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Development of models of intrabeam scattering for charged beams in

storage rings

E. MikhaylovaJoint Institute for Nuclear Research

Dubna, Russia

The First seminar of FRRC Fellows FAIRMoscow, June, 9 – 10, 2009

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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

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FAIR - Facility for Antiproton and Ion Research

100 m

UNILAC SIS 18

SIS 100/300

HESR:PANDAPAX

SuperFRS

NESR

CRRESR

ESR

FLAIR

Rare-IsotopeProduction Target

AntiprotonProduction Target

What have we done for FAIR?

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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

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Simulation of long-term processes

The general goal

What is it? How long?

Processes which lead to variation ofthe ion distribution function in 6 dimensional phase space: cooling processes, IBS

In comparison withthe 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

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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

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Model Beam algorithm

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1jjijiii DttFtpttp

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 thesame mass and charge asreal particles, BUT numberof model particles is muchless than real particle number

Way

We take intoaccount effectsof particle lossHow to do it

Initial model particlemomentum

Acting forces(cooling forces)

Coefficientsof diffusion

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Principle of growth rates calculation

Modelparticles

Distribution overthe coordinatesand velocities

Gaussianshape

IBS growth rates

increase incalculation

speed

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4 analytical models of IBS

1. Piwinski2. Martini3. Jie Wei4. Gas Relaxation

Works with average parameters of ringIntegrates over each optic elementSimplified version for high energy storage ringDoes not describe relaxation betweendegrees of freedom

Which model of IBS do we prefer?

Martini modelAs 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 toinvestigate the integrals and the all integrands

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Martini Model

0 0

2

0

21ln),(exp),(sin dzddzzDgkf iii

221 cossin31),(g

adg /cossinsin~6sinsin31),( 222

23 cos31),(g

2

222222 coscos~sinsincossin),(

c

bdaD

We use Martini model for calculation of the growth rates. According to thismodel we have to calculate some functions to find characteristic times

We calculate growth rates in momentum space. But it is better to transferrectangular coordinates to cylindrical coordinates in order to simplify somecalculations. According to this transformation the necessary functionswill look like this:

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IBS Program CodeThe IBS program code was created in order to investigate the integrals and the all integrands

What happens?

0 0

2

0

21ln),(exp),(sin dzddzzDgkf iii

the D(μ,ν) value at some beamparameters can be close to zero: critical points

0

0

2

),(

21ln),(exp DC

D

LdzzzD

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The problemThe result of calculations can depend onnumber of integration steps a lot!!!

is that

Howto escape?

To use avariableintegrationstep

),(1 DVariablestep near

criticalpoints

Constantstep

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Comparison of Results We made calculations for a single lattice elementof a ring in order to check IBS Program work

1. BETACOOL2. Mathematica

Coincidence witha sufficient accuracy

Comparisons withexperimental data

nowWith help ofBETACOOL

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Application of IBS Program

Why should we use it?

1. IBS is an independent program for everybody who wantsto calculate the IBS rates in storage rings

2. A simple way of calculations of IBS growth rates3. Comfortable graphical interface under Windows4. Possibility of getting a ring lattice structure from a MAD file5. 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 useit for them own program codes

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The graphical interface

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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 :

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Thank you for your attention!