Theory of electron cooling - CERN
Transcript of Theory of electron cooling - CERN
Theory of electron cooling
Daria Astapovych
03/12/2014 – HSC Meeting
Outline● Motivation and idea of the particle beam cooling● Cooler● Lowenergy, highenergy beam● Electron beam● Kinetics of electron cooling and electron cooling force● Positive and negative charge particles● Application● Simulation of electron cooling● Conclusions
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)
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 phasespace distribution function is constant along the trajectories of the system”.
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 nonfully ionized beam;● Electron cooling: heavy particles, ions.
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
● The angular spread in proton beam
mv e2=M v2
θ=√ mM
θe
Cooler
1974 NAPM, Novosibirsk
ElectronGun
ElectronCollector
1-5% of the ringcircumference
Electron beam
Ion beam
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.
Lowenergy ● < 2–3 MeV electrons
(< 46 GeV p, )
● Energy recuperation to decelerate the electrons to the lowest possible energy
● Transport over large distance: Longitudinal magnetic field accompanying the electron beam
Highenergy ● > 2–3 MeV electrons
(> 46 GeV p, )
● At low energy – closed and toroidal longitudinal magnetic field
● At higher energy – radiation cooling of electrons
● or – through periodic shortterm lowering of the cooled particles energy and the use of EC at a comparatively low energy
p̄
Electron beam for cooling
● Transverse:
– at high intensity the beam has a tuneshift 0.15–0.2;
– 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.
● “Magnetized” electron beam depends on the intrabeam heating.
● If the magnetic field is strong enough, that average Larmor radius of the transverse rotation of electrons becomes much smaller than the distance between them
then the electron collisions will be adiabatic.
Electron beam for cooling (2)
H⃗
ρL=mv⊥ c
eH≪n−1 /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 .
● The presence of a plateau on the experimental curves indicates the strong influence of the longitudinal magnetic field, which suppresses the process of transverselongitudinal temperature relaxation.
Electron beam for cooling (3)
Dependence between the electron energy spread at the end of the section and the magnetic field (and the current).1 – (theory) 2–4 –
B⃗=0B⃗=1, 3, 4 kG
I e1/2
Kinetics of electron cooling
● Significant contribution to the collision integral can give the area
rL Larmor radius, b – impact parameter
r L<b<bmax
● 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.
Nonmagnetized 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!
● Numerical integration
● In case of electron distribution f(ve)
● The Coulomb logarithm is kept under the integral due to the dependence of min impact parameter on electron velocity
Nonmagnetized EC force (2)The Coulomb logarithm should be large!
Nonmagnetized EC force (3)
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.
● DerbenevSkrinsky formula:
where ne, m– electron density and mass,
ion velocity,
relative velocity of the ion and an electron Larmor circle.
● The Coulomb logarithm
DerbenevSkrinsky function has asymptotes:
● V >> ΔII , can be approximated by the deltafunction f(ve)= (vδ e)
● V << ΔII
These formulas were originally derived based on a perturbative treatment of the collective plasma response.
Magnetized EC force (2)
● An empirical expression was suggested by Parkhomchuk
where Δe, eff – effective electron velocity spread.
● The Coulomb logarithm
Magnetized EC force (3)
Magnetized EC force (4)
Magnetized or nonmagnetized?
Cooling rate
Transverse and longitudinal cooling rates with BETACOOL
Dependence of the cooling rate on the time: a) using BETACOOL (black curve), b) by formula of G. Budker (red curve).
– BETACOOL
– Budker's formula
NAPM Measurements (1)
Dependence of the ion energy of the electron energy, B = 4kG, Ie = 3mA.
NAPM Measurements (2)
Dependence of the friction force of the electron current, B = 3kG.
NAPM Measurements (3)
Dependence on the magnetic field of the maximal friction force and optimal electron beam current.
Applications
● Particle physics: LEAR (CERN), Fermilab REC, BNL cooler, GSI, COSY (JulichFZ)
● Nuclear physics: ESR and SIS (GSI)
● Atomic physics: TSR, CryRing, ASTRID
● Antihydrogen generation: LEAR (CERN)
● Beam physics: NAPM (INP, Novosibirsk), ESR and SIS (GSI), CryRing
● Cancer therapy: HIMAC (NIRS, Japan)
Simulation of electron cooling
BETACOOL – JINR, Dubna, A. Smirnov
MOCAC (MONteCArlo 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
Conclusions
● EC is an efficient tool of lowenergy 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.
References1. Budker G. Electron cooling and new possibilities in elementary particle physics / G. Budker, A. Skrinskii // Sov. Phys.
Usp. – 1978. – V.124, ed.4. – P. 561–595.
2. BETACOOL Physics Guide for simulation of long term beam dynamics in ion storage rings (since 1995) / Meshkov I., Sidorin A., Smirnov A. –
Dubna, 2007. – 145 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, 2007. – 199 p. – ISBN 9783540698531
4. Rathsman K. Modeling of Electron Cooling. Theory, Data and Applications 56 / K. Rathsman. – Uppsala, 2010. – 148 p. – ISBN 9789155478711.
5. 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. – 2001.
6. 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.319.
7. I. Meshkov, A. Sidorin, Electron Cooling, Proc. of ECOOL'03, Japan 2003, NIM A, v. 532, 2004, p. 1925
8. Skrinskii A.N. and Parkhomchuk V.V. : Melthods of cooling beams of charged particles. Sov. J Part. Nucl. 12 (1981) 223