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Space Charge for the ERLP Injection Line

Space Charge for the ERLP Injection Line. Bruno Muratori ASTeC Daresbury Laboratory. Energy Recovery Linac Prototype. Emittance Growth in Injector Line due to Space Charge. ASTRA - used for Gun to Booster (C Gerth & F Hannon) How to treat dipoles in Injector line ?

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Space Charge for the ERLP Injection Line

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  1. Space Charge for the ERLP Injection Line Bruno Muratori ASTeC Daresbury Laboratory

  2. Energy Recovery Linac Prototype

  3. Emittance Growth in Injector Line due to Space Charge • ASTRA - used for Gun to Booster (C Gerth & F Hannon) • How to treat dipoles in Injector line ? • Analytical approach (N Vinokurov) • GPT (General Particle Tracer) • TRACE-3D (Linear Space Charge only)

  4. Elliptical beam with charge density Electric field Transverse motion (round beam) paraxial approximation, laminar flow ASTRA & Drifts - Analytical Approach

  5. ASTRA & Drifts - Analytical Approach • On boundary, , • With external focusing • Envelope for KV distribution (only KV ? – FIND OUT !) • Therefore laminar flow given by

  6. ASTRA & Drifts - Analytical Approach • Horizontal focusing given by (equivalent for vertical) • Sigma matrix transformation • New emittance • Gaussian bunch

  7. Results & Comparisons for ASTRA & Drifts

  8. Results & Comparisons for ASTRA & Drifts

  9. Results & Comparisons for ASTRA & Drifts

  10. Results & Comparisons for ASTRA & Drifts

  11. Results & Comparisons for ASTRA & Drifts • Vinokurov’s argument goes here (when I can find it)

  12. Results & Comparisons for ASTRA & Drifts

  13. CHECK THAT ENVELOPE EQUATIONS (AS QUOTED IN SPACE CHARGE PAPER) ARE *ONLY* TRUE FOR STANDARD KV DISTRIBUTION – don’t think so, but … • CHECK THAT THE STATEMENT MADE BY VINOKUROV IN E-MAIL IS UNDERSTOOD (RE: THE REALM OF VALIDITY OF FORMULA) – ESPECIALLY GIVEN WE HAVE EXAMPLES ABOVE AND BELOW THIS LIMIT …

  14. ASTRA/GPT & Injector line (TL2)

  15. ASTRA/GPT & Injector line (TL2) • Try to ignore dispersion effects • Replace dipoles with quadrupoles • Make sure resulting Twiss parameters almost identical • Look at emittance growth using both ASTRA/GPT for Gaussian parameters • Validity of analytical formula with quadrupoles ?

  16. ASTRA/GPT & Quadrupoles for TL2

  17. ASTRA/GPT & Quadrupoles for TL2 – Short model

  18. ASTRA/GPT & Quadrupoles for TL2 – Short model • ASTRA distribution from gun and booster (CG & FH) • Emittance outside transverse planes

  19. ASTRA/GPT & Quadrupoles for TL2 – Long model

  20. GPT • Includes bends • All results so far agree • Different algorithms also agree • Emittance increase appears to be less than analytical estimate • Dispersion may be left out for a rough estimate

  21. TRACE-3D • Include z component • Update continuously (no averaging) • Take into account longitudinal dispersion • Match R16 (dispersion) to zero • Match R26(angular dispersion) to zero • Match R15 (bunch spatial width) to zero • Match R25 (bunch angular spread) to zero • First two only done

  22. Conclusions • Good agreement between ASTRA and GPT without dipoles • Good agreement between ASTRA/GPT and analytical result for drifts • Can analytical estimate be used as an upper bound ? • Try to take into account space charge by rematching at several stages in injector line. However, this cannot take into account transverse & longitudinal coupling • Start to end simulations only real answer to see if bunch is acceptable for lasing at FEL

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