Electron Cooler

What is electron cooling?   Electron temperatures and adiabatic beam expansion   The CRYRING electron cooler   Cooling forces   Recombination experiments   Beam ordering   Publications

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 magnets.
 
 

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 kT_perp = 100 meV. The transverse temperature can be reduced, however, by letting the electron beam pass through a region of decreasing axial magnetic field. When the field changes adiabatically with respect to the cyclotron motion of the electrons, the ratio between their transverse energy and the field strength is an invariant. In this way, the transverse temperature can be reduced by a large factor, up to 100 at CRYRING.

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, kT_par, is around 0.1 meV.
 
 
 

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 N⁺), highly charged atomic ions (such as Kr³³⁺or Pb⁵⁴⁺), and molecular ions (such as H₂⁺ or (H₂O)₄H⁺) at energies between 0.021 and 22 MeV per nucleon or between 0.29 and 900 MeV total energy.

A 10 times expanded electron beam was introduced in August 1993, lowering the transverse electron energy spread from kT_perp = 100 meV to 10 meV. At the same time an electron gun with a 10 times smaller cathode area compared to the original gun but with the same perveance as the original one was installed. The expanded electron beam thus had the same diameter and current in the interaction region as the original beam. Since August 1997, the cooler has a 5-tesla superconducting gun solenoid and a cathode that is still 10 times smaller, that is, a diameter of 4 mm. This allows the beam to be expanded by a factor 100, giving a transverse electron energy spread of, theoretically, 1 meV. A longitudinal energy spread of approximately 0.05 meV was measured from the shape of a C³⁺ dielectronic-recombination peak by the group of Reinhold Schuch at Stockholm University. They were using a 25 mA electron beam at 3 keV.
 
 
 

Measured rate coefficient for dielectronic recombination of F6+. The red curve was obtained by fitting a theoretical cross section calculated by Eva Lindroth at Stockholm University to the large peak at 10-2 eV, the shape of which is sensitive to both transverse and longitudinal electron temperatures. This fit gave kTperp = 1.5 meV and kTpar = 0.10 meV. The rate is in arbitrary units and the calibration of the experimental energy scale is only approximate.

 
 
 

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 about 10⁴ m/s were made using another method, where an equilibrium between the drag force and the electrostatic force from the acceleration drift tube in the ring was used to calculate the drag force.

As seen from the figure, the data for kT_perp = 100 meV and 10 meV are in quite good agreement with the theoretical model. This is perhaps a little surprising since one would expect that the magnetic field, which is not included in the model, has a strong influence on the electron-ion interaction. On the other hand, the newest measurements for 1 meV are considerably lower than the theoretical model. This is a strong hint that the use only of binary collisions is insufficient. In a cold electron plasma, the strong correlation between the particles makes it necessary to use a many-particle or a plasma model to reproduce the measurements. It should also be said that the longitudinal electron temperature influences the drag force, and a value kT_par = 0.05 meV was used for the curves in the figure.
 
 
 

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 of ³HeH⁺ions as a function of the collision energy. Dissociative recombination is the process where a molecular ion picks up an electron and, as a result, breaks up into smaller atomic or molecular fragments. In the ³HeH⁺case, the dissociation results in neutral He and H atoms. The three sets of data represent measurements without beam expansion (red), with a 10 times expanded beam (green), and with a 100 times expanded beam (blue). The fact that the area under the curves are different is also due to the different electron temperatures.
 
 
 

Absolute rate coefficient for dissociative recombination of 3HeH+ions. The measurements were performed by the group of Mats Larsson at Stockholm University.

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 Xe³⁶⁺ ions in CRYRING, the ion beam can become so cold that it "condenses" into a state where the particle positions are correlated or ordered in a liquid-like way.

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 Ni¹⁷⁺, Xe³⁶⁺ or Pb⁵⁵⁺.
 
 
 

Relative momentum spread for a beam of Xe36+ ions i CRYRING. At t = 0 about 30 000 ions were injected into the ring. After 1 000 seconds there are only some 200 ions left, and the ordering appears. The particle number at which the ordering appears depends on how strong the cooling is, and this picture was taken with a rather weak cooling. Interestingly, but not seen in the picture, is that power of the Schottky noise can drop at the same time as the momentum spread. This is discussed in our Phys. Rev. Lett., 88, 174801 (2002).

Selected publications on electron cooling at CRYRING:

H. Danared,
Electron cooling at CRYRING,
Phys. Scr. 48, 405 (1993).

H. Danared,
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).

H. Danared,
Electron cooling for atomic physics,
Phys. Scr. T59, 121 (1995).

H. Danared,
Where are we after 30 years of electron cooling,
Proc. 5th Eur. Part. Acc. Conf., Sitges 1996, p. 153 (1996).

H. Danared,
Electron cooling at CRYRING with an expanded electron beam,
Nucl. Instr. Meth. A 391, 24 (1997).

H. Danared,
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).

H. Danared,
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, danared@msi.se

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Last updated 2003-10-17