Presentation on theme: "Wakefield Code ECHO 2(3)D"— Presentation transcript:
1Wakefield Code ECHO 2(3)D How it works, limitations, pros/cons and new/current developmentsIgor ZagorodnovICFA mini-Workshop on “Electromagnetic wake fields and impedances in particle accelerators“Erice, SicilyApril 2014
2Overview Motivation Numerical Methods Examples Code Status low-dispersive schemesboundary approximationindirect integration algorithmmodelling of conductive wallsExamplesCode Status
3MotivationWake field calculation – estimation of the effect of the geometry variations on the bunchMaxwell‘s EquationsFirst codes in time domain ~ 1980A. Novokhatski (BINP),T. Weiland (CERN)
4Motivation TBCI*, MAFIA*** rotationally symmetric and 3D longitudinal and transverse wakestriangular geometry approximation;arbitrary materialsmoving windowdispersion errorNOVO***only rotationally symmetriconly longitudinal wake“staircase” geometry approximation;only PECmoving meshlow dispersion error* T. Weiland, TBCI and URMEL - New Computer Codes for Wake field and cavity mode calculations, IEEE Trans. Nuclear Science, 30 (1983) 2489** MAFIA Collaboration, MAFIA Manual, CST GmbH, Darmstadt, 1997.*** A. Novokhatski, M. Timm, T. Weiland, Transition Dynamics of the Wake Fields of Ultra Short Bunches. Proc. of the ICAP 1998, Monterey, California, USA.
5Low-dispersive schemes New projects – new needsshort bunches;long structures;tapered collimatorsNew methods are requiredwithout dispersion error accumulation;“staircase” free;fast 3D calculations on PCSolutionszero dispersion in longitudinal direction;“conformal” meshing;moving mesh and “explicit” or “split” methods
6Low-dispersive schemes Dual gridMaxwell Grid Equations*Primary grid* T. Weiland, A discretization method for the solution of Maxwell’s equations for six-component fields, Electronics and Communication (AEÜ) (1977) 31, p. 116.
8Low-dispersive schemes FDTDImplicit Scheme* (2002)* I. Zagorodnov, R. Schuhmann, T. Weiland, Long-Time Numerical Computation of Electromagnetic Fields in the Vicinity of a Relativistic Source, Journal of Computational Physics, vol. 191, No.2 , pp , 2003.
9Low-dispersive schemes Implicit Scheme (2002)Our scheme in staircase approximation with =0.5 is reduced to the scheme realized in code NOVO.
10E/M and TE/TM* splitting (2004) Low-dispersive schemesE/M and TE/TM* splitting (2004)Subdue the updating procedureto the bunch motion* Zagorodnov I.A, Weiland T., TE/TM Field Solver for Particle Beam Simulations without Numerical Cherenkov Radiation, Phys. Rev. ST Accel. Beams, vol. 8, (2005)E/M splittingTE/TM splittingMAFIAECHO
16Low-dispersive schemes Stability, energy and charge conservationThe stability conditionE/M splittingTE/TM implicitTE/TM explicit*(FDTD scheme)* Dohlus M., Zagorodnov I., Explicit TE/TM Scheme for Particle Beam Simulations// Journal of Computational Physics, vol. 225, No. 8, pp , 2009.
17Low-dispersive schemes Explicit TE/TM vs FDTDExplicit TE/TM schemeE/M scheme (FDTD)Explicit TE/TM requires the same memory 6N as FDTDExplicit TE/TM requires only 18% more computational time than FDTD (the same transverse mesh)Explicit TE/TM allows “magical” time step to avoid the dispersion error
18Low-dispersive schemes Dispersion relation in the transverse planeImplicit TE/TM schemeExplicit TE/TM schemeexplicitimplicitNo dispersion in z-direction + no dispersion along XY diagonals
19Low-dispersive schemes Transverse Deflecting StructureGaussian bunch with sigma=300mmexplicitimplicit
20Standard Conformal Scheme* Boundary approximationStandard Conformal Scheme*PECreduced cell areatime step mustbe reduced* Dey S, Mittra R. A locally conformal finite-difference time-domain (FDTD) algorithm for modeling threedimensional perfectly conducting objects. IEEE Microwave and Guided Wave Letters 1997; 7(9):273–275..Thoma P. Zur numerischen Lösung der Maxwellschen Gleichungen im Zeitbereich. Dissertation Dl7: TH Darmstadt,1997.
21Time step is not reduced! Boundary approximationNew Conformal Scheme* (2002)PECPECvirtual cellTime step is not reduced!* Zagorodnov I., Schuhmann R.,Weiland T., A Uniformly Stable Conformal FDTD-Method on Cartesian Grids, International Journal on Numerical Modeling, vol. 16, No.2, pp , 2003.
22Square rotate by angle p/8. Boundary approximation204060801000.20.40.60.81PFCUSC1012-4-3-2-1USCPFCstaircaseSquare rotate by angle p/8.PFC (Partially Filled Cells) ~ Dey-MittraUSC (Uniformly Stable Conformal)
23Simple Conformal (SC) Scheme* Boundary approximationSimple Conformal (SC) Scheme** Zagorodnov I., Schuhmann R., Weiland T., Conformal FDTD-methods to avoid Time Step Reduction with and without Cell Enlargement , Journal of Computational Physics, vol. 225, No. 2, pp , 2007.
24Error in loss factor for sphere Boundary approximation?11staircasestaircase()Ohconformal0.010.01conformal2()Ohrrrz1e1e--44zzh?1010100100Error in loss factor for sphereGaussian bunch with σ=0.5 cm is passing through a spherical resonator. The sphere has the diameter 1.8 cm. The analytical loss factor L is equal to Vp/CThe error for stationary mesh is demonstrated by lines. The results for moving mesh are shown by triangles and circles.
25Error in loss factor for a taper Boundary approximation5101520253035405.822.214.171.124.8126.96.36.199.8staircaseconformalError in loss factor for a taperThe error δ relative to the extrapolated loss factor L= Vp/C for bunch with σ=1 mm is shown.
26Indirect Integration Algorithm 1C-1CCrzO. Napoly, Y. Chin, and B. Zotter, Nucl. Instrum. Methods Phys. Res., Sect. A 334, 255 (1993)
27Indirect Integration Algorithm 1C-1CCr2CzI. Zagorodnov, R. Schuhmann, T. Weiland, Journal of Computational Physics, vol. 191, No.2 , pp , 2003.
29Indirect Integration Algorithm Zagorodnov I., Indirect Methods for Wake Potential Integration, Phys. Rev. STAB vol. 9, (2006)H. Henke and W. Bruns, in Proceedings of EPAC 2006, Edinburgh, Scotland (WEPCH110, 2006)
343D simulation. Cavity Examples 3 geometry elements Moving mesh20 TESLA cells structure3 geometry elementsThe geometric elements are loaded at the instant when the moving mesh reach them. During the calculation only 2 geometric elements are in memory.
35Examples E/M ECHO-3D (TE/TM) Comparison of the wake potentials obtained by different methods for structure consisting of 20 TESLA cells excited by Gaussian bunchE/M splittingTE/TM splitting
37Examples1020304050010001500200025003000250.6%82.5%30%12.2%5.4%12.4%2.8%0.8%0.36%ref.E/MTE/TM-55-500The transverse dipole wake function (left) and loss factor for the collimators with and L=20cm (right). The solid lines show the results for the E/M scheme (Yee’s scheme) and the dashed lines display the results for the TE/TM scheme. The relative errors are given regarding the reference value (marked as ref. on the graphs) calculated by TE/TM method with the finest mesh.
38Examples E/M ECHO-3D (TE/TM) Comparison of the wake potentials obtained by different methods for round collimator excited by Gaussian bunchTE/TM method – fast, stable and accurate with coarse mesh