1. 12-й Международный семинар по проблемам ускорителей заряженных частиц, посвященный памяти В.П.Саранцева
CONCEPT OF A LOW-ENERGY ELECTRON-POSITRON COLLIDER TO SEARCH AND STUDY + BOUND STATE
A.V. Bogomyagkov, V.P. Druzhinin, E.B. Levichev
A.I. Milstein, S.V. Sinyatkin
Budker Institute of Nuclear Physics
Alushta, 3 – 8 September 2017

2. Motivation
Discrepancies between experiments and theory in the muon sector: Disagreement between the anomalous magnetic moment measurement and Standard Model prediction, the muonic hydrogen proton’s charge radius discrepancy, etc.
A discovery of a new lepton bound state, which has not been observed yet contrary to positronium (е+е) and muonium (+е), and its study is by far a challenging and interesting scientific enterprise.
Dimuonium is a Bohr atom and its study (including transition spectroscopy, lifetime precise measurement, etc.) allows verifying QED and quantum mechanics computations with great accuracy.
In such a research, (+) has higher new-physics reach potential in comparison with other exotic atoms.

3. Collider implementations:
Scientific case
Collider implementations:
Intersection of beams at a large angle;
Lower beam energy, Eb  400 MeV;
Small collider dimensions;
Cheapness of manufacture and operation;
Additional area of study:
The energy of the beams and the configuration of IR make it possible to investigate the processes of е+е pions and е+е ,.

4. LARGE ANGLE BEAM CROSSING
E1, p1
E2, p2
Head-on collision  = 0.
Collision invariant mass (c = 1):
Invariant mass energy resolution σМ:
– relative beam energy spread
- r.m.s. angular spread.

5. LARGE ANGLE BEAM CROSSING
Peak luminosity (w/o hour-glass effect) intersecting beams at  angle:
Estimation of dimuonium maximum production rate:
mµµ, Гµµ = 0.3710-6 keV and µµ – are dimuonium mass, leptonic width, and the peak cross section

6. - Factor defines the sign of the momentum compaction.
BEAM-BEAM EFFECTS
The beam-beam tune shifts for flat beams:
For some (not necessary large) intersection angle  :
- Factor defines the sign of the momentum compaction.

7. BEAM-BEAM EFFECTS Bunch current limitation
The linear Hamiltonian of longitudinal motion :
RF system
the colliding bunch electrical field
Suppression of longitudinal beam-beam effects:
Limitation of bunch intensity:

8. COLLIDER PARAMETERS SELECTION
Head-on collision:
Low energy of colliding beams (E = 105 MeV):
Compactness of the collider;
Strong current density effects (IBS, Impedance etc.);
Monochromatization (Renieri method);
Estimated luminosity: L0 ~ 1030 cm-2s-1;
Dimuonium maximum production rate Nμμ ~ 50 u/h;
Observation of the dimuonium by searching for X-rays from (+) Bohr transitions such as 2P1S => production and rapid annihilation of a single neutral system at rest inside the bunch are difficult to identify and separate from the dominating QED background;
In order to get sufficient positron rate after converter, the primary electron beam requires much higher energy that in the collider.

9. COLLIDER PARAMETERS SELECTION
Large angle beam crossing:
The scheme allows to reduce the vertical beta-function;
Dimium registration is facilitated by taking the µ+µ  е+е process out of the main beam region.
Increase in energy suppresses IBS;
The beam energy (E ~ 400 MeV) corresponds to the energy range of the existing injector with a production rate of ~0.511010 е+/е per second;

10. Collider specification
The crossing angle of 75 allows (+) production for the beam energy of Eb = 408 MeV (m = MeV).
The crossing angle of 75 provides 13S1 (+) decay path 2 mm, it is enough to detect the atom decay to е+е.
To increase the signal-background ratio the horizontal beam size at the IP should be σx* ≈ 0.15 mm << c.τμμ=0.54 mm.
For large crossing angle, horizontal angular spread at the IP is the main source of the invariant mass resolution degradation. To reduce the angular spread having the small beam size collider has to provide low horizontal emittance.

11. Collider specification
Momentum compaction  :
<0 - in such a mode microwave instability current threshold reduces, giving larger beam energy spread and transverse size and smaller luminosity;
>0 – The longitudinal beam-beam effects are observed.
>>0 ( ~ 0.06) – The current (N0_e+e- ~ 3.51010) is below on the longitudinal beam-beam effect current limitation and provides the optimal Touschek lifetime with the necessary luminosity. More compact structure;
The collider must have two separate rings to obtain required luminosity in a multibunch mode operation.
The vertical beta function (2 mm) at IP is limited by the lower limit due to the need for special chromatic correction scheme that require additional space.

12. Research of processes е+е pions and е+е ,
At 70 + (m = МэВ) can be generated at the same beam energy. The angle modification is available either by mechanical rearrangement of the interaction area or using corrector magnets.
Reverse of the beam circulation direction in one of the rings changes the crossing angle to 15, and makes it possible to study with high luminosity energy range from -meson (m = MeV, Eb  284 MeV at  = 15) to -meson (m = MeV, Eb  496 MeV).

13. COLLIDER Layout The dimensions of the collider 126 m2;
IP1
IP2
The dimensions of the collider 126 m2;
Ring circumference – 23 m.

14. COLLIDER Twiss functions
Twiss at IPs:
x* = 15 cm
y* = 2 mm
ηx* = 0 m
y_max = 50 m
DBA
MBA

15. Basic parameters of -collider
Beam energy (MeV)
408
Circumference (m) 23
Bunch intensity/current (mA)
3.51010/73
Revolution frequency/period (MHz)/(ns)
13.04/76.7
RF harmonic number/frequency (MHz)
26/338.98
Energy loss per turn (keV)
2.3
RF voltage (kV)
450
RF acceptance 2%
Synchrotron tune
1.7110-2
Momentum compaction 
6.410-2

16. Basic parameters of -collider
Damping time hor/ver/long (ms)
17.3/27.3/22.1
Damping partition hor/long
1.6/1.4
Horizontal emittance (without/with IBS) (nm)
26/90
Energy spread (without/with IBS), 104
4/8.4
Bunch length (without/with IBS) (mm)
5.4/11.6
Betatron coupling
0.3%
IP horizontal angular spread *x’104
6.7
Invariant mass resolution (keV)
390
Hor/vert betatron function at IP (mm)
200/2
Hor/vert betatron size at IP (m)
130/0.7
Hor/vert beam-beam parameter (x/y)
210-6/1.210-3
Longitudinal beam-beam parameter z
–210-3
Peak luminosity for 1 bunch (cm-2s-1)
41030
Peak luminosity for 20 bunches (cm-2s-1)
81031

17. Parameters of magnetic elements
Dipoles
Name N
L, m
R, m
alf,rad
B,T
G, T/m
B1_1 2
1.4
1.069
1.310
1.273
-1.354 B3 8
0.42
0.393
-3.349 B2
0.28
0.262
Quadrupoles
Name N
L, m
G, T/m Q2 2
0.200
0.00 Q8
7.05 Q7
0.2
9.49 Q3 1
12.72
Q6B
13.64
Q13 3
14.48
Q10
18.66
Q1B
20.38
Q11
22.54
QD0 4
32.70
Sextupoles
Name N
L, m
S, T/m^2
S5.1 6
0.05
188.2
S1.1 2
248.9
S3.1
612.4
S2.1 4
2133.1

18. EXA2017, 10-15 September 2017, Vienna, A. Bogomyagkov
Interaction region
Experimental chamber: flat box with 0.5-mm-thick beryllium windows on the top and on the bottom allowing passage of е produced by the dimuonium atoms decay.
Detector: tracking systems around the median plane, magnetic spectrometer
QD0: permanent magnet, G=-35 T/m,  30mm
QD/QF1: electromagnet
EXA2017, September 2017, Vienna, A. Bogomyagkov 18

19. Interaction Region Experimental chamber:
flat box with 0.5-mm-thick beryllium windows on the top and on the bottom allowing passage of е produced by the dimuonium atoms decay.
Detector:
tracking systems around the median plane, magnetic spectrometer
QD0:
– On permanent magnets
– Maximal gradient –35 Т/м
– Small transverse dimensions 45 mm

20. Dimuonium production rate of collider
(+) states distribution along the escape line

21. Measurements from  to -meason ( = 15  )
Reverse of one of the beams changes collision angle from 75 to 15 and opens additional possibilities for experiments.
The measurement range from the -meson (m = MeV, Eb  284 MeV) to the -meson (m = MeV, Eb  496 MeV);
Experiments with a traditional detector and a longitudinal magnetic field;
Replacement of permanent magnetic elements of the final focus.

22. Measurements from  to -meason ( = 15  )
Beam energy (MeV)
()
()
Invariant mass (MeV)
547.86
957.76
Energy loss per turn (keV)
0.535
4.997
RF voltage (kV)
300
550
Synchrotron tune
1.6710-2
1.7110-2
Horizontal emittance (without/with IBS) (nm)
11.4/105
34.8/75
Energy spread (without/with IBS), 104
2.8/10.6
4.8/8.4
Bunch length (without/with IBS) (mm)
3.7/14.2
6.3/11
IP horizontal angular spread *x’104
8.3
7.1
Invariant mass resolution (keV)
420
580
Hor/vert beam-beam parameter (x/y)
310-4/1.410-2
310-4/1.310-2
Longitudinal beam-beam parameter z
–1.810-3
–1.710-3
Peak luminosity for 1 bunch (cm-2s-1)
3.31031
5.21031
Peak luminosity for 20 bunches (cm-2s-1)
6.61032
11033

23. Conclusion
Preliminary design of the electron-positron collider for production and study of the (+) bound state is considered.
Two rings collider with large crossing angle is quite compact, the ring orbit length ~2030 m, and not expensive in development and maintenance.
Luminosity 41030 cm-2s-1 (Nb=1), 81031 cm-2s-1 (Nb=20)

24. Conclusion
When the injection scheme is changed it is capable to perform other experiments with high luminosity in the center-of-mass energy range ECM  5001000 MeV.
An additional detailed study of beam dynamics is necessary:
chromatic correction
dynamic aperture
collective effects
magnet and vacuum system designs …

25. -collider in the hall of the φ-factory.