LATTICE BEAM DYNAMICS STUDY AT LOW Β FOR SARAF/EURISOL DRIVER 40/60 MEV 4 MA D&P SUPERCONDUCTING LINAC

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1 WGB5 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA LATTICE BEAM DYNAMICS STUDY AT LOW Β FOR SARAF/EURISOL DRIVER 4/6 MEV 4 MA D&P SUPERCONDUCTING LINAC J. Rodnizki, B. Bazak, D. Berkovit, G. Feinberg, S. Halfon, A. Pernick, A. Shor, Y. Yanay, Soreq, Yavne 88, Irael Abtract In thi tudy we examine a lattice for the SARAF uperconducting (SC) linac at the low- range. The SC Half Wave Reonator cavitie in the firt cryotat are optimized for a geometric =.9 and hence the =.567 ion coming from the RFQ are mimatched. We developed a emi adiabatic tuning method for the low- portion of the SC linac. The guideline were derived from the tudy of two linac lattice that were conidered for the SARAF 4 MeV proton and deuteron linac, extended up to 6 MeV for the low energy part of the EURISOL driver. Simulation were run uing the TRACK and GPT code. The lattice were teted for energy gain along the linac, emittance growth and acceptance. Further, error run in GPT uing a tail emphai technique to enhance tatitic by focuing on the bunch tail allowed u to examine compatibility of the lattice with hand-on maintenance requirement. Our tudy may be relevant for other linac that begin with SC cavitie immediately following the RFQ, uch a SPIRAL, and perhap alo for IFMIF which i deigned to tart with imilar mimatch at the low- range. INTRODUCTION In thi tudy we examine a lattice for the SARAF [] uperconducting (SC) linac at the low velocity () range. The accelerator at SARAF i compoed of an ion-ource, a 4-rod 76 MHz.5 MeV/u RFQ and a 4 MeV proton and deuteron SC linac. The SC accelerator i decribed in detail in [] and the accelerator front-end in [,4,5]. Motivated by the lower contruction and operation cot, the SARAF linac tart with SC independent phae -gap HWR cavitie, right after the RFQ. The common olution of DTL in thi tranition (between the RFQ and the SC linac) wa rejected in order to have an efficient high energy gain acceleration of a large range of ma over charge ratio (M/q= ) ion. The SC Half Wave Reonator (HWR) cavitie at the firt cryotat are optimized for a geometric =.9 and hence the =.567 ion from the RFQ are mimatched. The development of an additional SC cavity with at the range of.6 at 76 MHz eemed to be technically complicated due to inner urface treatment in uch a narrow gap ize. The effort to accelerate light ion at the low- range with SC linac in a high acceleration rate i limited by the induced trong longitudinal focuing force [6]. High accelerating gradient could introduce high longitudinal phae advance reulting in beam loe [7]. A tuning method wa developed for the low- ide of the accelerator, which face the dual problem of mimatched 46 velocity and over focuing at high acceleration gradient. A preliminary approach of thi method i applied to the SARAF 4 MeV deuteron accelerator. We developed a new approach for beam lo calculation that place emphai on the tail of the particle ditribution. Thi cheme i ued for imulating the SARAF accelerator at a enitivity of the hand-on maintenance criterion. The imulation are preented at the end of thi paper, including error analyi, and are able to predict a reliable beam lo value, uing a ingle PC. BEAM TUNING METHOD For multi gap cavitie, the problematic region for the tune i the low ection. In thi area the acceleration in each gap i quite large in comparion to the particle initial velocity at the cavity entrance. The particle deviation from the reference particle at the econd gap of the cavity depend on the velocity gain of the particle at the firt gap. The evaluation of the particle trajectory, with ignificant velocity increae along the cavity, ha to be performed at each gap eparately, taking into account the particle phae deviation from the reference particle at each gap [8, p.89]. If the accelerating RF field along the bunch in one of the gap deviate from the linear range it could introduce ignificant emittance growth during the acceleration. The range of the accelerated particle' phae- φ i, at each gap i i defined by the reference particle phae φ ri and the bunch half length- Ψ i, φ ri Ψi φi φri + Ψi. Ψ i i etimated from the phae ditribution of the tuned bunch at the gap entrance. RF electric field (arb.).5 ψ phae (deg) ψ δ φ φ +π δ +π Figure : RF field a function of phae and phae definition for acceleration at mimatch a defined in the text.

2 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA WGB5 For a two gap cavity, i=, (Fig. ) the reference particle phae at each gap i evaluated from the ynchronou phae φ : φ r = φ δ φr = φ + δ δ = ( / ) * π / where δ i the difference between the ynchronou phae and the reference particle phae at both gap, i the geometric of the cavity and i the reference particle relative velocity at the firt gap exit. To minimize the emittance growth along the linac at the low ection, in each gap of the multi gap cavitie, it i validated that the acceleration RF field i linear along the bunch. A key factor for a good tuning i of coure a mall bunch width along the linac. The longitudinal phae advance per unit length i kept contant (baed on [8 p.75]). (The method developed here aumed a ingle cavity per period, further development i needed for few cavitie in a period): d( W W ) = qvt (coφ coφ ) / L d d( Φ φ ) = ( W W )π /( mc γ λ) d k = π /( mc γ λ) qv T inφ / L V lo ( γ T = V L ) T (inφ / inφ )( γ where: W i the bunch particle energy, W i the ynchronou particle energy, Φ i the approximated particle phae along the cavity gap, q i the particle charge, L i the ditance between cavitie, k lo i the phae advance per unit ditance, V T i the energy gain at zero ynchronou phae per unit charge at a cavity baed on the cavity voltage V (proportional to the cavity field amplitude) and the bunch tranient time factor T, i i the cavity index (i= i the uptream cavity, i= i the cavity to tune) and i the ditance at the beam direction. Thi formula implie that after applying a linear RF acceleration field along the bunch, in each gap, then, the energy gain of the cavity at zero ynchronou phae (V T ) i tuned according to the phae advance per unit length at the uptream cavity k lo, in order to avoid ignificant local variation of the phae advance per unit Figure : Schematic layout of the SARAF. L ) / length. The applied detuned phae advance per period σ l i evaluated by: L σ l = ˆ( d where ˆ i the Courant ) Snyder parameter [9 p. 5]. At the high range, in order to maintain the acceleration efficiency, the ynchronou phae i kept between - and -5 degree, but not above -5 degree in order to maintain tability. The tranvere phae advance hould be kept higher than 5% of the longitudinal phae advance to eliminate emittance growth and halo development []. LINAC LATTICE SETUP The linac lattice i decribed in detail in ref. [-] and reference there in. The linac i matched tranverely to the RFQ with three quad along the MEBT to convert the beam to a radial ymmetric hape (Fig. ). The linac i compoed of two =.9 cryotat followed by four =.5 cryotat. In thi work two option for the SC linac are tudied. The two are called here ymmetric and aymmetric and are differing in the internal cryotat arrangement. Each period at the baic linac aymmetric configuration i compoed of a leading SC olenoid followed by two SC cavitie (Fig. ). The firt SC cavity of the linac i ued a a buncher. Figure : The Prototype Superconductor Module with the aymmetric lattice deign []. 47

3 WGB5 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA At the RFQ exit Symmetric firt gap Aymmetric firt gap Figure 4: Longitudinal phae pace at the RFQ exit and at the entrance to the SC linac. At the ymmetric lattice the ditance between the firt and the econd MEBT quad i enlarged by 9 cm to increae the tranvere focuing. In thi cae the linac tart with a leading cavity operated a a buncher o the RFQ to buncher ditance i reduced by 6 cm with repect to the 7 cm ditance in the aymmetric lattice. The firt HWR at the aymmetric lattice tart cm downtream the warm to cold tranition. Thi ditance (partially inide the olenoid) act a a cold trap in the firt cryotat, which protect the SC cavitie from contamination emerging from the injector. Both lattice enable acceleration of a 4 ma deuteron and proton CW beam up to 4 MeV. The lattice i extended by more =.5 cryotat to reach 6 MeV a a preliminary option for the EURISOL driver. The current deign of the EURISOL driver include modification uch a uing one HWR at each internal period of the =.9 cryotat downtream the RFQ []. End to end imulation of the SARAF linac have been performed uing TRACK [] from the kev/u ion ource to 4 MeV, extended to 6 MeV for the EURISOL driver and in GPT [] from the RFQ entrance and up to 4 MeV. The D field of the LEBT olenoid and the fringe field of the LEBT bending magnet were modelled,. The RFQ accelerating tructure wa generated according to the RFQ deign data [5], D field were modelled for the radial matcher with EM Studio. The field in the regular cell are preented by the 8-term Fourier Beel expanion. The D field of the SC olenoid were calculated and the D field of the SC cavitie were included in the imulation. BEAM TUNING RESULTS AND COMPARISON The longitudinal phae pace diagram of 5k macro particle at the RFQ exit and at the entrance to the firt HWR gap of the ymmetric and the aymmetric lattice are time=.5 n time=7.5 n GPT.9.9 poition (m) poition (m) GPT..68 time=9 n GPT poition (m) GPT 4 6 time (n) 8 M. Pekeler HPSL 5 Figure 5: Longitudinal phae pace along the firt accelerating two gap HWR after the buncher,.5 ma p beam. 48

4 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA WGB5 5 5 Bunch acceleration phae [deg.] σ gap +σ gap -σ gap +σ gap Poition [m] preented in Fig. 4. The high longitudinal phae advance of the macro particle and the ignificant increae in along the firt accelerating cavity are preented in Fig. 5. Thee reult are typical to accelerating light ion with a high accelerating field at low - with a high -mimatch. The RF phae i choen o that the bunch encounter the RF field in it linear portion at each low- gap uing the accelerating phae hown in Fig. 6. The effort to bunch the beam along the linac i preented in Fig. 7. The deuteron energy at the linac exit for SARAF and for EURISOL i [4., 65.] and [4.6, 66.] MeV for the ymmetric and the aymmetric lattice for a 4 ma deuteron beam (Fig. 8). The energy difference between the lattice i not ignificant. One can probably improve the aymmetric lattice by reducing the energy gain at the low ection. The emittance growth i imilar at both lattice for the rm and 99.5% envelope both for longitudinal and normalized tranvere emittance. The maximum envelope of 5k macro particle i larger at the longitudinal phae pace for the ymmetric lattice and vice vera for the tranvere phae pace (Fig. 9 and ). The ymmetric lattice give ignificantly higher acceptance than the aymmetric lattice (Fig. ). The aymmetric acceptance can be improved by changing the buncher ynchronou phae. BEAM LOSS CRITERION The beam lo criterion value wa deduced from a limit on reidual activation in the component bore radiu along the linac. Thi wa determined in order to limit the doe rate to mrem/h ( h of hand-on maintenance per technician per year give % of the annual doe limit), at cm away from beam line, 4 hour after accelerator hutdown after a full year of operation. The SARAF linac bore radiu i built of about half tainle till and half niobium. The beam operation program i compoed of about half deuteron beam time and half proton beam time. Earlier calculation howed that up to 4 MeV, the main contribution to the doe i due to deuteron (relative to proton) bombarding thick 56 Fe Bunch acceleration phae [deg.] σ gap +σ gap -σ gap +σ gap Poition [m] Figure 6: Aymmetric (left) and ymmetric (right) lattice bunch acceleration phae at the firt cavity gap (bottom curve) and the econd gap (top curve) along the low SC linac ection. target (relative to niobium). Figure preent the produced doe rate from year of operation (by the relevant produced radioiotope) along the m linac followed by high energy beam line toward the target. The reult are normalized to na/m deuteron beam lo, with energy evolution a preented in Fig. 8. Figure preent the decay of the doe from 4 hour until day after hutdown. Taking into account the linac compoition and beam operation, relative to the above conervative calculation, a beam lo criterion of l na/m wa ued for the linac deign tudy. ERROR RUNS AND BEAM LOSS USING THE TAIL EMPHASIS METHOD We have applied the tail emphai method [4] in order to tudy particle loe along the linac for the aymmetric lattice (Fig. 4). The method i baed on the aumption that loe begin longitudinally, and problem particle begin at the periphery of the longitudinal phae pace at the RFQ exit, and originate in the boundarie between the downtream bunche at the dc current entering the RFQ buncher ection. The method allow u to calculate loe along the linac at the na level with limited computational effort: A Tail Emphai deuteron beam with. million macro particle at the RFQ entrance i equivalent to the imulation of bunche containing 4.6 million macro-particle (each :, equivalent to. na) for 4mA CW at 76 MHz. The reduced computation time allow u to run a large number of imulation in a relatively hort pan of time. Thi allow u to explore the effect of manufacture and operational error on the beam and etimate loe due to thee factor, a decribed in [5]. Table ummarize the range of the tatic and dynamic error ued in the tudy. Static error are aumed to have a uniform ditribution ditributed within the limit hown on the table. Dynamic error are aumed to have a Gauian ditribution with a tandard deviation a pecified in the table. A erie of error run were performed for an input deuteron beam at the RFQ exit. Thi input i generated by imulating the 49

5 WGB5 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA 9 8 Bunch rm bunch envelope for 5k 4rm 99.5% envelope for 5k Bunch length (deg.) bunch emittance [kev/u*n] Poition (m) Poition [m] Figure 7: Bunch amplitude length for the ymmetric (dot) and the aymmetric (olid line) lattice. Figure 9: Bunch longitudinal emittance for the ymmetric (dot) and the aymmetric (olid line) lattice Energy [MeV/u] Bunch normalized tranvere emittance [cm mrad] rm x 99.5% x envelope for 5k x 4rm y 99.5% y envelope for 5k y Poition [m] Poition [m] Figure 8: Bunch energy along the linac for the ymmetric (dot) and the aymmetric (olid line) lattice. RFQ with an entrance normalized tranvere rm emittance of. π mm mrad. The tail emphai method wa applied within the GPT [] code to run the beam dynamic imulation A imilar error et wa then generated with a doubled dynamic phae error to tudy the enitivity of the realization to larger phae error at the HWR accelerating field. For the input. π mm mrad both error run were without loe, a hown in Fig. 5. However, according to the on ite tet and the pecification the tranvere normalized rm emittance at the RFQ exit i. π mm mrad. The imulated tranvere macro particle phae pace at the RFQ exit wa expanded to reach thi value (Fig. 6), and the error run were repeated for the new bunch, having the pecified. π mm mrad rm normalized emittance at the RFQ exit. Thee error run were conducted with the nominal phae error. Figure 7 how the reult. For two out of the 5 linac realization (Fig. 7a,b) the lot particle exceeded the deign beam lot criterion ( na/m). Figure : Bunch tranvere normalized emittance for the ymmetric (dot) and the aymmetric (olid line) lattice. Table : Fabrication mialignment and operation error Component Error Static Dynamic Quadruple Solenoid HWR Mialignment x,y,z [mm] Rotation θ [mrad] Magnetic field [%] Mialignment x,y,z [mm] Magnetic field [%] Mialignment x,y,z [mm] Rotation θ [mrad] field amplitude[%] Phae [degree] ±. ± ±.5 ±. ±.5 ±.4 ±6 ± ±.5.5 5

6 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA WGB5 Figure : Longitudinal phae pace acceptance for the ymmetric (left) and the aymmetric (right) lattice v. the bunch pread at the RFQ exit (relative energy pread v. phae (deg)). 6 5.E+.E- Co-56 (78.8 d) Co-55 (7.54) Co-57 (7.9 d) Mn-5 (5.6 d) Mn-54 (.7 d) Mn-56 (.6 h) Total.E-.E Poition (m) Figure : Doe rate reidual activity calculated for uniform na/m deuteron beam lo on 56Fe target along the SC linac and the HEBT, after one full year of operation, 4 hour after hut down and at a ditance of cm from the beam line. D o e r a te (m re m / h) D o e rate fo r n A /m lo e (m rem /h ).E+ 4.E-.E+.E+.E+.E+ Decay time (day) Figure : Reidual activity doe rate (of Fig. ) decay after hut down.. million (.4 ma) macro particle at RFQ exit equivalent to a imulation of bunche along the RFQ with initial ditribution of 4.6 million (:) macro-particle (each. na) for a 4 ma, 76 MHz, CW at RFQ entrance. Figure 4: Longitudinal phae pace along the RFQ. Top entrance. Middle end of bunching ection. Bottom exit. Three bunche are preented. The tail emphai method (right) enable u increae the reolution in the longitudinal phae pace tail ( macro particle per ) and to reduce the reolution in the neighbour bunche relative to the regular treatment (left). 5

7 WGB5 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA Figure 5: Tranvere envelope and rm radiu for erie of error run. Left: tandard run. Right: dynamic phae error doubled. Showing reult for k/9k core/tail particle ditribution with a normalized rm input emittance of. mm mrad,.4 ma d beam, at RFQ exit. The lat macro particle i equivalent to na current. The bore radiu i 9 mm within olenoid and 5 mm everywhere ele. Figure 6: Simulated tranvere phae pace (left: original) i expanded to. mm mrad (right) to match the meaured rm emittance at the RFQ exit At one of the two run the lot macro particle ( na each) were lot at energy of 5 MeV. Practically, the evaluated expoure rate baed on thi realization i lower than mrem/h (required for hand on maintenance). Each realization repreent a momentary configuration of the field dynamic error combined with tatic lattice error. If the major ource of loe i the dynamic error we might conider the average beam lo, a hown in Fig. 7c, and that remain within the required hand on limit. We are currently conducting further imulation to verify it. (a) (b) Figure 7: Simulation of.4 ma d beam with an input of. π mm mrad rm tranvere emittance. Showing the reult of 5 run of a deuteron beam containing k/9k macro particle in it core/tail. Overall 78 particle (equal to 78 na) were lot: of thee and 4 particle were lot in two pecific run, and in all other run - macro particle (=- na) were lot. Left (a): tranvere envelope and rm radiu. Right, top (b): exit point and energy of lot particle. Right, bottom (c): the expected lot at na/m averaged along realization (blue line); the red line denote acceptable beam lo along the linac a derived from expoure rate of m rem/h at cm from the beam line for hand on maintenance after 4 h from hutdown a explained in the ection above (Fig. ). (c) 5

8 Proceeding of Hadron Beam 8, Nahville, Tenneee, USA WGB5 SUMMARY A lattice conit of a SC linac at the RFQ exit deigned for light ion that have variable ma to charge ratio probably will need a dedicated tune method to allow acceleration at low with a mimatch. A method to accelerate efficiently at the low range wa derived and applied for two baic lattice ymmetric and aymmetric lattice. The ymmetric lattice eemed to be the favour lattice ince it ha a better acceptance and ince it tranvere envelope eemed to be eaier to control. A beam lo criterion for hand on maintenance wa derived, mrem/h at cm from the beam line, and related to the expected imulated beam lot, na/m, along the linac. The tail emphai method enable u to increae the reolution to evaluate the lot particle at na/m out of 4 ma nominal current for the required beam lo criterion for erie of error run. The method aume that the lot particle are getting radical value at the RFQ bunching ection at the longitudinal phae pace. The expected expoure for the aymmetric lattice, the current lattice of the PSM tand at the bean lo criterion of hand on maintenance auming the erie of error run are dominated by the dynamic error. REFERENCES [] A. Nagler, I. Mardor, D. Berkovit, K. Dunkel, M. Pekeler, C. Piel, P. vom Stein and H. Vogel, proceeding of LINAC 6, Knoxville, Tenneee, MOP54 (6) [] M. Pekeler, K. Dunkel, C. Piel and P. vom Stein, Development of a uperconducting rf module for acceleration of proton and deuteron at very low energy, Proceeding of LINAC 6, Knoxville, Tenneee USA TUP4 (6) -. [] C. Piel, K. Dunkel, M. Pekeler, H. Vogel, P. vom Stein, Beam operation of the SARAF light ion injector, Proceeding of PAC7, Albuquerque, New Mexico, USA, TUPAN (7) 4-4. [4] C. Piel, K. Dunkel, F. Kremer, M. Pekeler, P. vom Stein, D. Berkovit, I. Mardor, Phae Commiioning Statu of the 4 MeV Proton/Deuteron Accelerator SARAF EPAC8, Genova, June (8) [5] J. Rodnizki, B. Bazak, D. Berkovit, G. Feinberg, A. Shor, Y. Yanay, K. Dunkel, C. Piel, Beam Dynamic Simulation of the.5 MeV Proton Beam Meaured at the SARAF RFQ Exit, EPAC8, Genova, June (8) [6] Thoma P. Wangler Longitudinal Beam Dynamic Contraint on Accelerating Gradient in a Proton Superconducting Linac, American Phyical Society meeting, Albuquerque New Mexico, - April (), ab/s66.html [7] R. W. Granett, T. P. Wangler, F. L. Krawczyk and J. P. Kelley, Conceptual deign of a low- SC proton LINAC, Proc. of PAC, Chicago, June 8-, () 9. [8] T. P. Wangler, Principle of RF Linear Accelerator, John Wiley and Son, Inc., 998. [9] M. Reier, Theory and Deign of Charged Particle Beam, J. Wiley & Son, Inc., 994. [] P. N. Otroumov, DESIGN FEATURES OF HIGH- INTENSITY MEDIUM-ENERGY SC HEAVY- ION LINAC, proceeding of LINAC, Gyeongju, Korea, MO4 () [] A. Facco, A. Balabin, R. Paparella, D. Zenere, D. Berkovit, J. Rodnizki, J. L. Biarrotte, S. Bouon, A. Ponton, R. Duperrier, D. Uriot, V. Zvyagintev, Beam Dynamic Studie on the EURISOL Driver Accelerator, Proceeding of the 6 Linear Accelerator Conference, Victoria, Britih Columbia, Canada, 8 [] P. N. Otroumov, V. Aeev and B. Mutapha, TRACK a code for beam dynamic imulation in accelerator and tranport line with D electric and magnetic field, ANL, March 7, 6. [] General Particle Tracer (GPT), Pular Phyic, [4] B. Bazak A. Shor, D. Berkovit, G. Feinberg, J. Rodnizki and Y. Yanay, Simulation of ion beam lo in RF linac with emphai on tail of particle ditribution, to be publihed. [5] J. Rodnizki, D. Berkovit, K. Lavie, I. Mardor, A. Shor, Y. Yanay, K. Dunkel, C. Piel, A. Facco and V. Zviagintev, Beam Dynamic Simulation of the SARAF Accelerator Including Error Propagation and Implication for the EURISOL Driver, Proceeding of the 6 Linear Accelerator Conference, Knoxville, 6, p