DESY/TEMF Meeting - Status 2011

Transcription

1 Erion Gjonaj Technische Universität Darmstadt, Computational Electromagetics Laboratory (TEMF) Schlossgartenstr Darmstadt, Germany DESY/TEMF Meeting - Status 211 DESY, Hamburg,

2 Contents - Problem description - Simulation approaches - Results - Discussion Field map calculations - Mixed mesh high order FEM code - Field quality study for the 3.9 GHz 3 rd harmonic cavity Summary

3 Problem description Optimized machine parameters for Q = 1nC (simulations) talk from M. Krasilnikov, Zeuthen, 211

4 Problem description SPCH limit talk from M. Krasilnikov, Zeuthen, 211

5 Problem description Sources of discrepancy: Thermal energy spread at cathode Oxide layer effects and cathode impurities Limited knowledge of machine conditions during measurement Emittance measurement slit scan technique Wakefields Improper modeling of radiation fields? Inaccurate simulation of the emission process?

6 Problem description Bring particles to computational grid Solve for electrostatic field on the grid (DFT) Push particle positions and momenta Transform to average rest frame Transform (fields) back to lab frame Boosted frame approach (ASTRA): Retardation effects due to relative motion within bunch? Acceleration radiation? Relativistic correction for mirror charge fields?

7 Beam dynamics in the boosted frame Problem description Field of accelerated point charge: 2 ( )( 1 ) q n β β n ( n β) β E = πε ( 1 β n ) R ( 1 β n ) R retardation acceleration Retardation only wrt. mean bunch motion Effect is stronger when space charge is included t= t r v / c 1,9,8,7,6,5,4,3,2,1 Velocity sheer (space charge free simulation) Mean velocity Velocity sheer Beam uniformity assumption violated few mm away from cathode,2,4,6,8 1 1,2 1,4 1,6 1,8 2 z / (cm) Effect is stronger when mirror charges are considered

8 Effect of retardation for single electron fields.4 V ( ) p x F x m= m q F = e = e E E = 6 MV/m b x d x m = 1mm mv( x) v'( x) 2 vx ( ) (1 ) 2 c V p ( x) = 3/2 = F, v() = c F x( 2 c m+ F x) 2 2 cm+ Fx

9 Effect of retardation for single electron fields.8 V ( ) p x F x m= m q F = e = e E E = 6 MV/m X p t m.6.4 mv( x) v'( x) 2 vx ( ) (1 ) 2 c 3/2 = F, v() = μ μ μ μ μ μ 1-11 t s X () t = c( c m + F t cm) p F

10 t s Effect of retardation for single electron fields 3. μ μ μ μ μ μ1-12 t T r d,t V ( ) p x 5. μ μ μ μ μ μ1-11 t s observer F r x Retardation time at arbitrary observer position as a function of time: ( ) 2 ( T ( x, t), x X ( t) = 2 ( ct x) 2 c m+ F ( x ct) 2, ct > x > X p( t ) 2[ ccm+ F ( x ct)] 2 ct + x c m+ F x + ct) < 3 p 2c m+ 2 cf ( ct + x), x Xp[ Tr( x, t)] Tr (,) x t = t c x > ct

11 Effect of retardation for single electron fields Electron fields at fixed positions.12 Static LW x =.1 Static LW x = 1 mm E V m.6 E V m μ μ μ μ μ μ μ μ μ μ μ μ 1-11 t s t s

12 Effect of retardation for single electron fields F V () p t x.7.6 Driver and test particle trajectories X p t X 1 t X 2 t V ( p t Δ ) V ( p t+δ ).5 t =Δ Δ = 1 ps X t m.4.3 bunch tail bunch head x μ μ μ 1-11 t s

13 Effect of retardation for single electron fields Fields at head particle Fields at tail particle. Static.7 Static LW LW E (, Δ ) =.55 V/m s E V m E V m.4.3 E (, Δ =.86 V/ m lw ) t =Δ 5. μ μ μ μ μ μ 1-11 t s. 5. μ μ μ 1-1 t s

14 Effect of retardation for single electron fields Add mirror charge at conducting surface Retardation times of particle and its mirror V () p t F V () p t x 3. μ μ 1-11 t T r d,t T m d,t mirror charge V ( ) p t Δ V ( ) p t+δ t s 2. μ μ 1-11 Δ = 1 ps 1. μ μ μ μ μ μ μ μ 1-11 t s

15 Effect of retardation on single electron dynamics Total fields at head particle Total fields at tail particle..3 Static Static LW -.1 LW.25 E V m x 1 E V m.2.15 E (, Δ =.11V/m s ) E (, Δ =.17 V/ m lw ) t =Δ 5. μ μ μ μ μ μ 1-11 t s. 1. μ μ μ μ μ μ 1-11 t s

16 Lienard-Wiechert particle-particle approach r -ct now +ct Store full particle history huge memory r(t) R n r (t r ) macroparticles Search at every time step retarded times and positions for all particle positions - N p 2 N t operations cathode t r t n t n+1 t Full physics Accuracy depends only on Time step image charges Number of particles

17 The PIC approach Bring particles to computational grid Solve full set of Maxwell equations on the grid Push particle positions and momenta Includes all effects; can handle arbitrary geometry Numerically more efficient then LW approach Accuracy depends on: accuracy of field solution, number of particles, current smoothing, time step, 19. Juli 211 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj

18 High order DG-FEM method Very accurate field solutions using piecewise high order polynomial approximation with grid cells (DG-FEM)* E Ii 1 I i Field resolution is given by approximation order not by grid step use sparse grids Ei (, ) 1 xt Ei ( x, t) Spectral convergence (wrt. order) Very low dispersion errors E( xt, ) x xi 1 x x i i + 1 * E. Gjonaj at al., New J. of Phys., Vol. 8, (26), pp Juli 211 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj

19 Charge conserving current interpolation - Macroparticle current density: jr (,) t = Qpvp() t W p r rp() t p v q W q ( r rq) - DG-FEM current projection: ( ) j v r r r e 3 e i() t Qp p() t d Wp, t ϕi ( ) p Ω () t = ep Ω e Ω ep r p r q - Discrete current / time step / cell: J n+ 1 t e n n+ 1 e i( t, t ) = dtj ( ) n t i t v p W p ( r rp ) - Choice of particle size most critical parameter for simulation accuracy 19. Juli 211 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj

20 Beam dynamics in the gun: LW simulations 3,5 Projected transverse emittance for different particle numbers Q = 1 nc XY_rms =.75 mm non-optimized setup (data from 21) 3 εn / (mm mrad) 2,5 2 1,5 1,5 1. particles 5. particles 1. particles 2. particles 5. particles ~ 2 TB,5 1 1,5 2 2,5 3 3,5 4 4,5 5 z / (cm) t =.1 ps

21 Beam dynamics in the gun: LW simulations systematic different 3,5 behavior at the cathode 3 Projected transverse emittance: comparison with ASTRA Q = 1 nc XY_rms =.75 mm non-optimized setup (data from 21) 2,5 εn / (mm mrad) 2 1,5 1,5 1. particles 5. particles 1. particles 2. particles 5. particles ASTRA,5 1 1,5 2 2,5 3 3,5 4 4,5 5 z / (cm) t =.1 ps

22 Beam dynamics in the gun: PIC simulations 4 Projected transverse emittance for different approximation orders Q = 1 nc XY_rms =.75 mm non-optimized setup (data from 21) 3,5 3 εn / (mm mrad) 2,5 2 1,5 1,5 PIC - P1 PIC - P2 PIC - P3 PIC - P4,5 1 1,5 2 2,5 3 3,5 4 4,5 5 z / (cm) z = 1 mm s = 1 mm N p = 5.

23 Beam dynamics in the gun: PIC simulations 4 Projected transverse emittance for different approximation orders Q = 1 nc XY_rms =.75 mm non-optimized setup (data from 21) 3,5 3 εn / (mm mrad) 2,5 2 1,5 1,5 PIC - P1 PIC - P2 PIC - P3 PIC - P4 Lienard-Wiechert ASTRA,5 1 1,5 2 2,5 3 3,5 4 4,5 5 z / (cm) z = 1 mm s = 2 mm N p = 5.

24 Beam dynamics in the gun Q = 1 nc XY_rms =.75 mm ASTRA (z = 5cm) LW (z = 5cm) PIC (z = 5cm)

25 Beam dynamics in the gun Q = 1 nc XY_rms =.75 mm ASTRA (z = 5cm) LW (z = 5cm) PIC (z = 5cm)

26 Beam dynamics in the gun Slice emittances for the different codes (z = 5 cm) Q = 1 nc XY_rms =.75 mm non-optimized setup (data from 21)

27 Beam dynamics for PITZ-1.8 setup no SPCH limiting at XY_rms =.3 mm Projected transverse emittance for different XY_rms sizes Q = 1 nc PITZ-1.8 setup (M. Krasilnikov, 211)

28 Beam dynamics for PITZ-1.8 setup no SPCH limiting at XY_rms =.3 mm Projected transverse emittance for different XY_rms sizes Q = 1 nc PITZ-1.8 setup (M. Krasilnikov, 211)

29 Beam dynamics for PITZ-1.8 setup no SPCH limiting at XY_rms =.3 mm Projected transverse emittance for different XY_rms sizes Q = 1 nc PITZ-1.8 setup (M. Krasilnikov, 211)

30 Beam dynamics for PITZ-1.8 setup Restarted ASTRA simulations with LW bunch as initial distribution Q = 1 nc XY_rms =.4 mm PITZ-1.8 setup (M. Krasilnikov, 211) Emittance at EMSY1 vs. z EMSY1 (z = 5.74m)

31 Beam dynamics for PITZ-1.8 setup ASTRA (z = 5.74 m) LW (z = 5.74m) Q = 1 nc XY_rms =.4 mm PITZ-1.8 setup (M. Krasilnikov, 211)

32 Beam dynamics for PITZ-1.8 setup ASTRA (z = 5.74 m) LW (z = 5.74m) Q = 1 nc XY_rms =.4 mm PITZ-1.8 setup (M. Krasilnikov, 211)

33 Beam dynamics for PITZ-1.8 setup Slice emittances for the different codes (z = 5.74 m) Q = 1 nc XY_rms =.4 mm PITZ-1.8 setup (M. Krasilnikov, 211)

34 2,2 Beam dynamics in the injector 2 1,8 Q = 1 nc PITZ-1.8 setup (M. Krasilnikov, 211) 1,6 1,4 1,2 1,8,6 restarted LW,4,2,1,2,3,4,5,6,7,8

35 Beam dynamics for PITZ-1.8 setup Still no good agreement with experiment Could extract full bunch charge at XY_rms =.3 mm Slightly larger emittance than ASTRA Emittance minimum and curve pattern same as ASTRA Are other effects responsible for the discrepancy (wakefields?) Restart positions too close to cathode backplane Longitudinal density oscillations not fully understood Convergence of LW vs. time step is unclear 19. Juli 211 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj

36 Discussion on space charge at the cathode dt =.1 ps Np = 5 K dt =.1 ps Np = 5K z = 1cm dt =.5 ps Np = 5 K dt =.5 ps Np = 5K z = 1cm Q = 1 nc XY_rms =.3 mm dt =.1 ps Np = 1 M dt =.1 ps Np = 1M z = 1cm

37 Discussion on space charge at the cathode No convergence: need to refine dt and N p simultaneously LW slice emittances for different parameters (z = 1cm) Q = 1 nc XY_rms =.3 mm PITZ-1.8 setup (M. Krasilnikov, 211)

38 Discussion on space charge at the cathode V () p t σ F V () p t x mv( x) v'( x) 2 vx ( ) (1 ) 2 c 3/2 = F + F ( ), m x v() = cloud mirror charge Point charge emission from ideal surface not possible: Need a cloud mirror charge distribution v( x) = 1 2 2x 2x 2 Erf ( ) ( ) σ k ke Fm x = σ 2 2πxσ 4x Main branch solution π cmxσ 2x ( πσ (4cmx+ kerf( ) + 4 F x ) 2 2 π kx) σ 2 2 2

39 Discussion on space charge at the cathode Wall force modified by cloud charge Usual trajectory: small wall interaction -2. μ 1-17 Cloud force Coulomb force.4 σ = 1μm E = 6MV/m -4. μ F x V m -6. μ 1-17 b x.2-8. μ μ μ μ μ μ μ 1-6 x m. 2.μ μ μ μ x m

40 Discussion on space charge at the cathode Small size particle trajectory SPCH limited trajectory.1.8 σ = 2nm.1.5 σ = 17 nm E = 6MV/m E = 6MV/m b x.6 b x μ μ μ μ μ μ μ μ μ μ 1-8 x m x m

41 Discussion on space charge at the cathode Low field / large size particle trajectory SPCH limited trajectory.8.6 σ = 1μm σ = 1μm.5 E = E = 21 V/m 24 V/m b x.4 b x μ μ μ μ x m 2.μ μ μ μ x m

42 Discussion on space charge at the cathode Minimum separation distance between particle and its mirror: LW: ~time step PIC: macroparticle shape ASTRA: longitudinal grid step (?) Needs to be reduced at high charge densities: but end up with individual particle interactions σ < λ D No numerical convergence Only cure, increase number of particles in the simulation Full charge extraction at.3 mm possible with ASTRA (?) 19. Juli 211 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj

43 Field map calculations Field noise in eigenmode simulations E / [kv / m] Typical field noise on-axis for computations with unstructured grids k - quadratic E x E y z / [cm] Example tetrahedral mesh for the 3.9 GHz 3 rd harmonic cavity Need huge amount of DoFs to compensate for mesh asymmetry Special treatment for the coupler kicks (PAC 29, DESY / TEMF 21) So far completely noise-free field maps only possible with Cartesian grids

44 Field map calculations Mixed mesh high order FEM approach Data already available for field map at structured points Cartesian mesh: no near field noise Low frequency noise from far fields close to the boundary Tetrahedral mesh: necessary for fine geometry

45 Field map calculations Mixed mesh high order FEM approach

46 Field map calculations Mixed mesh high order FEM approach

47 Field map calculations Mixed mesh high order FEM approach

48 Field map calculations Mixed mesh high order FEM approach

49 Field map calculations Field quality study for the 3.9 GHz cavity Fields on axis: Mixed mesh with 35K elements Fields on axis: Tetrahedral mesh with 45K elements

50 Field map calculations Field quality study for the 3.9 GHz cavity Fields on axis: Mixed mesh with 35K elements Fields on axis: Tetrahedral mesh with 45K elements

51 Field map calculations Field quality study for the 3.9 GHz cavity Fields on axis: Mixed mesh with 35K elements Fields on axis: Tetrahedral mesh with 45K elements

52 Field map calculations Field quality study for the 3.9 GHz cavity Use of different orders in different parts of the mesh to increase smoothness (not accuracy),1,8,6,4 E / a.u.,2 -,2 -,4 -,6 E y : P-P E y : P-P2 -,8 E y : P-P3 E y : P3-P3 -,1 -,55 -,45 -,35 -,25 -,15 -,5,5,15 z / m

53 Field map calculations Field quality study for the 3.9 GHz cavity Transversal fields off axis: Mixed mesh with 35K elements Transversal fields off axis: Tetrahedral mesh with 45K elements

54 Thank you for your attention 23. Juli 21 TU Darmstadt Fachbereich 18 Institut Theorie Elektromagnetischer Felder PD Dr.rer.nat. Erion Gjonaj