Download The GANIL CYCLOTRONS

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.
The GANIL Cyclotrons
1
09/05/17
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
09/05/17
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 GANIL Cyclotrons
3
09/05/17
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.
The GANIL Cyclotrons
4
09/05/17
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)
The GANIL Cyclotrons
F = qB/2 π m.
5
09/05/17
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:
m
m0
1  2
,
then the variation of <B> with <r> has to follow the same rule as m in order to
keep the frequency constant.
The GANIL Cyclotrons
6
09/05/17
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)
Q 
W  C BR   
 A
2
2
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.
The GANIL Cyclotrons
7
09/05/17
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 finetune the local field values by adjusting the currents in such coils (Fig. 7).
The GANIL Cyclotrons
8
09/05/17
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
09/05/17
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.
The GANIL Cyclotrons
10
09/05/17
Diameter
Height
Weight
Volume
Total internal surface
9.6 m
4.3 m
57 tons
46 m3
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 Δφ 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
The GANIL Cyclotrons
11
09/05/17
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.
V(t)
L'ion C, arrivant en avance sur A, est
freiné par le potentiel positif
C
A
Temps (ou phase)
L'ion B, en retard sur A, est
accéléré par le potentiel
négatif
B
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 separatedsector 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.
The GANIL Cyclotrons
12
09/05/17
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.
The GANIL Cyclotrons
13
09/05/17
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:
2
(6)
Q 
W  392  ( MeV / n )
 A
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
09/05/17
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
100
90
Energy (MeV/n)
80
70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95 100
Atomic number
Fig. 13. The maximum energy achievable out of SSC2 at GANIL
The GANIL Cyclotrons
15
09/05/17
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.
The GANIL Cyclotrons
16
09/05/17