C172 AND C560 HAVE NMAC IN PATTERN AT UGN.

Narrative

I WAS WITH A STUDENT PLT FOR A TRAINING FLT DEPARTING WAUKEGAN REGIONAL (UGN). THE WX WAS PERFECT FOR A DAY VFR FLT. THE ILS FOR RWY 23 WAS UNDERGOING MAINT AND WAS OTS. WE WERE CLRED FOR TKOF ON RWY 5 WITH A L TURN TO THE W. AS MY STUDENT ROTATED; I HEARD THE TWR CLR A CITATION FOR A L DOWNWIND FOR RWY 5 (THAT WAS THE LAST RADIO CALL I RECALL HEARING). I CONTINUED TO MONITOR MY STUDENT AS HE CLBED OUT AND BEGAN A L TURN TO THE W (THE TURN BEGAN AT 1500 FT MSL). WE LEVELED OFF AT 2500 FT MSL WITH A HDG OF W. SHORTLY AFTER WE LEVELED OFF; MY STUDENT BEGAN TO SEARCH FOR HIS FIRST CHKPOINT AND BEGAN HIS AFTER TKOF CHKLIST. MOST OF THE TIME MY EYES WERE OUTSIDE; SCANNING AHEAD OF OUR ACFT; WHEN THE CITATION JET FLEW ACROSS OUR NOSE; WITHIN 100 FT; FROM R TO L BANKING SHARPLY. I IMMEDIATELY PITCHED THE ACFT DOWN BUT THE CITATION HAD ALREADY PASSED BY THE TIME I WAS ABLE TO REACT. SHORTLY AFTER; THE PLT FROM THE CITATION CALLED THE TWR TO INFORM THEM THAT THEY HAD TO TAKE EVASIVE ACTION FROM AN ACFT. THE TWR RESPONDED BY SAYING THAT THEY JUST SAW IT ON THEIR RADAR AFTER IT HAPPENED. THEY SAID THEY HAD THEIR COLLISION ALARM SILENCED DUE TO THE WORK THAT WAS BEING DONE WITH THE ILS. I RESPONDED BACK BY CONFIRMING THE INCIDENT AND ASKING IF OUR XPONDER WAS WORKING CORRECTLY. THE TWR REPLIED THAT HE DID HAVE US ON HIS RADAR SCREEN. AFTER LNDG I CALLED THE TWR AS REQUESTED. THE CTLR APOLOGIZED AND SAID THAT THERE WERE A LOT OF DISTRS IN THE TWR AND DID NOT NOTICE THAT THE CITATION AND US WERE ON A COLLISION COURSE. THE 2 RADAR RETURNS WERE TOGETHER BY THE TIME ANYBODY NOTICED A PROB. I DID NOT PAY ENOUGH ATTN TO THE CLRNC FOR THE CITATION TO FLY A L DOWNWIND. ALTHOUGH WE WERE CLRED TO TURN IN THAT DIRECTION; WE WERE HEADING DIRECTLY INTO THE PATH OF THE CITATION. I RELIED ON THE TWR TO PROVIDE SEPARATION AND DID NOT THINK THE CITATION WOULD BE A FACTOR. I ALSO WAS ALSO ONLY SCANNING FOR TFC DIRECTLY AHEAD OF OUR FLT PATH WHILE DIVIDING MY ATTN ON MY STUDENT FLYING THE PLANE. I SHOULD HAVE BEEN LOOKING IN ALL DIRECTIONS. I BELIEVE THAT OTHER CONTRIBUTING FACTORS INCLUDE MY RELIANCE ON THE TWR TO PROVIDE SEPARATION AND CALL OUT TFC THAT MAY BECOME AN ISSUE AND DISTRS FROM MY STUDENT HAVING DIFFICULTY WITH FLYING THE PLANE AND NAVING.