WO2012055958A1

WO2012055958A1 - Synchrocyclotron

Info

Publication number: WO2012055958A1
Application number: PCT/EP2011/068844
Authority: WO
Inventors: Jérôme MANDRILLON; Matthieu Conjat
Original assignee: Ion Beam Applications S.A.
Priority date: 2010-10-27
Filing date: 2011-10-27
Publication date: 2012-05-03
Also published as: BE1019557A3; CN103493603A

Abstract

A synchrocyclotron comprises a ferromagnetic structure (4) with a pair of poles (5, 5'), which have a generally circular cross section of radius R which are placed on either side of a mid-plane (2) and centred on a central axis (1). These poles (5, 5') are separated by a gap forming a cavity (9) having a profile substantially symmetrical with respect to the mid-plane (2). The height of this gap varies radially and the profile of the gap comprises, in succession, starting from the central axis (1): a first portion (6, 7) of circular section with a radius R2, which is centred on the central axis (1), the height of the gap at the centre thereof being equal to H_centre, and which includes an annular subportion (7) in which the height of the gap progressively increases up to a maximum height H_max at the radius R2, and a second portion, of annular section (8), which surrounds the first portion (6, 7) and in which the height of the gap progressively decreases down to a height H_edge at the edges of the poles (5, 5'). The height H_centre is greater than 10 cm and the ratio of the maximum height H_max to the height H_centre is between 1.1 and 1.5.

Description

synchrocyclotron

TECHNICAL AREA

The present invention relates to a synchrocyclotron. DESCRIPTION OF THE STATE OF THE ART

[0002] Synchrocyclotrons, like cyclotrons, are particle accelerators comprising a magnet structure comprising two magnetic induction coils radially surrounding a cavity intended for particle acceleration, between two poles, the cavity comprising a central axis and in which extends a median plane perpendicular to said central axis. The particles are produced in a source of particles located in the cavity in the vicinity of the central axis, and are extracted from the source to be accelerated, in the median plane along a spiral-shaped path, by accelerating electrodes fed by a high frequency alternating voltage generator. Such synchrocyclotrons are increasingly used for hadron therapy.

Unlike cyclotrons, where the particles are accelerated at the same frequency, in a synchrocyclotron, the frequency of the electric field applied to the accelerating electrodes is modulated so as to compensate for the increase in relativistic mass when the particle velocity increases. .

To reduce the size of a cyclotron, it is necessary to increase the magnetic field that guides the ions during acceleration. For isochronous cyclotrons, where the vertical focusing of the beam is obtained by magnetic sectors placed in the gap, it is difficult to increase the average magnetic field above 5 Tesla, because the vertical focus becomes insufficient. On the contrary, in synchrocyclotrons the magnetic field level can in principle be increased without limits. Synchrocyclotrons are also more compact than cyclotrons, the size of a synchrocyclotron decreasing proportionally with respect to to the magnetic field generated between the two poles.

US 7,541,905 and US 7,696,847 describe a synchrocyclotron whose induction coils are made of a superconducting material, cooled to a temperature of 4.5K, and capable of producing a magnetic field between 5 Tesia and 1 1 Tesla. Magnetic fields of 14 Tesla can be produced by decreasing the temperature up to 2K for induction coils made of Nb ₃ Sn. The cylinder head made of soft iron provides an additional field of about 2 Tesla. In order to reduce the size of a synchrocyclotron, the aforementioned documents suggest producing a high magnetic field in the pole gap. Nevertheless, by increasing the magnetic field above 6 Tesla, as suggested in the aforementioned patents, undesirable effects occur. Thus, it becomes impossible or very difficult to draw the central region of the cyclotron, because the very high magnetic field causes a decrease in the radius of the first orbits taken by the particles, in such a way that the particles do not succeed in bypassing the source of the cyclotron. ion in the first round. A second disadvantage of magnetic fields greater than 6 Tesla is that the realization of the extraction device becomes very complex. A third disadvantage of magnetic fields greater than 6 Tesla in the center of the cyclotron is that, for such magnetic fields, the magnetic field in the coils exceeds the magnetic field for which a Niobium-Titanium alloy can be used for the coils. One must then use a Nb ₃ Sn alloy, which is much more expensive.

The synchrocyclotron described above comprises two poles whose profile allows a low focusing of accelerated particles in the median plane and a phase stability so that the charged particles acquire enough energy to maintain the acceleration in the air gap of the poles. In the magnetic field produced in the air gap of a synchrocyclotron, a charged and accelerated particle oscillates radially and axially around an equilibrium orbit. The radial oscillation frequency v _r is given by: v _r = Vl - n (oscillations per revolution) (I) the axial oscillation frequency v _z is given by: v _z = V (oscillations per revolution) (II) with n the field focusing index given by:

r dB .....

n = - (III)

B dr '

where r is the radius of the particle's orbit, the origin of the ray passing through a point of the central axis, and B is the magnetic field in this radius.

It can theoretically be shown that there is an axial focusing force when n> 0, which implies that dB / dr is negative. The synchrocyclotron must therefore have a scalable field profile that decreases with the radius so as to satisfy the conditions set by the field focusing index. Generally, it is arranged to have a pole profile whose field focusing index is less than 0.2 in the cavity for accelerating particles. When approaching the maximum radius of the pole, the magnetic field decreases more rapidly as a function of the radius, the magnetic field index increases, the radial frequency v _r decreases and the axial frequency v _z increases. When n = 0.2, we have a special condition where v _r = 2 v _z . In this particular condition, known as Walkinshaw resonance, the energy of radial oscillations can be transferred to axial oscillations. This increases the axial size of the beam and generally causes the loss of the majority of the accelerated ions. To avoid this phenomenon, the synchrocyclotron includes pole wings located on the edge of the poles, causing a reduction of the air gap before the field index is equal to 0.2, so as to locally increase the magnetic field and to prevent the loss of particles.

In the case of a high magnetic field synchrocyclotron, as described in the two US documents cited above, to satisfy the conditions set by the field focusing index n and allow the focus of the particles in the median plane, the profile of the poles must evolve from a region around the central axis where the air gap is sufficiently narrow to produce enough magnetic field, to a region located near the pole wings where the air gap is maximum and whose height is at least twice greater than that of the zone of the air gap near the central axis. The poles comprise beveled surfaces so as to progressively widen the gap of the poles, the region of the poles where the gap is maximum is between two surfaces forming an acute angle between them. In FIG. 2 of US 7,696,847, the junction between flange 134 and surface 130 has an acute angle. Such a pole profile including a deep and narrow region is quite difficult to machine accurately.

[0009] A synchrocyclotron comprising an air gap in which a 5.5 Tesla magnetic field is generated is described in the Wu X document. "Conceptual Design and Orbit Dynamics in a 250 MeV Superconducting Synchrocyclotron" (PhD dissertation, Michigan State University, 1990). The losses of particles at the outlet of the source are less important for such a magnetic field. Nevertheless, the gap between the poles of this synchrocyclotron is relatively narrow, as in the previously described synchrocyclotron, which requires the drilling of a hole in the cylinder head along the central axis of the cylinder head for the introduction of a source of particles in the central region. The hole in the bolt hole locally changes the magnetic field at the center of the accelerating cavity, where the magnetic field in the vicinity of the source initially increases with the radius to a maximum, then falls slightly with the radius. The field focusing index is therefore initially negative, which causes a defocusing of the trajectory of the particles over a short radius. This effect increases with the radius of the source, hence the need to minimize the diameter of the hole in the cylinder head and the diameter of the source, which reduces the particle production capacity. Also, it is necessary to insert coins circular metal magnetic field compensation, commonly called "shims".

Another disadvantage of the synchrocyclotrons described above is the limited space available for the insertion of a high frequency oscillation circuit comprising accelerating electrodes and a transmission line. This lack of space imposes a reduced distance between the accelerating electrodes and the transmission line, which has the effect of increasing the capacity between these two elements. An increase in capacity requires more power at the voltage generator to produce the desired AC frequency in the accelerating electrodes.

In order to minimize the problems of extraction of the particles from the source, and to reduce the production costs of a synchrocyclotron, it is necessary to minimize the magnetic field in the gap between the two poles of the synchrocyclotron while minimizing the size of the synchrocyclotron.

It is also desirable to produce a synchrocyclotron whose pole profiles satisfy the conditions set by the field focusing index and are easier to machine.

It is also desirable to make a synchrocyclotron whose gap between the two poles allows the easy insertion of a source and a high frequency oscillation circuit so as to avoid problems as encountered in synchrocyclotrons of the prior art.

SUMMARY OF THE INVENTION

The present invention relates to a synchrocyclotron comprising a ferromagnetic structure, a cold mass structure and a source of particles. The ferromagnetic structure generally comprises: two disc-shaped cylinder heads located coaxially with respect to a central axis, parallel and substantially symmetrical with respect to a median plane; a pair of poles that have a section of generally circular shape, of radius R, which are arranged on either side of said median plane, centered on the central axis and separated from an air gap forming a cavity; flux returns that surround the poles and join the two plates of the cylinder heads. The cold mass structure generally comprises at least two magnetic induction coils, and is surrounded by flux returns and surrounds the poles. The source of particles is generally located in the cavity in a first circular zone of radius R1, less than the radius R of the cavity, its origin being a point of the central axis. The gap of the cavity normally has a substantially symmetrical profile with respect to the median plane, its height varying radially. The profile of the air gap comprises successively from said central axis: a first portion, of circular section with a radius R2, centered on the central axis, the height of the air gap in the center is equal to H _this ntre, and which comprises an annular sub-portion (also called: first annular zone) in which the height increases gradually to a maximum height H _max at the radius R2; and a second portion of annular section (also called: second annular zone), which surrounds the first portion, and wherein the height of the air gap gradually decreases to a height H _b ords at the edges of the poles. According to a first aspect of the invention, the height H of _this etween the air gap is greater than 10 cm, and the ratio of the maximum height H _max of the height H _that etween is between 1, 1 and 1, 5, advantageously between 1, 2 and 1, 5, and preferably between 1, 2 and 1, 4. It will be noted that with this profile of the gap, the average magnetic field produced in the cavity by the coils and the ferromagnetic structure can be between 4 and 7 Tesla.

Preferably, the first portion comprises a central sub-portion (also called central zone 6) of radius R1 less than R2, centered on the central axis, where the height of the air gap is constant and of height H _this ntre-

The poles advantageously comprise a succession of beveled annular surfaces centered on the central axis, each of these surfaces forming with its adjacent surface an angle a strictly greater than 90 °, preferably greater than 120 °, and even more preferably greater than 140 °.

Preferably, the central sub-portion (central zone) extends over a radius R1 less than 20% of the radius R of the cavity, and the annular sub-portion (first annular zone) extends between the radius R1 and a radius R2 less than 95% of the radius R of the cavity 9.

In a preferred embodiment, the central sub-portion (central zone) extends over a radius R1 of the order of 10% of the radius R of the cavity and the first annular sub-portion extends between the radius R1 and a radius R2 of the order of 70% of the radius R of the cavity.

The source is advantageously located in the central sub-portion and held by a support inserted into the cavity substantially parallel to said median plane.

It will be appreciated that, thanks to a height H _{this is} quite important to the air gap, the poles can be advantageously full, because the source of particles can be introduced radially in the central zone of the air gap.

It will be appreciated that, thanks to the magnetic field quite low, the magnetic induction coils can be made in NbTi.

[0022] According to another aspect, the present invention relates to a method for producing a synchrocyclotron comprising the steps of: fixing the height of the air gap between the poles in the vicinity of the central axis H _that etween such that the height _It is greater than 10 cm;

fix a maximum height H _max of the air gap such that the latter is greater than at least 1, 1 times the height H _that etween and less than 1, 5 times the height H of _this etween;

fixing a magnetic field in induction coils magnetic surrounding the poles forming the accelerating particle cavity;

optimization of the profile of the poles and the size and position of the magnetic induction coils 3 taking into account _this etween H and H _max and the magnetic field in the coils, so as to obtain a particle accelerating cavity between the poles, the gap between the poles satisfies the conditions set by the field focusing index n = -, where r is the radius of the orbit of a particle, the origin of the ray passing through a point of the axis central, and B is the magnetic field in this radius, n to be strictly between 0 and 0.2.

DESCRIPTION OF THE FIGURES

Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is a simplified section of a synchrocyclotron according to an embodiment of the present invention; the section plane containing the central axis of the synchrocyclotron, and the section illustrating above all a ferromagnetic structure of the synchrocyclotron;

FIG. 2 is a section identical to the section of FIG. 1, also schematically showing a source of particles.

DETAILED DESCRIPTION OF THE INVENTION

Figs. 1 and 2 schematically show a synchrocyclotron according to the present invention. It should be noted that some parts of the synchrocyclotron are not shown so as not to clutter the figures.

The synchrocyclotron shown in the figures to illustrate the invention in a non-limiting manner comprises:

a ferromagnetic structure 4 comprising: o two base plates, also called disc-shaped cylinder head plates 16, 16 'arranged coaxially with respect to a central axis 1 of the synchrocyclotron, parallel and substantially symmetrical with respect to a median plane 2; a pair of poles 5, 5 ', having a section of generally circular shape, of radius R, arranged on either side of the median plane 2 of the synchrocyclotron, centered on the central axis 1 and separated from a gap forming a cavity 9; and

flow returns 17 surrounding the poles 5,5 'and joining the two of the yokes 16, 16';

a cold mass structure comprising at least two magnetic induction coils 3, surrounded by the flux returns 17 and surrounding the poles 5, 5 ';

a source of particles 1 1 (see FIG 2), located in the cavity 9 in a first zone 6 of circular section, of radius R1 less than the radius R of the cavity 9 and whose origin is a point of said axis central 1;

a high frequency voltage generator 14 (see FIG.2) located outside the flow returns 17;

an accelerating electrode (see FIG 2) coupled to the high frequency voltage generator 14; this accelerating electrode comprising a pair of parallel plates, substantially semicircular and separated from one another by a gap, located inside the cavity 9, extending parallel and symmetrically on both sides the middle plane 2 facing the source; and

a transmission line 13 surrounding the accelerating electrode 12 and located at a distance from the electrode 12.

In a preferred aspect, the magnetic field generated in the gap between the poles 5, 5 'of the synchrocyclotron is chosen:

so that it is high enough to accelerate particles at an energy of between 200 and 250 MeV; to prevent the particles leaving the source from falling back on it under the action of a magnetic field too high; and

to minimize the size of the synchrocyclotron.

The magnetic field generated in the gap between the poles is advantageously between 4 and 7 Tesla, preferably between 4 and 6 Tesla. It will be appreciated that the production of such a magnetic field does not require the use of Nb ₃ Sn superconducting coils. Indeed, NbTi superconducting coils are suitable for the production of a field between 3 and 5 Tesla, which is combined the magnetic field generated by the ferromagnetic structure 4, which is generally of the order of 2 Tesla. NbTi superconducting coils are less expensive and easier to implement than Nb ₃ Sn coils.

In a preferred aspect, the cavity 9 formed by the poles 5 has a radius R whose origin passes through a point of the central axis 1 and whose end coincides with the edges 10 of the poles 5. The height of the gap varies according to the radius so as to satisfy the conditions set by the field focusing index n. Preferably, the gap comprises three zones 6, 7 and 8, starting from the central axis towards the edge of the poles:

a central zone 6, preferably flat (although this is not necessarily a limitation of the present invention) and circular radius R1 less than the radius R of the cavity and whose origin coincides with a point of the central axis 1, located in the vicinity of the central axis 1 and whose air gap between the poles 5 is of height H _{this is} ; a first annular zone 7, between a circle of said radius R1 and a second circle of radius R2, also smaller than the radius R of the cavity and whose origin coincides with that of radius R1, in which the height of the gap between the poles 5 progressively increases up to a maximum height H _max , so as to gradually reduce the magnetic field to ensure a focusing of the particles in the median plane 2;

a second annular zone 8, between a circle of radius R2 and the edges 10 of the poles, in which the gap between the poles decreases progressively to a minimum height H _min at the edges of the poles, so as to increase again the magnetic field and decrease the field focusing index n before the field focusing index n reaches a limit value at which the particles oscillating axially around an equilibrium orbit resonate with the particles oscillating radially around the same equilibrium orbit.

[0029] In a preferred aspect, the ratio between the maximum height H _max of the air gap and the height H _that etween the air gap in the vicinity of the central axis is strictly greater than 1 and less than 1, 5, of in order to facilitate the machining of the inside of the poles, while satisfying the conditions set by the field focusing index. More preferably, the ratio H _max / Hcentre is between 1, 2 and 1, 5.

According to another preferred aspect, still with the aim of facilitating the machining of the poles 5, the zone comprising the first annular zone 7 and the second annular zone 8, is characterized by a succession of bevelled annular surfaces, centered on the central axis 1, each of these surfaces forming with its adjacent surface an angle a strictly greater than 90 °, preferably greater than 120 °, and even more preferably greater than 140 °.

[0031] According to yet another preferred aspect, the height H of _this etween the air gap in the vicinity of the central axis 1 is greater than 10 cm, more preferably greater than 15 cm, more preferably greater than 18.4 cm. It will be appreciated that the height H of _this etween the air gap in the vicinity of the central axis higher relative to synchrocyclotrons of the prior art, allows an easier insertion of the source and the high-frequency oscillation circuit comprising the accelerating electrodes and the transmission line. The widening of the gap allows for example to increase the gap between the two plates 12 of the accelerating electrode so as to avoid a collision of particles with the plates 12. The widening of the air gap also allows to increase the distance between the accelerating electrode and the transmission line 13, which reduces the capacitance between these two components and allows the voltage generator 14 to supply a high frequency alternating voltage to the accelerating electrode with less power.

[0033] According to a preferred further aspect, the height H _that etween high in the region of the air gap surrounding the central axis 1, allows the insertion of a source 1 1 laterally rather than axially (cf. Fig. 2). The insertion of the source 1 1 can be done, for example, by means of a support 15 coming from outside the cavity 9 and comprising conduits for the circulation of the gas in the source, as well as electrical connections for ignition of the source. The insertion of a source laterally makes it possible to dispense with the drilling of a hole in the cylinder head 16, 16 'and the poles 5, 5', which eliminates the negative variation of the field focusing index in the region of the air gap near the central axis 1 and also allows the use of a source of larger diameter than in the prior art synchrocyclotrons. In this way, the source can produce a higher particle current. Also, with the suppression of the negative variation of the field index in the region of the air gap near the central axis, the defocusing problems of the particles at the exit of the source are minimized, and the field compensation rings as used in the prior art synchrocyclotrons become optional, simplifying this region of the gap.

In an example, not limiting, embodiment of a synchrocyclotron according to the present invention, the average magnetic field in the air gap between the two poles is 5.6 Tesla. The height of the gap between the poles in the region near the central axis H _that etween is 18.4 cm and the height of the maximum gap H _max is 25.3 cm. In this synchrocyclotron, the ratio H _max / Hcentre is therefore equal to 1 .375. The distance z (cm) separating the poles of the median plane as a function of the radius of the poles r (cm) is given in Table 1. The external radius and the height of the synchrocyclotron are respectively 125 cm and 156 cm. For a comparable magnetic field, the dimensions of this embodiment according to the present invention are lower than the cyclotron described by Wu (magnetic field produced in the cavity: 5.53 Teslas, height of the synchrocyclotron: 173.4 cm, external radius of the synchrocyclotron: 132 , 3 cm). Still in this same embodiment according to the present invention, the gap between the plates of the accelerating electrode is 2 cm, and the gap between these plates and the transmission line is 7.4 cm.

Table 1:

It should be noted that the skilled person can optimize the profile of the poles as a function of the position of the coils relative to the median plane, as well as the dimensions and shape of this coil, while placing itself in conditions where the height of the gap between the two poles in the first zone is greater than 10 cm, where the maximum air gap height ratio H _max of the height of the minimum gap H ours _that in the central zone (6) is between 1, 1 and 1, 5 more preferably between 1, 2 and 1.5. In the example above, the coils have an inner radius of 55.4 cm centered on the central axis 1, a width of 13 cm and a height of 28.1 cm, and are spaced one from the another 20 cm.

The present invention also relates to a method for manufacturing a synchrocyclotron comprising two poles separated by an air gap, the method comprising the following steps: fixing the height of the air gap in the vicinity of the central axis H such _that such that the height H etween _this is greater than 10 cm, preferably greater than 15 cm, preferably greater than 18.4 cm and less than 37 cm;

fix a maximum height H _max of the air gap as it is strictly greater than the height H _that etween and less than 1, 8 times the height H of _this etween;

fixing a magnetic field in magnetic induction coils surrounding the poles forming the accelerating particle cavity;

optimization of the profile of the poles and the size and position of the magnetic induction coils, taking into account _this etween H and H _max, and the magnetic field in the coils, so as to obtain a particle accelerating cavity between the poles, the air gap between the poles satisfies the conditions set by the field focusing index n.

Claims

Synchrocyclotron comprising:

a ferromagnetic structure (4) comprising:

two disk-shaped cylinder head plates (16, 16 ') arranged coaxially with respect to a central axis (1) of the synchrocyclotron, parallel and substantially symmetrical with respect to a median plane (2);

a pair of poles (5, 5 ') having a section of generally circular shape, of radius R, arranged on either side of said median plane (2), centered on said central axis (1) and separated from one air gap forming a cavity (9); and

o flow returns (17) surrounding said poles (5,5 ') and joining the two yoke plates (16, 16');

a cold mass structure comprising at least two magnetic induction coils (3), said cold mass structure being surrounded by said flux returns (17) and surrounding said poles (5, 5 ');

a source of particles (1 1) situated in said cavity (9) in a first zone (6) of circular cross-section of radius R1 less than said radius R of said cavity (9) and whose origin is a point of said central axis (1);

the air gap forming said cavity (9) having a substantially symmetrical profile with respect to said median plane (2), the height of which varies radially, said profile of the air gap comprising successively from said central axis (1):

- a first portion (6, 7) of circular section of radius R2 centered on said central axis (1), the height of the air gap at the center is equal to _this H ours, and that includes an annular sub-portion (7) wherein the height of the gap increases gradually to a maximum height H _max at the radius R2; a second portion, of annular section (8), surrounding said first portion (6, 7), where the height of the air gap gradually decreases to a height H _b at the edges of said poles

(5.5 ');

characterized in that said height H _that etween the air gap is greater than 10 cm, and the ratio of said maximum height H _max of said height H etween _this is between 1, 1 and 1, 5.

2. Synchrocyclotron according to claim 1, characterized in that said first portion (6, 7) comprises a central sub-portion (6), of circular section of radius R1 less than R2, centered on said central axis (1), where the height of the gap is constant and equal to the height H _this ntre-

3. Synchrocyclotron according to claim 1 or 2, characterized in that the ratio of said maximum height H _max to said height H _ce ntre is between 1, 2 and 1, 5.

4. Synchrocyclotron according to claim 1 or 2 characterized in that the ratio of said maximum height H _max on said height H _ce ntre is between 1, 2 and 1, 4.

5. Synchrocyclotron according to any one of the preceding claims, characterized in that said poles (5,5 ') comprise a succession of beveled annular surfaces centered on said central axis (1), each of said surfaces forming with its adjacent surface a angle a strictly greater than 90 °, preferably greater than 120 °, and even more preferably greater than 140 °.

6. Synchrocyclotron according to any one of the preceding claims, characterized in that said central sub-portion (6) extends over a radius R1 less than 20% of the radius R of said cavity, and said annular sub-portion (7 ) of said first portion (6,7) extends between the radius R1 and a radius R2 less than 95% of the radius R of said cavity (9).

7. Synchrocyclotron according to any one of the preceding claims, characterized in that said central sub-portion (6) extends over a radius R1 of the order of 10% of the radius R of said cavity (9), and said annular sub-portion (7) of said first portion (7) extends between the radius R1 and a radius R2 of the order of 70 % of the radius R of said cavity (9).

8. Synchrocyclotron according to any one of the preceding claims, characterized in that said source (1 1) is located in said central sub-portion (6) and held by a support inserted into said cavity (9) substantially parallel to said median plane (2).

9. Synchrocyclotron according to any one of the preceding claims, characterized in that each of said poles (5) is full.

10. Synchrocyclotron according to any one of the preceding claims, characterized in that said magnetic induction coils (3) are made of NbTi.

1 1. A synchrocyclotron according to any one of the preceding claims, characterized in that the average magnetic field produced in said cavity (9) by said coils (3) and said ferromagnetic structure (4) is between 4 and 7 Tesla.

12. Method of producing a synchrocyclotron according to claim 1, the method comprising the steps of:

fixing the height of the gap between said poles in the vicinity of the central axis Hcentre such that said height Hcentre is greater than 10 cm;

- Fixing a maximum height of the gap Hmax such that it is greater than at least 1, 1 times the height Hcentre and less than 1, 5 times the height Hcentre;

- Fixing a magnetic field in magnetic induction coils (3) surrounding the poles forming the accelerating particle cavity;

optimizing the profile of the poles and the dimensions and position of the magnetic induction coils (3) taking into account the center and the Hmax and the magnetic field in the coils, so as to obtain an accelerating particle cavity between said poles, the gap between said poles satisfies the conditions set by the field focusing index n = -, with r the radius of the orbit of a particle, the origin of said radius passing through a point of the axis central, and B the magnetic field at this radius, n to be strictly between 0 and 0.2.