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Superconducting Electron Linacs

Superconducting Electron Linacs. Nick Walker DESY CAS • Zeuthen • 15-16 Sept. 2003 . What’s in Store. Brief history of superconducting RF Choice of frequency (SCRF for pedestrians) RF Cavity Basics (efficiency issues) Wakefields and Beam Dynamics Emittance preservation in electron linacs.

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Superconducting Electron Linacs

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  1. Superconducting Electron Linacs Nick Walker DESY CAS • Zeuthen • 15-16 Sept. 2003 CAS Zeuthen

  2. What’s in Store • Brief history of superconducting RF • Choice of frequency (SCRF for pedestrians) • RF Cavity Basics (efficiency issues) • Wakefields and Beam Dynamics • Emittance preservation in electron linacs • Will generally consider only high-power high-gradient linacs • sc e+e- linear collider • sc X-Ray FEL TESLA technology CAS Zeuthen

  3. MV 16 59 69 92 310 400 75 Status 1992: Before start of TESLA R&D(and 30 years after the start) L Lilje CAS Zeuthen

  4. S.C. RF ‘Livingston Plot’ CAS Zeuthen courtesy Hasan Padamsee, Cornell

  5. TESLA R&D 2003 9 cell EP cavities CAS Zeuthen

  6. TESLA R&D CAS Zeuthen

  7. Ez z The Linear Accelerator (LINAC) standing wave cavity: bunch sees field:Ez =E0sin(wt+f )sin(kz) =E0sin(kz+f )sin(kz) c c • For electrons, life is easy since • We will only consider relativistic electrons (v c)we assume they have accelerated from the source by somebody else! • Thus there is no longitudinal dynamics (e± do not move long. relative to the other electrons) • No space charge effects CAS Zeuthen

  8. SC RF Unlike the DC case (superconducting magnets), the surface resistance of a superconducting RF cavity is not zero: • Two important parameters: • residual resistivity • thermal conductivity CAS Zeuthen

  9. SC RF Unlike the DC case (superconducting magnets), the surface resistance of a superconducting RF cavity is not zero: • Two important parameters: • residual resistivity Rres • thermal conductivity  surface area f-1 losses Rsf 2 when RBCS > Rres f > 3 GHz fTESLA = 1.3 GHz CAS Zeuthen

  10. SC RF Unlike the DC case (superconducting magnets), the surface resistance of a superconducting RF cavity is not zero: Higher the better! • Two important parameters: • residual resistivity • thermal conductivity LiHe heat flow Nb I skin depth RRR = Residual Resistivity Ratio CAS Zeuthen

  11. RF Cavity BasicsFigures of Merit • RF power Pcav • Shunt impedance rs • Quality factor Q0: • R-over-Q rs/Q0 is a constant for a given cavity geometry independent of surface resistance CAS Zeuthen

  12. Frequency Scaling normal superconducting normal superconducting normal superconducting CAS Zeuthen

  13. RF Cavity BasicsFill Time From definition of Q0 Allow ‘ringing’ cavity to decay(stored energy dissipated in walls) Combining gives eq. for Ucav Assuming exponential solution(and that Q0 and w0 are constant) Since CAS Zeuthen

  14. RF Cavity BasicsFill Time Characteristic ‘charging’ time: time required to (dis)charge cavity voltage to 1/e of peak value. Often referred to as the cavity fill time. True fill time for a pulsed linac is defined slightly differently as we will see. CAS Zeuthen

  15. RF Cavity BasicsSome Numbers CAS Zeuthen

  16. RF Cavity BasicsSome Numbers Very high Q0: the great advantage of s.c. RF CAS Zeuthen

  17. RF Cavity BasicsSome Numbers • very small power loss in cavity walls • all supplied power goes into accelerating the beam • very high RF-to-beam transfer efficiency • for AC power, must include cooling power CAS Zeuthen

  18. RF Cavity BasicsSome Numbers • for high-energy higher gradient linacs(X-FEL, LC), cw operation not an option due to load on cryogenics • pulsed operation generally required • numbers now represent peak power • Pcav = Ppk×duty cycle • (Cu linacs generally use very short pulses!) CAS Zeuthen

  19. Cryogenic Power Requirements Basic Thermodynamics: Carnot Efficiency (Tcav = 2.2K) System efficiency typically 0.2-0.3 (latter for large systems) Thus total cooling efficiency is 0.14-0.2% Note: this represents dynamic load, and depends on Q0 and V Static load must also be included (i.e. load at V = 0). CAS Zeuthen

  20. RF Cavity BasicsPower Coupling • calculated ‘fill time’ was1.2 seconds! • this is time needed for field to decay to V/e for a closed cavity (i.e. only power loss to s.c. walls). CAS Zeuthen

  21. RF Cavity BasicsPower Coupling • calculated ‘fill time’ was1.2 seconds! • this is time needed for field to decay to V/e for a closed cavity (i.e. only power loss to s.c. walls). • however, we need a ‘hole’ (coupler) in the cavity to get the power in, and CAS Zeuthen

  22. RF Cavity BasicsPower Coupling • calculated ‘fill time’ was1.2 seconds! • this is time needed for field to decay to V/e for a closed cavity (i.e. only power loss to s.c. walls). • however, we need a ‘hole’ (coupler) in the cavity to get the power in, and • this hole allows the energy in the cavity to leak out! CAS Zeuthen

  23. RF Cavity Basics cavity coupler circulator Generator (Klystron) matched load Z0 = characteristic impedance of transmission line (waveguide) CAS Zeuthen

  24. RF Cavity Basics impedance mismatch Generator (Klystron) Klystron power Pfor sees matched impedance Z0 Reflected power Pref from coupler/cavity is dumped in load Conservation of energy: CAS Zeuthen

  25. Equivalent Circuit Generator (Klystron) coupler cavity CAS Zeuthen

  26. Equivalent Circuit Only consider on resonance: CAS Zeuthen

  27. Equivalent Circuit Only consider on resonance: We can transform the matched load impedance Z0 into the cavity circuit. CAS Zeuthen

  28. Equivalent Circuit define external Q: coupling constant: CAS Zeuthen

  29. Reflected and TransmittedRF Power reflection coefficient(seen from generator): from energy conservation: CAS Zeuthen

  30. Transient Behaviour steady state cavity voltage: from before: think in terms of (travelling) microwaves: remember: steady-state result! CAS Zeuthen

  31. Reflected Transient Power time-dependent reflection coefficient CAS Zeuthen

  32. Reflected Transient Power after RF turned off CAS Zeuthen

  33. RF On note: No beam! CAS Zeuthen

  34. Reflected Power in Pulsed Operation Example of square RF pulse with critically coupled under coupled over coupled CAS Zeuthen

  35. Accelerating Electrons • Assume bunches are very short • model ‘current’ as a series of d functions: • Fourier component at w0 is 2I0 • assume ‘on-crest’ acceleration (i.e. Ibis in-phase with Vcav) t CAS Zeuthen

  36. Accelerating Electrons consider first steady state what’s Ig? CAS Zeuthen

  37. Accelerating Electrons steady state! Consider power in cavity load R with Ib=0: From equivalent circuit model (with Ib=0): NB: Ig is actually twice the true generator current CAS Zeuthen

  38. Accelerating Electrons substituting for Ig: introducing beam loading parameter CAS Zeuthen

  39. Accelerating Electrons Now let’s calculate the RFbeam efficiency power fed to beam: hence: reflected power: CAS Zeuthen

  40. Accelerating Electrons Note that if beam is off (K=0) previous result For zero-beam loading case, we needed b = 1 for maximum power transfer (i.e. Pref = 0) Now we require Hence for a fixed coupler (b), zero reflection only achieved at one specific beam current. CAS Zeuthen

  41. A Useful Expression for b efficiency: voltage: can show optimum where CAS Zeuthen

  42. Example: TESLA beam current: cavity parameters (at T = 2K): For optimal efficiency, Pref = 0: From previous results: cw! CAS Zeuthen

  43. Unloaded Voltage matched condition: hence: for CAS Zeuthen

  44. Pulsed Operation From previous discussions: Allow cavity to charge for tfillsuch that For TESLA example: CAS Zeuthen

  45. reflected power: Pulse Operation generatorvoltage RF on • After tfill, beam is introduced • exponentials cancel and beam sees constant accelerating voltage Vacc= 25 MV • Power is reflected before and after pulse cavity voltage beam on beaminduced voltage t/ms CAS Zeuthen

  46. Pulsed Efficiency total efficiency must include tfill: for TESLA CAS Zeuthen

  47. Quick Summary cw efficiency for s.c. cavity: efficiency for pulsed linac: fill time: • Increase efficiency (reduce fill time): • go to high I0 for given Vacc • longer bunch trains (tbeam) • some other constraints: • cyrogenic load • modulator/klystron CAS Zeuthen

  48. Lorentz-Force Detuning In high gradient structures, E and B fields exert stress on the cavity, causing it to deform. detuning of cavity • As a result: • cavity off resonance by relative amount D = dw/w0 • equivalent circuit is now complex • voltage phase shift wrt generator (and beam) by • power is reflected require = few Hz for TESLA For TESLA 9 cell at 25 MV, Df ~ 900 Hz !! (loaded BW ~500Hz) [note: causes transient behaviour during RF pulse] CAS Zeuthen

  49. Lorentz Force Detuning cont. recent tests on TESLA high-gradient cavity CAS Zeuthen

  50. Lorentz Force Detuning cont. • Three fixes: • mechanically stiffen cavity • feed-forwarded (increase RF power during pulse) • fast piezo tuners + feedback CAS Zeuthen

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