SuperB e+/e- main linac and diagnostics studies Freddy Poirier - LAL On behalf of A.Variola and P.Hermes (who did the work) SuperB general meeting Frascati 29/09/2010 poirier@lal.in2p3.fr

Global scheme “New” Scheme – M. Preger’s Elba talk f) b) d) a) c) 50 MeV CAPTURE SECTION THERMIONIC GUN 0.95 GeV PC 0.6 - 1 GeV SHB b) combiner DC dipole d) e+ a) BUNCH COMPRESSOR 5.7 GeV e+ 3.9 GeV e- 50 MeV CAPTURE SECTION POLARIZED SLAC GUN SHB 0.2 GeV e- c) a) Injector Design b) 1 GeV positron beam matching c) 0.2 GeV electron beam matching d) Design of Emittance measurement f) Design of Energy Dispersion measurement

Linac Requirements A) Transport and confinement of incoming 1 GeV e+ and 0.2 GeV e- beams from a periodic quadrupole structure B) 2 accelerating structure (SLAC type) between quads. Minimal distance between two tanks = 30 cm C) Use of same phase for each accelerating section

Main Linac Requirements B) 2 accelerating structure (SLAC type) between quads. Minimal distance between two tanks = 30 cm C) Use of same phase for each accelerating section Distance between 2 cavities = 4 l Distance between 2 cavities with quadrupole of 8.6 cm width = 84 cm (8 l) Total length for a FODO half period = 714 cm (68 l) RF= 2856 MHz, wavelength l = 10.5 cm Cavity length= 294 cm, i.e. 28 l Tank length = 304.8 cm, A) Transport and confinement of incoming 1 GeV e+ and 0.2 GeV e- beams from a periodic quadrupole structure with alternating gradient force Conclusions: Quad Focal distance for positrons |f1gev|>5/2L (L=distance between 2 quads) Nth gradient to be modified: gn~g1(1+nDE/E) Initial gradient chosen: g1=1.3 T/m; |f0.2GeV|=5.04m Constrain: Coupled focal distance: |f1GeV|~5|f0.2GeV| Need DE energy gain between 2 quads A lattice solution was found by Pascal: see later slides

Matching Section to Main Linac For positrons, 1 GeV, total length of matching section= 17.6 m ax = 0.47 bx = 11.8m ay = 0.52 by = 16.1m ax = 0 bx = 58.1m ay = 0 by = 43.6m x y From BC Quads To linac For electrons, 0.2 GeV, total length = 6.425 m ax = 0 bx = 24.4m ay = 0 by = 4.2m ax = 0.5 bx = 14.0m ay = −0.5 by = 14.0m From PA No e+/e- dipole combiner between matching section and main linac: This would require an other section BC: Bunch Compressor, PA: pre-accelerator

Quadrupole strength? Transport (*) is first used to check that the beam is well confined within the fodo lattice with the initial condition. This does not include acceleration. * Computer program for designing charge particle beam Transport: SLAC R-091 Quadrupole gradient = ±1.3 T/m Rather periodic for both beams The lattice is appropriate for e+ and e- beams Quadrupole dimension design based on Octagon Quads from Radiabeam Tech. with Leff= 10.2 cm, gmax=9T/m

Tank Space - Particle simulation 1000 particles are simulated using Parmela Initial bunch length= 10o Energy dispersion=1% 26 TW tanks, 2.856 GHz Eref=~2.2 GeV Energy difference with ref. particle If the distance inter tank is correctly calculated, the phase of each tank should be equal and fixed to get maximum energy gain along the linac. This is the case, we’re at crest and the phase is fixed for each tank i.e. j=0o e+ are well accelerated on crest. Also e- too if they are p away Phase difference with ref. particle

Acceleration and Betatron length 5.7 GeV e+ 1 GeV e+ bmax=58m 4 GeV e- 0.2 GeV e- bmax=55.6m Linac total length = 450m, 63 tanks are required. The quads gradient is adapted for e+ but not specific to the e- Average Energy gain per tank = 46.3 MeV with max tank gradient = 14.75 MV/m b is stable for the e+ and under 60m. For the e-, b diverge, but is still small at the extraction

Emittance measurement Design of a section to measure emittance (upstream the matching section and behind the BC) 1) a doublet (to blow the beam and get sufficient sizes on the downstream screen at 3 ) 2) A triplet (magnetic strength modified to measure s11 on a screen) gex1,2 Total length=27.65 m We want: gex1=gex2 and ax=ay=0 at the screen So we need: gex/gin=-1.0277 T/m gex=-8.8842 T/m to get minimum waist at the screen Choice of a large central quad (35 cm) of gradient strength gin to limit the total length of the section

Simulation of Emittance Meast Simulation with Transport The triplet focal length is modified by scanning the gradient strength from -10T/m down to -5.5 T/m 18 simulated measurements of x2max and y2max on the screen O (10-8 m2) From the parabolic fitting: ex=6.6 10-9 p m rad, ey=3.9 10-9 p m rad Which are the values we injected  System is appropriate

Energy Dispersion Measurements Design for an energy dispersion measurements system at the end of the positron pre-accelerator (1GeV) based on a single quadrupole and a screen Design of a compact system Dipole field = 0.5 T Central length = 1m Angle = 8.58o Minimal length after dipole = 1m Simulation Results of the screen readings with various energy dispersion

Conclusion & Perspective Linac: Found a suitable design to carry both positrons and electrons beams up to main ring energy Matching section designed Missing combiner Diagnostics for linacs: Design and Dimension done for Emittance and Energy dispersion measurements Perspective: Every calculation is done to the first order. Second order should be the next step More realistics beams should also be used for the linac to check energy/phase distribution. Simulation of the complete linac simulation, probably with ASTRA Alignment errors impact on emittance should also be checked