Accelerator Physics Issues of ERL Prototype Ivan Bazarov, Geoffrey Krafft Cornell University TJNAF ERL site visit (Mar 7-8, )
Part I (Bazarov). Optics. Space Charge Emittance Compensation in the Injector 3. Emittance Preservation 4. Longitudinal Dynamics Talk Outline Part II (Krafft). Multipass Beam Break-Up. Single Bunch Instability 3. Longitudinal Instability 4. Ions
Front-End Beam Dynamics Simulation Astra, Parmela TraFiC4, elegant elegant Space Charge CSR Optics, RF 3
Emittance Growth in the Injector cath GaAs electron bunch th =. r E ε µm mc 4
Space Charge Emittance Compensation E -φ E -φ DC Gun Buncher Solenoids Injector Cavities Invariant Envelope Flow: σ r = γ I 3I peak Alfen γ 5
ERL Injector Parameters Beam Energy Range 5 5 a MeV Max Average Beam Current ma Max Bunch Rep. Rate @ 77 pc.3 GHz Transverse Emittance* (norm.).5 b µm Bunch Length*. ps Energy Spread*. % * r.m.s. values are used throughout a at reduced average current b corresponds to 77 pc/bunch 6
Simulations Results ( E Injector RF = 5 MeV) 3 emittance [mm-mrad].5.5.5-4 - 4 - - -3 x [mm] 3 4 5 6 7 position [m] px/pz [mrad] bunch length [mm] 4 3.5 3.5.5.5 * r.m.s. value emittance* x,y. µm bunch length*.63 mm energy spread*. % 3 4 5 6 7 position [m] p/p [%].8.6.4. -.5 -.5.5.5 -. -.4 -.6 -.8 z [mm] 7
Laser Pulse Profiles Used in Simulations Transverse: Truncated Gaussian (+/- σ r ) σ r =.8 mm Temporal: Gaussian FWHM = 8 ps Pulse-To-Pulse Laser Tolerances Arrival Time Jitter. ps Intensity Jitter 3.5 % 8
Optics Requirements Low Chromatic and Geometric Aberrations Adjustable Momentum Compaction (R 56 ) Second-Order Momentum Compaction (T 566 ) Betatron Phase Advance Flexibility to study BBU and CSR Emittance Compensation 9
ERL I Optics optical functions [m] 3 5 5 5-5 beta y beta x beta y beta x *eta x *eta x 3 4 5 6 7 position [m]
JLAB Demo IR-FEL Arcs quads strength [/m**] Adjustable R 56 Q.8 Q.6.4. -3 - - 3 Q Q -. -.4 R56 [cm] trim quads Q R ηx ds 56 ρ = Path-length adjuster Q
Sextupole Linearizer b) E RF waveform CSR wakes higher order optics effects longitudinal phase space curvature B A B t Curvature can be fixed with Sextupoles sextupoles changing sextupoles strength in the Arc
Coherent Synchrotron Radiation CSR enhanced spectrum ρ l ρ λsr 3 λ γ CSR l 4 γ PSR N PCSR N 3 43 ρ ρ l Longitudinal Effect P [W/mrad/.%BW] E-3 E-5 E-7 E-9 E- E-3 E-5 E-5 E-4 E-3 E- E- E+ E+ E+ E+3 σ l wavelength [mm] Transverse Effect N I SR ( λ) λ cutoff E (ct) - - + + emittance growth head s tail Dispersion 3
CSR Calculation Tools Used For ERL I TraFiC4 (DESY/SLAC) Track and Field of Continuous Charges in Cartesian Coordinates Pros: calculates CSR from the first principles Cons: few bunchlets; slow; too noisy if coulomb forces are significant elegant (APS) electron generation and tracking -D CSR theory [Derbenev, Saldin] non-steady case, CSRDRIFT element Pros: much faster Cons: for small bend radii and large angles -D theory may not be strictly applicable 4
CSR Induced Emittance Growth (Merger) ε x,n,csr. µm elegant.5 three 5-deg dipole merger. bunch length before the merger is.6 mm CSR emittance growth [mm-mrad]..5..5 CSR emittance growth [mm-mrad].8.6.4. fixed bend radius fixed dipole length.6.65.7.75.8.85.9.95 bunch length after the injector [mm] 5 5 5 5 3 35 bend angle per dipole [deg]
Bunch Length in the Arcs Bunch length in the Arcs:, m σl t = σl, + R56 + second_ter l For off-crest of several deg: R l 56 rms bunch length [mm] 4 3.5 3.5.5.5 phi = phi = - phi = - phi = phi = nd term on crest nd term 4 6 8 4 6 position [m] R56 [m], eta x [m].5.5 5 5 -.5 - -.5 - eta x R56 position [m] R 56 = 4.4 cm (trim quads off) 6 R56 eta x
CSR Induced Emittance Growth (Arc) Linac phase scan (final energy is MeV); injection bunch length =.6 mm CSR emittance growth [mm-mrad] low emit regime.8.6.4..8.6.4. TraFiC4 elegant - -5 - -5 5 5 rf offset in the linac [deg] R 56 = 4.4 cm sub-ps regime 7
Bunch Length and Energy Spread Linac phase scan (final energy is MeV); injection bunch length =.6 mm Energy Spread Bunch Length After the st Arc.6.6 energy spread [%].5.4.3. TraFiC4 elegant rms bunch length [mm].4..8.6.4 TraFiC4 elegant σl, + R56α. R 56 = 4.4 cm. - -5 - -5 5 5 Energy Spread: rf offset in the linac [deg] σ Longitudinal Emittance: = σ + ασl + ε z = σ - -5 - -5 5 5 β 4 σ l l σ + β 4 σ l rf offset in the linac [deg] α β E = = l E = = l cavsin E cav fin fin ϕ D 8 RF cosϕ E D RF
Longitudinal Phase Space Manipulations c) l I. Low Emittance Regime II. Sub-ps Regime R 56,Arc = α c) l d) b) l l a) l e) l trim quads sextupoles α α β β b) Rule of Thumb: Match (R 9, d),b) 56 ),, d), (T 566 )
Sub-ps Regime Linac off-crest phase is 4.9 deg; injection bunch length =.6 mm R longitudinal phase space after the st 56, Arc = 4.4 cm arc ε x,n,csr.7. =.7 µm transverse phase space after the st arc bunch length = 6 fs ε z,csr = kev deg
Conclusions Producing and preserving a transverse emittance of microns appears feasible CSR behavior of the prototype is understood and within bounds based on simulation results Flexible optics have been developed that allow detailed longitudinal phase space manipulations The ultra-short bunch regime has been addressed, although some work remains