The GANIL CYCLOTRONS -...

The GANIL Cyclotrons 1 30/05/06

THE GANIL CYCLOTRONS1

INTRODUCTION

Accelerators are tools for giving atomic particles very high velocities. In what follows, the particles of interest are positive ions, that is, atoms from which one or more electrons have been removed. Any experiment related to the atomic nucleus consists in causing collisions between these ions (of which only the nucleus is of importance) and the nuclei of a fixed target, most frequently a thin layer of matter. The purpose of this paper is not to discuss the experiments based on the observation of these collisions between nuclei. Our subject will be limited to the instruments which provide the high energies required for these experiments. Many types of accelerators have been invented: cyclotrons, synchrotrons, synchrocyclotrons, betatrons, linear accelerators, etc., but all of them have a common feature. They have to generate an electric field to accelerate the ions. Fig. 1 illustrates the basic principle: a positive ion placed at rest between two electrodes with a voltage difference V is attracted by the negative electrode and it is therefore accelerated.

Fig. 1. Acceleration of positive particles through a potential difference.

1 This presentation does not include SPIRAL, a specific system to produce and accelerate exotic ions.

Nuclear collisions do indeed require very high velocities, often of the order of an appreciable fraction of the velocity of light, which in turn require accelerating voltages much higher than 20 to 30 MV, which is the technical limit for DC generators. In order to go beyond this limit, the method generally adopted consists in inducing a series of small accelerations by applying electric fields distributed along the ion trajectories, until the required velocity is attained. For example, one can easily imagine the ions passing through a series of hollow metal tubes, with each alternate pair connected to opposite terminals of AC generators: this is indeed how a “linear accelerator” works. In this scheme, the trajectory may extend over several hundred meters, so an additional idea was to wrap it up into a circle or a flat spiral by superimposing a magnetic field perpendicular to the velocity. Not only does this lead to a considerable reduction of the size of the machine, but it requires merely a single AC generator and a single set of electrodes, through which the particles pass repeatedly. In cyclotrons, which will be our only concern here, the orbits have a spiral shape. Figure 2 illustrates the effect of a magnetic field B on an ion travelling with a velocity v perpendicular to B: the ion is deviated with a radius of curvature r. If the magnetic field extends over a quite large area (shown on the left of the figure), the trajectory is just a closed circle. If B has a limited extension in space, as on the right of the figure, then the ion is simply deflected. In what follows, we will deal only with cyclotrons. Methods of production and of acceleration are described, with orders of magnitude both for the ion beams and for the physical characteristics of the accelerators.

Fig. 2. Deflection of ions in a homogeneous magnetic field. The GANIL Cyclotrons 2 30/05/06


ION SOURCES The easiest way to get an atomic particle up to the high velocity required for a specific collision consists firstly in making it an electrically charged particle, then to apply successive electric fields as stated above. For this purpose, atoms (which are neutral) are stripped of one or more of their peripheral electrons: they then become ions. The process most commonly used for ionisation is the bombardment of these atoms by other electrons of sufficient energy. At this stage, we have to introduce a unit of energy specifically used in atomic and nuclear physics: the electron-volt (eV, with multiples: keV, MeV and GeV). The eV is simply the kinetic energy gained by any singly-charged particle (e.g. an electron or an atom ionised by removal of only one electron) when it is accelerated by a potential difference of 1 volt. Since the charge of an electron is 1.6×10-19 coulomb, the MKSA equivalent of one eV is E=1.6×10-19 joule, a quantity much less easy to use. The energy necessary for these bombarding electrons to ionise the atoms must be at least equal to (or preferably 2 to 3 times larger than) the binding energy of the electron to be stripped off. Let’s give a few examples:

13.6 eV are required to remove the (single) electron from a hydrogen atom.

16 eV are required to remove the first electron from an argon atom.

469 eV are required to remove the 10th electron from an argon atom.

4.264 keV are required to remove all 18 electrons from an argon atom.

5.4 eV are required to remove the first electron from a uranium atom.

434 eV are required to remove the 18th electron from a uranium atom.

129 keV are required to remove all 92 electrons from a uranium atom.

Table 1. Examples of the minimum energy necessary to ionise some elements. The first step in the whole accelerating process is thus to immerse neutral atoms into a “soup” of electrons with an average energy corresponding to the desired charge state. In order to produce argon ions with 10 electrical charges (written Ar 10+), this electron energy has to be at least 469 eV. This ionising process takes place in an almost closed volume where ions and electrons are confined in a magnetic field configuration (a “magnetic bottle”) created either by coils carrying high electrical currents (~1000 A) or by permanent magnets, or both. The value of the confining magnetic field may be as high as 1 tesla.

The bombarding electrons can be generated by a high-temperature cathode, or by the electrons resulting from previous collisions. In this latter instance these are “electron cyclotron resonance” sources (abbreviated as ECR): the electrons’ kinetic energy is provided by an electromagnetic wave of the same type as the one used in microwave ovens (2.45 GHz), but with higher frequencies: 10, 14, 18 and even 28 GHz. For a precise magnetic field configuration and such UHF electric fields, a resonant phenomenon brings the electron energy up to several hundreds of eV and even several keV. The ions resulting from the collisions with the electrons are then extracted from the source through a small hole and accelerated by a few tens of kilovolts (20 kV is a current value). For ions with charge state Q we then obtain a continuous and well-directed jet (or “beam”) of ions with energies of 20×Q keV. Unfortunately, this ionising process is not selective and the extracted beam carries a distribution of charge states, which may contain as many as ten different values of Q, depending in particular on the atomic number of the element.

Fig. 3. Cross-sectional view of an ECR ion source. We mention here also that in such ion sources, it is often difficult to produce large currents of fully stripped ions. We shall see below the consequence of this limitation.



After extraction, it is necessary to select a single charge state (or rather a single energy) in order to drive it into the cyclotron, since these ECR sources are too bulky to be installed inside the accelerator. Since beams are comprised of charged particles, they are usually measured in units of electrical intensity, the ampere and its sub-multiples: mA, µA, pA, etc. Alternately, the number of particles per second (pps) is sometimes used. Now let’s look at the accelerator itself.

THE CYCLOTRON Figure 2 shows qualitatively the action of a magnetic field on a moving ion. Two simple relations between the characteristics of a projectile (mass m, charge q and velocity v) and the field B may be established. Here we just state that, along the trajectory, the centrifugal force mv²/r exerted on the ion is at all times equal to the magnetic restoring force qvB: (1) mv²/r = qvB. Putting the ion’s characteristics onto the right-hand side, we get: (2) Br = mv/q. It is then obvious that in a homogeneous magnetic field (B constant), the trajectory is a circle of radius r if the velocity v is constant. Equation (1) also provides additional information on the angular velocity ω: (3) ω = v/r = qB/m. Keeping the assumption that the field B is homogeneous, the angular velocity is also constant and independent of v, as long as there is no sizeable variation of mass due to the relativistic effect: the cyclotron is an “isochronous” accelerator, which simply means that whatever the orbit radius (or energy, or velocity) may be, the time for an ion to make one turn is constant. Instead of angular velocity, it is very convenient to think in terms of revolution frequency: F = ω/2π , or from (2) we get: (4) F = qB/2 π m.

Figure 4 shows how acceleration in such a circular accelerator works. An AC voltage varying with the same frequency as (or an integer multiple of) the rotation frequency F determined by equation (4) is applied to a set of two electrodes: ions passing between them “at the right moment” are accelerated and the radius of curvature of their trajectory increases. Ideally, these electrodes are made of a kind of big circular copper “pill-box” cut along a diameter into two hollow parts called the “dees” (from the shape of the capital letter D). The flat spiral along which the ions travel lies in the plane of symmetry of the magnet, which coincides with that of the dees.

Fig. 4. The accelerating principle of a cyclotron: ions move in circular paths inside the dees, and are accelerated each time they cross the gap between the

dees, close to the peak of the sinusoidally varying RF potential across the gap.

It is in fact not necessary for the magnetic field to have a constant value over the whole orbit: it is sufficient that the average value of B over one turn is constant versus the radius r. Equations (1) to (4) remain valid using <B> and <r>, where the brackets means “average over 2π”. As an illustration, figure 5 shows that cyclotrons are very often made with an azimuthal variation of the magnetic field, and even with separated sectors, for reasons related both to a better stability of the vertical motion of the ions and to a better accessibility to the interior of the machine. Two of the GANIL cyclotrons each have four separated sectors. Finally, it is necessary to mention that, when the ions reach “relativistic” velocities, i.e. when their mass begins to increase significantly according to:

2

0

1 β−=

mm ,

then the variation of <B> with <r> has to follow the same rule as m in order to keep the frequency constant.


Fig. 5. Acceleration of ions in a solid-pole cyclotron with pole sectors, i.e. a magnetic field with “hills and valleys”, and in separated-sector cyclotron, with

discrete magnets.

A BIT MORE ABOUT THE TECHNICAL ASPECTS.

Very large electromagnets are required to achieve the magnetic field topology (figure 6 illustrates the case of one sector magnet): a hollow copper conductor carrying some 1000 to 2000 amperes of DC current is wrapped around each of the two pole-pieces made of forged iron. When fully powered by 190 000 ampere-turns, these main coils provide a 1.6-tesla magnetic field in the 10-cm gap between the two pole-pieces. The return path of the field lines is channelled by an enormous yoke made of slabs of iron. Each sector of the GANIL cyclotrons weights 430 tons. The dimensions are indicated in figure 6. The extraction radius R is the radius beyond which the magnetic field falls off and therefore no longer meets the condition for “isochronism” (i.e. equal times for each orbit). The average value of R fixes the kinetic energy reached by the ions at the end of the acceleration process. In the non-relativistic approximation and for an ion with mass number A (A is just the total number of nucleons: neutrons and protons, in the nucleus), this energy can be expressed as:

(5) ( )2

2⎟⎠⎞

⎜⎝⎛=

AQBRCW

Here, we have just introduced a new quantity: rather than the kinetic energy E, it is often more convenient to refer to W, the energy per nucleon: W = E/A. Using MKSA units for B and r (A and Q are dimensionless), the value of the constant C is 48.26.


Fig. 6. Dimensions of one of the GANIL SSC sector magnets

Equation (5) prompts two remarks:

• Since the energy varies as Q², the higher the charge state obtained from the source, the higher the maximum energy for a given cyclotron. But at present it is still difficult to produce high intensities of fully stripped atoms, except for the very light ones.

• Ion beams with different energies can be obtained by changing either B or Q. But it is of course necessary to adjust the RF frequency accordingly, i.e. to have a variable frequency oscillator, in order to maintain isochronism.

For example, the average magnetic field in the GANIL SSCs may be adjusted between 0.39 and 0.95 tesla, while the RF frequency covers a 7-to-14-MHz range. It is not simple to design the correct field law versus radius, azimuth and level, just by shaping the poles pieces. These poles have in addition to be equipped with a series of flat trim-coils lying on their surfaces, thus allowing us to fine-tune the local field values by adjusting the currents in such coils (Fig. 7).


Fig. 7 The trim-coils arranged on the surface of the pole of one of

GANIL’s SSC magnets Some characteristics of typical SSC magnet are presented in Table II below. Main parameters Main coils : 2 per sector (North and South)

Number of sectors 4 Maximum power 100 kW

Azimuthal extent of a sector 52 degrees. Maximum intensity 1850 A

Gap 10 cm Number of ampere-turns 190.000

Magnetic field in the gap from 0.66 to 1.6 tesla Copper weight 3.4 tons

Weight of one sector (iron) 430 tons Water flow per main coil 10 m3/h

Weight of one pole 25 tons Output-to-input water temperature drop 10 °C

Table II. Parameters of the GANIL SSC magnets

We won’t give much detail here about RF oscillators and resonators since it is quite complicated technology. It is enough to know that an electromagnetic wave is injected into a large resonant copper cavity (Fig. 8) which, as can be seen by comparison with figure 4, no longer has much to do with the shape of a D! The resonant frequency can be adjusted by varying the capacitance of the system: this is obtained by changing the distance between the two corrugated panels shown on the figure. With such cavities, the potential (i.e. the accelerating voltage) may reach up to 250 kV. The GANIL Cyclotrons 9 30/05/06

Fig. 8. An exploded view of the RF resonators used at GANIL Magnetic and electric fields are the most prominent aspects of a circular accelerator. As essential is a third component: the vacuum. Actually, an ion moving in a gas at atmospheric pressure would immediately be slowed down by collisions with the numerous atoms of the gas. In addition, the ion could also either lose or capture one or more electrons from the neutral atoms. Then, any change of its electrical charge Q would destroy the condition of synchronism between the RF frequency and its rotation frequency, which as we have seen is a function of Q. It is therefore necessary for the ion beams to move in tanks or pipes which have been well evacuated, down to pressures as low as 10-7 mbar (about 1/10th of a billionth of atmospheric pressure). In a first step, mechanical pumps (working in a manner similar to a reversed compressor) reduce the pressure down to values of the order of 10-1 mbar. Then come either turbomolecular pumps (fast rotating turbines) or cryopumps, i.e. very low temperature surfaces (cooled by liquid nitrogen or helium) which capture molecules in the same manner as water vapour condenses on the coldest surfaces in a refrigerator. In order to reach these low pressures, it is also necessary that the tanks be very clean: stainless steel is the most common material used for this purpose. In addition, seals are made of soft metals (indium, lead) rather than rubber or synthetic plastics. Figure 9 give an idea of the complexity of the vacuum chamber for one SSC and some characteristics are indicated in the table below. About 24 hours are needed to reach a good operating pressure.



Diameter 9.6 m Height 4.3 m Weight 57 tons Volume 46 m3

Total internal surface 900 m²

Table III. Parameters of the GANIL SSC vacuum chamber shown in fig. 9.

Fig. 9. The structure of the vacuum chamber for one of GANIL’s SSCs

THE VOYAGE OF THE IONS BUNCHING AND INJECTION It was stated previously that the ions are extracted from the source as a continuous, low energy jet or beam. These are two important points: continuous beam: on the right-hand side of figure 4, we can observe that the ions which will be most efficiently accelerated are those located within a short time interval ∆φ around the peak of the sine wave. On the other hand, the ions traversing the electrical gap when the accelerating potential is zero are obviously not accelerated at all and are therefore lost. Using a buncher between the source and the cyclotron helps to reduce this loss by concentrating a good fraction of the beam into a small period around the peak of the accelerating potential. The simplest buncher is just a cylindrical hollow

electrode, through which the beam of ions passes, and which carries an AC voltage of the same frequency as the cyclotron RF voltage. The principle is shown on Figure 10: ion A sees no accelerating voltage and its velocity is thus unchanged; ion B, arriving late with respect to ion A, gets a velocity increment and will therefore catch up to A after some “drift” distance travelled. Conversely, C, arriving ahead of A, is slowed down and will therefore be caught up by A and B. (Of course the ions experience a similar bunching effect when they exit from the tube, by which time the RF voltage has reversed.) In this manner, a large fraction (more than 50%) of the DC beam from the source is compressed into a series of short bunches. In this simplified model, the bunching process is not a 100% efficient since this is true only for the (almost) linear part of the sine wave. Modern bunchers employ saw-tooth waves and may reach 75% to 80% efficiency. Voltages of the order of a few hundred volts are typically used to bunch the particles to within ~10° of phase of the (360°) sine wave, for drift distances of about a few meters.

Temps (ou phase)

V(t)

A

B

C

L'ion C, arrivant en avance sur A, est freiné par le potentiel positif

L'ion B, en retard sur A, est accéléré par le potentiel négatif

Fig. 10. Sinusoidal voltage on a buncher, seen by arriving ions, plotted against time (or phase of the sine wave).

low energy: as shown on the right part of figure 5, the centre of a separated-sector cyclotron is empty. This means that the first orbit has to have quite a large radius and therefore, an energy much larger than that delivered by the ion source. For example, the injection radius of the first SSC at GANIL is 0.8 m, which corresponds to energies of 0.25 to 1 MeV per nucleon in the ion (depending on Q/A), while the ions are extracted from the source at energies about 40 times lower. For this reason, it is necessary to add an intermediate (or “injector”) accelerator to provide the additional energy required.


Fig. 11. The C0 injector cyclotron

At GANIL, this injector is a compact cyclotron (C0, figure 11). The beam from the source (and buncher) is injected vertically through a cylindrical hole drilled along the axis of the poles. When entering the gap between the poles, the ion trajectories are bent by an electric field until they become horizontal and in the plane of symmetry of the cyclotron (also called the “median plane”) where they begin their spiralling race. The poles of injector cyclotron C0 have four sectors as indicated in the left part of figure 5. It operates at the same RF frequency as the SSC located downstream; the extraction radius is 0.50 cm and the average magnetic field may be adjusted between 0.8 and 1.6 tesla.

THE BEAM TRANSPORT SYSTEM The beam of ions travels down the centre of stainless steel pipes under vacuum from source to injector, and then to the SSC. In a manner similar to a beam of light, the ion beams have a natural tendency to diverge and it is necessary to correct this. For this purpose, quadrupole magnetic lenses which focus the ions, are periodically arranged along the beam pipes. When bending is necessary, a magnetic dipole (shown at right on figure 2) will do the job.


WHY IS THERE A SECOND SSC AT GANIL? GANIL is in fact comprised of three cyclotrons: a compact injector C0, then two (almost identical) SSCs in a row: SSC1 and CSSC2. Why? Applying equation (5) to one of the GANIL SSCs, we find that the maximum energy obtained with B = 0.95 T and r = 3 m is given by:

(6) )/(3922

nMeVAQW ⎟

⎠⎞

⎜⎝⎛=

If the ion source were capable of delivering fully stripped light ions (e.g. for light atoms having an equal number of protons and neutrons, like calcium-40 with 20 neutrons and 20 protons), the maximum energy would be 95 MeV/n, which was the goal for the GANIL project. Unfortunately, as indicated previously, the sources are not able to deliver reasonable intensities of fully stripped ions and another scheme has to be adopted. In order to reach higher charge states, the trick is to use stripping at high velocities. This makes use of the following physics: when a swift ion passes through a target, whether solid or gaseous, it suffers a series of captures and losses of electrons. A high-velocity ion beam, traversing an extremely thin film of material (typically 1 µm of carbon, which doesn't significantly modify the velocity), emerges with a charge state distribution, and the mean charge is higher as the input velocity increases. Here, high velocity means several MeV/n, which implies that this stripping process is only of interest downstream of the SSC. This explains why two SSCs are used, with a carbon foil as a stripper in between (Fig. 12).

Fig. 12. The use of a stripper between two cyclotrons. Let’s illustrate this scheme with the following example: if neon nuclei are to be accelerated up to about 100 MeV/n, the first process takes the neon atoms to the 4+ charge state, then accelerates them through C0 and SSC1 up to 15.6 MeV/n (equation 6). The ions are then stripped to charge state 10 (fully stripped, in this The GANIL Cyclotrons 14 30/05/06

case) when passing through the carbon foil. Assuming the magnetic field is the same in SSC2 as in SSC1, equation (2) tells us that the injection bending radius is 10/4 = 2.5 times less than the extraction radius of SSC1. The ions can therefore be injected into SSC2 with a 3/2.5=1.2 m radius and then accelerated up to r = 3 m (and W=95 MeV/n). For atoms heavier than calcium, the number of protons Z is less than A/2 and the it becomes are more and more difficult to remove a large number of electrons from the attraction of the nucleus, even through the stripping process occurs at quite a high energy. Therefore, a suitable Q/A ratio is impossible to reach by stripping. The maximum energy achievable out of SSC2 then varies as a function of the number of protons in the nucleus Z (the atomic number), as shown in figure 13.

GANIL beams out of SSC2

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Atomic number

Ene

rgy

(MeV

/n)

Fig. 13. The maximum energy achievable out of SSC2 at GANIL


SUMMARY

GANIL is composed primarily of three cyclotrons in a row: C01, CSS1, and CSS2 (figure 14). (C02 is just an alternative injector, and SPIRAL is another part of the facility for producing and accelerating secondary ion beams.) The ions generated from neutral atoms in the ion source, are first analysed for selection of a single charge state Q, then injected into a compact cyclotron C01 and accelerated to an energy high enough for them to be inserted on the first orbit of the first SSC, called CSS1. After extraction, they pass through a carbon stripper, thus reaching a higher charge state, and CSS2 accelerates them up to the final energy, ready to be directed towards the physicists’ experimental targets and detection apparatus.


Fig. 14. Sketch of the GANIL accelerators and related experimental devices.

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