Lab Report TEMF, TU Darmstadt

Transcription

1 Fachgebiet Theorie Elektromagnetischer Felder Lab Report Wolfgang F.O. Müller Thomas Weiland TESLA Collaboration Meeting Daresbury, 09/23/02 Technische Universität Darmstadt, Fachbereich Elektrotechnik und Informationstechnik Schloßgartenstr.. 8, Darmstadt, Germany temf.tu-darmstadt.de,

2 Outline PITZ-RF-Gun Dark Current Simulation Solenoid Simulation Design Study of a Booster Cavity Ensemble Model Beam Dynamics Calculations High Frequency Wakefields HOM-Damper for THz-Wakefields Surface Roughness Wakefields New Code for Wake Potential Calculation RF-Calculations on Deformed TESLA Cavities 1

3 2 Simulation of Dark Currents PITZ RF-Gun Mathematica RF-Gun Boundary Description (3D) x - Position / cm z - Position / cm x y z

4 3 Dark Currents Dark Current Density at Gun Exit vs. Initial Phase

5 Dark Currents 4 Particles Positions and Dark Current Density at Gun Exit Current Density / a.u.

6 Simulation parameters: cathode position bucking solenoid centre position main solenoid centre position mesh points solver time z cath = 0 mm z buck = mm PITZ Solenoid Simulation with CST EM Studio z main = mm 285,696 < 3 min (PIII 933 MHz) z-axis cathode position main solenoid N main = 109 I main = 200 A bucking solenoid N buck = 57 I buck = 103 A 5

7 Magnetic Field on Axis 0.02 Scaled Measurement EMS Simulation Measurement: I. Bohnet, DESY-Zeuthen 6 B z / Tesla z z / mm ( B z / B z,max ) / % Relative Deviation of Simulation from Measurement z / mm

8 Design Study of a Cut Disk Structure (CDS)asBoosterforPITZ MAFIA model Valentin Paramonov Institute for Nuclear Research Moscow, ,258,884 meshpoints 7 MWS model 47,915 meshpoints per cell

9 8 2 cells Accelerating Field in CDS drift tubes coupling cell Ez / arb. u. coupling cell coupling window accelerating cell accelerating cell accelerating cell z / mm

10 mid-cell r Frequency Optimisation r midcell = mm f midcell = GHz end-cell r endcell = mm f endcell = GHz 9

11 Field Flatness three cell cavity Field Flatness not optimised: 1.5 % frequency optimised: 0.1 % 10 E z / arb. u z / mm not optimised frequency optimised

12 Ensemble Model for Beam Dynamics Simulations Ensemble described by 27 parameters: 6 phase coordinates of the center and 21 second order moments 11 Ensemble Parameters r r ξ = ξψ dr dp, ξ = x, y, z, px, py, pz r r Mξν = ξ ν = ( ξ ξ )( ν ν ) ψ drdp rr ψ = ψ( tr,, p) is Ensemble Distribution Function Simulation of collective effects with Single Ensemble Multi Ensemble Model for simulation of nonlinear effects beam r d p ( ) d ct r d ( ) d ct r r r = F = Wˆ ( r, p ) r p ensemble ensemble ensemble ensemble ensemble Governing Equations dmˆ d ct pp X P X P = FMxp + FMpp + ( FMxp + FMpp ) ( ) T xp X P = pp + xx ( ) + xp ( ) ( ) ( ) ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ, dmˆ T VM ˆ ˆ M ˆ F ˆ M ˆ F ˆ, d ct dmˆ d ct xx = M ˆ V ˆ + VM ˆ ˆ The Multi Ensemble Model allows for space charge simulations A Multi Centered Gaussian Expansion is being developed xp T xp T

13 Simulations of the Beam Longitudinal Phase Space Simulation of longitudinal phase space development in a drift space: The Single Ensemble Model (SEM) shows no longitudinal emittance growth The Multi Ensemble Model (MEM) is conform to ASTRA 100 kev RMS Energy Spread Interface ASTRA SEM MEM* z / m 20 mm-kev Longitudinal Emittance ASTRA SEM MEM* z / m 12

14 RF-Gun + Drift Space Interface: Conventional Tracking Particles -> Ensembles Particle Distribution Function Ensembles Envelope Particle Distribution Function particles variables Ensembles Envelope 7 Ensembles 189 variables 13

15 Absorption models for HOM-absorbers 14 Power deposition per accelerator module due to wake fields: 12.7 W at f > 10 GHz coaxial HOM-absorbers between the modules operative at 70 K shall absorb > 90% of this power. planned material: Mo grains embedded in Al2O3 Ceramics Absorption believed to be magnetic. grain size determines absorption characteristics Existing absorption measurements: at 70 K for f < 13 GHz at room temperature for f < 40 GHz scetch of coaxial HOM-absorber (from M. Dohlus) Current investigation: Will the anomalous skin effect influence absorption characteristic (and needed grain size) at higher frequencies?

16 New Literature concerning the Thin Dielectric Layer Model Surface roughness wakefield measurements at the Brookhaven Accelerator Test Facility F. Zhou, J.H. Wu, X.J. Wang et al. "see above" Proc. EPAC 2002, Paris. smooth vacuum tube: diameter = 6mm length = 970mm artificial roughness on inner surface: metal drops # per cm² = 16 height = 0.6mm diameter = 1.2mm schematic view of the rough surface (bumps should be more dense) (from K. Bane, G. Stupakov, slac-pub 8023) wavelength of the rough tube mode according to TDLM is roughly the same as the distance between adjacent bumps. TDLM not applicable to this geometry. The observed difference in behaviour of periodic and random structures is suspected to be due to poor statistics 15

17 New Literature concerning the Thin Dielectric Layer Model (cont.) Analytic calculation of surface roughness wake fields for rectangular geometry. A. Mostacci et al.: Wakefields due to surface waves in a beam pipe with a periodic rough surface. PRST-AB, Vol 5, (2002) 16 Existence and frequency of rough tube mode (RTM) comparable to Timm-Novokhatski-Weiland-model but: Amplitude of RTM is predicted to be two orders of magnitude lower than Timm-Novokhatski-Weiland-model (allowed roughness depth < 10 m vs. < 100 nm!!) Current work: Decide between different predictions by MAFIA-T3 simulations. (Results not yet available.)

18 j = cρ A New Code for Wake Potential Calculation r ϕ z 17 A new code for calculation both longitudinal and transversal wake potentials of very long smooth structures TBCI, ABCI MAFIA-T2/3 / grid dispersion / staircase geometry approximation / moving mesh the new scheme - zero dispersion in longitudinal direction. - staircase free (second order convergent) - travelling mesh easily (mesh step is equal to time step) For the pure longitudinal case (m=0) and staircase approximation the new scheme is reduced to the Novokhatskis algorithm

19 Implicit scheme r ϕ z longitudinal direction transversal plane Discrete curl operator is split 0 P z 0 C2 = Pz Maxwell s Grid Equations C= C1 + C2 0 0 P ϕ C1 = 0 0 Pr Pϕ Pr 0 ) d ) ) d ) ) ) ) ) ) ) Ce= b, Ch % = d+ j, Sb= 0, Sd % ) = q, e= M 1d, h= M 1b ε µ dt dt Implicit Time Stepping ) ) ) ) ) n n ) n+ 12 ) n+ 12 ) n 12 T n T n n h = h tm 1Ce, e = e + tm 1( C1h + C2h j ), µ ε ) ) ) ) n n+ 1 n n 1 h θh + (1 2 θ) h + θh 18

20 Implicit scheme Vector Potential Formulation Implicit Scheme for Vector Potential ( θ ) ( θ θ ) ( θ ) ( θ θ ) n n n n n n n I + T a = 2 a a T (1 2 ) a + a La + F, F = I + T a + 2 a a T (1 2 ) a + a La, n n n n n n n T = t M CM C, L = t M CM C, 2 T 2 T µ ε µ ε 2 tn tn n 1 = sdτ, 0 0dτ, S 1 a = h µ 0 + a = n a h ) ) M ( a ) 0 Stability Condition (spectral) c t = z Implicit Time Stepping c t z, 0.25 θ. magic time step the scheme features zero dispersion in longitudinal direction 19

21 Wake for long collimator 20 r NOT to scale!! 40mm 4900mm 10mm 10mm z V pc -2-4 Wake potential of a collimator staircase σ / h = 5 σ / h = 10 σ / h = 20 analytical conformal σ / h = 5,10, The figure demonstrates the wake potential for a collimator of 490 cm length and the bunch with σ = 0.1 cm. The solution is compared to the analytical estimation. The conformal scheme shows second order convergence and gives results of high accuracy with only 5 mesh steps per s. Note that the staircase scheme in the last example gives at the same resolution an error in excess of 300 %. z σ

22 Wake for TESLA cryomodule W(s) / V/pC r/cm without bellows with bellows s/cm Longitudinal wake for one cryomodule, σ = 1 mm 100:1 30:1 10:1 1:1 z/cm

23 22 Mechanical Deformation Calculation for TESLA Cavities Elongation of 1 mm Calculation by Huimin Gassot

24 23 Deformation times 10 1mm

25 24 Deformation times 100 Stiffening Ring

26 25 Import in CST MicroWave Studio with Splines

27 26