Some features of accelerating section field computation presented by the development of power and HOM couplers for TESLA linear collider are considered. The devices mentioned produce electromagnetic field asymmetry in the beam area, thus causing transverse kick. For this kick and its influence on beam under acceleration parameters estimation the dynamics modelling calculations were done. 3D-simulation code MAFIA was used for field computation. These data were further used in beam dynamics calculations by means of TRMTrace code. Standing wave mode was simulated while considering HOM couplers, and travelling wave in case of power couplers. Transverse kicks and focussing forces are calculated for one HOM coupler design and two coaxial FM couplers

Dohlus, M.

Kostin, D.V.

Lalayan, M.V.

Shvedunov, V.I.

Sobenin, N.P.

Zavadtzev, A.A.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

ELECTROMAGNETIC FIELDS AND BEAM DYNAMICS SIMULATION FOR THE SUPERSTRUCTURE OF TESLA LINEAR COLLIDER CONSIDERING FIELD ASYMMETRY CAUSED BY HOM AND POWER COUPLERSM.V. Lalayan,  D.V. Kostin, N.P. Sobenin, V.I. Shvedunov1, A.A. Zavadtzev2, M. Dohlus3MEPhI (Technical University),1 Scientific Research Institute JAF of the Moscow State University,2 RTI Russian Academy of Science,3 DESY (Germany)Some features of accelerating section field computation presented by the development of power and HOM couplers for TESLA linear collider are considered. The devices mentioned produce electromagnetic field asymmetry in the beam area, thus causing transverse kick. For this kick and its influence on beam under acceleration parameters esti-mation the dynamics modelling calculations were done. 3D-simulation code MAFIA was used for field computa-tion. These data were further used in beam dynamics calculations by means of TRMTrace code. Standing wave mode was simulated while considering HOM couplers, and travelling wave in case of power couplers. Transverse kicks and focussing forces are calculated for one HOM coupler design and two coaxial FM couplers.PACS numbers: 29.27.Bd, 71.15.Pd1  INTRODUCTIONThe superstructure layout according TESLA collider scheme proposal [1] is shown in Fig. 1, where one could see the FM coupler along with HOM couplers position. Estimation  of  the  transverse  kick  seen  by  a  particle moving through asymmetry field regions was based on field components obtained by MAFIA electromagnetic modelling code.  Then the values  of  field  components were exported to RTMTRACE code, and by means of it the dynamics calculations of the beam under accelera-tion were performed.Fig. 1. Superstructure layout with FM and HOM couplers positions.For correct beam dynamics simulation while moving through  accelerating  structure  one  must  consider  the electromagnetic fields in relatively long part  of it.  To avoid excessive memory consumption and long compu-tation  time  the  full  superstructure  model  was  divided into separate parts with computation followed by fields merging. The following elements were used: cavity end cell with drift tube and input coupler attached, two half-cells and drift tube with HOM coupler, and cavity mid-dle cell. Latter two elements computation was done in SW mode using MAFIA’s eigenvalue solver module. In the  input  coupler  region  the  electromagnetic  wave  is travelling, and in order to make a correct evaluation one have to apply another approaches.a) FM3 b) FM5Fig. 2. End cell with two types of input couplers.Fig. 3. Two half-cells and HOM coupler.2  TW FIELDS COMPUTATIONTwo different  ways were used to solve this task - two  standing  waves  combining  method  and  the  one based on time-domain computation.Models used in each case were the same in order to make  the  results  comparable.  Considerable  attention was put to obtain model’s azimuthal symmetry in order to  eliminate  pretended  field  unsymmetry  effects.  But quadrupole effects could not be completely eliminated because of MAFIA’s way of rounded borders approxim-ation with straight lines.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №3.Серия: Ядерно-физические исследования (38), с. 138-140.1382.1  Two standing waves combining methodTravelling wave in coaxial  input coupler  could be treated as two standing waves interferention. To get the correct  simulated  fields  vales  it  is  sufficient  to  apply two types of boundary – magnetic and electric one in coaxial  line,  provided  the  reference  plane  position  in line is  chosen correctly.  For this task one could only deal with eigenvalue problem, solvable by many well-developed codes, for example by E module of MAFIA.Reference  plane coordinate is to be chosen so that the frequencies fe, fm, and operating frequency fo were equal (fe = fm = fo), where fe  – frequency corresponding to electrical boundary conditions in reference planes 1 and 2, fm - the same for magnetic ones.                     Reference plane 1reference plane 2Fig. 4. Input coupler model with reference planes positions showed.At the second stage travelling wave fields in input coupler are computed. This computation uses two fields components: Еx,y,z(e) , Bx,y,z(e) for electrical boundary con-ditions in reference planes, and Еx,y,z(m) , Bx,y,z(m) for mag-netic ones, obtained by two MAFIA runs. The following normalising procedure is essential: the Еz мах(е)  и Еz мах(m) components maxima along coaxial line inner conductor surface (at z = r) are to be equal.  After this the field amplitude and phase of travelling wave in coaxial wave-guide calculation became possible.( ) ( ) 2)m( z,y,x2)e( z,y,xz,y,x EEE += =ϕ )e(z,y,x)m(z,y,xz,y,xE EEarctg( ) ( ) 2)m( z,y,x2)e( z,y,xz,y,x EBB += =ϕ )e(z,y,x)m(z,y,xz,y,xB BBarctgIn order to make an Еx,y,z and Bx,y,z amplitudes corres-pond to some power P transmitted along the waveguide the second normalisation is to be done. In the reference plane  1  vicinity  one  should  calculate  the  following factor( )rRlnP120rrz,y,0xEz2⋅⋅===αand then divide all Еx,y,z and  Bx,y,z  amplitudes by it.2.2  Method using MAFIA T3 module for TW fields calculationModel  used  for  calculations  consisted  of  one  cell with magnetic boundary placed at the iris, drift tube and the coaxial coupler, all having the geometry like corres-ponding TESLA ones. Drift tube was long enough to the field considerably decayed along it.Because  of  very  small  coupling  the  only  way  to solve this problem using MAFIA is to reverse the power flux. The field excitation was realised by two currents. They are high-frequency Gaussian pulse modulated sine with determined pulse width of 300 MHz. At the first stage the frequency of this signal has been chosen equal to 1300.0 MHz, which is  close to yet  unknown reso-nance frequency.Excitation currents pass the cell parallel to the beam axis  with  each  having  45  degrees  off  the  symmetry plane with the displacement equal to the drift tube radi-us (see Fig. 6). Two beams were used during the calcu-lation because in the task description for MAFIA it is not allowed to have magnetic boundary and beam on the same  plane.  Otherwise  we could  have  used  only  one beam passing the model along cavity axis.As it  was already mentioned,  at  the  first  stage  of computation the excitation pulses frequency was chosen just close to resonance, and signal propagating along the coaxial line was of interest. This signal was obtained by placed in coaxial line virtual monitor – special MAFIA means for calculation data storing during the time integ-ration loop.Having pulse length determined one could get excit-ation pulse length (tpuls), and take into account for the later treatment only part of output signal, in the region from about 1.2 ⋅ tpuls  to 3 tpuls. Applying harmonical ana-lysis to this signal we could determine the exact reson-ance frequency of excited oscillations, those apparently became free after excitation pulse ended. This was done by determining a complex function( ) ( ) t*fest*2*ie*f*41tAitAf,tCestestpi−−⋅+= ,where A(t) is the output signal, fest is the estimation for the resonant frequency.Proper choose of this estimation gives us a constant argument of  C(t,  fest).  During the second MAFIA run fields in the entire volume were monitored after the ex-citation pulses pass. Signal decreasing has substantially low rate, so one could put the amplitude to be constant in some short time period. Using special MAFIA means having resonant frequency known online vector Fourier transformation was performed, thus providing us travel-ling wave fields.3  BEAM DYNAMICS CALCULATIONWhile  beam  dynamics  calculating  transverse  kick could be treated as following [4]:)yxxy(S)yyxx(Q)yyxx(FyDxDp0000000y0xt++−+++++=∆where  tp∆  - transverse kick,  00 , yx - unit vectors for horizontal and vertical plane, x, y - initial particles dis-placements, Dx, Dy - dipole kick components, F, Q, S - azimuthal,  quadruple  and  skew  quadrupole  focussing strengths,  all  but  F  are  energy-independent.  Thus  the simulation  results  obtained for  some energy could be applied to the cases having other beam energy. All the simulation were done assuming the particles are elec-trons with charge sign taking into account. Beam energy 139on particles phase with respect to field dependence al-lows us to derive a transverse kick to maximal accelera-tion phase relation. For the estimation HOM and FM couplers shares in transverse kick independent simula-tions  were  done  for  the  superstructure  having  five identical HOM couplers and the one with input coupler of different constructions.Fig. 5 illustrates simulation done by the RTMTrace code for the energy of particles leaving superstructure (a) dependence on their initial phase along with dipole momentum (b) computed for the input coupler construc-tion #5 and both dependencies approximation by cosine function.a. b.Fig. 5.In Table 1 the simulation results for HOM couplers and two variants of input coupler are presented.Table 1. Transverse kick dipole components and quad-ruple focussing strengths for different couplers.Coupler type Dy0, KeV/sϕDy0 Q0, KeV/s/mϕQ0HOM, SW 6.7±0.1 3930 212±7 2180FM #3, SW 1.4±0.1 1250 40±7 2930FM #3, TW 2.3±0.1 1290 69±7 2910FM#5a TW 11.7±0.1 930 337±7 2660In  order  to  make  these  results  easily  comparable they were normalised for the same energy gain by the superstructure equal to 60 MeV having initial  particle energy of 100 MeV. Besides in each case the reference plane for particles phase definition was placed with its offset of the first cell centre corresponded to maximum acceleration at ϕ = 180o.For input coupler #3 the simulation results for TW and SW calculations  are presented.  These  cases  have close transverse kick phase values, but 1.6 to 1.7 times differ in its amplitude. Taking into account an asymmet-rical  field component high sensitivity to the reference plane  position  in  the  input  coupler  simulations  using SW mode we assume these results of less accuracy and exclude them from further analysis.Transverse kick caused by the input coupler was es-timated  also  by  travelling  wave  field  integrals  using MAFIA  code  means.  Transverse  kick  absolute  value calculated using the integral for field normalisation ac-cording  to  Table  1  data  is  2.37  KeV for  coupler  #3 which is pretty close to Dy0 values. It is worth to be men-tioned that only a dipole kick component could be es-timated using integrals along the beam axis calculation.For asymmetric component role studying the trans-verse kicks and focussing strengths corresponding to a particle phase of maximal acceleration are of significant interest. These data are presented in Table 2.Table 2. Transverse kick dipole components and quadruple focussing strengths for different couplersCoupler type Dx0, KeV/sDy0, KeV/sQ0, KeV/s/mS0, KeV/s/mHOM, SW -1.1±0.1 -5.6±0.1 167±7 14±7FM, #3, TW – 1.4±0.1 -25±7 –FM, #5a, TW – 0.6±0.1 23±7 –4  CONCLUSIONSInput coupler #5 has the largest transverse kick amp-litude and quadrupole focusing strength, but at the phase corresponding to maximal acceleration these parameters values  for  HOM  couplers  are  greater  than  for  input ones. For example trajectory tilt angle at the end of su-perstructure caused by HOM couplers for the beam in-jected along it axis will be about 50 µrad and focal dis-tance about 6⋅105m. Transverse kick caused by couplers to the particles bunch under acceleration couple be par-tially compensated with beam correctors. Most danger-ous with respect  to  emittance dilution is  the kick de-pendence on the particles position in the bunch. Trans-verse kick dependence on particle phase in the bunch could  be  evaluated:  dDy/dϕ =  –Dy0sin(ϕ+ϕDyo).  This value for three couplers mentioned in Tables 1 and 2 is 3.6,  1.8,  11.7  KeV/s/rad,  respectively.  Assuming  the bunch having the length of 1 mm at the superstructure entrance (phase length of 0.027 rad) one could estimate transverse kick in bunch occupied region, dσDy = 0.097, 0.049 and 0.320. To make normalised mean-squared re-spective emittance growth we could use the following expression  [5]:  dεn,y/εn,y =  dσDy/σpy.  Impulse  mean-squared  scattering  for  the  bunch  to  be  injected  in TESLA collider is  σpy ≅ 1.5 KeV [5]. So, the relative transverse  emittance  growth  after  the  superstructure passing by a bunch in maximal acceleration phase is 6, 3, 21% and of this reason the input coupler construction #5 is less suitable.REFERENCES1. J.Sekutowicz  et  al.  Superstructure  for  TESLA  // Phys.Rev.Special Topics, 1999, v. 2, p. 062001.2. V.I.Shvedunov et al. PTMTRACE // VINITI. 1989, N 183-В89.3. M.Dohlus,  S.G.Wipf.  Numerical  investigations  of waveguide  input  couplers  for  the  TESLA  super-structure  //  Proceedings  of  EPAC,  2000,  Vienna, Austria, p. 2096-2099.4. Z.Li,  J.J.Bisognano  and  B.C.Yunn.  //  Proc.  of  PAC’93, p. 179.5. M.Zhang and Ch.Tang. TESLA 98-17.140

Electromagnetic fields and beam dynamics simulation for the superstructure of TESLA linear collider considering field asymmetry caused by HOM and power couplers

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Electromagnetic fields and beam dynamics simulation for the superstructure of TESLA linear collider considering field asymmetry caused by HOM and power couplers

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