1. 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

2. Global scheme “New” Scheme – M. Preger’s Elba talk f) b) d) a) c)
50 MeV
CAPTURE
SECTION
THERMIONIC
GUN
0.95 GeV PC
GeV
SHB b)
combiner
DC dipole d) e+ a)
BUNCH
COMPRESSOR
5.7 GeV e 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

3. 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

4. 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 = 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

5. 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 = 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

6. 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

7. Tank Space - Particle simulation
1000 particles are simulated using Parmela
Initial bunch length= 10o
Energy dispersion=1%
26 TW tanks, 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

8. 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 = MV/m
b is stable for the e+ and under 60m. For the e-, b diverge, but is still small at the extraction

9. 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= T/m
gex= 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

10. Simulation of Emittance Meast
Simulation with Transport
The triplet focal length is modified by scanning the gradient strength from T/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= p m rad, ey= p m rad
Which are the values we injected  System is appropriate

11. 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

12. 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