FLC OF ACR LTT TYPE ACFT INVOLUNTARILY DSNDED BELOW ASSIGNED APCH VECTORING ALT DUE TO EXTREME DOWNDRAFT TURB IN TSTMS.

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FLT BEGAN WITH CAPT AS PF. IMMEDIATELY AFTER DEP FROM RWY 20R BNA AT NIGHT; WITH TSTMS IN ALL QUADRANTS; VIVID CLOUD TO CLOUD LIGHTENING; LOST OUR ONBOARD WX RADAR. WITH VIVID LIGHTENING; HVY RAIN AND MODERATE TURB; PRESSURIZATION BEGAN TO SPIKE TO 3000 FPM DSCNT; THEN 3000 FPM CLB NEVER ACTUALLY STABILIZING. WE WERE INSTRUCTED TO CLB TO 7000 FT. PRIOR TO LEVEL OFF DECISION TO WAS MADE TO RETURN TO NASHVILLE. CAPT TRANSFERRED FLT CTLS TO ME. WE WERE ASSIGNED TO DSND; MAINTAIN 2000 AND TURN FOR HDG TO INTERCEPT APCH COURSE. WE INFORMED APCH CTLR OF OUR SITUATION AND ASKED FOR HELP STEERING CLR OF WX. APCH CTLR SEEMED TO QUESTION OUR DECISION TO RETURN. WE REPEATED REQUEST FOR VECTORS CLR OF WX; WHEREBY CTLR SAID WOULD DO BEST HE COULD. ASSIGNED SPD WAS 170 KTS. UPON FINAL VECTOR ONTO LOC 20R BNA AND ARRIVING AT 2000 MSL ENCOUNTERED EXTREME CONTINUOUS DOWNDRAFTS (1000-2000 FPM) AND MODERATE TURB. APCH AND NAV MODE ARMED AND NAV WAS CAPTURED. WE MOMENTARILY DROPPED 500 FT BELOW ASSIGNED ALT. I APPLIED MAX PWR AND AS I WAS CORRECTING CTLR SAID 'MAINTAIN 2000 FT.' WE WERE BELOW 2000 FT ASSIGNED ALT. NO MORE THAN 5 SECONDS. REJOINED GS GOT APCH CAPTURE ANNUNCIATION AND FLEW REMAINDER OF APCH WITH NO INCIDENT.