Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and acceleration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing influence (RF focusing concept). Investigation of intensive ribbon beam dynamics features is carried out. The space charge effects are studied numerically by means of "super particles" approach. The proposal of 80% transmission 1 A limit current ribbon beam accelerator for the ITER neutral injection system and some another applications is presented

Masunov, E.S.

Polozov, S.M.

Vinogradov, N.E.

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

SPACE CHARGE EFFECTS AND RF FOCUSING OF RIBBON BEAM IN ION LINACE.S. Masunov, N.E. Vinogradov, S.M. PolozovMoscow State Engineering Physics Institute,115409, Kashirskoe Shosse 31, box 14, Moscow, Russiamasunov@dinus.mephi.ru.Version of the plane structure ion linac which is designed for intensive low energy ribbon beams bunching and ac-celeration is considered. Transverse stability is achieved by the use of nonsynchronous field harmonic focusing in-fluence (RF focusing concept). Investigation of intensive ribbon beam dynamics features is carried out. The space charge effects are studied numerically by means of ″super particles″ approach. The proposal of 80% transmission 1 A limit current ribbon beam accelerator for the ITER neutral injection system and some another applications is pre-sented.PACS numbers: 41.75.L, 41.85.E, 29.27.F1  INTRODUCTIONUsing of a neutral injection system (NIS) is known to be effective way to heat  thermonuclear plasmas. It can be realized as a combination of a high intensive ion beam linac with funneling and stripping systems. Ap-plying of the well-known RFQ linac is not suitable for this  purpose  because  of  the  insufficient  output  beam current. Early in [1] it was suggested to use the undula-tor linear accelerator of a ribbon D −  beam. Applying of plane  structures  with  ribbon beams has  the  following specific features: 1) large value of bunch cross-section allows to  increase greatly  the output  current;  2)  large beam surface is convenient for effective neutralization; 3) it is suitable to combine the plane channel and high-intensity ion source. The most of aspects of the undula-tor accelerator design was investigated in [1]. In the pa-per [2]  studying intensive ribbon beam dynamics was carried out in the 2D model. In this paper concept of the RF focusing intensive ribbon beam accelerator  is  dis-cussed.  Space  charge  effects  are  investigated  in  3D model. Differences between this kind of accelerator and the undulator accelerator are considered.2  PARTICLE MOTION EQUATIONThe acceleration system discussed is supposed to be realize as an interdigital H-type structure. It consists of a cavity, some vanes inside it and a number of electrodes alternatively connected to the vanes.  Usually only the ribbon beam thickness keeping is investigated To create the RF field components which can provide the trans-verse focusing along the ribbon width it is suggested [1] to  apply the curved electrodes  of  a  special  form (see Fig. 1). Let us assume the beam to interact with only two space harmonics of the RF field. Then the field po-tential can be presented asU U k x k y h dz tp xpyppp s n= ∫∑=ch( ) ch( ) sin( ) cos( ),ω . (1)Here  s,  n are  numbers  of  synchronous  and  nonsyn-chronous harmonics respectively; U p  are harmonic am-plitudes;  k xp ,  k yp ,  hp  are  wave  numbers; h p Dp = +( ) /µ pi2 ,  µ is the phase advance per period of the structure D . Formula (1) determines the RF field of the structure considered. The motion equation in this field in a smooth approximation can be obtained using the  averaging  method  [1].  In  the  single  particle  ap-proach does not  taking into account the space charge field it givesddU eff22RRτ∂∂= −   ,                 (2)where U eff  is the effective potential function which can be expressed as U U Ueff = +0 1 ,[ ]U ezs0 12= − + −ch( ) ch( ) sin( ) cosρ η ψ χ χ ψ  , (3)Ue ens nps pp s n122221161 1161=−+−− +=∑ ∆ ∆, ,,.Here [ ]R = ρ η χ, , ,ee k X k Ye k X k Ye k X k Ypxpxpypypxpypxpxpyp=sh( ) ch( )ch( ) sh( )ch( ) ch( ),  ee Emcx y zp x y zpc, ,, ,=λpi β2 2  are the  dimensionless  field  harmonic  amplitudes, ρ piλ β=2cX ,  ηpiλ β=2cY ,  χ ω ψ= − −∫ h dZ ts ,  X, Y, Z  are the slowly varying coordinates,  ψ  and  β c  are the synchronous  particle  phase  and  velocity  respectively, ∆ s pp ssh hh,±=±.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.Серия: Ядерно-физические исследования (39), с. 71-73.71Fig. 1. The plane structure.Effective  potential  function (3)  determines  the  3D beam motion completely.  Term  U 0  describes interac-tion of particle with synchronous harmonic accelerating and defocusing the beam. Summand U1  evaluates only the transverse focusing and is being independent of the synchronous particle phase. The form of equation (2) al-lows the Hamilton analysis to be used. Existence of a total  minimum of  the  function  U eff  is  the  necessary condition  of  simultaneous  transverse  and  longitudinal focusing. Expanding the U eff  near the synchronous par-ticle coordinate one can formulate this condition in the formω χ2 0> , ω ρ2 0> , ω η2 0>  ,          (4)where ω χ , ω ρ , ω η  are frequencies of small longitudi-nal  and transverse oscillations.  If  the condition (4)  is satisfied, the effective potential function U eff  is the 3D potential well in the bunch frame. Therefore, in the RF focusing ribbon beam accelerator discussed the particle energy gain is  achieved by affecting the synchronous wave field. The ribbon transverse stability is achieved using the focusing influence of a nonsynchronous field harmonic (RF focusing concept).3  CHOICE OF CAVITY PARAMETERS3.1  RF field harmonic structureSo, for the plane structure  k kxpyp< < ,  one can as-sume  e e eypzpp≅ ≡ ,  p=s, n.  Because of the shielding effect (i.e. interaction between bunch space charge and channel  walls)  the  defocusing  influence  of  Coulomb field along the ribbon width is weak. The focusing in this direction is  provided using the curved electrodes. The focusing condition ω η2 0>  can be presented in the formα ψ χ αsin( ), ,+ < + +− +121 1 12 422 22 2e hhens n s nnsn∆ ∆, (5)where α ≡ e es n/ . Formula (5) defines the value of the parameter  α which allows the transverse stability to be achieved for all values of particle phase. It can be seen from condition (5) that  a large phase capture under a good transverse focusing may be  obtained if  α < < 1 . On the other hand, this parameter is bounded below be-cause the acceleration gradient  dW dz En/ . cos= 0 5α ψ  is proportional to α. Parameter en  also defines the value of the frequency ω η . The value of en  is bounded above by a sparking criteria. Formula (5) also gives that the RF focusing is more effective in the case of low beam velocity. One can optimize the set {s, n,  µ} calculating value of  ω η  at fixed  α,  en ,  ψ. The system providing the most strong transverse focusing is to be chosen. It should be noted that structures with a large harmonic number are not effective. Firstly, realization of systems with p>2, p=s, n is hardly possible since it is necessary to set many electrodes per structure period. Secondly, the value of the field amplitude which corresponds to separatrices overlapping decreases fast versus growth of harmonic number. It may lead to longitudinal instabili-ty. One can see from (5) that if the inequality α < < 1  is satisfied, systems with s>n are ineligible because of in-sufficient transverse focusing. For the cavity parameters we consider (see below) the acceleration structure {s=0,  n=1,  µ=pi} is to be regarded as the best. The optimum ratio k kxpyp/  can be obtained using a computer simula-tion of beam dynamics. For the cavity parameters of ac-celerator discussed (see below), the transmission coeffi-cient is maximal if k kxpyp/ =1/23. In this case the trans-verse frequency  ω ρ  is very small. Actually, the beam particles do not have time to complete even one oscilla-tion along the ribbon width. It means that such a plane structure can be considered as an analogy of multibeam system.3.2  Acceleration channel parametersLet the acceleration cavity consists of two subsec-tions: the gentle buncher subsection and the acceleration one.  In  the  gentle  buncher  the  synchronous  particle phase decreases linearly from  ψ=pi/2 to some nominal value and the RF field  amplitude  increases  as  a  fair-curve. Here the beam is being bunched carefully and ac-celerated insignificantly. In the acceleration subsection these parameters are fixed making the bunch to gain the necessary energy. The approach described allows to en-large  the  transmission  coefficient  greatly.  During  the bunching process the averaged separatrix is slowly de-formed. In the undulator ribbon beam accelerator [1] RF field inside the channel is primary transversal. So fast oscillation amplitudes of a longitudinal coordinate and velocity are very small, and difference between the lon-gitudinal motion in phase space and its smooth approxi-mation is  insignificant.  Therefore the phase motion is not very sensitive to the slow changing of cavity param-eters. In the accelerator of this type to achieve a large transmission the field amplitude versus longitudinal co-ordinate  in  the  gentle  buncher  can  be  chosen  as  any growing function (for instance, it may be proportional to sine). In the RF focusing ribbon beam accelerator dis-cussed here the RF field in the interaction area is prima-ry longitudinal. In this case fast oscillation amplitudes of a longitudinal coordinate and velocity are not small, and transmission is very sensitive to the choice of the field amplitude as a function of the longitudinal coordi-nate. The reason is loosing of bunch particles with ve-locities of large fast oscillation amplitudes from within the deforming separatrix. In paper [3] a special method of gentle buncher parameter choice for the acceleration system with a primary longitudinal RF field was sug-gested. It is based on the concept of longitudinal limit current nondecreasing. Value of this characteristic is ap-proximately proportional to longitudinal acceptance. To provide a high transmission the longitudinal acceptance should  be  increasing  function.  This  statement  defines the  relationship  between  the  field  amplitude,  syn-chronous particle phase and beam velocity in the gentle 72bunching  subsection.  Such  approach  can  be  used  for cavity parameter choice in the RF ribbon beam accelera-tor described. The electrode form depends on the equi-librium particle velocity and is defined by relationship ( ) ( ) ( )k k hxpypp2 2 2+ = ,  p=s, n, which can be derived from Maxwell’s equations. The ratio  k kxpyp/ =const is the system parameter. Construction of the structure peri-od is  defined by the phase  advance  µ and harmonics number  s, n. The form and size of electrode cross-sec-tions should provide the necessary harmonic spectrum of the RF field. It can be obtained by computer simula-tion in the 2D model.4  NUMERICAL SIMULATIONThe  computer  simulation  of  high-intensity  ribbon beam dynamics in the plane structure described was car-ried out by means of the  ″superparticles″ method. The Coulomb  field  is  calculated  using  the  Cloud-in-Cell method. Here the space charge density is computed on the grid which is set into the bunch area. The Poisson equation  on  the  grid  is  solved  using  the  fast  Fourier transform. Gentle buncher parameters (see Fig. 2) were optimized numerically by means of the component-wise descent method. The starting parameters for computer optimization were calculated by the approach described in previous chapter.Fig. 2. Gentle bunching subsection parameters.Fig.3. Dimensionless space-charge filled potential  without taking into account (1) and with taking into account (2) the shielding effect.It was shown that for acceleration of a high-intensity beam the  shielding  effect  is  significant.  This  circum-stance is very important for large transmission obtain-ing.  Fig.  3  shows  the  difference  between  the  space charge field potential with and without shielding effect. Table 1 contains results of computer simulation. It can be seen that the RF focusing ribbon beam accelerator which is suggested in this paper provides a high trans-mission under a  large input current.  Fig. 4  shows the transmission coefficient versus input current. It  proofs the efficiency of the plane structure using for high-in-tensity beam acceleration. To test the averaging method applicability  the  computer  simulation  was  carried  out for both RF field and averaged one. All results obtained in a smooth approximation and for the RF field coincide up to 5-10%.Fig. 4. Transmission versus input current, A.Table 1. Numerical simulation results.Parameter ValueOperating frequency, MHz 150Parameter α 0.1Maximum field amplitude Emax , kV/cm 280Input/Output Energy, MeV 0.1/2.0Total length, m 3x-aperture, cm 0.2y-aperture, cm 55  CONCLUSIONThe RF focusing ribbon beam accelerator concept is discussed. Methods of transmission coefficient increas-ing are suggested. High intensity ribbon beam 3D dy-namics is studied by means of computer simulations. It is shown that applying of RF focusing plane structure for intensive ion beam acceleration allows to realize a 1 A output current under more than 80% transmission.REFERENCES1. E.S.Masunov //  Sov.  Phys.  –  Tech.  Phys.  1990, v. 35, № 8, p. 962-965.2. E.S.Masunov, A.S.Roshal. // Proc. of the 1997 Par-ticle  Accelerator  Conference,  Vancouver,  BC, Canada, May 1997, v. 3, p. 2835-28373. E.S.Masunov,  N.E.Vinogradov.  //  Phys.  Rev.  ST Accel. Beams. 2001, No 7, 070101.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2001. №5.Серия: Ядерно-физические исследования (39), с. 73-73.73

Space charge effects and RF focusing of ribbon beam in ion linac

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Space charge effects and RF focusing of ribbon beam in ion linac

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