EP2410823B1 - Cyclotron for accelerating at least two kinds of particles - Google Patents

Description

TECHNICAL AREA

The present invention relates to the field of cyclotrons, and in particular to cyclotrons capable of accelerating several types of charged particles having different charge (q) / mass (m) ratios, such as for example protons (equal q / m ratio at 1), alpha particles (ratio q / m equal to ½) or deuterons (ratio q / m also equal to ½).

DESCRIPTION OF THE PRIOR ART

We know from the document WO8606924 a cyclotron. With reference to the figure 2 of this document, such a cyclotron comprises acceleration electrodes 28, commonly called dice, each coupled to a vertical pillar 29 also called stem. Said die 28 and said pillar 29 are surrounded by a conductive enclosure which together constitute a resonant cavity.

où q est la charge de la particule à accélérer, m sa masse et B le champ magnétique principal, normal au plan médian de circulation des particules. Un cyclotron peut également fonctionner en mode harmonique : dans ce cas plusieurs oscillations de la tension RF se produisent alors que les particules circulent encore à l'intérieur du dé.The resonant cavities are generally excited by an RF power source and the successive passage of the charged particles in the accelerator gap consisting of dice and sectors brought to different potentials produces the acceleration of said particles. The frequency of the applied RF voltage shall be equal to the "cyclotron frequency" expressed by the following equation: $${\mathrm{f}}_{\mathrm{RFcyc}}=\frac{q\mathrm{.}\overrightarrow{B}}{2*\pi \mathrm{.}m}$$

where q is the charge of the particle to accelerate, m its mass and B the main magnetic field, normal to the median plane of circulation of the particles. A cyclotron can also operate in harmonic mode: in this case several oscillations of the RF voltage occur while the particles still circulate inside the die.

chargé par la capacité de dé à une extrémité, son autre extrémité étant court-circuitée. Le pilier forme une ligne de transmission axiale se comportant essentiellement comme une inductance destinée à compenser l'impédance capacitive du dé afin de minimiser la puissance RF réactive. En fonction de la configuration du cyclotron, les cavités sont disposées asymétriquement ou symétriquement par rapport au plan médian de circulation des particules. Dans le cas d'une topologie asymétrique (figure 1a de la présente demande), les deux plaques constituant le dé sont mécaniquement et électriquement solidaires et constituent un seul ensemble porté par le pilier. Dans le cas d'une topologie symétrique (figure 1b de la présente demande), les piliers inférieur et supérieur supportent respectivement le demi-dé inférieur et le demi-dé supérieur. Ces derniers sont reliés électriquement entre eux en quelques endroits de leur périmètre dès que le cyclotron est fermé.In the case of these known cavities, it is in the presence of a resonator $\frac{\mathit{\lambda }}{\mathbf{4}}$

loaded by the die capacity at one end, its other end being short-circuited. The pillar forms an axial transmission line essentially having an inductance for compensating the capacitive impedance of the die to minimize reactive RF power. Depending on the configuration of the cyclotron, the cavities are arranged asymmetrically or symmetrically with respect to the median plane of circulation of the particles. In the case of an asymmetric topology ( figure 1a of the present application), the two plates constituting the die are mechanically and electrically integral and constitute a single assembly carried by the pillar. In the case of a symmetric topology ( figure 1b of the present application), the lower and upper pillars respectively support the lower half-die and the upper half-die. These are electrically connected to each other at a few points in their perimeter as soon as the cyclotron is closed.

The die is part of a resonant cavity 5 as schematically shown in FIG. figure 1 at. This cavity comprises the actual dice 10, a vertical cylindrical pillar 20 and a conducting enclosure 40. figure 1c represents an equivalent circuit diagram of the cavity, in which the inductance L represents the pillar 20 and the capacitance C is that formed at the space between the die 10 and the conducting enclosure 40. The resonance frequency such a parallel LC circuit is given by the expression: $${\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="imgf0003.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=\frac{1}{2.\pi \mathrm{.}\sqrt{\mathrm{The}\mathrm{.}\mathrm{VS}}}$$

1. a) utiliser des modes harmoniques différents tout en conservant la fréquence RF identique
2. b) utiliser le même mode harmonique tout en variant la fréquence RF

La première solution comporte les désavantages suivants:

• une complexité accrue de la région centrale du cyclotron
• à haut courant, des pertes de faisceau à l'intérieur de la machine provoquant l'activation de pièces mécaniques.

En revanche, la seconde solution présente les avantages suivants:

• un même centrage des particules de masse différentes qui suivront donc une trajectoire similaire, au moins dans les premiers tours à basse énergie
• moins de pertes de faisceau réduisant ainsi l'activation des pièces mécaniques situées à proximité de la trajectoire du faisceau
• un meilleur gain par tour pour les particules de rapport q/m=1
• un meilleur isochronisme.

In order to accelerate several types of particles of different ratios q / m in the same cyclotron, the field B being determined, there are several solutions:

1. a) use different harmonic modes while maintaining the same RF frequency
2. b) use the same harmonic mode while varying the RF frequency

The first solution has the following disadvantages:

• increased complexity of the central cyclotron region
• at high current, beam losses inside the machine causing the activation of mechanical parts.

On the other hand, the second solution has the following advantages:

• the same centering of the different mass particles that will follow a similar trajectory, at least in the first low energy rounds
• fewer beam losses, thus reducing the activation of mechanical parts near the beam path
• a better gain per revolution for particles of ratio q / m = 1
• better isochronism.

The implementation of this second solution requires the ability to modify the resonant frequency of the cavity formed by the die, the pillar and the conductive enclosure. Such solutions have been proposed by M. Eiche et al. ("Dual Frequency Resonator System for a Compact Cyclotron", Proc.XIII Intern, Conf., Cyclotrons and Their Applications, (World Scientific, Singapore, 1992, 515). ), by P. Lanz et al. ("A Dual Frequency Resonator," Proceedings of the 1993 IEEE Particle Accelerator Conference, 17-20 May 1993, Washington, DC; 15th IEEE Particle Accelerator Conference, p.1151 ) and by Miura Iwao et al. ("Accelerating Resonance Cavity" , JP07-066877B, 1995 ).
The first two authors perform the RF frequency shift using sliding shorts, actuated by means of pistons, to change the length of the resonator. The last author proceeds to the change of frequency RF thanks to movable plates pivoting of 90 ° which modify the capacity of the electrodes and therefore the frequency of resonance.

• a. pour les courts-circuits mobiles :
  • la taille du piston est en rapport avec celle du court-circuit car celui-ci exerce une force de friction non négligeable sur les parois du résonateur ;
  • l'usure causée par les mouvements linéaires répétés du court-circuit lors des changements de fréquence. A terme, la dégradation de l'état de surface des contacts et/ou de la paroi sur laquelle ils glissent entraîne l'apparition de points plus résistifs qui dès lors qu'ils sont parcourus par des courants RF provoquent un échauffement localisé ;
  • la destruction pure et simple du court-circuit lorsque la pression exercée par celui-ci sur les parois n'est plus suffisante. Le cas échéant, la résistance de contact étant devenue trop importante eu égard aux courants RF à transporter entraîne ainsi une élévation de température qui peut provoquer la fusion des contacts.
• b. pour les plaques mobiles :
  • l'axe de rotation des plaques nécessite la traversée de la partie sous vide du cyclotron afin d'assurer sa connexion sur le piston ou sur le moteur qui l'entraîne. Si ces derniers étaient contenus dans le vide, il faudrait néanmoins les alimenter électriquement ce qui nécessite quand même une traversée de câble vers l'extérieur.
  • le facteur de qualité de la cavité dans la fréquence basse est assez mauvais dû aux courants RF importants passant dans cette capacité mobile. La stabilité en fréquence peut également être problématique.

This modification of the resonance frequency requires a relatively complex and expensive RF structure, to which reliability problems are added. Indeed, the devices of the prior art have certain disadvantages listed below:

• at. for mobile short circuits:
  • the size of the piston is related to that of the short circuit because it exerts a significant frictional force on the walls of the resonator;
  • the wear caused by repeated linear movements of the short circuit during frequency changes. Eventually, the degradation of the surface state of the contacts and / or the wall on which they slide leads to the appearance of more resistive points which, when they are traversed by RF currents, cause a localized heating;
  • the pure and simple destruction of the short circuit when the pressure exerted by it on the walls is no longer sufficient. If necessary, the contact resistance having become too great with regard to the RF currents to be transported thus causes a rise in temperature which can cause the melting of the contacts.
• b. for moving plates:
  • the axis of rotation of the plates requires the passage of the vacuum part of the cyclotron to ensure its connection to the piston or the motor that drives it. If the latter were contained in the vacuum, it should nevertheless feed them electrically which still requires a cable crossing to the outside.
  • the quality factor of the cavity in the low frequency is bad enough due to the large RF currents passing in this mobile capacity. Frequency stability can also be problematic.

SUMMARY OF THE INVENTION

The present invention aims to solve at least partially the aforementioned difficulties.

According to a first aspect, the present invention relates to a resonant cavity for accelerating charged particles in a cyclotron, comprising a die, a pillar and a conductive enclosure at least partially including said pillar and said die, an end of said pillar supporting the die. , the conductive enclosure and the pillar thus forming a transmission line, an opposite end of said pillar being integral with a base of the conductive enclosure, characterized in that the linear capacitance of an intermediate portion of said transmission line located between said ends of the pillar is substantially greater than the linear capacity of the other portions of said transmission line.

Such a configuration makes it possible to make the cavity resonate according to two modes thus producing two distinct frequencies, without having to make use of mobile elements such as, for example, sliding shorts or moving plates, which resolves many of the problems mentioned. previously.

Preferably, the linear capacitance of the intermediate portion of the transmission line is greater than twice the linear capacitance of the other portions of said transmission line. More preferably, the linear capacity of the intermediate portion of the transmission line is greater than ten times the linear capacity of the other portions of said transmission line.

Even more preferably, the characteristic impedance of the intermediate portion and the characteristic impedances of the other portions of the transmission line are such that the cavity is able to resonate in two modes to produce two distinct frequencies in a substantially double ratio.
By substantially double, it is necessary to understand a frequency ratio lying between 1.7 and 2.3.
Such a cavity makes it possible to accelerate, in the same cyclotron, particles having values of q / m in a ratio of two, such as for example protons and alpha particles or protons and deuterons.

Even more preferably, the pillar comprises a plurality of superimposed cylinders, one of these cylinders corresponding to said intermediate portion of the transmission line and having a mean diameter substantially greater than the average diameter of the other cylinders. Alternatively or jointly, the conductive enclosure comprises a plurality of superposed hollow cylinders, one of these hollow cylinders corresponding to said intermediate portion of the transmission line and having a mean diameter substantially smaller than the average diameter of the other hollow cylinders. A such cylindrical configuration of the pillar and / or the conductive enclosure makes it possible to obtain good mechanical rigidity of the assembly, to facilitate its construction and to ensure a good distribution of equipotentials of the electric field from the pillar.

According to a second aspect, the invention relates to a method for designing a dual-frequency resonant cavity as claimed.

These and other aspects of the invention will be clarified in the detailed description of particular embodiments of the invention.

BRIEF DESCRIPTION OF THE FIGURES

The figures are given for information only and do not constitute a limitation of the present invention. Moreover, the proportions of the drawings are not respected. Identical or like components are generally designated by the same reference numerals among all the figures.

The figure 1a represents a section of an asymmetric resonant cavity of a cyclotron of the prior art;

The figure 1b represents a section of a symmetrical resonant cavity of a cyclotron of the prior art;

The figure 1c represents a simplified equivalent electrical diagram of the resonant cavity of the Figure 1a or 1b ;

The figure 2a schematically represents a section of a cavity according to the invention with indication of the circulation of the current and the magnetic field during resonance at the low frequency;

;The figure 2b represents the evolution of the voltage and the current along the pillar during the operation of the cavity of the figure 2a in mode $\frac{\mathit{\lambda }}{\mathbf{4}}$

;

The Figure 2c represents a simplified equivalent electrical diagram of the resonant cavity of the figure 2a ;

The figure 3a schematically represents a section of a resonant cavity according to the invention with indication of the circulation of currents and magnetic fields during resonance at the high frequency;

;The figure 3b represents the evolution of the voltage and the current along the pillar during the operation of the cavity of the figure 3a in mode $\frac{\mathbf{3}\mathit{\lambda }}{\mathbf{4}}$

;

The figure 3c represents a simplified equivalent electrical diagram of the resonant cavity of the figure 3a ;

The figure 4a represents a real geometrical shape and a distribution of the equipotentials of a static electric field of a cavity of the prior art;

The figure 4b schematizes a cavity of the prior art in the form of a coaxial transmission line whose characteristic impedance is a function of the diameters d and D;

The figure 5 represents a graph illustrating the power dissipated in a resonant cavity according to the invention for each of the two resonance frequencies as a function of the value of the capacitance of the characteristic low-impedance line portion;

The figure 6a represents an impedance diagram of a pillar in an embodiment of the invention;

The figure 6b schematically represents a section of the cavity according to the invention, to be related to the impedance diagram of the figure 6a ;

The figure 7 represents a section of a bi-frequency cyclotron equipped with four cavities according to the invention;

The figure 8 schematically represents a graph showing the two distinct frequencies in a double ratio obtained by frequency scanning of a cavity according to the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

The figure 2a schematically represents an exemplary embodiment of a dual-frequency cavity according to the invention. This is a symmetrical cavity relative to the median plane of the cyclotron (represented by a mixed dotted line in the figure), but it is obvious that an asymmetrical cavity would also be suitable. The cavity 6 comprises two half-dice 10 and 10 'electrically connected together and between which will circulate the particles to accelerate, two pillars each comprising three portions 20a, 20b and 20c (20a', 20b 'and 20c'), and two conductive speakers 40 and 40 'surrounding the whole. The speakers have a cross section which, in this example, is substantially constant over the height of the pillars. Each pillar respectively supports a half-die at one end, the opposite ends being respectively electrically connected to the bases 45 and 45 'of the conductive speakers 40 and 40' to constitute a short circuit from the radiofrequency point of view. The different portions of the pillar are superimposed and preferably aligned along the same axis. Said portions consist, in this example, of cylindrical tubes of different diameters, examples of dimensions of which will be given below when a method of designing a cavity according to the invention will be described. The diameter of the intermediate portion 20b is substantially greater than the diameter of the other two portions 20a and 20c, so that the linear capacity (in Farad per meter) of this intermediate portion 20b is substantially greater than the linear capacity of the other two portions 20a and 20c. Consequently, the intermediate portion 20b will have a substantially capacitive behavior while the other portions 20a and 20c will have an essentially inductive behavior, in the operating frequency range of the cavity (which is in the megahertz).

A simplified equivalent electrical diagram of such a cavity is presented at Figure 2c .

(λ étant la longueur d'onde), ce qui permet d'obtenir une première fréquence de résonance (ci-après « la fréquence de résonance basse », par exemple 33 MHz).
La figure 2b représente l'évolution de la tension (U_x) et du courant (I_x) dans ce mode en fonction d'une position axiale x le long du pilier. La tension est maximale au niveau du dé tandis que le courant correspondant y est nul ou très faible. Cela s'inverse lorsqu'on se ramène au pied du pilier. Cette configuration de tension convient particulièrement bien pour accélérer des particules évoluant dans le plan médian d'un cyclotron.A first type of operation is obtained by exciting the cavity in $\frac{\mathit{\lambda }}{\mathbf{4}}$

(λ being the wavelength), which makes it possible to obtain a first resonance frequency (hereinafter "the low resonance frequency", for example 33 MHz).
The figure 2b represents the evolution of the voltage (U _x ) and the current (I _x ) in this mode as a function of an axial position x along the pillar. The voltage is maximum at the die while the corresponding current is zero or very low. This is reversed when one comes back to the foot of the pillar. This voltage configuration is particularly suitable for accelerating particles moving in the median plane of a cyclotron.

The magnetic field B is oriented identically on either side of the intermediate portion 20b (hereinafter "the low impedance line 20b"). The resulting current i ₁ of this mode circulates axially and is distributed radially around the pillar as shown in FIG. figure 2a .

, ce qui permet d'obtenir une deuxième fréquence de résonance (ci-après « la fréquence de résonance haute », par exemple 66 MHz), plus élevée que la première fréquence. La figure 3b représente l'évolution de la tension (U_x) et du courant (I_x) dans ce mode et, de manière identique au premier mode de résonance, la tension est toujours maximale au niveau du dé tandis que le courant correspondant y est nul ou très faible. Par ailleurs, le courant s'inverse en un point intermédiaire situé environ à mi-hauteur de la ligne faible impédance 20b, ce qui a pour effet de diviser l'effet capacitif de cette portion de ligne 20b en deux.A second type of operation is illustrated in figure 3a . The physical structure is identical to that of the figure 2a but we excite the mode $\frac{\mathbf{3}\mathit{\lambda }}{\mathbf{4}}$

, which makes it possible to obtain a second resonance frequency (hereinafter referred to as the "high resonance frequency", for example 66 MHz), higher than the first frequency. The figure 3b represents the evolution of the voltage (U _x ) and of the current (I _x ) in this mode and, like the first resonance mode, the voltage is always maximum at the dice level, while the corresponding current is zero or very weak. Furthermore, the current is reversed at an intermediate point about halfway up the low impedance line 20b, which has the effect of dividing the capacitive effect of this portion of line 20b in two.

In view of the above, the magnetic field B is in opposition on both sides of this intermediate point. The figure 3c represents a simplified equivalent electrical diagram with the circulation of currents i ₂ and i ₃ respectively present in the upper and lower part of the half-cavity. They are distributed radially around the pillar, in opposition to a virtual horizontal plane transversely sharing the low impedance line 20b, in which they cancel each other out.

It will be obvious to one skilled in the art that many other geometric configurations of the cavity are possible, provided that an intermediate portion of the cavity has a linear capacity substantially greater than the linear capacity of the other portions, preferably greater than twice the linear capacity of the other portions, even more preferably greater than ten times the linear capacity of the other portions. One could alternatively provide a pillar of constant section over its height and a conductive enclosure having an intermediate portion of section substantially smaller than that of the other portions. One could also provide a combination of these two solutions, namely an enclosure having an intermediate narrowing and a pillar having an intermediate expansion, as illustrated for example by the figures 6b and 7 , or any other combination.

A calculation method for designing and dimensioning a structure of a cavity according to the invention is provided below.

1. 1. calcul de la capacité linéique du pilier d'une cavité dont le pilier et l'enceinte conductrice présentent une section constante, permettant de déduire l'impédance caractéristique de la ligne de transmission ainsi formée par ledit pilier et l'enceinte conductrice ;
2. 2. calcul de l'impédance caractéristique pour différents diamètres de pilier ;
3. 3. détermination du diamètre extérieur moyen équivalent de l'enceinte conductrice ;
4. 4. simulation électromagnétique 2D de la cavité s'appuyant sur les dimensions trouvées précédemment et détermination du diamètre d'un dé équivalent, supposé circulaire, produisant la même fréquence de résonance que ladite cavité de l'art antérieur ;
5. 5. calcul des paramètres intrinsèques de la cavité, tels que le facteur de qualité Q, la puissance dissipée, l'énergie stockée et comparaison des résultats avec des valeurs mesurées.

Prior to the calculation of the dual-frequency cavity according to the invention, a modeling of a known cavity as described in the document WO8606924 - that is to say a cavity whose pillar and the conductive enclosure have a constant section - is carried out according to a method described below to precisely determine the diameter of an equivalent die, supposed circular, and the impedance of the pillar of such a known cavity:

1. 1. calculation of the linear capacity of the pillar of a cavity, the pillar and the conductive enclosure have a constant section, to deduce the characteristic impedance of the transmission line thus formed by said pillar and the conductive enclosure;
2. 2. Calculation of the characteristic impedance for different pillar diameters;
3. 3. determination of the equivalent mean outside diameter of the conductive enclosure;
4. 4. 2D electromagnetic simulation of the cavity based on the dimensions previously found and determination of the diameter of an equivalent die, assumed circular, producing the same resonance frequency as said cavity of the prior art;
5. 5. Calculation of the intrinsic parameters of the cavity, such as the quality factor Q, the dissipated power, the stored energy and comparison of the results with measured values.

Details of step 1

The characteristic impedance of the known pillar is evaluated, for example using the Tricomp program of Field Precision LLC. This program solves the electric field by the finite element method.
The figure 4a shows for example the distribution of electric field equipotentials obtained by applying a voltage of 1 V on a known pillar of diameter d = 90 mm, while the conducting enclosure is at the potential of the mass. A stored energy of 18.53 pJ / m is obtained.

, ce qui donne C = 37,06 pF/m dans le cas de l'exemple.The value of the capacitance C is then obtained from the expression: $$E=\frac{\mathrm{VS}\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0003.png"\; state="\{\{state\}\}">V</figure-callout>}}^2}{2}$$

which gives C = 37.06 pF / m in the case of the example.

Then, combining the two following expressions: $$Z_{\mathrm{vs}}=\sqrt{\mathrm{The}/\mathrm{VS}}\mathrm{and}{\mathrm{vs}}_0=\frac{\mathrm{1}}{\sqrt{\mathit{The}\mathit{.}\mathit{VS}}}\mathrm{with}{\mathrm{vs}}_{\mathrm{0}}\mathrm{=}\mathrm{speed\; of\; light},$$

, de laquelle on obtient une valeur de Z_c, qui vaut 90,1 ohms dans le cas de l'exemple.the expression of the characteristic impedance Z _c can be rewritten in the form: $$Z_{\mathrm{vs}}=\frac{1}{\mathrm{VS}\mathrm{.}{\mathrm{vs}}_0}$$

from which a value of Z _c is obtained, which is 90.1 ohms in the case of the example.

Details of step 2

• pour d = 100mm : C = 39,88pF/m et Zc = 83,58 ohms
• pour d = 80mm : C = 34,36pF/m, Zc = 97,01 ohms

The same characteristic impedance calculation is performed for other pillar diameters. For example, the following values are obtained:

• for d = 100mm: C = 39.88pF / m and Zc = 83.58 ohms
• for d = 80mm: C = 34.36pF / m, Zc = 97.01 ohms

Details of step 3

Pour l'exemple fourni, cela donne : D = 404,02 mm pour un diamètre de pilier de d = 90 mm.
En effectuant par ailleurs le même calcul avec les données obtenues à l'étape 2, on remarque que D ne varie quasi pas pour différents diamètres de pilier. On obtient en effet que D = 402,69 pour d = 100 mm, et que D = 402,97 pour d = 80 mm. Nous choisissons dans cet exemple la valeur de D= 400mm (+/- 3mm sont alloués à l'épaisseur de cuivre de l'enceinte conductrice).The known conducting enclosure does not necessarily have a circular section (as seen for example on the figure 4a which shows a more or less triangular section for the example of known enclosure), an equivalent mean diameter D is then determined (see figure 4b ) of this conducting enclosure by the following expression: $$\mathrm{D}\mathrm{=}\mathrm{d}\mathrm{.}{e}^{\left(\frac{{\mathrm{<figure-callout\; id="60"\; label="Z\; VS"\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">Z\; </figure-callout>}}_{\mathrm{VS}}}{60}\right)}$$

For the example provided, this gives: D = 404.02 mm for a pillar diameter of d = 90 mm.
Moreover, by performing the same calculation with the data obtained in step 2, it is noted that D does not vary substantially for different pillar diameters. We obtain in fact that D = 402.69 for d = 100 mm, and that D = 402.97 for d = 80 mm. We choose in this example the value of D = 400mm (+/- 3mm are allocated to the copper thickness of the conductive enclosure).

Details of step 4

In order to determine the diameter of an equivalent die, assumed to be circular, producing the same resonance frequency as said cavity of the prior art, a 2D electromagnetic simulation of the cavity based on the dimensions found previously, for example, is carried out. using the Wavesim program from Field Precision LLC. This is done by successive approximations until the good resonance frequency.

In the case of the example, there is an equivalent diameter of the dice of 378 mm for a resonance frequency of f ₀ = 66 MHz (measured on the actual cavity).

Details of step 5

The surface currents in the cavity are then determined so as to evaluate the dissipated power and the quality factor. This can for example also be done using the Wavesim program.

For a voltage of 50 kV present in the accelerator gap, the power dissipated in a cavity known according to the example provided is 1300 W and the quality factor Q is 10600.
These values will serve as benchmarks for subsequent steps.

pour une fréquence basse d'environ 33 MHz et un second mode à $\frac{\mathbf{3}\mathit{\lambda }}{\mathbf{4}}$

pour une fréquence haute d'environ 66 MHz. Il sera évident pour l'homme du métier d'adapter ce qu'il est nécessaire d'adapter à ces étapes suivantes pour d'autres fréquences et/ou d'autres rapports de fréquence.The numerical values obtained during these first five steps then make it possible to calculate the structure of a two-frequency cavity according to the invention. The following steps of the calculation method according to the invention concern, by way of example, a cavity according to the Figures 2a and 3a and exploiting two resonant modes: a first mode to $\frac{\mathit{\lambda }}{\mathbf{4}}$

for a low frequency of about 33 MHz and a second mode to $\frac{\mathbf{3}\mathit{\lambda }}{\mathbf{4}}$

for a high frequency of about 66 MHz. It will be obvious to those skilled in the art to adapt what is necessary to adapt to these next steps for other frequencies and / or other frequency ratios.

• l'impédance caractéristique et la longueur de la ligne 20c ;
• l'impédance caractéristique et la longueur de la ligne faible impédance 20b, assimilable à un condensateur ;
• l'impédance caractéristique et la longueur de la ligne 20a.

The shape of a two-frequency cavity according to the invention is determined by several physical components whose following characteristics can be obtained, and preferably optimized, for example using the Genesys radio frequency simulation software from Agilent:

• the characteristic impedance and the length of line 20c;
• the characteristic impedance and the length of the low impedance line 20b, comparable to a capacitor;
• the characteristic impedance and the length of the line 20a.

Once these elements have been determined, a final optimization of the two-frequency cavity is preferably carried out by 2D electromagnetic simulation, for example using the Wavesim program. It examines the variation of the resonant frequency as a function of the variation of the geometrical characteristics of the different portions of the pillar.
In particular, the most delicate point is the optimization of the low impedance line 20b. Indeed, if its capacity is chosen too low, the dissipation at the high frequency (eg at 66MHz) is important, as is the voltage developed at this point, in some cases as important as that present on the die. By increasing the value of the capacitance, the voltage decreases as well as the power dissipated in the bottom of the cavity. Taking into account the maximum acceptable value of the electric field as well as the value of the capacitance making it possible to obtain the desired frequency ratio, for example a double ratio (referenced point C _min ), an optimum point C _{opt is} preferably determined. the dissipated power is almost identical to the two resonance frequencies, as illustrated by figure 5 .

1. i. avoir un pilier de diamètre supérieur ou égale à 80 mm dans la portion 20c pour des raisons de rigidité mécanique ;
2. ii. avoir une longueur totale du pilier la plus courte possible ;
3. iii. prolonger la ligne faible impédance 20b hors de la culasse du cyclotron, permettant ainsi une injection de la puissance RF et un accord cavité optimum ;
4. iv. permettre une puissance RF d'excitation des cavités aussi basse que possible, en particulier à la fréquence haute (p.ex. à 66 MHz), afin d'avoir une réserve pour l'accélération du faisceau de particules.

A multitude of solutions exist. However, certain technical criteria have guided the design of a more preferred cavity according to the invention:

1. i. have a pillar of diameter greater than or equal to 80 mm in the portion 20c for reasons of mechanical rigidity;
2. ii. have a total length of the pillar as short as possible;
3. iii. extend the low impedance line 20b out of the cyclotron breech, thus allowing RF power injection and optimum cavity tuning;
4. iv. to allow RF excitation power of the cavities as low as possible, particularly at the high frequency (eg at 66 MHz), in order to have a reserve for the acceleration of the particle beam.

• portion 20c (en deux parties) :
  • ○ première partie : diamètre = 80 mm, longueur = 520 mm, Zc = 96,5 ohms ;
  • ○ deuxième partie : diamètre = 80 mm, longueur = 145 mm, Zc = 70 ohms ;
• portion 20b : diamètre = 258 mm, longueur = 285 mm, Zc = 5 ohm (portion à faible impédance)
• portion 20a : diamètre = 184 mm, longueur = 405 mm, Zc= 60 ohms.

Applying the above method, the following preferred dimensions for the pillar are finally obtained:

• portion 20c (in two parts):
  • ○ first part: diameter = 80 mm, length = 520 mm, Zc = 96.5 ohms;
  • ○ second part: diameter = 80 mm, length = 145 mm, Zc = 70 ohms;
• portion 20b: diameter = 258 mm, length = 285 mm, Zc = 5 ohm (low impedance portion)
• portion 20a: diameter = 184 mm, length = 405 mm, Zc = 60 ohms.

This result is illustrated in Figures 6a and 6b , the figure 6a being an impedance diagram of the different line portions constituting the pillar and the figure 6b being a schematic view in longitudinal section of a corresponding physical embodiment of the preferred cavity example according to the invention (only half of the cavity is shown).

The total length of the cavity is 1355 mm, of which 600 mm out of the cylinder head 60 of the cyclotron. The low and high resonance frequencies are evaluated at 33.094 MHz and 66.486 MHz, respectively. The dissipated powers are of the order of 2768 W at 33 MHz for a dc voltage of 25 kV and 2699 W at 66 MHz for a dc voltage of 50 kV. The quality factors are 6700 to 33 MHz and 10000 to 66 MHz.

A practical embodiment of a cavity according to the invention and its implantation in a cyclotron is illustrated in FIG. figure 7 . The vertical section of this cyclotron makes it possible to distinguish four cavities according to the invention, only one of which has been annotated for clarity and comprehension.

The resonance frequencies of the cavity can be verified by performing a frequency sweep ("wobbulation"). This provides a curve of variation of the impedance as a function of the frequency revealing two distinct peaks. According to the preferred example provided, there is a peak at substantially 33 MHz and a second peak at substantially 66 MHz, as shown schematically in FIG. figure 8 .

During its operation, the resonant frequency of the cavity will drift, mainly because of thermal drifts changing its dimensions. According to the prior art, it is known to place a tuning capacitor motorized and controlled in the median plane of the cyclotron and intended to adjust the RF frequency injected into the cavity. This configuration, however, would have little effect at low frequency, for example at 33 MHz.
According to a preferred version of the invention, the cavity 6 comprises a tuning capacitor 50 comprising a movable electrode electrically connected to the conducting enclosure 40 and placed opposite the pillar and substantially at the intermediate portion 20b. of the transmission line. This tuning capacitor 50 is visible on the figure 7 . By simulation, it has in fact been determined that such a tuning capacitor 50 placed at such a place makes it possible to obtain an adjustment amplitude very close to the two resonance frequencies, namely, in the case of a low frequency of 33 MHz and a high frequency of 66 MHz, a variation of 12.6 KHz / pF at 33 MHz and a variation of 12.2 KHz / pF at 66 MHz.

In summary, the invention can also be described as follows: a resonant cavity (6) bi-frequency cyclotron which comprises a die (10), a pillar (20) and a conductive enclosure (40) encompassing said pillar and said die , one end of the pillar being integral with the base of the conductive enclosure and an opposite end of said pillar (20) supporting the die (10). The conducting enclosure and the pillar form a transmission line comprising at least three portions (20a, 20b, 20c) each having a characteristic impedance (Z _c1 , Z _c2 , Z _c3 ). The characteristic impedance Z _c2 of the intermediate portion (20b) is substantially lower than the characteristic impedances Z _c1 and Z _c3 of the two other portions (20a, 20b), which makes it possible to make the cavity resonate according to two modes in order to produce two frequencies separate without having to use moving parts such as for example sliding shorts or moving plates.

The present invention has been described in relation to specific embodiments, which have a purely illustrative value and should not be considered as limiting. In general, it will be apparent to those skilled in the art that the present invention is not limited to the examples illustrated and / or described above. The invention includes each of the novel features as well as all their combinations. However, it is the claims that determine the extent of its protection. The presence of reference numbers to the drawings can not be considered as limiting, even when these numbers are indicated in the claims.
The use of the verbs "to understand", "to include", "to include", or any other variant, as well as their conjugation, can in no way exclude the presence of elements other than those mentioned. The use of the indefinite article "a", "an", or the definite article "the", "the", or "the", to introduce an element does not exclude the presence of plurality of these elements.

Claims (9)

1. Resonant cavity (6), for accelerating charged particles in a cyclotron, comprising a dee (10), a rod (20), and a conductive chamber (40) at least partially surrounding said rod and said dee, one end of said rod (20) supporting the dee (10), the conductive chamber and the rod (20) thus forming a transmission line, one opposite end of said rod (20) being securely fastened to a base (45) of the conductive chamber (40), characterized in that the capacitance per unit length of an intermediate portion (20b) of said transmission line located between said ends of the rod is substantially higher than the capacitance per unit length of the other portions (20a, 20c) of said transmission line.
2. Resonant cavity according to Claim 1, characterized in that the capacitance per unit length of the intermediate portion (20b) of the transmission line is twice as high as the capacitance per unit length of the other portions (20a, 20c) of said transmission line.
3. Resonant cavity according to Claim 2, characterized in that the capacitance per unit length of the intermediate portion (20b) of the transmission line is ten times higher than the capacitance per unit length of the other portions (20a, 20c) of said transmission line.
4. Resonant cavity according to any one of the preceding claims, characterized in that the characteristic impedance (Z _c2 ) of the intermediate portion (20b) and the characteristic impedances (Z _c1 , Z _c3 ) of the other portions (20a, 20c) of the transmission line are such that the cavity (6) is able to resonate in two modes so as to produce two separate frequencies, one being substantially double the other.
5. Resonant cavity according to any one of the preceding claims, characterized in that the rod (20) comprises a number of superposed cylinders (20a, 20b, 20c), one of these cylinders (20b) corresponding to said intermediate portion (20b) of the transmission line and having an average diameter that is much larger than the average diameter of the other cylinders (20a, 20c).
6. Resonant cavity according to any one of the preceding claims, characterized in that the conductive chamber (40) comprises a number of superposed hollow cylinders, one of these hollow cylinders corresponding to said intermediate portion (20b) of the transmission line and having an average diameter substantially smaller than the average diameter of the other hollow cylinders.
7. Resonant cavity according to any one of the preceding claims, characterized in that it furthermore comprises a matching capacitor (50) comprising a moveable electrode electrically connected to the conductive chamber (40) and placed facing the rod and substantially level with the intermediate portion (20b) of the transmission line.
8. Method for designing a dual-frequency resonant cavity according to any one of the preceding claims, comprising the following steps:

   - calculating the capacitance per unit length of a cavity the rod and the conductive chamber of which have a constant cross section, allowing the characteristic impedance of the transmission line thus formed by said pillar and conductive chamber to be deduced;

   - calculating the characteristic impedance for various rod diameters;

   - determining the equivalent average outside diameter of the conductive chamber;

   - producing a 2D electromagnetic simulation of the cavity using the dimensions found beforehand and determining the diameter of an equivalent dee, hypothesized to be circular, producing the same resonant frequency as said cavity, the rod and the conductive chamber of which cavity have a constant cross section;

   - calculating the intrinsic parameters of the cavity, such as the quality factor Q, the power dissipated, the energy stored and comparing the results with measured values; and

   - characterizing, using a radiofrequency simulation, the various line portions forming the rod of a cavity, two resonant modes of which are used to produce two separate frequencies.
9. Method for designing a dual-frequency resonant cavity according to Claim 8, furthermore comprising a final step of optimizing the dual-frequency cavity using 2D electromagnetic simulation.

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