A new phys i cal scheme for femto second X-ray la sers, where the up per lasing is pumped by X-ray pho tons and the lower lasing level is de pop u lated via a Coster-Kronig radiationless tran si tion, is an a lyzed for Ca. The tran si tion wave length is 4.1 nm, which is in side the wa ter win dow. The peak spec tral bright ness of the X-ray la ser out put at 4.1 nm is pre dicted to be as large as 5 10 25 pho tons/sec./(mm 2 mrad 2 0.1% band width), which is 4 to 5 or ders of mag ni tude brighter than a typ i cal undulator ra di a tion in the sim i lar spec tral re gion. In ad dition to the high flux, the ex pected du ra tion of X-ray lasing of ~3 fs. will be use ful for the study of fast dy namics in phys i cal and bi o log i cal sci ences.
IN TRO DUC TIONNew re gimes of la ser mat ter in ter ac tion have opened due to re cent ad vances in 10-fs-range, high-peak-power la ser de vel op ment.1-4 These la sers are ideal for the gen er a tion of femto second high-order har monic ra di a tion in the soft X-ray range, 5-9 and for pump ing X-ray la sers based on innershell atomic tran si tions. [10][11][12][13][14][15][16] While the past 15 years have seen signif i cant prog ress in the X-ray la ser re search and de vel opment, most X-ray la sers op er ate at low-repetition rates with pulses in pi co sec onds or lon ger. High-repetition-rate, femtosecond X-ray la sers would be use ful for dy nam i cal stud ies of ultrafast phe nom ena in na ture.
17Duguay and Rentzepis 18 first pro posed Innershell X-ray la ser schemes in 1967. In their scheme the lower level of the lasing tran si tion was the ground level of the first ion and could not de cay. The idea of us ing an atomic sys tem in which the lower level de cays was sug gested by Stankevich,19 elab o rated by Arecchi 20 and Elton, 21 and cal cu lated in de tail by Axelrod for K-shell tran si tions. 22 The tech ni cal bar rier for the suc cess ful re al iza tion of these schemes has been the devel op ment of a suf fi ciently fast and en er getic X-ray pump source whose time-scale is on the or der of the life time of the keV lasing tran si tions, i.e., in the 10-fs-range. 10,11,15,22 Such pump ing sources are now be com ing avail able due to the advent of femto second ul tra-high peak-power la sers. Such systems with peak pow ers of 10's to 100's of terawatt (TW) have been dem on strated 1 -4 and plans ex ist for ex tend ing peak powers to 1 petawatt at a 20 fs. pulse du ra tion. Even with these new la sers, in trin sic prob lems with the K-shell tran si tion X-ray la ser scheme still ex ist. In par tic u lar, elec trons produced dur ing photo-ionization and sub se quent Au ger de cays are en er getic enough to collisionally ion ize neu tral at oms, pro duc ing the lower level of the lasing tran si tion and de stroying the in ver sion. If it were pos si ble to cre ate an in ner-shell pop u la tion in ver sion via atomic pro cesses in volv ing only elec trons, the in ver sion in any photo-ionization pumped X-ray la ser schemes based on the same tran si tions would be (1)...