What is electron cooling?
The electron cooler at CRYRING. The metal cylinder on top at the left
side and the red piece below it is the superconducting gun solenoid, containing
the electron gun. The other red pieces are normal-conducting magnets guiding
the electron beam to the collector on top at the right side. You also see
three yellow dipole magnets in the ring and some smaller yellow quadrupole
Ions circulating in a storage ring such as CRYRING always have some spread in velocity. The velocity variations can be regarded as a thermal motion, and the task of the electron cooler is to reduce these variations, that is, to "cool" the ion beam. This improvement of the beam quality allows, for example, for a higher precision in measurements and experiments performed at the ring.
The cooling occurs when the hot ion beam is merged, over a distance of about 1 m, with a beam of cold electrons having the same average velocity as the ions. Heat is then transferred from the ions to the electrons. (To create a cold electron beam is comparatively easy.) The electron beam is surrounded by magnet coils which produce a magnetic field directed along the electron trajectory. The field prevents the electron beam from blowing up under its space charge and bends it in and out of the ion beam. The magnetic field has only a small influence on the ions due to their much greater inertia.
Apart from being used for cooling of the ion beam, the electron cooler
serves as an electron target in experiments with the stored ions, such
as studies of recombination between ions and electrons.
|Here are two Schottky spectra, showing the distribution of revolution frequencies in a deuteron beam in CRYRING before cooling (wide distribtion) and after cooling (narrow distribution). The change in width indicates that the velocity spread of the beam has shrunk by almost a factor 100 due to the cooling. (Actually, the double structure of the narrow peak tells that this is not a true Schottky signal, but instead a result of density waves propagating through the ion beam. The distribution of revolution frequencies is narrower than the width of the blue peak.)|
An important property of an electron cooler is the temperature of its electron beam. A low electron temperature improves the cooling. More important is the effect of a low electron temperature on resolution and count rates when the cooler acts as an electron target in atomic-physics experiments.
In general, the transverse temperature of electrons emitted from the
cathode is equal to the cathode temperature, around 900°C, which corresponds
to a thermal energy spread
The longitudinal electron temperature is much lower than the transverse
temperature due to the acceleration of the electrons. In fact, the longitudinal
temperature is hardly influenced by the cathode temperature, but is instead
dominated by relaxation processes in the electron plasma that the beam
constitutes. Typical values for the longitudinal energy spread,
|This is the orbit of an electron through a decreasing magnetic field. The electron has an unrealistically high transverse temperature, that is, a too large spiral radius, but otherwise the orbit is correctly drawn.|
The cooler has been in operation since May 1992. It has been used for
cooling and/or recombination experiments with singly charged atomic ions
(such as protons or
A 10 times expanded electron beam was introduced in August 1993, lowering
the transverse electron energy spread from
Measured rate coefficient for dielectronic recombination of
Some design parameters for the superconducting cooler (values used for
cooling or recombination within parentheses if not the same as design values):
|Gun diameter||4 mm|
|Electron energy||0-20 (0.011-8.1) keV|
|Electron current||0-500 (<0.1-110) mA|
|Perveance||0-5 (<0.01-4.8) µA/V3/2|
|Magnetic field, gun solenoid||0-5 (0.3-4) T|
|Magnetic field, cooling solenoid||0-0.3 (0.015-0.18) T|
An ion that moves with respect to the electrons in the cooler experiences a drag force due to the Coulomb interaction with the electrons. This force depends on the electron temperature and can be calculated using different models. The figure below shows this force as a function of the relative velocity between the ion and the electrons according to a simple binary-collision model. No effects of the magnetic field in the cooler were taken into account.
Most measurements of the drag force were made by first cooling the ions
so that the ions and the electrons get the same average velocity. Then
the electron energy was shifted rapidly in order to get a certain velocity
difference between ions and electrons. At the same time the Schottky spectrum
of the circulating ion beam was monitored, and measurements were made of
the rate at which the Schottky frequency changed as the ions were accelerated
by the electrons. Knowing the circumference of the ring and the momentum
compaction factor, the frequency change per unit time is easily and accurately
converted to an acceleration and then to a force. The measurements below
As seen from the figure, the data for
|Drag forces measured at CRYRING. The points are measured data at various beam expansions. The curves are calculated values obtained from binary collisions without magnetc field.|
Many of the experiments in atomic and molecular physics at CRYRING study recombination between free ions and electrons in the cooler. Recombination is often studied as a function of the relative energy between ions and electrons. The ions are then first cooled using electrons that have the same average velocity as the ions. Then the electron velocity is detuned, creating the desired collisions energy, and the measurements start.
The energy resolution in a recombination spectrum is normally determined entirely by the energy spread of the electrons. At low collision energies, it is the transverse energy spread that is important, and the adiabatic beam expansion then improves the energy resolution considerably.
The figure illustrates this by showing the rate for dissociative recombination
Absolute rate coefficient for dissociative recombination of
In an ordinary ion beam in a circular accelerator, the
particles move with random relative velocities, like molecules in
a gas. A gas that gets sufficiently cold can condense into a liquid, where
the positions of the nearby molecules are correlated to each other. The ion
beam in CRYRING has a temperature that is determined by the balance between
the cooling in the electron cooler and heating that is due to collisions
between the ions (intra-beam scattering). This balance shifts toward
lower temperatures when the number of particles in the ring decreases, since
then there are less collisions and less heating. When the number of particles
becomes sufficiently small, less than about 5000 for
As discussed above, the beam temperature can be observed by looking at Schottky signal from the beam. This signal reflects the velocity spread of the ions, which is directly related to the longitudinal beam temperature. When the transition to the liquid-like ordered state occurs, the velocity spread and the width of the Schottky peak drop abruptly as illustrated in the figure below.
In the ordered state, the kinetic energy of the ions (in the frame of reference
moving with the beam) is of the same magnitude or smaller than the potential
energy between neighbouring ions. The result is that ions cannot "overtake"
as they move around the ring. Instead they become trapped in a one-dimensional
configuration where an ion can only move between the one in front and the
one in the back, but not past them. Since the potential energy between the
ions is higher for highly charged ions, and since they also cool better
because of a stronger interaction with the cooler electrons, electron-cooled
ordered beams have only been observed for heavy, highly charged ions like
Relative momentum spread for a beam of
Selected publications on electron cooling at CRYRING:
Electron cooling at CRYRING,
Phys. Scr. 48, 405 (1993).
Fast electron cooling with a magnetically expanded electron beam,
Nucl. Instr. Meth. A 335, 397 (1993).
H. Danared, G. Andler, L. Bagge, C.J. Herrlander, J. Hilke, J. Jeansson,
A. Källberg, A. Nilsson, A. Paál, K.-G. Rensfelt, U. Rosengård,
J. Starker, and M. af Ugglas,
Electron cooling with an ultracold electron beam,
Phys. Rev. Lett. 72, 3775 (1994).
Electron cooling for atomic physics,
Phys. Scr. T59, 121 (1995).
Where are we after 30 years of electron cooling,
Proc. 5th Eur. Part. Acc. Conf., Sitges 1996, p. 153 (1996).
Electron cooling at CRYRING with an expanded electron beam,
Nucl. Instr. Meth. A 391, 24 (1997).
Simulation of relaxation process in electron beams at high magnetic fields,
Hyperfine Int. 115, 61 (1998).
H. Danared, A. Källberg, G. Andler, L. Bagge, F. Österdahl,
A. Paal, K.-G. Rensfelt, A. Simonsson, Ö. Skeppstedt, and M. af Ugglas,
Studies of electron cooling with a highly expanded electron beam,
Nucl. Instr. Meth. A 441, 123 (2000).
H. Danared, G. Andler, L. Bagge, A. Källberg, F. Österdahl,
A. Paál, A. Simonsson, and M. af Ugglas,
Studies of transverse electron cooling,
Proc. 7th Eur. Part. Acc. Conf., Vienna 2000, p. 301 (2000).
Numerical calculations of the electron cooling drag force in a magnetic field,
Proc. 7th Eur. Part. Acc. Conf., Vienna 2000, p. 1238 (2000).
H. Danared, A. Källberg, K.-G. Rensfelt, and A. Simonsson,
Model and observations of Schottky-noise suppression in a cold heavy-ion beam,
Phys. Rev. Lett, 88, 174801 (2002).
H. Danared, A. Källberg and A. Simonsson,
One-dimensional ordering in coasting and bunched beams,
J. Phys. B, 36, 1003 (2003).
For more information about the electron cooler, contact Håkan Danared, firstname.lastname@example.org
Top of page
MSL main page
Last updated 2003-10-17