Computer class: Linear Optics in JLAB: Longitudinal Dynamics and BBU

Transcription

1 USPAS course on Recircuated and Energy Recovered Linacs Ivan Bazarov, Corne University Geoff Krafft and Dave Dougas, JLAB Computer cass: Linear Optics in JLAB: Longitudina Dynamics and BBU

2 JLAB IRFEL Spreadsheet mode of JLAB IRFEL incudes: - fu first-order optics - ongitudina phase space visuaization - beam break-up simuations January 6, 008 USPAS 08 R & ER Linacs

3 Downoading the esson Downoad the spreadsheet and bbu code to a singe writeenabed directory from Make sure macros are enabed. Start the spreadsheet (note: it may take a whie to initiaize a formuas). January 6, 008 USPAS 08 R & ER Linacs 3

4 Spreadsheet organization The spreadsheet is organized into three main parts ---> eements matrices ayout and attice contro products twiss ---> bbu bbu_atfie bbu_homs bbu_param ---> ong_phase_space R56 z pz beam breakup simuation ongitudina phase space January 6, 008 USPAS 08 R & ER Linacs 4

5 Organization: ayout and attice ---> eements sheet contains optics contros January 6, 008 USPAS 08 R & ER Linacs 5

6 Spreadsheet: beam break-up ---> bbu contros execution of beam break-up code January 6, 008 USPAS 08 R & ER Linacs 6

7 Spreadsheet: ongitudina phase space ---> ong_phase_space tracks a bunch in the ong. p.s. January 6, 008 USPAS 08 R & ER Linacs 7

8 A brief overview of ongitudina dynamics first- and second-order correation in ongitudina phase space second-order momentum compaction requirements for energy recovery January 6, 008 USPAS 08 R & ER Linacs 8

9 First- and second-order correations = 0 + = 0 +! 0 + α + β = 0 +K σ 4 4 = σ + α σ 0 + βσ ε - = σ σ + 0 βσ Einac α = krf sinϕ E fina k = π / λ = RF RF 3.5 m - Einac β = krf cosϕ E fina for.5 GHz January 6, 008 USPAS 08 R & ER Linacs 9

10 After acceeration after the main inac: α k RF ϕ β k RF assuming arge E fina /E injection and sma energy spread energy spread: ongitudina emittance: σ σ α σ for ϕ > krfσ 3 ε - β σ β σ for ϕ < krf σ January 6, 008 USPAS 08 R & ER Linacs 0

11 = + R56 T566 + = Longitudina transform momentum compaction (times the path ength): R 56 η = ds ρ second-order momentum compaction: T L = ( + x / ρ) + x + y ds 566 η () η η = + + ds ρ ρ α β α = + R 56 α = β T566α ( + R α ) January 6, 008 USPAS 08 R & ER Linacs

12 for maximum compression need T 566 R Compression = α k RF ϕ 56 for maximum compression need T 566 = β 3 3 α k RF ϕ actua (absoute) vaue of T 566 can be smaer comp comp σ σ T comp = 566, σ α σ k σ ϕ no is needed beyond a certain off-crest phase ange σ krf ϕ > ϕt = 566= 0 comp σ RF January 6, 008 USPAS 08 R & ER Linacs

13 Achieving the right vaues of R Q Q quads strength [/m**] trim quads Q Q -0.4 R56 [cm] Adjustabe R 56 R ηx ds 56 ρ = January 6, 008 USPAS 08 R & ER Linacs 3

14 Achieving the right vaues of T 566 sextupoes changing sextupoes strength in the Arc T 566 η () η η = + + ds ρ ρ 3 η ( ) + K ( s) η() = h + kη kη + ( h + kh) η + hη + h η η + h η January 6, 008 USPAS 08 R & ER Linacs 4

15 Bunch ength in the Bates rms bunch ength [mm] Bunch ength in the Arcs:, m σ t = σ,0 + R56 + second_ter For off-crest of severa deg: R phi = -0 phi = 0 phi = -0 phi = 0 3 phi = 0.5 nd term.5 on crest 0.5 nd term position [m] R56 [m], eta x [m] eta x R56 position [m] R 56 = 4.4 cm (trim quads off) R56 eta x January 6, 008 USPAS 08 R & ER Linacs 5

16 Energy recovery 3 = ~ R 56 σ β T ~ 566σ ~ σ dump R σ dump ~ 56 3 βσ T σ dump ~ βσ Genera rue of thumb for successfu energy recovery is having the fu recircuating arc isochronous to first and second order (R 56 = T 566 = 0). In IRFEL, the main difficuty is an additiona energy spread generated at the wigger due to FEL interaction. January 6, 008 USPAS 08 R & ER Linacs 6

17 Controing Bates quads ---> eements sheet, yeow region st Bates nd Bates January 6, 008 USPAS 08 R & ER Linacs 7

18 Off-crest phase, FEL energy spread and T > ong_phase_space sheet Off-crest ange FEL energy spread st Bates nd Bates January 6, 008 USPAS 08 R & ER Linacs 8

19 Exercises (ongitudina gymnastics) Set the off-crest phase ange in the main inac to 0 and turn-off aser interaction. Observe how the ongitudina phase space ooks throughout the acceerator and at the beam dump. Set the off-crest phase ange in the main inac to 0. Achieve the shortest bunch possibe at the wigger ocation using inear optics ony (T 566 shoud be 0). Compare cacuated R 56 with the vaue in the mode. Use T 566 to maximay compress the bunch at the wigger. Compare cacuated T 566 with the vaue in the spreadsheet. How much shorter is the bunch ength when both second- and first-order compaction is used, as opposed to ony the first-order compression? Achieve ess than 50 fs rms bunch duration. NOTE: R 56 from the inac to the wigger consists comes from two parts: Bates turn-around and a chicane January 6, 008 USPAS 08 R & ER Linacs 9

20 Exercises (optiona) Turn-on the aser interaction (actua max. energy spread of 5 %). Observe the ongitudina phase space at the dump. Is the beam being successfuy recovered? Adjust R 56 in the second Bates section to minimize energy spread at the dump. Note the smaest energy spread you were abe to achieve. Use T 566 to minimize energy spread at the dump. Note the vaues of R 56 and T 566 of the whoe recircuating arc that aowed the resut. What is the smaest energy spread you were abe to achieve? Achieve ess than 5 % max energy spread at the dump. January 6, 008 USPAS 08 R & ER Linacs 0

21 Two basic concerns: Higher order modes Mutipass beam breakup (dipoes) Resonant excitation of a higher order mode (monopoes) monopoe (m = 0) y TM 0 -ike y dipoe (m = ) y TM -ike y quadrupoe (m = ) y TM -ike y z x z x z x E B E B E B high energy osses, no kick kick and osses when beam is not centered kick, couping and osses when beam is not centered January 6, 008 USPAS 08 R & ER Linacs

22 BBU threshod for a singe dipoe mode NO NO use code! YES NO YES YES, is independent of January 6, 008 USPAS 08 R & ER Linacs

23 Controing BBU code ---> bbu contros execution of beam break-up code contros ength (time) of code execution output votage and coordinate at a given cavity (must have a HOM!) January 6, 008 USPAS 08 R & ER Linacs 3

24 bbu_homs spreadsheet Controing BBU code: HOMs comments are denoted by! and are ignored; use it to disabe HOMs HOM data that goes into BBU code January 6, 008 USPAS 08 R & ER Linacs 4

25 Exercises (beam-break up) By commenting out modes in bbu_homs sheet, determine the worst mode (the one with highest threshod). How does the threshod due to the singe worst mode compares to the situation when a modes are present? Work with the worst offending mode (for faster computing speed). Sighty change the frequency of the mode and obtain dependence of threshod vs. the mode frequency. Pot the dependency. What is the ratio of max over min threshod that you found in this manner? What is the frequency difference between the two adjacent maxima? Add fake 000 m to the recircuation ength (---> bbu sheet) and repeat the steps from ). What is the ratio of max over min threshod in this case? What is the frequency difference between the two adjacent maxima? Try to expain the resut. January 6, 008 USPAS 08 R & ER Linacs 5