▁the ▁angular ▁frequency ▁domain . ▁ ▁Ens emble ▁of ▁ ▁of ▁the ▁total ▁ ▁electrons ▁in ▁the ▁ ▁beam ▁is ▁a ▁st ochastic ▁process ▁taking ▁into ▁account ▁statistical ▁distributions ▁in ▁phase ▁space ▁( special ▁distribution , ▁energy , ▁and ▁angular ▁spread ings ). ▁ ▁Solution ▁of ▁the ▁mode ▁amplitude ▁ ▁together ▁with ▁equation ▁of ▁motion ▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁is ▁the ▁mass ▁of ▁the ▁particle . ▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁is ▁the ▁super - rad i ant ▁emission . ▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁is ▁the ▁elect romagnet ic ▁field ▁in ▁terms ▁of ▁eigen mod es ▁of ▁the ▁medium ▁which ▁the ▁radiation ▁is ▁excited . ▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁is ▁the ▁instant aneous ▁velocity . ▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁is ▁the ▁magnetic ▁field ▁in ▁terms ▁of ▁eigen mod es ▁of ▁the ▁medium ▁which ▁the ▁radiation ▁is ▁excited . ▁ ▁enables ▁one ▁to ▁calculate ▁sp ont aneous ▁and ▁super - rad i ant ▁em issions , ▁including ▁stim ulated ▁interaction ▁resulting ▁in ▁ampl ification ▁of ▁the ▁excited ▁radiation ▁as ▁occurr ing ▁in ▁self - am pl ified ▁sp ont aneous ▁emission ▁( S ASE ). ▁ ▁Inst ru ments ▁Inst ru ments ▁that ▁uses ▁the ▁super ▁radi ant ▁emission . ▁ ▁Free ▁Electron ▁Las er ▁( F EL ) ▁ ▁Far ▁Inf ra red ▁( FI R ) ▁Las er ▁▁▁ ▁Und ulator ▁allows ▁to ▁obtain ▁the ▁super ▁radi ant ▁emission . ▁ ▁Application ▁Super rad i ant ▁emission ▁using ▁instruments ▁such ▁as ▁F EL ▁are ▁used ▁in ▁materials ▁science , ▁chemical ▁technology ▁and ▁surface ▁analysis . ▁Using ▁the ▁super rad i ant ▁emission ▁from ▁the ▁instruments , ▁prote ins