Emittance Partitioning in Photoinjectors

Transcription

1 Emittnce Prtitioning in Photoinjectors Bruce Crlsten, Robert Rne, Kip Bishofberger, Steven Russell, nd Nikoli Ympolsk Los Almos Ntionl Lbortor Lwrence Berkele Ntionl Lbortor

2 Motivtion We need ver smll trnsverse emittnces for future XFEL driven b energ diffusion: E rms E eb 4πε m Induced rms energ spred (-m wiggler) is.5% t GeV (probbl ok) nd.6% t 35 GeV (probbl not ok) We wnt 5-keV photons overlp of electron bem nd photon bem puts n upper bound of bout.5 µm for the trnsverse emittnces We wnt 5 pc to 5 pc of bunch chrge (from the needed number of photons), violtes the ccepted scling: 3 5 c 6 L / q ε µ m nc / (which would indicte bout pc) (for emple Brun from Mond)

3 Motivtion continued Phse spce from photoinjector is ver cold overll volume is more thn sufficient for our needs: tpicl photoinjector t.5 nc: ε.7 mm mrd ε.7 mm mrd ε.4 mm mrd our needs: ε.5 mm mrd ε.5 mm mrd ε mm mrd volume.7 (µm) 3 volume.3 (µm) 3 this comes from.% energ spred nd 8 fs t GeV Cn we control the phse-spce prtitioning?

4 Motivtion continued We cn get huge gins in pek photon flu if we cn prtition the phse spce: Blck line: q ε µ m nc / Red line: Optiml prtitioning Dshed line: CSR vlidit questions

5 Review of FBT Correltions plus Three Skew Qudrupoles: Shove some of the horiontl emittnce into the verticl emittnce b introducing correltion t the cthode nd removing it with the downstrem optics ( ε ) instrinsic ε ε L L where ct eb R L ct 8 βcm

6 Limittions of Current Photoinjector nd FBT/EEX Technologies Photoinjector SOA t.5 nc (s ~mm cthode rdius nd ps drive lser) ε.7 mm mrd ε.7 mm mrd ε.4 mm mrd Emittnce genertion pln (KJK AAC8) Strt with fs lser, bigger cthode: ε. mm mrd ε.4 mm mrd ε.4 mm mrd ε. mm mrd ε 35 mm mrd ε.4 mm mrd ε.4 mm mrd ε.4 mm mrd ε 35 mm mrd Stndrd FBT stge Stndrd EEX stge The problem is tht photoinjectors don t scle this w

7 FBTs nd EEXs Arise From Conservtion of Certin Quntitites: Eigen-Emittnces Let s denote the bem second moment mtri The eigenvlues of Js re clled eigen-emittnces J Eigen-emittnces re invrint under ll liner smplectic trnsformtions, which include ll ensemble electron bem evolution in n ccelertor however, the eigen-emittnces cn be echnged mong the -p, -p, -p phse plnes We cn control the formtion of the eigen-emittnces b controlling correltions when the bem is generted (like in FBT) We recover the eigen-emittnces s the bem rms emittnces when ll correltions re removed

8 More About Eigen-Emittnces Drgt s code MrLie hs procedure, since the 99 s, to clculte eigen-emittnces nd the mtri needed to recover the eigen-emittnces (so we re not blind in this process) Invrince of eigen-emittnces lso known to Cournt (966). Origin of this goes bck to J. Willimson (936). Strightforwrd to generte the right eigen-emittnces, issue with implementing this concept is to ensure tht nonlinerities (especill nonliner correltions) do not interfere with our bilit to unwind the liner correltions Not cler how nonliner emittnce growths ffect the prtitioning The FBT (nd FNAL demonstrtion) is n eistence proof tht ou cn in one regime Emittnce compenstion is n eistence proof tht ou cn in nother regime (well, sort of; mostl nonliner correltion)

9 Some Definitions Definitions: ( c t) ( c t) ( c t) ( c t) ( c t) ( c t) ( c t) ( c t) ( c t) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ( β ) ε n, β ε n, β ε n, ( β ) β ( c t) t ( c ) ( β ) ( β )

10 Slides to Build Phsicl Intuition Smplectic trnsformtions look like: And led to these tpes of correltions: R skew T skew skew R R Note the signs B dl mc e β JM M J T Smplectic trnsformtions obes: I I J

11 Nonsmplectic correltions look like: A trnsversel deflecting rf cvit looks like skew qud in -: field il bem B cth R R cth mc e β R rf c m b ead β π With trnsversel deflecting rf cvities nd fnc drifts, we cn build - FBTs Slides to Build Phsicl Intuition

12 More generll for non-smplectic bem correltion we cn diddle with the correltions to leve onl one (b using smplectic trnsformtions): which does reduce nicel to KJK s FBT cse. But it lso tells us how to design rbitrr FBTs with initill non round bems (like for - FBTs)., α α α reduced, α α α reduced [ ] ( ) ±, 4 α α ε [ ] ( ) ±, 4 α α ε Slides to Build Phsicl Intuition

13 We Know of 3 Correltions tht Work. If the initil bem hs 5: spect rtio (meets the emittnce requirement in one trnsverse direction, there is the trivil solution of n - correltion where we build n - FBT. Also, with the sme 5: spect rtio, simple - correltion works 3. With n spect rtio ner (ellipticl bem), n - correltion with il mgnetic field works Bseline is this lst correltion - net step is to model this design to understnd if we cn preserve the correltions through ccelertion to ~ GeV

14 How We Find the Eigen-Emittnces JS λj Scle for smll norm M e JS Tlor epnsion, eigenvlues will be on unit circle N A MA Look in Ale Drgt s book to construct A (from eigenvlues) where N is in norml form clled Willimson form E AA T Sme A is used to find eigen-emittnces (onl strictl if the re not degenerte, but we hven t seen n filures of this lgorithm et)