1. BINP, Novosibirsk, Russia
Calculation and Measurement of Non-Gaussian Beam Tails due to Scattering on Residual Gas Targets
O.I.Meshkov, E.B.Levichev, A.N.Zhuravlev, E.V.Kremyanskaya, N.Yu.Muchnoi, Yu.A.Pahotin, N.A.Selivanov, D.N.Shatilov, S.A.Glukhov,
BINP, Novosibirsk, Russia
Sergey Glukhov
Beam Dynamics meets Vacuum, Collimations, and Surfaces, 8-10th March 2017, Karlsruhe, Germany

2. History The experiment was carried out in 2004:
O.I.Meshkov, E.B.Levichev, A.N.Zhuravlev, E.V.Kremyanskaya, N.Yu.Muchnoi, Yu.A.Pahotin, N.A.Selivanov, D.N.Shatilov, Study of Beam Tails with the Optical Coronagraph
For simulation purposes the following theory was used:
K.Hirata, K.Yokoya. Non-gaussian Distribution of Electron Beams Due to Incoherent Stochastic Processes
Then a few theoretical calculations were performed:
The present talk
Now there are plans to repeat the experiment with the X-ray pinhole camera.
O.I.Meshkov, A.N.Zhuravlev, V.V.Smaluk, Multi-Pinhole Camera for Beam Position and Vertical Angle Stabilization

3. Theoretical part

4. Campbell–Rice theorem
Consider a random value ω with distribution density ρ(ω):
It is changing due to some stochastic process:
This process has single-collision distribution density:
Consider its Fourier image:
Number of collisions has Poisson distribution:
Then Fourier image of the distribution density is the following:
Now we can obtain the distribution density function:

5. Beam density distribution
Consider normalized transversal betatron coordinates:
Then
initial Gauss distribution:
new distribution:
where
and

6. Residual gas scattering
Elastic scattering on residual gas atoms has the following cross-section:
Single-collision distribution density:
Then
and

7. Some maths... Bessel function was decomposed into Taylor series:
Two “tabular” integrals were calculated by hands:
The integral of interest was transformed into the rapidly converging series:

8. Ĉ-function

9. Experiment and simulations

10. VEPP-4M facility layout
Coronagraph 2 (optical)
Pinhole camera (X-ray)
Coronagraph 1 (optical)

11. Optical coronagraph layout

12. Coronagraph test (I) 0.8mm × 3mm light source (close to beam sizes):
without mask:
with mask:

13. Coronagraph test (II)
Integrated coronagraph signal vs time during the artificial variations of residual gas pressure:

14. Simulation results
Simulated beam distribution for different energies of VEPP-3, P = 2·10-9 Torr

15. Experiment at VEPP-3 and simulation
Difference between distribution functions at different residual gas pressures, E = 356 MeV, P1 = 2·10-9 Torr, P2 = 3·10-9 Torr

16. Experiment at VEPP-4 (I)

17. Experiment at VEPP-4 (II)

18. X-ray pinhole camera layout (I)
* O.I.Meshkov, A.N.Zhuravlev, V.V.Smaluk, Multi-Pinhole Camera for Beam Position and Vertical Angle Stabilization

19. X-ray pinhole camera layout (II)
Unused diagnostic channel at VEPP-4
CCD-camera
scintillator
mask
pinhole
primary scintillator

20. Summary Beam tails measurement is important for
detector background assessment,
collimation design,
lifetime improvement,
dynamic aperture measurement,
etc.
Experiments at VEPP-4M have shown the possibility of such studies using coronagraph.
Theory proposed by Hirata & Yokoya and its analytical improvement can be applied to the scattering on residual gas atoms and to other stochastic processes with non-Gaussian distribution tails.

21. Thank you for your kind attention!