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Here you can find a list of useful references and a list of effects one should keep in mind (still to be completed!) Use the left menu for details on e-coolers in different machines at CERN and on the available software for simulation.

Interesting external websites

  • Summary of measurements performed at TSR link
    • Good source of ideas on what to do next
  • COOL’21 conference (Novosibirsk) link
  • COOL’19 conference (Novosibirsk) link
  • COOL’17 conference (Bonn) link
  • COOL’15 conference (JLAB) link
    • with list of previous conferences
  • Wiki space from JLAB about e-cooling and Electron guns.

E-cooling in the world

List of some known e-coolers in the world (to be completed/verified):

I_e [A] e^- E_k [keV] B_{gun} - B_{drift} [G] Ions In operation Reference
AD (CERN) <2.5 27 590 - 590 \bar{p} y PS-LI-Note-87-6
ELENA (CERN) <0.005 0.355 1000 - 100 H^-, \bar{p} y IPAC2016
LEIR (CERN) 0.6 2.3 2300 - 750 ^{208}Pb^{54+} y 10.1016/j.nima.2004.06.072
CELSIUS (Uppsala) 3 300 1500 - 1000(?) n 10.5170/CERN-1994-003.235 ISBN 978-91-554-7871-1
CSR (Heidelberg) 0.165 ~50 y COOL2009
TSR (Heidelberg) 16 12000-3000 n
NICA Booster (Dubna) <1 <60 700 ^{4}He^{1+}, ^{56}Fe^{14+} y RuPAC2021 RuPAC2018
NICA Collider (Dubna) 1 2450 2000 - 500 p, ^{194}Au^{79+} n COOL2019
CSRe (Lanzhou) 3 300 5000 - 1500 ^{12}C^{6+} y COOL2009 NIMA, 2000,441:87
CSRm (Lanzhou) 3 35 2400 - 1500 ^{12}C^{6+}, ^{36}Ar^{18+} y COOL2009
HIAF (Lanzhou) 2 50(450) 2500(4000) - 1500 COOL2017
SIS (Darmstadt) 35
ESR (Darmstadt) 1 230 2000 - 100
HESR (Darmstadt) n
CRYRING (Darmstadt) 13 y
COSY (Julich) 4 <100 1650 - 800 p, ^{2}H^{+} y arxiv, 1993, 1992
COSY (Julich) <0.5 <908 p, ^{2}H^{+} y arxiv
RHIC-LEReC (BNL) 2000 y COOL2021
IOTA (FNAL) 0.01 1.36 1000 p n arxiv
NAP-M (Novosibirsk)
S-LSR (Kyoto) 4
TARN II (Tokyo) 110

References about Electron Cooling and related topics, in descending chronological order:

  • May 2022: "Magnetic design of the new AD electron cooler (PXMLCEANWC)" EDMS
  • Nov 2021: D. Gamba et al. Presentation on AD/ELENA electron cooling experience during and after CERNs Long Shutdown (LS2) COOL21-S503 proceedings
  • Aug 2021: H. Zhao et al. Rate redistribution in dispersive electron cooling PRL 24.083502
  • May 2021: C. Krantx et al. Transverse electron cooling of heavy molecular ions link
    • Interesting source of data points for cooling simulations
    • No much information about cooling time as a function of optics functions
  • May 2021: G. Stancari et al. Beam physics research with the IOTA electron lens link
    • Detailed description of physics aspect for electron cooling and related at IOTA. Good starting point for physics aspect one should take into account in a low-energy ring with e-cooling-like devices.
  • Jul 2020: H. Zhao et al. Cooling simulation and experimental benchmarking for an rf-based electron cooler PRL 23.074201
    • Cooling simulations using `TRACKIT' - an BNL in-house devoloped code for bunched beam cooling simulations
  • Nov 2020: S. Seletskiy et al. Obtaining transverse cooling with nonmagnetized electron beam PRL 23.110101
    • Experience of high-energy electron cooling (with nonmagnetized electron beam) at RHIC
  • Nov 2020: Markus Steck, Yuri A. Litvinov Heavy-ion storage rings and their use in precision experiments with highly charged ions j.ppnp.2020.103811
    • Excellent review of running accelerators and general concepts used (including cooling) with many references
  • 26/03/2019: AD Cooler review indico
  • 2018: N.S. Dikansky et al. Development of techniques for the cooling of ions inspire
    • Very interesting review (maybe) but in Russian...
  • Fall 2017: V. N. Litvinenko et al. Hadron Beam Cooling slides
    • Short presentation with main results of cooling (both electron and stochastic)
  • 3/10/2017: Electron Cooling Studies (LEIR) indico
    • Results from steering test in LEIR electron cooler
    • Big horizontal emittance/cooling variation while scanning in vertical
      • To be continued
  • 7/08/2017: LEIR activities follow up, indico
    • status of LEIR multi-injeciton, high intensity.
    • plans to do orbit scan in the cooler.
  • Jun 2017: Andrea Latina indico
    • RF-track approach to e-cooling simulations
  • 2017: Yaroslav S. Derbenev Theory of electron cooling arxiv
    • Interesting theory review, translated from Russian
  • 2016: J. Resta-López et al. Non-Gaussian beam dynamics in low energy antiproton storage rings link
  • Sep 2015: Vsevolod Kamerdzhiev Introduction to electron cooling indico
    • interesting presentation with theory from 1990 paper I think…
  • 2015J. Resta-López et al. Simulation studies of the beam cooling process in presence of heating effects in the Extra Low ENergy Antiproton ring (ELENA) link
  • 2015: Igor Meshkov et al. Storage and cooling of ion beams link
    • review of techniques for accumulation in storage rings, including electron cooling (with references) and stochastic cooling.  
  • 2014: Beam Dynamics Newsletter no65 on Beam Coolings
  • July 2014I.Meshkov Beam Cooling Techniques indico
    • Very interesting presentations with a lot of details!
  • Apr 2014Daria Astapovych (2).pdf
    • Interesting presentation with references
    • Some parts were extracted from K. Rahsman - Modeling of Electron Cooling (2010) - thesis
  • SAP2014: L.J. Mao et al., Electron cooling experiments at HIRFL-CSR (link)
    • Interesting measurements of dragging force as done at LEIR
  • PRSTAB 2013: Hrachya B. Nersisyan et al., Cooling force on ions in a magnetized electron plasma PhysRevSTAB.16.074201
  • IPAC2012: V.V. Parkhomchuk, Development of electron coolers in Novosibirsk WEXA02
    • Review of the e-cooler technology used by BINP team to build their e-coolers, from NAP-M to LEIR to COSY.
    • Shows picture of Andrey Sery measuring cooling force on H- and H+.
    • Also stating that one should maximise magnetic field for having strongest cooling force!
    • Discussion on physical requirements for 2 MeV e-cooler for COSY.
    • Magnetic field straightness requirement of better than 1e-5.
    • Showing gun design with grid split in 4 to allow for measuring space charge effect (and therefore neutralisation) on e- beam transport
  • 2011: H. J. Stein et al. Present Performance of Electron Cooling at Cosy-Julich arxiv
    • Status of COSY e-cooling (similar to AD e-cooler).
    • Despite very good magnetic field quality measured in 1993 (see referecens below), in this paper it is quoted that cooling force was more inline to nonmagnetized coling.

i - Measurement of cooling force using CSR Main ring with e-cooler similar to the one of AD, but gun similar to the one of LEIR (multiple profiles measured) - Estimate of magnetic field quality from cooling force measurement down to 8e-5 (using formula of Parkhomchuk’s semi-empirical formula, with details!) - Measurement compatible field quality measurement in "Test Results of HIRFL-CSR Main Ring Electron Cooling Device" (2003, Chinese Physics C - CAS2008: F. Caspers, Lecture on Schottky Signals (link) - COOL2007: Cooling Results from LEIR, link - (to be read) - PhysRevSTAB 2006 A. V. Fedotov et al. Numerical study of the magnetized friction force, link - Overview of different approaches to simulate friction force - First brute force approach to simulate cooling force using VORPAL - EPAC06: LEIR ELECTRON COOLER STATUS, link - Nice overview of the commissioning of LEIR e-cooler - (to be read) - 2006: A. V. Fedotov et al. Experimental studies of the magnetized friction force PRE73 - Report on experiments in CELSIUS aimed at a detailed study of the magnetized friction force. - 2006: A.O. Sidorin et al. BETACOOL program for simulation of beam dynamics in storage rings link - 2006: Valentin Bocharov et al. First Tests of LEIR - Cooler at BINP DOI - Report by BINP with measurements of magnetic field and electron currents achieved - 2006: Valentin Bocharov et al. Precise Measurements of a Magnetic Field at the Solenoids for Low Energy Coolers doi - Details on the design of the pancake structure of LEIR ecooler and measurement of magnetic field. - 2006: V. V. Parkhomchuk Development of a New Generation of Coolers with a Hollow Electron Beam and Electrostatic Bending doi - Details on the physics of using electrostatic bending - Also details on definition of effective velocity taking into account magnetic field straightness! - Also details on the gun design with variable profile - 31/05/2005: Hakan Danared Beam Cooling - CAS - link - Some detailed derivation of friction force - There are also proceedings CDS - Link to possibility to measure the electron temperatures - 15/09/2004: G. Tranquille Specification of a new electron cooler for the low energy ion accumulator ring, LEIR. link - 11/10/2004: G. Tranquille Recent highlights from the CERN-AD NiMA - General report with serveral e-cooler (but not only!) tests in AD (neutralisation, dispersion in the e-cooler, ...) - Provides a table with performance reached in AD - Oct. 2004: M.Nishiura et al. Simulation studies of the electron cooler for MUSES at RIKEN link - Study of electron trajectory into toroids of e-cooling. - Sep. 2004: J. Bosser et al. Optimum lattice functions for electron cooling link - Summary of previous reports on Optimum Parameters for Electron Cooling - It contains some attempt to demonstrate reasons for faster cooling with dispersion - 2003: G. Tranquille Diagnostics for Electron Cooled Beams link - Overview of different instruments to measure e- and ions (Schottky, IPM, screen, Faraday Cup, neutrals monitor, laser, antenna, ...) - 2003: M. Beutelspacher et al. Dispersive electron cooling experiments at the heavy ion storage ring TSR link - Observation of better cooling at TSR with D=1.8 m. (Note that beam parameters probably close to CERN coolers) - Some theory to attempt to describe the effect - 2001: G. Tranquille Optimum Parameters for Electron Cooling cds - 2001: A. Skrinsky ELECTRON COOLING and ELECTRON-NUCLEI COLLIDERS link - Some math of e-cooling - 2001: V.V. Parkhomchuk Electron Cooling for RHIC link - 2000: V.V. Parkhomchuk, Aleksandr N Skrinskii Electron cooling: 35 years of development link - Interesting review of Parkhomchuk's cooling force and details - 2000: V.V. Parkhomchuk New insights in the theory of electron cooling link - Reference of Parkhomchuk semi-empirical model of cooling force - 2000: Bosser, J. et al. Stability of cooled beams, NIMA - Review of previous studies in LEAR and recomandation for controlling neutralisation and impedance - 2000 N St J Braithwaite, Introduction to gas discharges link1 link2 - Interesting summary with physics about particle interaction in plasmas. - 1999 Bosser, Jacques et al. Stability of cooled beams NIMA - Review - 1999 Bosser, Jacques et al. On the Optimum Dispersion of a Storage Ring for Electron Cooling with High Space Charge CERN-PS-99-045-OP - 1999 Bosser, Jacques et al. Experimental investigation of electron cooling and stacking of lead ions in a low energy accumulation ring CERN-PS-99-033-DI - Some generic formula for cooling time - Main summary of cooling experiments done at LEAR (with the AD-like cooler) - Includes data from cooling time as a function of optics parameters in the cooler - 1999 N. Madsen, Simulations of Electron Cooling Using BETACOOL link - Comparison of LEAR cooler performance and extrapolation to AD. Very extensive study! - 1998 S. Mannervik et al., Strong Relativistic Effects and Natural Line widths Observed in Dielectronic Recombination of Lithiumlike Carbon link - Measurement of electron temperatures using dielectronic recombination spectrum of C^{3+}. - 1997: J.Bosser et al. Experimental studies of electron beam neutralisation link - Details on measurement of e- neutralisation in LEAR - See also earlier paper of 1995 by J.Bosser on this topic - 1997: I.Meshkov Electron cooling — the first 30 years and thereafter link - interesting overview. Some formulas (e.g. cooling time). - 1996: Bosser, Jacques Review of recent work on electron cooling at LEAR CERN-PS-96-013-AR - This paper describes the measurements made on the cooling and lifetimes and on the neutralization technique implemented on the LEAR electron cooler. - Also reports on lifetime of different Pb charge states, see paper from 1995 below - 1995: Baird, S A et al. Measurement of the lifetime of Pb^{52+}, Pb^{53+} and Pb^{54+} beams at 4.2 MeV per nucleon subject to electron cooling CERN-PS-95-35-AR - 1995: Bosser, J. et al Neutralisation of the LEAR electron-cooling beam: experimental results DOI - Details about how neutralisation was implemented/studied in LEAR e-cooler - 1995: Bosser, Jacques Electron cooling (storage rings), CAS School 10.5170/CERN-1995-006.673 - Refers to e-cooling physics by Helmut Poth (see ~1990) - List of effects on the circulating beam (instabilities, kicks due to toroids, rest-gas interaction) - Also provides a table with existing e-cooler at the time - 1994: I.Meshkov Electron Cooling Status and Perspectives, Physics of Particles and Nuclei link linkCDS - theory explained, but not fully... - 1993: Prasuhn, D et al. Technical Features and Final Electron Beam Tests of the COSY Electron Cooler and First Proton Beam Cooling cds - Details about COSY e-cooler (very similar to AD e-cooler in some ways). Magnetic field quality measured at the the level of 10^-5 - 1993: Bosser, Jacques (ed.) Workshop on Beam Cooling and Related Topics CDS - General overview of all cooling techniques and experience at the time (stochastic cooling, laser cooling, electron cooling, muon cooling...) - theory of e-cooling by I. Meshkov - Interesting details of longitudinal Schottky and Impedance effects (double peak distribution) - Several experiences, also on hardware part designs, for e-cooling in different labs - 1993: Burov, A.V et al. Experimental Investigation of an Electron Beam in Compensated State CDS - Very detailed study at NAP-M of e- space charge compensation with ions and impact on e- stability - Sep 1992: S.P. Moller Cooling Techniques link - CAS school lecture - Feb 1990: Helmut Poth Further results and evaluation of electron cooling experiments at LEAR link - Nov 1990: Helmut Poth Electron cooling: Theory, experiment, application link - Used as reference in Gerard's 40 years of cooling presentation - 1989: R. Calabrese et al. A VERY COLD, LASER INDUCED ELECTRON BEAM FOR STUDIES ON THE FRICTION FORCE IN AN ELECTRON COOLING EXPERIMENT link - 1989: K. Schindl Space charge Theory link - CAS school proceedings - 1988: N. S. Dikansky et al. Influence on the Sign of an Ion Charge on Friction Force at Electron Cooling EPAC88 - 1987: A. Wolf, "Electron cooling of stored ions", link - 1987: C. Habfast et al. "Status report on the LEAR electron cooler", link PS-LI-Note-87-6 - Details on e-cooling adaptation for LEAR, including measurement of e- temperatures! - 1985: H. Poth at CAS1985, "Electron cooling theory", CERN-87-03-V2 page 534. - Details of cooling theory with many details and passages - Dec 1982: V. I. Kudelainen et al. Temperature relaxation in a magnetized electron beam link  - Study of perturbation of temperatures of electron beam along the cooler. - 1978: Derbenev, Yaroslav S; Skrinsky, A N The Effect Of An Accompanying Magnetic Field On Electron cooling Part. Accel. 8 (1978) pp.235-243 - Detaild theory of cooling force at that time with estimates on the effect of magnetic field line straightness - May 1967: G. I. Budker An effective method of damping particle oscillations in proton and antiproton storage rings link

Some theory

A great reference with detailed derivations of physics around e-cooling and e-cooler is Nov 1990: Helmut Poth Electron cooling: Theory, experiment, application CERN-EP/90-04

Effects on electrons

Perveance limit of gun

Space charge in e-: velocity distribution

Temperatures after acceleration

Transverse drift in toroids


Nice derivations in Introduction to plasma physics

In a toroidal field the e^- follow the B field lines. However, due to Centrifugal force, e^- are also subject to a lateral drift with speed given by:

\vec{v}_d = \frac{m v_\parallel^2}{q} \frac{\vec{B} \times \vec{R_C}}{|B|^2 |R_C|^2}

Assuming a toroid where R_C = R_{tor} is perpendicular to B and v_\parallel = \beta c and L_{tor} = R_C \Theta_{tor}: $$ \Delta X = \frac{m}{q} (\beta c)^2 \frac{1}{B R_C} \frac{L_{tor}}{\beta c} = \frac{m}{q} (\beta c) \frac{\Theta_{tor}}{B} $$

Then knowing that for electron \frac{q}{m} = −1.759e11 [C kg^{-1}]; For the ELENA e-cooler the lateral offset of the electrons is: $$ \begin{align} \Delta X_{ELENA} &= −1/1.759e11 [kg/C] * 0.0146 * 3e8 [m/s] * 3.14/2 * 1/0.01 [C s / kg] \\ &= - 3.9 \mathrm{ mm} \end{align} $$ at 100~keV, and, since it scales with \beta, it is about 10 mm for the mid plateau at 653~keV.

Effect of B field imperfection

Effects on ions

kick due to toroidal field

Considering derivation form Helmut Poth and its toroid schematics, The total the ion beam path, S=r_{tor} \tan \phi_0. Therefore \frac{dS}{d\phi} = \frac{r}{\cos^2 \phi}, while B_y(\phi) = B_{tor} \sin \phi. Integrating over the whole path, i.e. from \theta_0 to zero, one obtains: $$ \begin{align} \theta_{x} &= (\cos^{-1} (\phi_0) - 1) \frac{B_{tor} r_{tor}}{B \rho} \end{align} $$ For the AD e-cooler (B_{tor} = 620 Gauss at 400 A, \phi_0=0.628319 rad, r_{tor} = 1.133 m), one obtains: \frac{.00497}{p} where p is in units of [GeV/c], i.e. up to 50 mrad at 100 MeV/c.

In a similar way, one could compute equivalent integrated solenoidal field of a toroid. The integral involves integrating 1/\cos \phi which is equal to \ln |\sec \phi + \tan \phi| + C, therefore $$ \begin{align} B_s L &= \frac{B_{tor} r_{tor}} * \ln |\sec \phi_0 + \tan \phi_0| \end{align} $$ For AD e-cooler (B_{tor} = 620 Gauss at 400 A, \phi_0=0.628319 rad, r_{tor} = 1.133 m) one obtains 474 Gm to be compared to about 410 Gm in EDMS 2340163.