Algorithms for emittance evaluation

1. Algorithms for emittance evaluation

2. Emittance measurements

3. Slit-grid devices • Trusted method • Wire current resolution 1pA • Integration time 1us..Nsec • Spatial resolution ~100um • Measurement time minutes

4. Slit-grid control software

5. Pepper-pot measurements without scintillating screen

6. Use of optical registration

7. An example of optimal resolution ratio for single shot operation

8. Dedicated algorithms and outputs

9. Scattering effects in screens, holes and slits

10. Pepper-pot calibration • Pinhole effective radius calibration • Estimation of the light scattering effect in the screen • Pinholes zero position calibration with low-emittance light beam

11. Use of multiple profile monitors

12. Use of variable quadrupole strengths

13. Longitudinal emittance measurements Timo Milosic. Thursday. 10:50

14. Ellipses and linear optics

16. Canonical distributions

17. Universal algorithms • Mostly exist for two-dimensional phase space • Applicable for any measurement type • Data transformation: applying of linear optics element, resampling etc. • Noise and fraction reduction • Data healing tools • 2-D emittance calculation

18. Use of KV-plane for the emittance estimation

19. Use of statistical momentums

20. Use of optimal fitting methods

21. Use of parametric data fit

22. A comparison of different methods

23. Errors estimation • Noise added to the data value • Errors due to the model simplification • Limitation of the parameterized model • Limited accuracy of parameters of involved beam optics elements • Non-ideal registration equipment (non-linearity, aberrations, cross talk,… )

24. Typical output of the emittance evaluation results

25. Typical preliminary data evaluation in 2-D space

26. An example of an interactive tool for 2-D emittance evaluation

27. Few nice output plots which good to have for report and publications • For standalone applications – OpenGL primitives library • To save some time one may use TeeChart • Tools based on MATLAB or MathCAD could be easily adapted to any new ideas. License cost is critical.

28. Typical preliminary data evaluatin in 2-D space

29. A data manipulation possibilities are always demanded

30. The basic evaluation uses only first order integration algorithms Main calculations in EmitView are executed on the data matrix. Each element of this matrix owned an elementary current. In the assumption that the current density is uniformly distributed on the surface of elementary cell, this current is equal to product Ii,k=Ji,k*dx*dy. Where J is the current density in the phase space coordinates. Thresholds and KV levels are defined as a percentage of the maximum elementary current value. Captured current and KV plane are defined as a part of full current, which is sum of all elementary currents. RMS emittance for defined KV level is calculated by formula . Statistical parameters for given formula are calculated for current density weighted elementary cells. Only cells with current higher then KV level are taking into account.

31. Pepper pot algorithms • Image processing technique • Limited spatial resolution • 4- dimensional phase space

32. Pepper-pot ‘classical’ data preparation EMITTANCE MEASUREMENTS AT THE NEW UNILAC PRE-STRIPPER USING A PEPPER-POT WITH A PC-CONTROLLED CCD-CAMERA. M.Dolinska et al. DIPAC 1999, Chester. UK.

33. Noise cancellation

34. Local spot filtering

35. Parametric nonlinear data fitting

36. Image evaluation cycle

37. Horizontal profile

45. An example of a heavy ion beam investigation Beam divergence as a function of applied potential 7kV 10kV 14kV

46. An example of a heavy ion beam investigation(2)

47. An example of a heavy ion beam investigation(3)

48. An example of a heavy ion beam investigation(4)

49. Parametric nonlinear data fitting