CSRtrack: Faster Calculation of 3d CSR Effects

Transcription

1 CSRtrack: Faster Calculation of 3d CSR ffects M. Dohlus, T. Limberg, DSY, Hamburg, Germany Projected Method / Sub-Bunch Approach Field Calculation: Convolution Method Iterative Tracking CSRtrack xample Pseudo Green s Function Approach Meshed Fields 4 2 effort (sub-bunch approach # of point to point interaction ~ N 2 5 6

2 Projected Method (1d approach ( (ext e ( s, t + v B p & ν = q ν ν ν no transverse self- t ( δ λ ( s tc = qν δ (( s tc ( sν s s s ν ( t ( δ λ s t c = λ ( s t c g s σ σ ( ( ( rigid 1d charge distribution: very low numerical effort 1d -field without γ 2 singularity: s, t = λ ( u + s ct K( s, u du ( no transverse dependency of longitudinal see: Saldin, Schneidmiller, Yurkov: NIM A398 ( Dohlus: TSLA-FL-23-5

3 Sub-Bunch Approach individual trajectories N source distributions (sub-bunches self-consistent tracking: pairs of source- and test- + additional test M N perturbative tracking: source- and test- independent macro distribution M test effort per field calculation: = MN p to p

4 Iterative Tracking ( (self (ext F + v B p & ν q = ν ν integration with fine steps t 2 t 1 but: are calculated on time mesh (self (self with larger steps F t, F ( t,l linear interpolation: t2 t F F ( t = ( 1 2 (self ( ( t + ( t t (self (self 1 1 ( 2 new force F (self (t 2 depends on new phase space coordinates x ph (t 2 that depend on F (self (t 2 iterative tracking t 2 t 1 F t

5 Iterative Tracking n:= n:=n+1 x (t2,n-1 force calculation t1 X (t1 F (t1 t2 F (t1 linear interpolation F(t F (t2, = F (t1 linear interpolation F(t F (t2,n x (t1 x (t2, x (t1 x (t2,n x (t2,n -x (t2,n-1 > ε < ε X (t2 F (t2 error

6 Convolution Method source distributions: 1d distribution 2d distribution 3d distribution λ (s η ( r, z ρ(r em fields: ( r, B ( r, η (3d ( r, B (3d ( r, singular (s and non-singular (ns parts: ( B λ ( r = ( r = K s ( r + ns ( r (3d ( r = η η s s analytical functions ( r + η ( r + ns ns ( r ( r numerical 1d integration see: M.Dohlus, A.Kabel, T.Limberg: fficient field calculation of 3D bunches on general trajectories. NIM A445 (

7 Pseudo Green s Function Approach reference path r ( t B ( ( q ν q ( r,t ( r,t path of subbunch ν (t r ν reference path after shift&rotation transformation r ν ( r ( t r ( ( t r ν ( t + R t

8 the Green s functions are calculated numerically on a 2d-mesh with M g points B ( ( (, t (, t = x ( x, y u x + y ( x, y u y M-field of reference (, t = Bz ( x, y u z sub-bunch effort per field calculation: f. c. = M g p to p + NMi,g p to p = effort per point to point interaction i,g N = effort for interpolation on grid << p to p = number of source distributions M = number of test (> N

9 Meshed M Fields not now in CSRtrack density of large compared to fine structure of field: calculate field on mesh (M em points and interpolate to M test- effort: f.c. = M em N pto p + M i,em (~ linear with M-field macro-distribution

10 Meshed M Fields + Pseudo Green s... not now in CSRtrack effort: f.c. = M g p to p + M em N i,g + M i,em M-field of reference sub-bunch M-field of Macro distribution

11 4 2 2 effort a.u Scaling of ffort (simplified M N = 6 Green s M-mesh + Green s p to p M-mesh

12 MATLAB pre-processor LINUX cluster, MPI windows XP MATLAB post-processor

13 xample: BC2-TTF1 overcompression initial distribution from ASTRA (2 γ = qtot = 2.61 nc top view slice slice 4 sub-bunches (CSRtrack

14 xample: BC2-TTF1 initial distribution horizontal slice after BC: longitudinal phase space x /µrad x/mm s/µm

15 xample: double BC (proposal for TTF2 ASTRA (space charge LGANT (geom. Wakes, CSR CSR-Track

16 xample: double BC p to p : d on 2x1GHz CPU greens :.5d on 1x1GHz CPU projected : ~15min on 1x1GHz CPU d/ d/ (d-d(/ s[µm] (d-d(/ s[µm] s[µm] RMS((d-d(/ 8* -4 6* -4 4* -4 2* s[µm] RMS((d-d(/ 8* -4 6* -4 4* -4 2* s[µm] s[µm]