RU2212121C2 - Method and device for accelerating and focusing charged particles by constant field - Google Patents

Abstract

FIELD: direct- action electrical accelerators for producing high-intensity charged- particle beams. SUBSTANCE: method intended for simultaneous acceleration, filtering, and production of charged particle beams with electric field unchangeable with time includes generation of constant longitudinal accelerating component of electric field strength with aid of electrostatic electrodes and linear focusing of transverse one. Field is built up by means of elongated electrodes of quasi-cylindrical quadruple form whose inner contour in cross- sectional area is described by four half-hyperbolas of equilateral hyperbola and in longitudinal direction, as square root of longitudinal coordinate value. Potentials and other parameters of electrodes are set in compliance with required acceleration and focusing of charged particles. EFFECT: enhanced voltage gradient across acceleration tube, reduced size and cost of accelerator. 2 cl, 2 dwg

Description

 The invention relates to the field of acceleration of electrically charged particles, and in particular to the technique of acceleration, focusing and formation of charged particle beams by a constant electric field in time and can be used in direct-acting electric and electrostatic accelerators to produce high intensity charged particle beams.

 In modern accelerators, to focus the beam and increase the intensity of accelerated particles, they are focused using various techniques that keep particles in the accelerator. The principles of strong focusing of charged particles are known, based on the use of azimuthal variation of the magnetic field in cyclic circular accelerators, on the application of a spatially periodic gradient magnetic field, and in particular, the focusing-defocusing quadrupole magnetic field in cyclic ring accelerators, and finally, on the use of a time-variable electric quadrupole field (high-frequency quadrupole focusing) in linear resonant accelerators. All these methods make it possible to obtain, with the help of accelerators of the indicated types, fairly well formed beams of accelerated charged particles with an average intensity of up to several tens of mA.

 In direct action accelerators, i.e. In accelerators with a time-constant accelerating electric field created either by means of an electric step-up transformer and current rectifier, or by means of an electrostatic generator, mainly weak electric focusing due to the action of a scattered edge electric field is used to form a beam of charged particles [1], [ 2]). To do this, either breaks are created in the accelerator in the plane electric field of the accelerating tube, breaking up the continuous tube into sections, or changing the longitudinal gradient of the intensity of the accelerating electric field, setting the potentials of the accelerating electrodes in a special way. The open-end accelerator tube section, due to the solenoidality of the electric field, acts on the particles as a collecting single lens at the entrance to the section and as a scattering lens at the exit of the section. As a result, the difference in the actions of the scattered field at the two ends of the section creates a weak focusing effect.

 Weak electrical focusing does not provide effective confinement of charged particles in a beam with a high spatial electric charge density. Therefore, in order to ensure efficient beam passing through the accelerator, direct focusing accelerators introduce additional focusing elements, for example, short solenoidal lenses of permanent magnets for focusing soft particles in a magnetic field, for example, electrons with energies up to 1.5 MeV [3], or multiplets of electric cylindrical quadrupole lenses for focusing harder heavy ions with energies of more than a hundred MeV [4]. The requirement of a strong focusing action is especially significant in electrostatic tandems, which use strippers to peel their electron shell to increase the ion energy. However, even with the use of cylindrical quadrupole lenses, the transported current of accelerated heavy ions [4] does not exceed several μA, while the supply current of the accelerator electrostatic conductor, which determines the maximum possible value of the current of accelerated particles, is several mA. In addition, the placement of additional focusing, but not accelerating cylindrical quadrupole lenses between the accelerating electrodes and the separation of a single accelerating tube into separate sections, leading to the formation of so-called “dead” zones, increases the length of the acceleration path, reduces the average acceleration rate, and thereby increases the overall dimensions the accelerator itself and the external gas tank under a pressure of 10-15 atm, increasing the cost of the accelerator.

 In an electrostatic tandem of type 25URC of two accelerators for a total voltage of 25 MB [4], manufactured by the National Electric Company of the United States and designed to accelerate heavy ions, multiplexes of electrostatic cylindrical quadrupole lenses are installed in four breaks of the accelerator tube. In this case, the voltage gradient along the accelerator tube is only 1.6 MV / m, while in other similar accelerators it is noticeably higher (up to 2.2 MV / m).

 The above method and device for focusing and forming a beam of ions accelerated in a direct-acting electrostatic accelerator [4], containing additional cylindrical quadrupole lenses between the sections of the accelerating tube, are here taken as a prototype of the invention.

где v(r, φ, z) - электрический потенциал поля в цилиндрической системе координат r, φ, z, Е_z - ускоряющая постоянная составляющая напряженности электрического поля, направленная вдоль продольной оси z электрического поля во всей области поперечного сечения z= const, G_r - градиент радиальной (поперечной) фокусирующей или дефокусирующей составляющей напряженности электрического поля, V(0, 0, z₀) - потенциал в точке z₀ на оси поля.The present invention solves the problem of creating a static electric field for use in a linear high-voltage accelerator of direct action, effectively accelerating and simultaneously focusing charged particles using a specific device - accelerating-focusing electrodes of a special shape. This method and device solves the problem of accelerating, focusing and forming a beam of accelerated charged particles with high intensity, increasing the voltage gradient on the accelerating tube and thereby reducing the size and cost of the accelerator. This goal is achieved by the formation of a constant in time electric field with a constant longitudinal accelerating component and a transverse linearly growing component of the electric field strength, defined by the following formula:

where v (r, φ, z) is the electric potential of the field in the cylindrical coordinate system r, φ, z, Е _z is the accelerating constant component of the electric field strength, directed along the longitudinal axis z of the electric field in the entire cross-sectional area z = const, G _r is the gradient of the radial (transverse) focusing or defocusing component of the electric field strength, V (0, 0, z ₀ ) is the potential at the point z ₀ on the field axis.

где r_e(φ, z) - радиус-вектор внутреннего профиля электрода, V_e - потенциал электрода, а сами электроды расположены в порядке чередования их фокусирующего и дефокусирующего действий, определяемых знаком градиента радиальной напряженности поля G_r.A device for realizing field (1) is a system of monopotential electrodes, the internal profiles of which are made in accordance with the formula

where r _e (φ, z) is the radius vector of the internal profile of the electrode, V _e is the potential of the electrode, and the electrodes themselves are arranged in alternating order of their focusing and defocusing actions, determined by the sign of the gradient of the radial field strength G _r .

Для решения поставленной задачи зададим базовое поле в плоскости симметрии φ=0 и на оси z в виде

Как можно видеть, условия (5) представляют электрическое поле, ускоряющее заряженные частицы вдоль оси z постоянной составляющей напряженности Е_z и фокусирующее (дефокусирующее) частицы поперечной линейно растущей составляющей напряженности электрического поля с градиентом G_r в плоскости φ=0, G_r<0 или G_r>0. Из уравнения (3) имеем равенство ∂E_φ(r,φ,z)/∂φ = ∂[rE_r(r,φ,z)]/∂r = -2G_rr, интегрируя которое по φ от 0 до φ и используя начальные условия (5), получаем
E_φ(r,φ,z) = -2G_rrφ. (6)
Подставив полученный результат (6) в уравнение (4), приходим к

интегрируя которое снова по φ, получаем
E_r(r,φ,z) = G_rr[1-(2φ)²/2]. (7)
Используя результат (7) и уравнение (3) и снова интегрируя по φ, приходим к
E_φ(r,φ,z) = -G_rr[(2φ)-(2φ)³/3!].
Продолжая так далее бесконечное число раз и используя формулы разложения тригонометрических функций sinφ и соsφ в ряды, в итоге находим

Интегрируя выражения (8), получаем формулу (1) для потенциала поля V(r, φ, z) в любой его точке.The accelerating-focusing static electric field (1) was found by our proposed method for solving electrical problems, the inverse of the traditional method of directly solving electrostatic problems based on the Laplace equation. The inverse method consists in the fact that based on the requirements for the structure of the electric field in any physical or technical device, we analytically set the base, reference field on the physically selected axis or surface of the device. The electric field in the remaining space of the device aperture is determined by integrating the Maxwell equations

To solve the problem, we set the base field in the plane of symmetry φ = 0 and on the z axis in the form

As can be seen, conditions (5) represent an electric field accelerating charged particles along the z axis of the constant component of intensity E _z and focusing (defocusing) particles of the transverse linearly growing component of electric field with a gradient of G _r in the plane φ = 0, G _r <0 or G _r > 0. From equation (3) we have the equality ∂E _φ (r, φ, z) / ∂φ = ∂ [rE _r (r, φ, z)] / ∂r = -2G _r r, integrating which over φ from 0 to φ and using the initial conditions (5), we obtain
E _φ (r, φ, z) = -2G _r rφ. (6)
Substituting the obtained result (6) into equation (4), we arrive at

integrating which again over φ, we obtain
_{E r (r, φ, z} ) = G r r [1- (2φ) ^2/2]. (7)
Using the result of (7) and equation (3) and again integrating over φ, we arrive at
_{E φ (r, φ, z} ) = -G r r [(2φ) - (2φ) ^3/3!].
Continuing so on an infinite number of times and using the formulas for expanding the trigonometric functions sinφ and cosφ into series, we finally find

Integrating expressions (8), we obtain formula (1) for the field potential V (r, φ, z) at any of its points.

 The electric potential (1), as one can easily see directly, satisfies the Laplace equation.

When the azimuthal angle φ passes through the values π / 2, 3π / 2, 5π / 2, and 7π / 2, as follows from formula (1), the field potential reverses its sign. Along with it, changes sign to the inverse and the gradient of the radial component of the electric field strength G _r . This corresponds to the fourth-order axial symmetry of the electric field structure, which makes it possible to focus charged particles in two mutually perpendicular planes by alternately focusing and defocusing actions of the field on moving charged particles. From formulas (8) and (1) it follows that the obtained field provides constant continuous longitudinal acceleration of charged particles of the axial component of tension E _z and alternate transverse focusing of the radial component E _r in its entire volume.

A field with potential (1), like any other electrostatic field, can be formed by local electrodes of relatively small sizes with corresponding potential values located at the aperture of the device. However, monopotential extended electrodes of a special shape are more convenient for practical use in high-voltage accelerators of charged particles of direct action. From (1) follows equation (2) of the internal profile r _e (φ, z) of the equipotential electrode under the potential V _e .

It follows from formula (2) that, in any cross section z = const, the electrode profile is described by four branches of an equilateral hyperbola, and in the section φ = const, by the square root of the coordinate difference (zz ₀ ).

The general scheme of a system of four electrodes (2) forming a field (1) is shown in FIG. 1, where 1 and 2 are “quasicylindrical” hyperbolic electrodes made of sheet metal (trough electrodes), as shown in FIG. 1, or in the form of solid rod electrodes, with an internal profile according to formula (2), 3 - a cylindrical metal holder for attaching the electrode in the accelerating tube and supplying an electric potential to the electrode. In the upper part of figure 1 shows the projection of the electrodes on the plane φ in the first quadrant. The azimuthal profiles of the electrodes in the other three quadrants have mirror symmetry in the horizontal and vertical planes. In the lower part of figure 1 shows the projection of the electrode 1 on the half-plane φ = 0, z and electrode 2 on the half-plane φ = π / 2, z, and _min , and _max - the minimum and maximum distances from the optical axis z to the crest of the quasi-cylindrical hyperbolic electrode, L is the length of the electrode.

The parameters of the electrodes are selected according to (2) in accordance with the requirements for the acceleration and focusing of ions and taking into account the size and current of the beam in a specific section of the accelerating tube. For example, by requiring a longitudinal accelerating field strength equal to E _z = 22 kV / cm (2, 2 MV / m), and setting the dimensions of the electrodes a = 1.5 cm (determines the minimum clearance in the aperture of the electrode system equal to 3.0 cm) , and _max = 2.5 cm and 1 = 3.5 cm, from formula (2) we obtain the radial gradient of the field strength equal to G _r = 38.5 sq / cm ² in the upper and lower quarters of the quasi-cylindrical quadrupole (focusing of positively charged particles ) and equal to G _r = 38.5 kV / cm ² in the left and right quarters (defocusing). The potentials of the electrodes with respect to the potential of the field axis at the point of least distance of the electrode from the axis are V _e = ± 43.3 kV, respectively. The maximum electric field strength on the inner surface of the considered quasi-cylindrical quadrupole electrodes, equal to E _e = (E $\genfrac{}{}{0ex}{}{\text{2}}{\text{r}}$ + E $\genfrac{}{}{0ex}{}{\text{2}}{\text{φ}}$ + E $\genfrac{}{}{0ex}{}{\text{2}}{\text{z}}$ ) ^1/2 , does not exceed the permissible in vacuum 100 kV / cm. The maximum electric field strength E _φ is set, as in the known cylindrical quadrupoles, by choosing the azimuthal size of the hyperbolic electrode.

 The necessary electric potentials of the electrodes for accelerating and focusing the charged particles are supplied from the full voltage divider to the accelerator conductor through the electrode holders 3 and do not require other power sources.

In FIG. Figure 2 shows the conditional placement of two quasicylindrical quadrupoles in a focusing doublet with an initial doublet potential equal, for example, v ₀ = -1000 kV in a direct action accelerator for positively charged particles with a grounded ion source. The doublet is constructed according to the principle of FD and DF focusing, respectively, in the planes φ = 0, φ = π, z and φ = π / 2, φ = 3π / 2, z. The potentials of the electrodes V _e in the plane φ = 0, φ = π, z are - 956.7 and - 1000.7 kV and in the plane φ = π / 2, φ = 3π / 2, z - 1120.3 and - 1077.7 kV. The electric strength of the vacuum gaps between the electrodes is ensured by the choice of their sizes and radii of rounding of the boundaries of the electrodes, also presented in figure 2.

где j - плотность тока пучка, v - скорость ускоряемых частиц. Например, жесткость приведенных выше квадруполей по отношению к ионам с отношением ионного заряда к массовому числу иона Q/M= 1/30 при плотности тока в пучке j≅10 мА/см² снижается всего в два раза в фокусирующей плоскости и возрастает в три раза в дефокусирующей. Это не мешает все еще приемлемой фокусировке ионов.The calculation of the focusing of continuously accelerated particles is possible by known calculation methods, including analytical ones. Numerical estimates show that the doublet of quasi-cylindrical quadrupoles with the parameters presented above has a focal length determined by the transformation of the particle beam by the type of “parallel to the point” and counted from the exit boundary of the doublet, equal to ≅15 cm in the FD plane and equal to ≅70 cm in the DF plane without taking into account the defocusing effect of the space charge of the beam. The wave number of each of the two quasi-cylindrical quadrupole lenses is about 0.13 cm ^-1 . Accounting for the space charge determined by the Maxwell equation divD = 4πρ, where ρ is the space charge density of the beam of accelerated particles, shows that the action of the beam charge reduces to defocusing the beam by its internal radially linear field with a gradient

where j is the beam current density, v is the velocity of the accelerated particles. For example, the rigidity of the above quadrupoles with respect to ions with the ratio of the ion charge to the mass number of the ion Q / M = 1/30 at a current density in the beam of j≅10 mA / cm ² decreases only two times in the focusing plane and increases three times in defocusing. This does not interfere with the still acceptable ion focusing.

 The accelerating-focusing field found during the acceleration of positive ions eliminates the counter current of secondary electrons knocked out from the electrodes and molecules of the residual gas, due to the strong difference in the focusing effects of the field with respect to ions and electrons, due to a significant difference in their energies. This eliminates the so-called "full voltage effect", which in existing high-voltage electrostatic accelerators is eliminated by tilting the flat accelerating electrodes to the axis of the system and the removal of electrons from the optical axis of the accelerator.

 Quasicylindrical quadrupoles can be used to sort ionic charges after stripping ions by strippers in the accelerator in the same way as applied cylindrical quadrupoles by their transverse displacement.

The proposed method and device can find application in solving some fundamental scientific problems of modern nuclear physics, requiring high currents and precision energy from accelerated ions, as well as in some applied problems requiring economical methods of accelerating charged particles with a high beam intensity (ion propulsion for spacecraft , nuclear fusion of neutrons for energy purposes). The most tempting seems to be the application of the proposed method for electro-nuclear generation of intense neutron fluxes, for example, in the D + ⁹ Be reaction at a deuteron energy of about ten MeV for economically viable energy production by the accelerator-controlled safe subcritical nuclear reactor proposed by Rubbia.

LIST OF REFERENCES
1. A. P. Greenberg "Methods of acceleration of charged particles", M. L., GITTL, 1950. S. 27-58.

 2. E. G. Komar. "Fundamentals of accelerator technology", M., Atomizdat, GITTL. 1950.S. 27-58.

2. E. G. Komar. "Fundamentals of accelerator technology", M., Atomizdat, 1975, S. 33-47,
3. E.A. Abrahamyan and V.A. Gaponov. A.E. 1966.Vol. 20, issue 5, p. 385.

 4. Heavy Ion Laboratory, Newsletter, (Oct.-Dec. 1975) no. 4, Oak Ridge National Laboratori.

 5. J.B. Ball et al. Journ. de Phys. 1976, vol. 37, n. 11, p. S-227.

Claims (2)

1. The method of acceleration and focusing of charged particles by a constant electric field containing a longitudinal accelerating and transverse focusing components of the electric field created by a system of electrodes mounted on metal holders passing through the wall of the accelerating tube, through which electric potentials are supplied, characterized in that the charged particles are simultaneously accelerated and focused by a quasi-cylindrical quadrupole field formed in accordance with the formula

where V (r, φ, z) is the electric potential of the field in the cylindrical coordinate system r, φ and z;
E _z is the constant accelerating component of the electric field strength;
G _r is the gradient of the radial component of the electric field strength;
V (0, 0, z ₀ ) is the potential of the field on its axis at the initial point z ₀ . 2. Device for accelerating and focusing charged particles with a constant electric field, containing a system of electrodes mounted on metal holders passing through the wall of the accelerating tube, through which electric potentials are supplied to the electrodes, characterized in that the electrodes are made with quasi-cylindrical hyperbolic profiles in accordance with the formula

where r _e (φ, z) is the radius vector describing the profile of the electrode;
V _e - constant potential supplied through a metal holder with a divider of the full accelerating potential,
and the electrodes themselves are arranged in alternating order of the sign of the gradient of the radial component of the electric field.

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