUSED BY RCS. THEY NOTED THAT FOR MANY OF THESE FLARES THE ENERGY LOST BY BEAM ELECTRONS IN THE CORONAL PORTIONS OF LOOPS IS DOMINATED BY RC EFFECTS SINCE CORONAL DENSITIES (AND HENCE COLLISIONS) ARE TYPICALLY LOW WHEREAS ENERGY LOST IN THE DENSE FOOTPOINT IS PRIMARILY DUE TO COULOMB COLLISIONS (CC). HENCE IN MANY CASES RC EFFECTS CAN BE SEPARATED FROM THOSE DUE TO CC. WITH THIS ASSUMPTION THEY USED A 1D ANALYTICAL MODEL TO FIT THE X-RAY SPECTRA THEREBY OBTAINING ESTIMATES OF THE ACCELERATED ELECTRON SPECTRA FOR THOSE FLARES. HOWEVER IN THEIR SAMPLE THEY ALSO FOUND MANY CASES WHERE THE CORONAL DENSITY WAS NOT LOW. IN WHICH CASES THE RC AND CC ARE NEITHER SEPARABLE NOR TREATABLE BY 1D ANALYTICAL METHODS. FOR THIS PROJECT WE WILL USE THE STATE-OF-THE-ART CODE RADYN TO MODEL BOTH THE ELECTRON BEAM TRANSPORT AND THE HYDRODYNAMIC RESPONSE OF THE SOLAR ATMOSPHERE TO ELECTRON BEAM HEATING. RADYN HAS RECENTLY BEEN ENHANCED TO INCLUDE A SOLVER OF THE FOKKER-PLANK EQUATION THAT TREATS THE FEEDBACK BETWEEN RC AND CC SELF-CONSISTENTLY. WE PROPOSE TO ANALYZE THE RHESSI OBSERVED X-RAY SPECTRA OF THESE FLARES TO ACCURATELY DERIVE ELECTRON SPECTRA. THIS WORK DIRECTLY ADDRESSES HELIOPHYSICS DECADAL SURVEY GOAL #4: TO "DISCOVER AND CHARACTERIZE FUNDAMENTAL PROCESSES THAT OCCUR BOTH WITHIN THE HELIOSPHERE AND THROUGHOUT THE UNIVERSE." WE ALSO WILL ADDRESS RHESSI'S MISSION GOALS #1 2 AND 4 OF THE 2017 SENIOR REVIEW: TO UNDERSTAND THE "EVOLUTION OF SOLAR ERUPTIVE EVENTS " "ELECTRON ACCELERATION " AND "THE ORIGIN OF THE THERMAL PLASMA" DURING FLARES.