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## ‘Multi-pass-Droplet’ Experiment

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**‘Multi-pass-Droplet’ Experiment**Kevin Beard, Alex Bogacz, Vasiliy Morozov, Yves Roblin Discussion • Why multi-pass arcs? Recent development of Dogbone RLAs Alex 15 min. • Proof-of-principle optics for a two-pass arc Vasiliy 15 min. • Scaled super-cell test with electrons Yves 25 min. • Discussion All 20 min. Why? How? What? ????**Why multi-pass arcs?**Recent development of Dogbone RLAs Alex Bogacz**A Decade of Muon RLAs**• Racetrack RLA – NF Study I (2000) (Bogacz/Lebedev) • Switchyard (single bend, horizontal) • Individual energy return Arcs for recirculation • Dogbone RLA – NF Study II (2005) (Bogacz) • Better separation of passes • Compact arcs, saving on beamlines • Simultaneous acceleration of both charge species • Increasing number of passes (ISS/IDS-NF): • Bi-sected linac Optics (2006) (Bogacz) • Ramped linac quads (2007) (Johnson) • Reducing number of return Arcs – Multi-pass Arcs (IDS-NF): • Non-scaling FFAG arcs with sextupoles (2008) (Trbojevic/Bogacz/Wang) • Linear Non-scaling FFAG arcs (2010) (Morozov) • Arcs based on combined function magnets (2011) (Morozov)**Racetrack vs ‘Dogbone’ RLA**DE/2 DE DE/2 2.5 DE • the droplets can be reduced in size according to the required energy • better orbit separation at linac’s end ~ energy difference between consecutive passes (2DE) • allows both charges to traverse the Linac in the same direction (more uniform focusing profile) • both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) DE 4**Dogbone RLA – IDS**900 MeV 244 MeV 0.9 GeV 3.6 GeV 86 m 0.6 GeV/pass**Pre-Linac and RLA I to RLA II …**244 MeV 3 GeV 900 MeV 1.8 GeV 1.2 GeV 2.4 GeV 3.6 GeV 6**Injection/Extraction Chicane**FODO lattice: 900/900 (h/v) betatron phase adv. per cell 7**Droplet Arcs**top view 1.2 GeV 2.4 GeV side view 1.2 GeV 1 m 2.4 GeV**Mirror-symmetric ‘Droplet’ Arc – Optics**3 20 BETA_X&Y[m] DISP_X&Y[m] -3 0 0 BETA_X BETA_Y DISP_X DISP_Y 130.618 (bout = bin and aout = -ain , matched to the linacs) disp. sup. cells out 2 empty transition cells disp. sup. cells out 2 empty transition cells 10 cells in 2 vertical steps 2 vertical steps**Switchyard - Arc 1 and 3**1.2 GeV 2.4 GeV 1.2 GeV**Switchyard - Arc 1 and 3**1.2 GeV 2.4 GeV 1.2 GeV**Multi-pass Linac Optics – Bi-sected Linac**5 15 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 39.9103 5 15 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 78.9103 ‘half pass’ , 900-1200 MeV initial phase adv/cell 90 deg. scaling quads with energy 6 meter 90 deg. FODO cells 17 MV/m RF, 2 cell cavities quad gradient 1-pass, 1200-1800 MeV mirror symmetric quads in the linac quad gradient**5**30 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 389.302 Multi-pass bi-sected linac Optics bx = 13.0 m by = 14.4 m ax=-1.2ay=1.5 bx = 7.9 m by = 8.7 m ax=-0.8ay=1.3 Arc 2 Arc 3 Arc 4 Arc 1 bx = 6.3 m by = 7.9 m ax=-1.2ay=1.3 bx,y → bx,y axy → - axy bx = 3.2 m by = 6.0 m ax=-1.1ay=1.5 bx,y → bx,y axy → - axy bx,y → bx,y axy → - axy bx,y → bx,y axy → - axy quad grad. 3.0 GeV 0.9 GeV 1.2 GeV 1.8 GeV 2.4 GeV 3.6 GeV length**100**5 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 100 5 DISP_X&Y[m] BETA_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 ‘Fixed’ vs ‘Pulsed’ linac Optics (8-pass) Fixed Pulsed**A Decade of Muon RLAs**• Racetrack RLA – NF Study I (2000) (Bogacz/Lebedev) • Switchyard (single bend, horizontal) • Individual energy return Arcs for recirculation • Dogbone RLA – NF Study II (2005) (Bogacz) • Better separation of passes • Compact arcs, saving on beamlines • Simultaneous acceleration of both charge species • Increasing number of passes (ISS/IDS-NF): • Bi-sectedlinac Optics (2006) (Bogacz) • Ramped linac quads (2007) (Johnson) • Reducing number of return Arcs – Multi-pass Arcs (IDS-NF): • Non-scaling FFAG arcs with sextupoles (2008) (Trbojevic/Bogacz/Wang) • Linear Non-scaling FFAG arcs (2010) (Morozov) • Arcs based on combined function magnets (2011) (Morozov)**2-pass ‘Droplet’ Arc**• Dipole and quadrupole field components of the remaining magnets adjusted so that at both momenta • Each super-cell has periodic solutions for the orbit and the Twiss functions • At the cell’s entrance and exit, periodic orbit offset, dispersion and their slopes are all zero Vasiliy Morozov * Trajectories are shown to scale**Proof-of-principle optics for a two-pass arc**VasiliyMorozov**RLA with Two-Pass Arcs**Alex Bogacz RLA with FFAG Arcs 0.9 GeV 244 MeV 146 m 79 m 79 m 0.6 GeV/pass 3.6 GeV 264 m 12.6 GeV 2 GeV/pass • Two or potentially more regular droplet arcs replaced by one multi-pass arc • Simplified scheme • No need for a complicated switchyard • Compactness • More efficient use of RF by maximizing the number of passes • Potentially cheaper • Potential for other applications 19**Schematic Layout of a Two-Pass FFAG Arc**simple closing of geometry when using similar cells = 41.3 m 300 60 C = 302.4 m 20**Non-Linear FFAG: 1.2 GeV/c Linear Optics of Unit Cell**• Combined-function bending magnets are used • 1.2 GeV/c orbit goes through magnet centers • Linear optics controlled by quadrupole gradients in symmetric 3-magnet cell • Dispersion compensated in each 3-magnet cell 3-magnet cell in + out + in = in MAD-X (PTC) 21**Non-Linear FFAG: 2.4 GeV/c Linear Optics of Unit Cell**• Unit cell composed symmetrically of three 3-magnet cells • Off-center periodic orbit • Orbit offset and dispersion are compensated by symmetrically introducing sextupole and octupole field components in the center magnets of 3-magnet cells sextupole and octupole components symmetric unit cell MAD-X (PTC) 22**Cell Matching**• 1.2 GeV/c • 2.4 GeV/c outward inward outward inward 23**Issues with Non-Linear FFAG Arcs**• Small dynamic aperture and momentum acceptance • Compensation of non-linear effects is complicated • Matching to linac is difficult • Hard to control the orbit lengths and therefore the difference in the times of flight of the two momenta • Combined function magnets with precise control of field components up to octupole 24**Two-Pass Linear FFAG Arcs**• Same concept as with the non-linear FFAG arcs • Droplet arcs composed of symmetric FFAG cells • Each cell has periodic solution for the orbit and the Twiss functions • For both energies, at the cell’s entrance and exit: • Offset and angle of the periodic orbit are zero • Alpha functions are zero • Dispersion and its slope are zero • Outward and inward bending cells are automatically matched 25**Two-Pass Linear FFAG Arcs**• Combined function magnets with dipole and quadrupole field components only • Much greater dynamic aperture expected than in the non-linear case • Easier to adjust the pass length and the time of flight for each energy • Easier to control the beta-function and dispersion values • Initial beta-function values chosen to simplify matching to linac • Much simpler practical implementation without non-linear fields • More elements are used in each unit cell to satisfy the diverse requirements and provide enough flexibility in the orbit control 26**Linear FFAG: Linear Optics of Unit Cell**• Initial conditions set; orbit, dispersion and -function slopes zero at the center • Path lengths adjusted to give time of flight difference of one period of RF • 1.2 GeV/c • 2.4 GeV/c 27**DesignBased on Linear Combined-Function Magnets**• Same concept as the linear FFAG design • Linear combined-function magnets • Droplet arc composed of symmetric super cells • Each super-cell has periodic solutions for the orbit and the Twiss functions • At the cell’s entrance and exit, periodic orbit offset, dispersion and their slopes are all zero • Two cells bending in the same or opposite directions automatically matched at both momenta • First few magnets of the super cell have dipole field component only, serving as spreader/recombiner • Both dipole and quadrupole field components of the remaining magnets used as parameters to meet the constraints • Synchronization with linac accomplished using path-length adjusting chicanes and/or vertical beam bypasses 29**Advantages of New Arc Design**• All the advantages of a linear FFAG at a greater compactness • Alternating in-out-in or out-in-out pattern no longer required • Variation of the bending angles increases the number of available parameters and reduces the number of magnets required • Reduced orbit excursion • Spreader/recombiner incorporated into the arc design • Large dynamic aperture and momentum acceptance expected • Simple linear combined-function magnet design 30**300**60 C = 117.6 m Arc Layout • Still simple closing of arc geometry when using similar super cells • 1.2 / 2.4 GeV/c arc design used as an illustration can be scaled/optimized for other momenta preserving the factor of 2 momentum ratio of the two passes 31**Super-Cell Optics for P2 / P1 = 2**• P • 2xP 32**Droplet Arc Spreader/Recombiner**• First few magnets of the super cell have dipole field component only, serving as Spreader/Recombiner * Trajectories are shown to scale 33**Two 2-Pass Arc Switchyard**• Two 2-pass arcs • Lower momentum arc is the most challenging because of the highest momentum ratio; have a solution but still plenty of room for optimization * Trajectories are shown to scale 34**Future Studies and Optimization Paths**• Lower momentum ratio • In case of a race-track design or in the inner droplet super cells, quadrupole field component can be used in the super-cell’s first magnets • Introduce sextupole component in the spreader/recombiner to control orbit deviation • Study the possibility of more than two passes • Study sextupole compensation of chromatic effects • Study error sensitivity • Tracking using realistic field maps 35**Scaled super-cell test with electrons**Yves Roblin**goal of the project**• Validate the concept of combined function magnet return arcs • Demonstrate feasibility, establish leadership • The scaled down test is a fertile ground for beam physics: • Dynamic aperture, • Effect of non linearities, • Tunability, • Envelope control, • Exploring the range of momenta that can be transported • Etc..etc.. 37**Closed orbit in cell**20cm aperture 38**scope**• Build a fully functional half-cell (first phase) and eventually a full arc using electrons rather than muons. • Use this arc to characterize and demonstrate the concept for the MAP program • Great teaching tool. Can partner with local universities (ODU Beam physics program) 39**feasibility**• Electron is 206 times lighter than muon. We only need a few MeV to 10’s of MeV to carry out the tests. Canonical 2.4 GeV/c lattice requires 11.6 MeV/c electrons. • Real arc will have superconducting magnets. We can build small normal conducting magnets in house to test the concept (more about this later) • We have the expertise with electron beams and can deliver the needed beam • We have the room at JLAB (see next slides) for testing a half cell, maybe even a full cell and later a full arc. 40**Testing a Half-Cell with Electrons**Cell with 12 combined function magnets bending a totalof 30 degrees. Each magnet is a dipole+quad+sextupole. L=50cm, aperture=20cm Need instrumentation between each magnet (beam position monitors and means of measuring beam profile at some locations) Low current is adequate. 5 to 40 MeV/c of electron beam is good 41**Footprint of the apparatus**Full cell About 8x3 meters on floor for the half cell. 42**Possible Locations at Jefferson Lab**Where 0L07 spectrometer is. In a Hall after setting up CEBAF in energy recovery mode to get a Low energy beam. Good option if one want to test a bigger device. In the test lab !! Using the injector group test gun along with a cavity to bring beam to 5 MeV. Maybe some paperwork involved.. 43**Magnet specifications**Aperture of 20 cm, length of 50 cm. The real thing will have to provide around 1.8 Tesla. Our prototype only needs to put out 1.8/206 or about 87 Gauss. These magnets can be easily (maybe??) made in house. 44**Printed Circuit design(cont)**And it works.. Phys. Rev. ST Accel. Beams 3, 122401 (2000) 45**Printed Circuit design**That’s a quad ! Back Front 46**Full scaled down simulation of RLA with return arcs**Eventually two of these return arcs can be build. A small recirculating linac would accelerate from 11.6 GeV to 46.4 GeV/c over several recirculations. This would be a full scaled down test of the neutrino factory and/or muon colliders. 47