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## The lattice variations Loss estimation using tail emphasis method END

Guild, Carol, Features Editor & Prospect Editor (Local Entertainment) has reference to this Academic Journal, PHwiki organized this Journal J. Rodnizki SARAF, Soreq NRC HB2008, August, 2008 Nashville TN Lattice Beam dynamics study in addition to loss estimation as long as SARAF/ EURISOL driver 40/60 MeV 4mA d/p superconducting Linac Content of talk Introduction- Acceleration at low b with b mismatch The tune method The lattice variations Loss estimation using tail emphasis method Acceleration at low b with b mismatch The SARAF is SC linac design as long as 4 mA p/d acceleration up to 40 MeV with the TRACK code, P. Ostroumov, ANL in addition to benchmarked with GPT,www.pulsar.nl/gpt Inlet energy 1.5 MeV/u (b = 0.0567) 6HWR module (geometric b = 0.09) 8HWR module (geometric b = 0.15)

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Acceleration at low b with b mismatch The SARAF SC linac inlet energy is 1.5 MeV/u, b=0.0567 while the HWR start at b=0.09 At low energy as long as light ions the acceleration is limited by the induced strong longitudinal focusing as long as ce accompanied by transverse defocusing due to the induced space charge High accelerating gradient could introduce high longitudinal phase advance resulting in beam losses Our study is relevant as long as other linacs that start with SC cavities right after the RFQ, such as SPIRAL2, in addition to maybe IFMIF too, which start with similar b mismatch at the low b range with the TRACK code, P. Ostroumov, ANL in addition to benchmarked with GPT,www.pulsar.nl/gpt Beam tuning method For multi gap cavities, the problematic region as long as the tune is the low section In this area the acceleration in each gap is quite large in comparison to the particles initial velocity at the cavity entrance The particle deviation from the reference particle at the second gap of the cavity depends on the velocity gain of the particle at the first gap Beam tuning method cont. The evaluation of the particle’s trajectory, with significant velocity increase along the cavity, has to be per as long as med at each gap separately, taking into account the particles phase deviation from the reference particle at each gap If the accelerating RF field along the bunch in one of the gaps, deviates from the linear range it could introduce a significant emittance growth during the acceleration The range of the accelerated particle’s phase fi, at each gap i is defined by the reference particle phase in addition to the bunch half length

Longitudinal phase space along the first accelerating two gaps HWR after the buncher, 3.5 mA p M. Pekeler HPSL 2005 The longitudinal emittance DEDt (proportional to gz, g 1) is an invariant along the linac as long as a conservative system. The accelerating range at each gap The reference particle phase at each gap as function of the synchronous phase For a two gap cavity the reference particle phase at each gap is a function of: – bunch b at the first gap exit – the geometric b of the cavity

The effective voltage as function of the selected synchronous phase The effective cavity voltage is tuned to keep the upstream phase advance: The development in addition to the notation followed T. P. Wangler, Principles of RF Linear Accelerators, John Wiley in addition to Sons, Inc., 1998. p 175 The tune method steps at low b with b mismatch Bunch the RFQ exit beam to apply linear fields along the acceleration at each cavity gap Select an appropriate synchronous phase as long as a multi gap cavity to reach a linear accelerating field at each gap Find the cavity field amplitude base on the cavity synchronous phase in addition to the upstream phase advance The lattice variations

Symmetric the period is composed of [cavity – solenoid – cavity] Asymmetric the period is composed of [solenoid – cavity – cavity] Comparison between symmetric in addition to asymmetric lattice extended to 60 MeV as long as the EURISOL driver Lattice symmetry variations Pekeler linac 2006 40 MeV 60 MeV The lattice variations Two basic lattices were considered: a symmetric lattice in addition to an asymmetric one. The internal period of a symmetric module is consisted of [HWR, solenoid, HWR], The Internal period of an asymmetric module is consisted of [solenoid, HWR, HWR]. Both lattices consist of 3 internal periods as long as 0=0.09 in addition to 4 internal periods as long as 0=0.15. The symmetric lattice MEBT is longer, including an extra drift between the quadrupoles to enhance the focusing since the symmetric module starts with a HWR. The distance to the first HWR which act like a buncher could be 16 cm shorter at the symmetric lattice. The asymmetric lattices have a SC solenoid which acts like a cold trap after the normal MEBT. The diagnostic space between the modules is 15 cm (except the first space of 10 cm at the asymmetric lattice). Tune parameters The tune acceptance was fitted to the expected RFQ exit particles phase space distribution including an errors study. The errors are based on ACCEL designed in addition to measured values. The tune was optimized as long as : Deuterons/ Protons 4 mA moderated beam emmitance increase moderated beam envelope

Longitudinal phase space at the RFQ exit in addition to at the entrance to the SC linac. RF Acceleration phase at each gap along the low b SC linac section, 4mA d Bunch energy in addition to spread along the linac Bunch length as long as the symmetric (dots) in addition to the asymmetric (solid line) lattices. Bunch energy along the linac as long as the symmetric (dots) in addition to the asymmetric (solid line) lattices.

Bunch normalized emittance along the linac Bunch transverse envelope along the linac Bunch transverse size along the linac as long as the symmetric (dots) in addition to the asymmetric (solid line) lattices. Lattice longitudinal phase space acceptance Longitudinal phase space acceptance as long as the symmetric (left) in addition to the asymmetric (right) lattices vs. the bunch spread at the RFQ exit (relative energy spread vs. phase (deg)).

Loss estimation using tail emphasis method Tail as long as mation during RFQ bunching SNS Jeon linac02 1.4% Longitudinal phase space: Dz Df z DE RFQ longitudinal phase space 3bl – regular 3bl tail emphasis 2.1 million (3.4 mA) macro particles at RFQ exit equivalent to simulation of 3 bunches with 42.6 million (1:10) macro-particles (each 0.3 nA) at RFQ entrance as long as 4mA CW at 176 MHz. 10000 1000 10 B. Bazak et al. submitted 2008 RFQ entrance norm rms ex,y=0.2 p mm mrad. Emittance growth <10%. 10000

Superconducting linac simulation with error analysis Simulations shown in next slides. 4 mA deuterons at RFQ entrance. Last macro-particle=1nA: RFQ entrance norm rms ex,y=0.2 p mm mrad Similar to 1 with double dynamic phase error Similar to 1 with RFQ exit norm rms exp in addition to ed to ex,y=0.3 p mm mrad Errors are double than in: J. Rodnizki et al. LINAC 2006, M. Pekeler HPSL 2005 B. Bazak et al. submitted 2008 d beam envelope radius along the SC linac RFQ exit 3.4 mA deuterons 32k/193k particles in core/tail Last macro-particle = 1 nA HWR bore radius = 15 mm SC solenoids bore radius = 19 mm Asymmetric lattice General Particle Tracer 2.80 2006, Pulsar Physics S.B. van der Geer, M.J. de Loos http://www.pulsar.nl/ rmax rRMS nominal 200 realizations 70 realizations No loss observed Increased Emittance Originally we took ex = 0.2 mm mrad Measurements show ex = 0.3 mm mrad Run simulations with exp in addition to ed bunch

beam envelope along the linac – entrance distribution exp in addition to ed to the specified value Total 78 particles (=nA) lost over 50 runs. At 48/50 runs the lost are 0-1nA At 2/50 runs the lost are 31 in addition to 40 nA Simulation as long as 50 realizations 3.4 mA deuterons 32k/193k particles in core/tail Last macro-particle = 1 nA Still to do Updated lattice: As made MEBT in addition to PSM Initial deuteron distribution as measured Exp in addition to ed distance between module as long as diagnostics from 100 to 156 mm Check options: Robustness (one or some elements are malfunctioning) Replace second HWR with solenoid (semi Eurisol improvement) Operation ability (related to the available beam diagnostics) Summary A lattice consist of a SC linac at the RFQ exit designed as long as light ions that have variable mass to charge ratio probably will need a dedicated tune method to allow acceleration at low b with a b mismatch In the presented study a method to accelerate efficiently at the low b range was derived. The method was applied as long as two basic lattices symmetric in addition to asymmetric lattice. The symmetric lattice seemed to be the favor lattice since it has a better acceptance in addition to since its transverse envelope seemed to be easier to control. Improved transverse tune as long as the GPT simulation (not verified yet with the TRACK simulation) seemed to reduce the losses at the asymmetric lattice. The tail emphasis enable us to increase the resolution to the required safety level. It assumes that the losses originated at the longitudinal phase space.

END Collaboration B. Bazak (Soreq) D. Berkovits (Soreq) A. Facco (LNL) G. Feinberg (Soreq) P. Ostroumov (ANL) A. Shor (Soreq) Y. Yanay (Soreq) Parallelization of a beam dynamic code is adopted as long as large scale RFQ simulation TRACK @ BlueGene J. Xu, B. Mustapha, V. N. Aseev, in addition to P. N. Ostroumov, Parallelization of a beam dynamics code in addition to first large scale radio frequency quadrupole simulations, Phys. Rev. ST Accel. Beams 10, 014201 (2007)

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