Theory of electron cooling

Transcription

1 Theory of electron cooling Daria Astapovych 03/12/2014 HSC Meeting

2 Outline Motivation and idea of the particle beam cooling Cooler Low energy, high energy beam Electron beam Kinetics of electron cooling and electron cooling force Positive and negative charge particles Application Simulation of electron cooling Conclusions

3 Motivation From experiments with targets to experiments with colliding beams => To improve beam quality Precision experiments Luminosity increase Compensation of heating To increase the intensity by accumulation Weak beams from source can be increased Secondary beams (antiprotons, rare isotopes)

4 Particle beam cooling reduction of the beam temperature in the storage ring due to some mechanism of dissipation. Temperature = phase space volume, emittance and momentum spread is a violation of conditions of Liouville's theoreme: the phase space distribution function is constant along the trajectories of the system.

5 Methods of beam cooling Radiation cooling (synchrotron radiation): electron, positron; Ionization cooling: muon; Stochastic cooling: for long bunches, small number of particles, large velocity spread; Laser cooling: atoms and non fully ionized beam; Electron cooling: heavy particles, ions.

6 The idea of electron cooling In 1966 Budker proposed to cool a proton beam by an electron beam. The velocity of the electrons is made equal to the average velocity of the ions. During the cooling the temperatures become equal 2 m v e =M v 2 The angular spread in proton beam m θ= θe M

7 Cooler 1974 NAP M, Novosibirsk Electron Gun Electron Collector Electron beam Ion beam 1-5% of the ring circumference 1 electron gun; 2 magnetic coils and electrostatic plates; 3 toroidal solenoid; 4 main solenoid; 5 magnetic shield; 6 collector solenoid; 7 correction coil of ion beam orbit; 8 vacuum channel of ion beam orbit.

8 Low energy < 2 3 MeV electrons High energy (< 4 6 GeV p, p ) Energy recuperation to decelerate the electrons to the lowest possible energy Transport over large distance: Longitudinal magnetic field accompanying the electron beam > 2 3 MeV electrons (> 4 6 GeV p, ) At low energy closed and toroidal longitudinal magnetic field At higher energy radiation cooling of electrons or through periodic short term lowering of the cooled particles energy and the use of EC at a comparatively low energy

9 Electron beam for cooling Transverse: at high intensity the beam has a tune shift ; at low intensity the average transverse size < 10 μm. Longitudinal: at high intensity Δp can not be easily determined from either the Shottky spectra or the bunch length; at low intensity the the beam may exhibit effects of ordering; Typically, the ultimate momentum spread is determined by the IBS.

10 Electron beam for cooling (2) Magnetized electron beam depends on the intrabeam heating. is strong enough, that average Larmor radius of the If the magnetic field H transverse rotation of electrons becomes much smaller than the distance between them m v c 1/ 3 ρl = n eh then the electron collisions will be adiabatic.

11 Electron beam for cooling (3) At low currents, there is a plateau, the length of which depends on the magnetic field. At high enough currents the curve reaches its asymptotic I 1/e 2. The presence of a plateau on the experimental curves indicates the strong influence of the longitudinal magnetic field, which suppresses the process of transverse longitudinal temperature relaxation. Dependence between the electron energy spread at the end of the section and the magnetic field (and the current). 1 B=0 (theory) 2 4 B=1,3,4 kg

12 Kinetics of electron cooling Significant contribution to the collision integral can give the area r <b<b L max rl Larmor radius, b impact parameter Due to the electrostatic acceleration of the electron beam the longitudinal electron temperature is much smaller than transverse. The longitudinal magnetic field will magnetize the transverse motion of electrons, that with small longitudinal electron temperature caused the growth of contribution to cooling of collisions with large impact parameters.

13 Non magnetized EC force (1) The Vlasov technique (dielectric model) takes into account the collective interaction of the electrons in the plasma. The binary collisions: the momentum transfers from individual electrons scattered against one ion are summed. In the case of ultra cold electron plasma The Coulomb logarithm should be large!

14 Non magnetized EC force (2) Numerical integration In case of electron distribution f(ve) The Coulomb logarithm should be large! The Coulomb logarithm is kept under the integral due to the dependence of min impact parameter on electron velocity

15 Non magnetized EC force (3)

16 Magnetized EC force (1) Due to the influence of magnetic field to transverse motion of electrons, transverse degree of freedom doesn't take part in the energy exchange. Derbenev Skrinsky formula: where ne, m electron density and mass, ion velocity, relative velocity of the ion and an electron Larmor circle. The Coulomb logarithm

17 Magnetized EC force (2) Derbenev Skrinsky function has asymptotes: V >> ΔII, can be approximated by the delta function f(ve)=δ(ve) V << ΔII These formulas were originally derived based on a perturbative treatment of the collective plasma response.

18 Magnetized EC force (3) An empirical expression was suggested by Parkhomchuk where Δe, eff effective electron velocity spread. The Coulomb logarithm

19 Magnetized EC force (4)

20 Magnetized or non magnetized?

21 Cooling rate BETACOOL Budker's formula Dependence of the cooling rate on the time: a) using BETACOOL (black curve), b) by formula of G. Budker (red curve). Transverse and longitudinal cooling rates with BETACOOL

22 NAP M Measurements (1) Dependence of the ion energy of the electron energy, B = 4kG, Ie = 3mA.

23 NAP M Measurements (2) Dependence of the friction force of the electron current, B = 3kG.

24 NAP M Measurements (3) Dependence on the magnetic field of the maximal friction force and optimal electron beam current.

25 Applications Particle physics: LEAR (CERN), Fermilab REC, BNL cooler, GSI, COSY (Julich FZ) Nuclear physics: ESR and SIS (GSI) Atomic physics: TSR, CryRing, AS TRID Antihydrogen generation: LEAR (CERN) Beam physics: NAP M (INP, Novosibirsk), ESR and SIS (GSI), CryRing Cancer therapy: HIMAC (NIRS, Japan)

26 Simulation of electron cooling BETACOOL JINR, Dubna, A. Smirnov MOCAC (MONte CArlo Code) ITEP, Moscow, P. Zenkevich, A. Bolshakov SIMCOOL (SIMulation of COOLing) BINP, Novosibirsk, V.Parkhomchuk, V.Reva PTarget (Pellet Target) GSI, Darmsdadt, A.Dolinsky CodeK2 (Katayma & Kikuchi) Tokyo University, T.Katayama, T,Kikuchi

27 Conclusions EC is an efficient tool of low energy heavy particle beams formation in storage ring. Particle beam physics is enriched significantly with development of EC method and its application to formation of intense and dense heavy particle beams.

28 References 1. Budker G. Electron cooling and new possibilities in elementary particle physics / G. Budker, A. Skrinskii // Sov. Phys. Usp V.124, ed.4. P BETACOOL Physics Guide for simulation of long term beam dynamics in ion storage rings (since 1995) / Meshkov I., Sidorin A., Smirnov A. Dubna, p. 3. Nersisyan H. Interactions Between Charged Particles in a Magnetic Field: A Theoretical Approach to Ion Stopping in Magnetized Plasmas / Nersisyan H., Toepffer C., Zwicknagel G. Springer, p. ISBN Rathsman K. Modeling of Electron Cooling. Theory, Data and Applications 56 / K. Rathsman. Uppsala, p. ISBN Simulation of electron cooling process in storage rings using BETACOOL program / Meshkov I.N., Sidorin A.O., Smirnov A.V. // Proceedings of Beam Cooling and Related Topics A. V. Fedotov, D. L. Bruhwiler, D.T. Abell, A. O. Sidorin, in Proceedings of International Workshop on Beam Cooling and Related Topic (COOL05, 2005), edited by S. Nagaitsev and R. J. Pasquinelli (American Institute of Physics, 2006), p I. Meshkov, A. Sidorin, Electron Cooling, Proc. of ECOOL'03, Japan 2003, NIM A, v. 532, 2004, p Skrinskii A.N. and Parkhomchuk V.V. : Melthods of cooling beams of charged particles. Sov. J Part. Nucl. 12 (1981) 223