CPR PIC MAKES A MISSED APCH GAR AFTER TCASII RA ON UNKNOWN VFR NORAC TFC INDICATED BELOW HIS ACFT WHILE ON AN ILS APCH. POTENTIAL CONFLICT.

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WE WERE CLRED FOR AN ILS AND LNDG ON RWY 4 AT MIDWAY (CHICAGO). WHEN DSNDING THROUGH APPROX 2000 FT ON THE GS OUR TCASII GAVE A TA SHOWING AN ACFT 700 FT BELOW US. WE LOOKED BUT COULDN'T SEE IT. THE TWR WAS TALKING AND WE COULDN'T BREAK IN TO ASK. THE TWR HAD NOT ISSUED AN ADVISORY ON TFC. WHEN DSNDING THROUGH APPROX 1600 FT; WE RECEIVED AN RA TO CLB. WE STILL COULD NOT SEE THE ACFT. I IMMEDIATELY BEGAN A CLB AND MY COPLT CALLED TWR WITH A MISSED APCH ADVISORY. THE TWR THEN STATED THE TFC WAS A HELI MANEUVERING BELOW US TO CONTINUE THE APCH. WE WERE TOO HIGH TO SAFELY LAND. I LEVELED AT 2200 FT WHEN WE RECEIVED AN ADVISORY 'CLR OF TFC' AND THEN FOLLOWED TWR INSTRUCTIONS FOR MISSED APCH BY FIRST DSNDING TO 2000 FT; R TURN TO 090 DEGS; THEN CLB TO 2600 FT AND TURNED OVER TO APCH CTL FOR SECOND APCH AND LNDG. ALL THE WAY AROUND ON THE SECOND APCH AFTER RECONTACTING THE TWR; WE RECEIVED TFC ADVISORIES ON ACFT THAT WERE OBVIOUSLY NOT IN CONFLICT WITH US. THEY WERE OBVIOUSLY UPSET WITH OUR MISSED APCH AND ENDED OUR CONVERSATION WITH 'YOU ARE LUCKY THERE WERE NO ACFT ABOVE YOU AT 2000 FT.' I CONTACTED MDW TWR VIA PHONE AFTER THE FLT AND TALKED TO THE CTLR; WHO DECLINED TO GIVE ME HIS NAME. HE SAID HE FELT THE TCASII SYS 'DEMEANED HIS POS' AS A CTLR. I FEAR I WAS UNABLE TO CONVINCE HIM OUR INTENTION WAS TO MISS UNRPTED TFC AND NOT TO OPENLY DEFY HIM. SUPPLEMENTAL INFO FROM ACN 240478: THE TWR OPERATOR WAS UPSET WITH US FOR TAKING AN EVASIVE ACTION AND TOLD US IT WAS HELI TFC; THAT WE HAD BEEN TOLD ABOUT; THAT WE HAD MANEUVERED TO AVOID. FIRST THE TFC WAS NEVER POINTED OUT TO US; AND SECOND; IN THE TERMINAL AREA WITH NO VISUAL CONTACT WITH THE TFC I AM GOING TO HEED THE TCASII. IF I CAN'T VISUALLY SIGHT THE TFC AND THE TCASII GIVES A COMMAND I WILL FOLLOW IT. IF WE CAN'T TRUST THE TCASII LET'S GET THEM OUT OF ALL ACFT.