Computational models, algorithms & computer codes in accelerator physics. Valentin Ivanov Stanford Linear Accelerator Center 23 February 2006

Transcription

1 Computatonal models, algothms & compute codes n acceleato physcs Valentn Ivanov Stanfod Lnea Acceleato Cente 23 Febuay 2006

2 Intoducton The aeas of actvty Types of the poblems Contents Statonay poblems Scala Felds F/T-doman Electomagnetsm Vecto Felds Beam Dynamcs & Image Electon Optcs Optmzaton & Stuctual Synthess

3 Physcal Electoncs Plasma Physcs Fokke-Plank equaton u f f F f f + v + = + S t M v t Patcle Tackng model & 1 P = q Et, + v Ht, U vt,, + U&, c 1/2 2 & P P R = M M c B ot E =, t D ot H = + j0 + qnv, t ρ 1 dv D = + qn, ε0 ε0 dv B = 0. & ρ + dv j = 0. c, Acceleato Physcs vacuum electoncs Lase Physcs non lnea optcs Semconducto mco electoncs

4 The aeas of actvty Statonay felds Electodynamcs Electon optcs Plasma physcs Hydodynamcs Posson equaton F-doman T-doman Electo statcs Themal physcs Magneto statcs Helmholtz Eq.+PIC Maxwell Eq.+PIC Beam dynamcs Tack-3p Image optcs Beamplasma nteacton Stess analyss Semconducto Cystal gowth n low gavty Nave-Stokes, Heat & Mass Tansfe eqs. Posson-2 Maxwell-2 Optcs-2 Elast-2 Nave-2 Posson-3 Maxwell-3 Optcs-3 Elast-3 HYDMIG-3 Posson-C Maxwell-T

5 Types of the Desgn Poblems Feld & patcle Analyss Paametc Optmzaton Stuctual Synthess Toleance Analyss

6 Compaatve featues of dffeent numecal methods Method FDM FEM BEM Matx Solve Iteatve Iteatve, Dect Dect Matx dmenson 2D 3D Advantages Unfom opeatons; Smple stuctue of the mesh Dsadvantages Less accuacy fo complexshape egons Flexble bounday-ftted mesh Analytcal ntegaton ove the element s volume Complex meshgeneato n 3D; Hgh accuacy; 2. Open bounday; 3. Hgh-ode devatves; 4. Edge sngulaty 5. Extenal asymptotc; 1. Dense matx; 2. Moe complex analytcs

7 Bounday Element Method fo An ntegal epesentaton fo the electostatc potental ϕ at obsevaton pont s a sum of the suface souces wth the densty σ and space chage densty ρ : 1 σ 1 ρ ϕ = ds + dv, S, V, R =. 4πε R 4πε R S Statonay Poblems V Applyng the Dchlet, Neumann condtons and contnuty of electc nducton at the bounday gves a set of ntegal equatons fo unknown functon σ ϕ ϕ ϕ ϕ = U, = E, ε = ε n n n Lnea System afte dscetzaton GX S1 0 S2 0 + S+ S 4 1 ψ m, η = F, Gj = J, η d h h, η η m= 1 dη.

8 Paametc epesentaton of the bounday Paametc epesentaton of the bounday,,,,,,,,, 1 η η η η η d d J ds z z y y x x S S k k k k N k k = = = = = = U Polynomal appoxmaton fo suface souces [ ] [ ] { },, 1 1, 1 1, 1 1, 1 η η η σ σ η η σ σ η σ h h j j j j j j = Lnea system G σ = F wth matx elements.,,, η η η η ψ η d d J h h G m m j = =

9 Mult-flow Gun fo Klyston Gun schematc sketch Ion geomety Smulaton of mult beam gun by TOPAZ 3D Fle fo beam envelope and tajectoes: F:\mam\170kV new\fnal wth washes\no washes\15 kv wthout washes Tajectoy data fle: F:\mam\170kV new\fnal wth washes\no washes\15 kv wthout washes\testf2.tl Input fle: ~\testf2.tsk -> do not foget cosssecton Fle fo magnetc feld coecton fo anode-cathode aea: CCR-1xxxx.dwg Fles of extenal off-axs Bx,y,z: nx.pn, ny.pn, nz,pn dated by Fles of extenal on-axs Bx,y,z:nxon.pn, nyon.pn, nzon.pn dated by Bz_max= 922G, Bb= 369G, Bz_cath= 24G Ib=1.46A, V0=15 kv Adjusted coeffcents fo TOPAZ nput fle: dx=0.063 m, dy = 0.0 m, dz=0.046 m, #4=0.0381, #12= Ognal & optmzed beam envelopes

10 The esults of sheet-beam gun smulaton Focusng electode 2. Emtte 3. Anode

11 Dode, tode & gd guns Cathode Assembly Computatonal Models Gun Pototype, Calabazas Ceek, Inc.

12 Non Elastc Collsons n Gas Flled Dode 2D model of collsons * α = M / Mdnσ e 0 Reacton tees J/Jb alpha Cuent multplcaton. Blue 1D model, geen onzaton; ed onzaton+echagng

13 Fequency-doman Electodynamcs Maxwell equatons Integal epesentaton e Geen functons [ ] Integal equatons ote = ωb, oth = ωd + J, e EP = J QG PQ, β αβ ds 2π n S Q, 1 m H P = J Q G P, Q β αβ ds 2π n G = α φ β, φ = cos kr/ R, G αβ m αβ S 2 1 φ αr βr φ 1 φ = αβ kφ kr R kr R R R 1 m m H P = H Q Gη P, Q H Q G P, Q η dsq, Ω4π S 1 m m Hη P = H Q Gηη P, Q H Q G P, Q η η dsq. Ω4π S Q.

14 Egen modes of RF cavtes The codes MAXWELL-2 and MAXWELL-3 can smulate azmuthally hamoncs and 3D modes of oscllatons

15 Tme-doman Electodynamcs Maxwell equatons B t k kαβ ε + αeβ = g 0, Mateal equatons D t k kαβ ε αh β = g J k. J = σ E + J, t, B = µ H H, D = ε E E. k k 0 k k Consevaton law ρ + dv J = c t 0.

16 RF-gun desgn fo LCLS. The code MAXWELL-T UV Lase Lght RF Photonjecto 10 ps, 1 nq bunch dynamcs Electc feld dstbuton Tansvese nomalzed emttance vs. z Space chage dstbuton Space chage pofle

17 Tansvese chage dstbuton At the cathode At the ext

18 Beam Optcs Klyston gun desgn usng dffeent numecal methods U = 500 kv I = 266 A Statonay poblem. BEM. The code POISSON-2. T=5 Non Statonay poblem. FDM + PIC. The code MAXWELL-T, Mesh: 400x500. Np=3500, T= 65

19 Tme-of of-flght flght Mass-Spectomete Potable hgh esoluton TOF MS fo analyss of Geen-house gases Detectos Spal-Quaduple Lens Lens Tempoal Resoluton fo Geen-house gases

20 Dak Cuent smulaton model Feld emsson β E ϕ 6+ ϕ β E J f, t = e, ϕ Seconday emsson σ = Isec / Ip = δ + η+ δ n 1 m ε + n z δ = g zm, g z = z 1 e, gm ε m Seconday emsson spectum Lye-Dekke model

21 SLAC X-band X TW-stuctue 30-cell stuctue, GHz, G=62MV/m Dstbuted mesh fo paellell Mawxell solve Tansent EM-feld. Electc feld oveshoot fo se-tme 15 ns Dak cuent evoluton. Redpmay pat., geen secondaes

22 NLC Dak Cuent Pulse Dak cuent pulses wee obtaned fo the FIRST TIME fom Tack3P smulaton fo dect compason wth measuement 10 ns se tme 15 ns se tme 20 ns se tme Dak 3 pulse setmes nsec nsec nsec Tack3P Expemental data by J.Wang

23 X-Ray spectum smulaton fo Squae bend wavegude X-Ray Attenuaton, Cu - 5 mm Electc feld Magnetc feld En, kev Squae bend wavegude & EM felds X-ay enegy spectum. Expemental data by C. Adolphsen, smulaton by V. Ivanov N Smulaton E, ev

24 Multpactong n supe conductng cavty Multpactong effect s the man facto lmtng feld gadent n SC cavtes MultPac smulatons Tack3P smulaton Meshng fo SNS Cavty G = 59 MV/m

25 Tajectoy equaton Abeatonal appoach * * 1+ ϕ ϕ q 1+ ψ 2 ψ * ψ + 2 0, x y. * = = + * ε + ϕ 2 z 2m ε + ϕ z Feld expanson * * 2 IV ϕ, z = Φ z Φ z+ Φ zl 4 64 Paaxal equaton Φ zu Φ z + ρ z/ ε + q/2 mb z ξ z + + = 0, =. Φ z + ε Φ z + ε 0 z u u u e z z Pncpal tajectoes Abeatonal expanson υ z = 0, w z = 1, υ z = 1/ ε, w z = 1/ R z 0 = ευe + we + εε He + ε Ke + ε Be + εεpe + α β α β 3/2 α α 0 z 0 z z Qe Ce De Fe Ge E L β 2 2 βα α 2 αβ β 3 0εz + 0 ε + + 0ε c

26 Hgh-speed steak camea Infaed mage convete Nght vson glasses X-ay lght amplfe

27 Optmzaton Poblem Objectve functonal Constants { } F0 u, E u, H u mn u U { F,, } u Eu Hu < 0, = 1, n; F u, Eu, Hu = 0, = nn, ; { } Optmzaton doman U: u u + < < u, j = 1, m. j j j Ognal equaton S σ G ds + λσ = U Q PQ Q P P. Equaton n vaatons S δσ λδσ δ σ δ QGPQdSQ + P = UP Q GPQdSQ. S

28 Types of the geomety petubatons

29 Bounday poblems Foue expanson ϕ,, zθ =Φ z + ϕ, zcos[ m θ + θ ] m m m Helmholtz equatons ϕm ϕm 1 ϕm m + + ϕ m = z ρ m wth the bounday condtons ϕ ϕ = U, z; = E, z. m m S1 m m n S 2

30 Algothms of BEM Integal equaton S1 σ Q G P, Q ds = U P ρ t G P, Q dv, σ m P 2 m σ, m m m ρ, m V σ QG PQdS, = E P ρ tg PQdV,. S2 m σ, m m m ρ, m V Kenels G σ, m = 2π 0 cos mθ dθ + 2 cos θ + zz 2 2 2, G [ z z sn ne cos θ cos ne ]cos mθ dθ. [ + 2 cos θ + zz ] 2π z z ν, m = /2

31 Bounday Vaatons fo the Electon Optcal Devce a 1 change of the tube damete; a 2 change cuvatue adus fo the cathode ; a 3 change of the adus fo the anode hole; a 4 change of the oute adus fo the anode cone; a 5 change of the cathode-anode dstance; a 6 change of the cathode-anode dstance

32 30 Non petubed potental and devatves Vaaton of the cathode adus m=1 Petubed feld fo vayng Rc V V' V" V'" V"" V V' V" V''' V"" z, mm -25 z, mm Tlt of the axs m=1 Ellptcal defomaton m= V V' V" V''' V"" V V' V" V''' V"" z, mm -20 z, mm

33 Numecal esults fo the toleant Resoluton mm -1 Cathode da, mm defects a, mm ,25 a a a a a a

34 Stuctual Synthess Classcal appoaches 1. Scheze sees Numecal nstablty; ϕ, z = Φ z, Φ z ϕ0, z 2 = 0! 2 2. Confomal mappng Mappng sngulaty; 2π 1 ϕ, z = f z + cosα dα. 2π 0 3. Fnte-dffeence appoxmaton fo the Cauchy poblem. Numecal nstablty; 4. No addtonal equements lke constant functonals F j ; 5. No toleance analyss.

35 The deal analytcal model and the pactcal Pece gun ϕ, z = C 2 + z 2 2 / 3 cos actg z 1- heate; 2 cathode; 3 focusng electode; 4 anode; 5 ceamc nsulato; 5 collecto.

36 The esults of classcal appoach The absence of techncal constants n classcal synthess poduces the solutons unealzable n pactcal manufactung.

37 New fomulaton of the synthess poblem s suggested 1. Obtan the Cauchy data Φz by mnmzng the objectve functonal F 0; 2. Intoduce 3 types of sufaces: a fxed-shape electodes wth the bounday condtons; b suface wth the Cauchy data and c skeleton suface wth the feld souces chages, dpoles. 3. Detemne the feld souce values fom the soluton of mxed bounday/cauchy poblem; 4. Obtan the electode shape fom the map ϕ =c; 5. Obtan the eal shape n the toleance ange.

38 Algothms of BEM Algothms of BEM Bounday condtons Cauchy data on the axs Integal equatons mxed fomulaton n S ψ s, ϕ β αϕ = +, 0 ϕ Φ = S. 2,,, 2, 2, s d t s G t d t s G t s d t s G n t s d t s G n t s S S πν ν σ πν β α ν πσ β α σ ψ ν σ ν σ Γ + Γ + = Φ Γ Γ + + = Γ Γ+ Γ Γ+

39 Appoxmaton and lnea system Appoxmaton and lnea system Souce appoxmaton wth cubc splne Geen functons sngle & double laye potentals Lnea Poblem n weak fomulaton h t t h M X h t t h M X h t t M h t t M t X + =. cos cos 2 1,, = + + = = e z n z z k E z z ne k K k E z z G z z k K G δ δ πε δ δ πε ν σ mn * * * = R F GX D F G X,, Φ ψ ν σ F X

40 The Synthess of Matchng Lenses Ideal lens Apetue hole a=0.3 Apetue hole a=0.4 Ctcal apetue: a0 = 2 / 31 λ

41 The Synthess of Sngle Lens Ideal Lens Apetue hole a=0.25

42 The Butle Lens Fomng an Ideal Cylndcal Beam W = 0.09 W = 0.2 Beam paametes : U=4KeV; P=0.55µA/V 3/2

43 Summay New appoaches n fomulaton fo complex poblems of analyss, optmzaton and synthess ae suggested; Set of pecson methods and algothms ae mplemented. The effectveness was demonstated fo dffeent applcaton aeas; The numecal tools and compute codes fo 2D and 3D poblems ae successfully used n pactcal desgn dung moe than 30 yeas. Many unque devces have been constucted usng numecal desgn.