1. 1 Development of models of intrabeam scattering for charged beams in storage rings E. Mikhaylova Joint Institute for Nuclear Research Dubna, Russia The First seminar of FRRC Fellows FAIR Moscow, June, 9 – 10, 2009

2. 2 BETACOOL application over the world (since 1995) RIKEN, Wako NIRS, Chiba Kyoto Univ. Hiroshima Univ. Beijing Univ. IMP, Lanzhou Fermilab, Batavia BNL, Upton Tech-X, Boulder FZJ, Jülich GSI, Darmstadt Erlangen Univ. MPI, Heidelberg CERN, Geneva München Univ. TSL, Uppsala MSL, Stockholm JINR, Dubna ITEP, Moscow ITMP, Sarov BINP, Novosibirsk http://lepta.jinr.ru/betacool.htm

3. 3 FAIR - Facility for Antiproton and Ion Research 100 m UNILAC SIS 18 SIS 100/300 HESR: PANDA PAX Super FRS NESR CR RESR ESR FLAIR Rare-Isotope Production Target Antiproton Production Target What have we done for FAIR?

4. 4 BETACOOL for FAIR ESR – experiments with electron cooling and gas cell target, ordered beams, injection with RF system, etc. SIS18 – estimation of electron cooling NESR – accumulation with electron cooling HESR – optimization of electron cooling system PANDA – effective luminosity with internal pellet target PAX – optimization of colliding experiment with electron cooling system FLAIR – optimization of electron cooling

5. 5 Simulation of long-term processes The general goal What is it? How long? Processes which lead to variation of the ion distribution function in 6 dimensional phase space: cooling processes, IBS In comparison with the ion revolution period We can do the simulation on condition that: The ion beam motion inside a storage ring is supposed to be stable and is treated in linear approximation Linear matrixes

6. 6 Advantages 1.Many different effects (ECOOL, IBS, Target, RestGas etc.) can be simulated simultaneously at the same parameters using different algorithms 2. Fast estimations on PC 3.Graphical interface under Windows 4. Control the results and vary parameters during simulation

7. 7 Model Beam algorithm Ion beam is presented by array of model particles. Each effect calculates a kick of the ion momentum components and changes the particle number To numerical solve Langevin equation What is it? Model particles have the same mass and charge as real particles, BUT number of model particles is much less than real particle number Way We take into account effects of particle loss How to do it Initial model particle momentum Acting forces (cooling forces) Coefficients of diffusion

8. 8 Principle of growth rates calculation Model particles Distribution over the coordinates and velocities Gaussian shape IBS growth rates increase in calculation speed

9. 9 4 analytical models of IBS 1.Piwinski 2. Martini 3. Jie Wei 4. Gas Relaxation Works with average parameters of ring Integrates over each optic element Simplified version for high energy storage ring Does not describe relaxation between degrees of freedom Which model of IBS do we prefer? Martini model As the most accurate model (need more simulation time) BUT! There is an irregular dependence on an integration step A special program code was created in order to investigate the integrals and the all integrands

10. 10 Martini Model We use Martini model for calculation of the growth rates. According to this model we have to calculate some functions to find characteristic times We calculate growth rates in momentum space. But it is better to transfer rectangular coordinates to cylindrical coordinates in order to simplify some calculations. According to this transformation the necessary functions will look like this:

11. 11 IBS Program Code The IBS program code was created in order to investigate the integrals and the all integrands What happens? the D(μ,ν) value at some beam parameters can be close to zero: critical points

12. 12 The problem The result of calculations can depend on number of integration steps a lot!!! is that How to escape? To use a variable integration step Variable step near critical points Constant step

13. 13 Comparison of Results We made calculations for a single lattice element of a ring in order to check IBS Program work 1.BETACOOL 2. Mathematica Coincidence with a sufficient accuracy Comparisons with experimental data now With help of BETACOOL

14. 14 Application of IBS Program Why should we use it? 1.IBS is an independent program for everybody who wants to calculate the IBS rates in storage rings 2. A simple way of calculations of IBS growth rates 3. Comfortable graphical interface under Windows 4. Possibility of getting a ring lattice structure from a MAD file 5. The IBS program will appear on the Internet soon as a public resource + library of Martini integral calculations. http://lepta.jinr.ru/ 6. We changed object-oriented structure of the program to procedure one in order to other programmers could use it for them own program codes

15. 15 The graphical interface

16. 16 My plans for FAIR 1.Improvement of numerical models of electron and stochastic cooling in common with the University of Tokyo and scientific centre GSI and FZ-Juelich (calculations of cooling processers and balance with intrabeam scattering for NESR, HESR) 2.Beam dynamics simulation for NESR and HESR storage rings (calculation of charge particle accumulation process for NESR) 3.Beam dynamics simulation for FLAIR project (calculation of cooling process for LSR, USR) I suppose to do in the future :

17. 17 Thank you for your attention!