Longitudinal Issues for a Full-Scale ERL. Topics for discussion

Transcription

1 Longitudina Issues for a Fu-Scae ERL Topics for discussion first- and second-order correation in ongitudina phase space requirements for momentum compaction of the ring attice options second-order momentum compaction unduator performance ERL mtg (Nov 5), then (Dec 4, 00) with sight modifications

2 dump / energy recovery requirement on energy spread dump E E dump ring 0 3 require 6σ momentum cearing σ dump dump or.7 MeV Sources for energy spread in the ring (rms) spontaneous radiation CSR wakes?? Linac and optics ony are treated in what is to foow

3 st- and nd-order correation in ongitudina phase space ! 0 + α + β 0 +K energy spread: ongitudina emittance: σ 4 4 σ + α σ 0 + βσ ε - σ σ + 0 βσ st- and nd-order correation after RF Einac α krf sinϕ, E fina k π / λ RF RF 7 m - Einac β krf cosϕ E fina 3

4 after acceeration after the main inac: α k RF ϕ β k RF energy spread: ongitudina emittance: σ σ ασ for ϕ > krfσ 3 ε - β σ β σ for ϕ < k σ RF 4

5 ongitudina transform + R T6 + α β α + R α β T6α ( + R α ) 3 3 L ( + x / ρ) + x + y ds momentum compaction (times the path ength): R η ds ρ second-order momentum compaction: T 6 η () η η + + ds ρ ρ 5

6 first-order business for maximum compression need e.g. R cm for ϕ 0 or R 4 cm for ϕ 5 R α k RF ϕ accruing R N d η θ d 3 ) DBA: R / bend 6 ρθ, e.g. ρ 50 m, θ d d 4 R / bend 3 mm ) TBA, QBA shoud be adequate L / 3) FODO: / bend FODO θd R for a matched ce sin µ e.g. η ~ m, θd FODO / 5 R / bend ~ 0 cm 6

7 constraints for momentum compaction of the ring α α < dump * denotes vaues after the oop toerabe deviation from the idea isochronous condition: R < dump α σ or R R ϕ 0 ϕ 5 < dump α haf-ring vaue somewhat arbitrariy assuming 3σ (e.g. can be 6σ) e.g. for attice shoud be within R R < 4.6 cm R <.0 cm need arcs with R and R uness we recover (π ϕ) off-phase (need detuning of 8*ϕ [deg] Hz ~ khz) 7

8 e.g. these tricks won t work for our parameters ) increasing the bunch ength on the return pass through the inac over that of injection to mitigate HOM dissipation ) fipping ongitudina phase space coud work ony for (π ϕ) phase shift recovery 8

9 attice options ) DBA won t work (woud work if no compression desired) ) TBA, QBA, etc. is fine 5 0 R /ce cm b e ta x b e ta y e ta x TBA ce exampe from ERL Study beta function (m) dispersion function (m) R adjustabe /ce ( ) cm p o s itio n (m ) R /ce 0 cm b e ta x b e ta y e ta x beta function (m) dispersion function (m) p o s itio n (m )

10 attice options (contd.) 3) FODO shoud work at the expense of arger dispersion, beta (if R < 0) and need to have matching sections to create zero-dispersion sections for unduators increase decrease exampe: RHIC 3 FODO ces perturbed to obtain negative momentum compaction [D. Trbojevic and E. Courant] R 0.7 mm 4) introduce negative bends 0

11 second-order business for maximum compression need T 6 β 3 3 α k RF ϕ actua (absoute) vaue of T 6 can be smaer by T comp 6, σ σ σ comp comp α σ krfσ ϕ no T 6 is needed beyond a certain off-crest phase given by σ krf comp ϕ > ϕt 6 0 comp e.g. σ σ, σ 00 fs ϕ >5

12 dependence on bunch ength in the inac T E- 3.0E- 8 7 T 6 vs.ϕ - RF phase offset [deg] σ 3 σ.5e-.0e-.5e-.0e- 5.0E-3 reative energy spread T6 [m] σ 0 0.0E bunch ength [mm] RF phase offset [deg]

13 constraints for second-order momentum compaction β β < dump toerabe deviation from the idea T 6 0 (for π offset recovery): T 6 < dump dump α krfϕ comp Summary for σ and 00 fs, ϕ 0 ϕ 5 R ± 4. ± 0.7 [cm] σ T 6 [m] 3.4 ±..0 ±.0 R 3σ [cm] < 4.6 <.0 T 6 [m] < 3.6 <. 3

14 T 6 achieving the right vaue of T 6 η () η η + + ds ρ ρ 3 η ( ) + K ( s) η() h + kη kη + ( h + kh) η + hη + h η η + h [from Georg s TESLA TN] η ) T 6 /R ~ 0 seems feasibe, higher vaues are difficut ) proper soution with toerabe chromatic aberrations coud not be found for energy spread of 0% (coud be o.k. for %) 4

15 momentum compaction of the ring for on-crest running 3 β R T 6 R < dump 4 dump dump < T 3 6 < 3 5 β β for our parameters this transates to successfu energy recovery when momentum compaction of the ring is R < m and T 6 < 750 m (for 6σ, R < 3 cm and T 6 < 4 m). 5

16 matching unduators to ERL parameters scaing with number of periods N& ph( dω) sma detector: Np dω dω / ω N& ph( dωθ ) brightness: N ( rθ ) dω / ω scaing rues above hod true ony when spectra bandwidth is dominated by unduator natura broadening ~ / N b.w. rms 0.4 ( γ + σ θ ) + (σ beam Np ) p p If N p N p, max 0. σ then brightness stays approximatey constant 6

17 energy spread effect on unduator performance for ERL parameters 0. 0 N p, max ~ (performance of the predicted) engthening unduator by 50 % beyond this point improves brightness by 5 %, i.e. coherent properties of radiation do not improve much, ony fux does comp comp when bunch is compressed, N ~ 000 /( σ / σ ) N N > comp p N p, max < comp p N p, max p,max comp average brightness is decreased by σ / σ peak brightness stays constant average brightness stays constant peak brightness is increased by σ / comp σ 7

18 preiminary concusions ERL with current parameters requires eaborate optics with controed first- and second-order momentum compaction we woud need arcs with something ike R ±0 cm, T 6 / R /ϕ ~ 5 for an off-crest phase of 0 high brightness favors uncompressed bunches not ony because of smaer transverse emittance, but because of smaer energy spread as we (true for a but very short unduators) on-crest operation without compression is rather forgiving of optics, T 6 in particuar 8