Start2End Simulations for Micro Bunching Experiments at FLASH. reloaded :-(

Transcription

1 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded StartEnd Simulations for Micro Bunching Experiments at FLASH reloaded :-( 9..7 Mathias Vogt (MPY) Two Slides of Theory... A Revised Set Up (thanx to N.G. & V.B.) Scans & Evaluation A New Candidate... Double Humps

2 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded A Simple Purely Longitudinal Model of Micro Bunching () long. phasespace R : v := (z, p z ) ps density Ψ(z, p z ), Ψ d v = (linear!) projection operator ˆQ : Ψ ρ := ˆQΨ = Ψ dp z ultra relativistic ρ(z) =const, except in BunchCompressor cavity, space charge (any long. wake) : KICKS all kicks commute cav+sc : (z, p z ) (z, p z + cav(z) + (g sc ρ)(z)) g sc ρ := g sc (z, z )ρ(z )dz collective kick : K[ρ] = Id + [ρ] : (z, p z ) (z, p z + (g ρ)(z)) Property: K[ρ + ρ ] = K[ρ ] + [ρ ] with K [ρ + ρ ] = K [ρ ] [ρ ] BunchCompressor : (generalized) DRIFT with R 56 /p length FEL w/o undulator := Cascade : (ACC BC ) n D n K n [ρ n ]... D K [ρ ] ( FLASH : n = ) all the former maps are measure preserving!!! Ψ k = Ψ k K k [ ˆQΨ k ] D k linear operator M[ρ] : Ψ M[ρ]Ψ := Ψ K [ρ] D Ψ k = M[ ˆQΨ k ]Ψ k time discrete Vlasov system, nonlinear integro-difference-eqn. as

3 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 3 A Simple Purely Longitudinal Model of Micro Bunching () Now assume we already now Ψ := M[ ˆQΨ ] Ψ (Ψ suff. smooth)... and add a tiny modulation : Ψ Ψ + ɛφ, ɛ, R Φ d v = Ψ := M[ ˆQ(Ψ + ɛφ )] (Ψ + ɛφ ) NONLINEAR EVOLUTION! ( ) can lead to increasing amplitudes for certain wavelengths GAIN can be micro bunching Gain Functions: evolution eqn. ( ) can in principle be completely studied numerically using so called -D Perron Frobenius codes (for PF see e.g. papers by Bassi, Ellison, Sobol, Venturini, Vogt, Warnock) (Gain Functions ctd.) M. Dohlus: quasi analytic model of modulation: z z/π c + R{a(δp z )e ikz } + cδp z p z p + χz/π c + R{b(δp z )e ikz } + dδp z with iteration procedure for all parameters for transport through Cavity, BunchCompressor and SpaceCharge USED IN THIS STUDY!!! to linear order in ɛ, ( ) gives (for smooth Ψ and gain ɛ ) Ψ = Ψ + ɛφ + O(ɛ ) with Φ = M[ ˆQΨ ]Φ ( Ψ [ ˆQΦ ]) D spectral analysis seems at least possible. treatment of short wavelength modulations is hardly possible in 6-D collective simulations. However, indications for micro bunching effects exist in SE simulations

4 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 4 Revised Set Up SE range Gun φ_ ACC φ_ φ_3 BC φ_4 ρ_ ACC φ_5 ACC3 BC3 ρ_3 BC : ρ =.76,.8m (lattice: ρ =.6m) R () 56 =.5,.4m (lattice: -.5m) BC3 : ρ 3 = 5.7m - m (lattice: ρ 3 = 7.5m) R (3) 56 =.9m -.5m (lattice: -.5m) φ φ φ 3 φ 4 φ 5 (gun) ACC. ACC.-4 ACC.5-8 ACC& , 5-5 VB!! accel. corr. chirp extra chirp fixed DONE 96 fixed scan scan with long. Gaussian bunch from cathode

5 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 5 Goal of SE Scans : I(z) moderately large over sufficiently large length... separated from spike! transv. ps: not first priority check µ bunching gain (model & spread sheet by M.Dohlus) Scanning φ 4, φ 5, ρ and ρ 3 Evaluation : scan of φ (see talk from 4.9.7) not affected by revised setup φ = 96 for different choices of φ 4 and ρ look at length scales supporting various currents as function of φ 5 and ρ 3 EXAMPLE : φ =8deg, ρ 3 =3.8m (after BC3) bins L >A /mm fract. of bunch with I > A excl. peak (after BC3) φ 5-8 =-4deg Θ =6deg L >A >=.4mm L >A <.4mm I(z) /ka z /mm L >5A =.mm L >4A =.5mm L >3A =.5mm L >A =.35mm /deg 5.7

6 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 6 L >3A /mm fract. of bunch with I > 3A excl. peak (after BC3) φ 5-8 =-4deg Θ =6deg L >3A >=.mm L >3A <.mm L >3A /mm fract. of bunch with I > 3A excl. peak (after BC3) φ 5-8 =-4deg Θ =6.5deg L >3A >=.mm L >3A <.mm /deg /deg 5.7 L >3A /mm fract. of bunch with I > 3A excl. peak (after BC3) φ 5-8 =-5deg Θ =6deg L >3A >=.mm L >3A <.mm L >3A /mm fract. of bunch with I > 3A excl. peak (after BC3) φ 5-8 =-5deg Θ =6.5deg L >3A >=.mm L >3A <.mm /deg /deg 5.7

7 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 7 L >4A /mm fract. of bunch with I > 4A excl. peak (after BC3) φ 5-8 =-4deg Θ =6deg L >4A >=.mm L >4A <.mm L >4A /mm fract. of bunch with I > 4A excl. peak (after BC3) φ 5-8 =-4deg Θ =6.5deg L >4A >=.mm L >4A <.mm /deg /deg 5.7 L >4A /mm fract. of bunch with I > 4A excl. peak (after BC3) φ 5-8 =-5deg Θ =6deg L >4A >=.mm L >4A <.mm L >4A /mm fract. of bunch with I > 4A excl. peak (after BC3) φ 5-8 =-5deg Θ =6.5deg L >4A >=.mm L >4A <.mm /deg /deg 5.7

8 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 8 L >5A /mm fract. of bunch with I > 5A excl. peak (after BC3) φ 5-8 =-4deg Θ =6deg L >5A <.5mm L >5A /mm fract. of bunch with I > 5A excl. peak (after BC3) φ 5-8 =-4deg Θ =6.5deg L >5A >=.5mm L >5A <.5mm /deg /deg 5.7 L >5A /mm fract. of bunch with I > 5A excl. peak (after BC3) φ 5-8 =-5deg Θ =6deg L >5A >=.5mm L >5A <.5mm L >5A /mm fract. of bunch with I > 5A excl. peak (after BC3) φ 5-8 =-5deg Θ =6.5deg L >5A <.5mm /deg /deg 5.7

9 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 9 ε n,s x /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-4deg Θ =6deg x <= 3.5µm x > 3.5µm ε n,s x /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-4deg Θ =6.5deg x <= 3.5µm x > 3.5µm /deg /deg 5.7 ε n,s x /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-5deg Θ =6deg x <= 3.5µm x > 3.5µm ε n,s x /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-5deg Θ =6.5deg x > 3.5µm /deg /deg 5.7

10 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded ε n,s y /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-4deg Θ =6deg y <= 3.5µm y > 3.5µm ε n,s y /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-4deg Θ =6.5deg y <= 3.5µm y > 3.5µm /deg /deg 5.7 ε n,s y /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-5deg Θ =6deg y <= 3.5µm y > 3.5µm ε n,s y /µm averaged (I>A) normalized slice-emittance (after BC3) φ 5-8 =-5deg Θ =6.5deg y <= 3.5µm y > 3.5µm /deg /deg 5.7

11 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded A New Candidate... 5 After BC3: φ =6deg φ 4 =-4deg ρ =.76m ρ 3 =m x bins / smooth σ bin =.5 p z /MeV z /mm

12 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 8 After BC3: φ =6deg φ 4 =-4deg ρ =.76m ρ 3 =m x bins / smooth σ bin =.5 6 After BC3: φ =6deg φ 4 =-4deg ρ =.76m ρ 3 =m x bins / smooth σ bin =.5 p x /kev p y /kev e-5 Ψ x /mm y /mm.6 After BC3: φ =6deg φ 4 =-4deg ρ =.76m ρ 3 =m x bins / smooth σ bin =.5.3 After BC3: φ =6deg φ 4 =-4deg ρ =.76m ρ 3 =m x bins / smooth σ bin =.5 x /mm y /mm Ψ e-5 Ψ z /mm z /mm

13 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 3 3 After BC3: φ =6deg φ 4 =-4deg ρ =.76m φ 5 =-5deg ρ 3 =m tot const-len bins (smooth.5)/ suppr <5 part <P z > +/- σ pz I(z) <P z > +/- σ pz /MeV I /ka (z-<z>) /σ z

14 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 4 ε n x /µm ε n y /µm ε n x I(z) After BC3: φ =6deg φ 4 =-4deg ρ =.76m φ 5 =-5deg ρ 3 =m tot const-len bins (smooth.5)/ suppr <5 part ε n y I(z) (z-<z>) /σ z After BC3: φ =6deg φ 4 =-4deg ρ =.76m φ 5 =-5deg ρ 3 =m tot const-len bins (smooth.5)/ suppr <5 part (z-<z>) /σ z I /ka I /ka

15 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 5 I(z) /ka sum (head) (tail) Before BC: φ =6deg φ 4 =-4deg sub-ensembles / 5 part/bin (smooth.5) - - z /mm

16 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 6 I(z) /ka sum (head) (tail) After BC: φ =6deg φ 4 =-4deg ρ =.76m sub-ensembles / 5 part/bin (smooth.5) z /mm

17 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 7 I(z) /ka.5.5 After BC3: φ =6deg φ 4 =-4deg ρ =.76m φ 5 =-5deg ρ 3 =m sub-ensembles / 5 part/bin (smooth.5) sum (head) (tail) z /mm

18 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 8 I(z) /ka : pre bc 6 : pre bc 7 : pre bc 5 : post bc 6 : post bc 7 : post bc 5 : post bc3 6 : post bc3 7 : post bc3 Before and after BC and after BC3 sub-ensembles 5-7 / 5 part/bin (smooth.5) z /mm

19 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 9 Gain Curve : Φ 3 8 = 5 / SubEnsemble= 5 C bc =.3, C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

20 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded Gain Curve : Φ 3 8 = 5 / SubEnsemble= 6 C bc =., C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

21 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded Gain Curve : Φ 3 8 = 5 / SubEnsemble= 7 C bc =., C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

22 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded Gain Curve : Φ 3 8 = / SubEnsemble= 5 C bc =.3, C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

23 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 3 Gain Curve : Φ 3 8 = / SubEnsemble= 6 C bc =., C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

24 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 4 Gain Curve : Φ 3 8 = / SubEnsemble= 7 C bc =., C bc3 = ( g k ) ( g k ) ( g k ) ( g k )...5 λ k 5.

25 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 5 Is This Micro Bunching in SE-Simulations?.5 After BC3 (5 prt/bin) / φ 5-8 =-4deg ρ =.765m ρ 3 = φ = -deg φ = -5deg.5 I /ka z /mm

26 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 6 Double Humped Densities p z /kev At Gun-Cathode: Gaussians, 3σ separated x const bins (smooth.5) τ /ns 7e-5 6e-5 5e-5 4e-5 3e-5 e-5 e-5 p z /MeV After BC3: Gaussians, 3σ separated x const bins (smooth.5) z /mm

27 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 7 I(z) /ka sum (head) (tail) After BC3: Gaussians, 3σ separated sub-ensembles / 5 part/bin (smooth.5) z /mm

28 XFEL BD meeting 9..7 / M.Vogt / SE for µ bunching reloaded 8 Summary Proposed set of parameters φ φ φ 3 φ 4 ρ φ 5 ρ 3 (gun) ACC. ACC.-4 ACC.5-8 BC ACC&3 BC m 5 m VB accel. corr. chirp extra chirp decent z region with high current outside spike 5µm with I > 5A, µm with I > 3A decent transcerse phase space no strong mixing in high I region estimated gain > +4 for µm < λ < µm, > +3 for λ < µm proposed µ bunching switch : vary φ 5 from to 5 possibly try double humped initial densities from cathode