RLA WITH NON-SCALING FFAG ARCS V.S. Morozov, S.A. Bogacz, Y.R. Roblin Thomas Jefferson National Accelerator Facility K.B. Beard Muons, Inc. Muon Accelerator Program - Winter Meeting, March 2, 2011

RLA with Two-Pass FFAG Arcs Alex Bogacz RLA with FFAG Arcs 244 MeV 0.6 GeV/pass 3.6 GeV 0.9 GeV 146 m 79 m 2 GeV/pass 264 m 12.6 GeV 79 m Two regular droplet arcs replaced by one two-pass FFAG arc Simplified scheme No need for a complicated switchyard Non-linear and linear FFAG solutions with linear solution perhaps more preferable Muon Accelerator Program - Winter Meeting, March 2, 2011

Two-Pass FFAG Arcs 300 60 simple closing of geometry when using similar cells  = 41.3 m 300 60 C = 302.4 m Muon Accelerator Program - Winter Meeting, March 2, 2011

Non-Linear FFAG: 1.2 GeV/c Linear Optics of Arc 1 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 MAD-X (PTC) Muon Accelerator Program - Winter Meeting, March 2, 2011

Non-Linear FFAG: 2.4 GeV/c Linear Optics of Arc 1 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 symmetric unit cell sextupole and octupole components MAD-X (PTC) Muon Accelerator Program - Winter Meeting, March 2, 2011

Cell Matching 1.2 GeV/c 2.4 GeV/c outward inward outward inward Muon Accelerator Program - Winter Meeting, March 2, 2011

Non-Linear FFAG: Linear Optics of Arc 2 Unit Cell Same concept as 1.2 GeV/c linear optics of Arc #1 1.8 GeV/c 3.0 GeV/c Muon Accelerator Program - Winter Meeting, March 2, 2011

Matching of Non-Linear FFAG Arcs to Linac Horizontal  functions of the higher momenta overfocused at the unit cell ends Matching sections introduced in arcs to reduce  function values in linac Muon Accelerator Program - Winter Meeting, March 2, 2011

Issues with Non-Linear FFAG Arcs Small dynamic aperture and momentum acceptance Compensation of non-linear effects is complicated Matching to linac is difficult, the matching sections break the arcs’ superperiodicity 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 Muon Accelerator Program - Winter Meeting, March 2, 2011

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 Muon Accelerator Program - Winter Meeting, March 2, 2011

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 Muon Accelerator Program - Winter Meeting, March 2, 2011

Linear FFAG: Linear Optics of Arc 1 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 Muon Accelerator Program - Winter Meeting, March 2, 2011

Linear FFAG: Linear Optics of Arc 2 Unit Cell Path lengths adjusted to give equal times of flight for the two momenta 1.8 GeV/c 3.0 GeV/c Muon Accelerator Program - Winter Meeting, March 2, 2011

Multi-pass linac Optics 355.552 80 5 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 1.2 GeV 0.9 GeV 3.0 GeV 2.4 GeV 1.8 GeV 3.6 GeV Arc 1 bx = 8 m by = 2 m ax = 0 = ay Arc 2 bx = 9 m by = 2 m bx = 2 m by = 4 m bx = 10 m by = 3 m Alex Bogacz

Dynamic Aperture Muon Accelerator Program - Winter Meeting, March 2, 2011

Tracking Bunch with p/p = 0 p = 2.4 GeV/c, xN = 300 m, yN = 300 m, z = 1 cm, x = 2 m, y = 4 m, 3000 particles, 1 turn Muon Accelerator Program - Winter Meeting, March 2, 2011

Tracking Bunch with p/p = 0.01 Muon Accelerator Program - Winter Meeting, March 2, 2011

Tracking Bunch with p/p = 0.027 Muon Accelerator Program - Winter Meeting, March 2, 2011

Conclusions Non-linear and linear NS FFAG schemes developed for muon RLA return arcs Droplet arcs are composed of symmetric FFAG cells having Periodic solution for the orbit and the Twiss functions Orbit offset, dispersion and their slopes are zero at the cell’s entrance and exit for both energies Automatic matching of the cells with each other and between the outward and inward bending cells from the optics and geometry points of view The non-linear FFAG scheme has issues with dynamic aperture, momentum acceptance, orbit control and linac matching The linear FFAG scheme Promising dynamic aperture and momentum acceptance The orbit length were adjusted to compensate for the time of flight difference Simpler linac matching Future plans Sextupole compensation to improve the momentum acceptance Study of the error sensitivity Muon Accelerator Program - Winter Meeting, March 2, 2011