VACUUM SYSTEMS OF ELECTRON ACCELERATORS

A. G. Vlasov, V. P. Ponomarev, M. T. Shavyrtalov, P. M. Shanin

General Considerations

The problem of creating vacuum systems for electron accelerators and obtaining in them a sufficiently low pressure is a rather complex task. The operating characteristics and efficiency of the accelerator depend on the solution of this problem.

The main element of an accelerator vacuum system is the vacuum chamber. The dimensions of the cross section and the radius of the chamber are determined by the pole gap of the electromagnet and by the radius of the equilibrium orbit, whose magnitude depends on the acceleration principle, the energy of the accelerated electrons, etc. The material from which the chamber is made must satisfy a number of requirements [1].

1. It must possess sufficient mechanical strength to prevent destruction of the chamber by atmospheric pressure.

2. It must possess good vacuum properties, i.e., be gas-impermeable and have a low sorption capacity.

3. The chamber walls must not distort the magnetic field in the pole gap.

On the basis of these requirements, accelerator chambers may be made either from dielectrics—glass, porcelain, ceramics, plastics—or from metals, provided that conditions are met which ensure a minimum magnitude of the eddy currents that arise. The choice of one or another chamber material is made on the basis of the specific conditions. For cyclic electron accelerators with energies up to 25–30 MeV, vacuum chambers are usually made as one-piece (seamless) chambers of molybdenum glass ZS-5 or porcelain. For accelerators with energies of 100 MeV and above, the chamber dimensions become considerable, and it has to be made from separate sectors with subsequent cementing together.

In the case where the accelerator magnet has a split and the upper part of the magnet can be raised for installation of the chamber, the chamber is cemented from sectors and subsequently is non-demountable. Such a chamber is shown in Fig. 1 and is usually made for accelerators with energies not exceeding 200–300 MeV.

Accelerator magnets for energies above 300 MeV are in most cases made in the form of the letter “C” and have no split. In addition,

therefore, the chambers of these accelerators are so large in diameter that making them non-dismountable is impractical. Therefore, for such accelerators the vacuum chambers must be made demountable. The individual parts of a demountable chamber are glued together from sectors and joined by means of flanges with a vacuum-rubber gasket. The cross section of the chambers may be either oval or rectangular with rounded sharp corners, and should enclose the interpole space as completely as possible.

Fig. 1. Non-dismountable chamber of a 100 MeV betatron.

The inner surface of the vacuum chamber must be sufficiently conducting to prevent the accumulation of charges as a result of particles leaving the acceleration process and settling on the chamber walls. Otherwise, the electrostatic fields that arise would lead to deflection and scattering of the accelerated beam.

The choice of the resistance value of the conducting coating is subject to two opposite conditions.

1. The resistance of the conducting coating must be sufficiently small for charges to have time to drain from the layer during one revolution of the electrons.

2. The resistance of the layer must be no less than the minimum permissible value, so that large eddy currents are not induced in it.

An analytic expression for the first condition is difficult to obtain. In practice, if the resistance of the coating is large, this condition can be satisfied by grounding at several azimuths.

Satisfaction of the second condition is necessary so that the eddy currents induced by the alternating magnetic field are small and do not distort the main magnetic field of the accelerator, and also do not heat the chamber wall. Proceeding from this condition, the value of the specific resistance of a continuous uniform conducting coating, i.e., a coating having no electrical break around the circumference, can be determined from the expression [2]

\[ \rho = \frac{8 \cdot 10^{-9} R_0^2 \dot{H}_{oi}} {\Delta n\, h\, H_{oi}} . \tag{1} \]

If there is an electrical break in the conducting coating along the circumference of the chamber, the main field of the accelerator in the region of the equilibrium orbit is not noticeably disturbed by the eddy currents, and the distortions occur mainly at the edges of the chamber cross section, i.e., in the region remote from the equilibrium orbit. In this case the minimum permissible specific resistance of the conducting coating is determined [2] by

\[ \rho = \frac{16 \cdot 10^{-9} \pi a R_0^2 \dot{H}_{oi}} {\Delta n\, h\, H_{oi}} . \tag{2} \]

Here \(H_{oi}\), \(\dot{H}_{oi}\) are the magnetic-field intensity and the rate of its rise on the equilibrium orbit at the moment of injection, in gauss,

\(a\)—the radial half-dimension of the cross section of the accelerating chamber, in centimeters,

\(R_0\)—the radius of the equilibrium orbit, in centimeters,

\(h\)—the height of the interpolar space at the radius of the equilibrium orbit, in centimeters,

\(\Delta n\)—the permissible deviation of the index of decrease of the magnetic field with radius.

In order that electrons not be lost because of scattering by residual gas during acceleration in the chamber, a high vacuum must be created. Calculations and experiments carried out to study the effect of pressure in the vacuum chamber on the radiation intensity of the accelerator show that, for normal operation of the accelerator, the pressure in the chamber must be such that electron losses due to scattering by the residual gas do not exceed 5–6%. On this basis, the operating pressure in the vacuum chamber, in mm Hg, can be determined from the following expression [3, 4]:

\[ P_p = \frac{n b^3 T_i eV T^{5}\eta} {2 z^2 R_0^3 n_z z_z^2 e^4 \ln \dfrac{180 b \sqrt{n}(\gamma_0^2-1)^{1/2}}{R_0 z^{1/3}}}, \tag{3} \]

where \(n\)—the index of decrease of the magnetic field,

\(b\)—the half-dimension of the vacuum chamber in the axial direction, in centimeters,

\(T_i\)—the injection energy, in electron-volts,

\(eV\)—the energy acquired by the electron per revolution, in electron-volts/revolution,

\(T\)—the temperature of the gas filling the chamber, in degrees Kelvin,

\(\eta = 0.06\)—a coefficient determining 5% losses due to scattering,

\(R_0\)—the radius of the equilibrium orbit, in centimeters,

\(n_z, z_z\)—the number of atoms in a molecule of the gas filling the chamber and its atomic number,

\[ \gamma = \frac{1}{\sqrt{1-\beta^2}}, \qquad \beta = \frac{v}{c}. \]

In determining the operating pressure, both single and multiple scattering and losses due to radial and axial oscillations were taken into account by means of the coefficient “4,” since expression (3) without this coefficient is valid only for multiple scattering in the axial direction. The introduction of this coefficient gives an uncertainty of 5–10%, which is quite permissible for the present calculation. Elastic and inelastic scattering were taken into account in determining the value of \(\eta\). Calculations and operating experience with accelerators show that the pressure in the vacuum chamber must be of the order of \(1\)–\(5 \cdot 10^{-6}\) mm Hg. To produce such a pressure in the chamber, the second principal element of accelerator vacuum systems is used—the pumping system. As the pumping system, diffusion oil-vapor pumps are usually used, paired with fore-vacuum pumps and connected to the vacuum chamber and to one another by a system of pipelines and valves. Recently, instead of diffusion pumps, ion-sorption pumps have increasingly begun to be used, since they do not contaminate the chamber with oil vapors, and this is very important during prolonged operation of accelerators.

Below, the calculation of the pumping system and the fabrication technology of accelerator vacuum systems will be considered.

Pumping System of the Vacuum Chamber

When calculating a vacuum system for producing a vacuum in the chamber of charged-particle accelerators, if the operating pressure is known, it is necessary to determine:

1. The arrangement of the high-vacuum pumps and their pumping speeds.
2. The pumping speed of the backing pumps.
3. The cross sections of the pipelines connecting the backing and high-vacuum pumps.

The cross sections of the pipelines connecting the high-vacuum pumps with the chamber, and the arrangement of the backing pumps, are usually selected on the basis of design considerations and ease of operation of the system. In view of the fact that, in the calculation, it is difficult to take into account all factors affecting the rate of gas evolution and leakage, as well as the final dimensions of the elements of the vacuum system, the pumping speeds of the high-vacuum and backing pumps must be selected with some margin in comparison with the calculated values.

In molecular gas flow (at pressures of the order of \(1 \cdot 10^{-4}\)–\(1 \cdot 10^{-6}\) mm Hg), the calculation of the vacuum system is carried out for the pumping of gases and vapors entering the vacuum chamber as a result of gas evolution and leakage. Since the length of the chamber is usually considerably greater than its transverse dimension, it will have resistance to the gas flow, as a result of which a pressure difference will be created between the pumping point and a point located at some distance from it.

Neglecting the curvature of the vacuum chamber, the latter may be represented in the form of a straight pipeline of length

\[ l = 2\pi r_{\mathrm{av}} + ml, \tag{4} \]

where \(r_{\mathrm{av}}\) is the mean radius of the quadrant,
\(l\) is the length of the straight section,
\(m\) is the number of straight sections.

The resistance of a chamber of oval cross section may be determined as the resistance of a pipeline of rectangular cross section equal in area to the transverse section of the chamber:

\[ Z = \frac{\Pi l}{61.8\, k A^{2}}, \tag{5} \]

where \(\Pi\) is the perimeter of the chamber section,
\(A\) is the area of the chamber transverse section,
\(k\) is a coefficient depending on the ratio of the sides of the reduced rectangle.

The value of \(k\) can be determined from the Clausing formula [5]:

\[ k = \frac{3}{8}\, \frac{1-r^{2}}{r^{2}} \left\{ r \ln \left(r+\sqrt{1-r^{2}}\right) + r^{2}\ln \frac{1+\sqrt{1-r^{2}}}{r} + \frac{1}{3} \left[ 1-r^{2}-(1-r^{2})^{3/2} \right] \right\}. \]

where

\[ r=\frac{b_1}{a_1} \]

is the ratio of the sides of the reduced rectangle,

\(x\) is the length of the section of the chamber under consideration.

On an infinitely small section of the chamber \(dx\) (Fig. 2), the pressure drop will be equal to

\[ dP=Q_x\,dz, \tag{6} \]

where \(Q_x\) is the gas flow passing through the chamber cross section at a distance \(x\) from the pumping point and determined by the formula

\[ Q_x=q\Pi(L_1-x), \tag{7} \]

where \(L_1\) is the distance between the pumping point and the point most remote from the pumping point,

\(q\) is the specific gas evolution and leakage of the chamber (leakage of the chamber per unit time from unit surface area).

Fig. 2. Schematic of the vacuum system. 1—vacuum chamber, 2—branch pipe; 3—valve, 4—trap.

Substituting the values of \(Q_x\) and \(dz\) into formula (6), after integration we obtain the value of the pressure drop over the segment \(x\):

\[ \Delta P_x=P_x-P_0= \frac{q\Pi^2 L_1^2}{61.8\,\kappa A^2} \left[ \frac{x}{L_1}-\frac{1}{2}\left(\frac{x}{L_1}\right)^2 \right]. \tag{8} \]

For \(x=L_1\), the maximum pressure drop in the chamber will be equal to

\[ \Delta P_{\max}=P_{0\max}-P_p= \frac{\Pi^2 L_1^2 q}{2\cdot 61.8\,\kappa A^2}. \tag{9} \]

From the last expression it is evident that, in order to obtain the specified pressure \(P_p\) in the chamber, it is necessary to obtain, at the pumping point, a pressure no worse than \(P_{0\max}\). Hence the distance between pumps must be equal to

\[ L_2=2L_1= \frac{2A}{\Pi} \sqrt{\frac{123.6\,\kappa\,(P_{0\max}-P_p)}{q}} \tag{10} \]

and the number of pumps was not less than

\[ N=\frac{2n r_{\mathrm{av}}+ml}{l_2}. \tag{11} \]

In order to create, at the inlet of the pumping connection, a pressure not higher than \(P_{omax}\), it is necessary to pump the chamber at a speed

\[ S_0=\frac{Q}{N}=\frac{2\Pi q}{P_{omax}}\sqrt{123.6\,k\,\frac{P_{omax}-P_p}{q}}, \tag{12} \]

where \(Q\) is the rate of leakage and gas evolution, reduced to the pressure \(P_{omax}\).

Usually the pump is connected to the chamber not directly, but through intermediate elements (a connection pipe, valve, trap, etc.); therefore, in the calculation it is necessary to take into account the resistance of these elements. Then the limiting pressure produced by the pump must be

\[ P_0=P_{omax}-\Delta P_{\mathrm{el}}, \tag{13} \]

where \(\Delta P_{\mathrm{el}}\) is the pressure drop in the intermediate elements, and the pumping speed of the high-vacuum pumps is determined as

\[ S_n=\frac{1}{\dfrac{1}{S_0}-Z_{\mathrm{el}}}, \tag{14} \]

where \(Z_{\mathrm{el}}\) is the resistance of the elements connecting the chamber with the high-vacuum pumps. After calculating the capacity of the high-vacuum pumps, their type is selected.

The arrangement and number of fore-vacuum pumps are usually chosen on the basis of design considerations and ease of operation. In this case it is necessary that, at the point where the fore-vacuum system is connected to the exhaust connection of the high-vacuum pumps, a pressure be produced not lower than their exhaust pressure \(P_{\mathrm{ex}}\). This condition is satisfied if the pumping speed at the inlet to the high-vacuum pumps is equal to

\[ S_{\phi}=\frac{Q}{N P_{\mathrm{ex}}}. \tag{15} \]

In the molecular-viscous regime of gas flow, the conductance of a pipeline is determined from the expression

\[ u_{\phi}=\frac{u_{\mathrm{tab}}\,l_{\mathrm{tab}}}{l_{\phi}}, \tag{16} \]

where \(u_{\mathrm{tab}}\) is the conductance of a pipeline of diameter “\(D\)” and length \(l_{\mathrm{tab}}=1\ \mathrm{m}\). Values of \(u_{\mathrm{tab}}\) are given in [6]. The required pumping speed of the fore-vacuum pump will be

\[ S_{n\phi}=\frac{2S_{\phi}}{1-\dfrac{2S_{\phi}}{u_{\phi}}}. \tag{17} \]

From condition (17) the type of pump is selected. However, condition (17) is necessary but not sufficient for selecting the fore-vacuum pump.

The second condition is the time during which the pressure required for switching on the high-vacuum pumps is established in the vacuum chamber. This time is determined from the equation

\[ t=\frac{1}{2}\,\frac{V}{S_{\mathrm{eff}}}\ln\frac{P_a}{P_v}, \tag{18} \]

where

\[ \begin{aligned} V &\text{ is the volume of the entire system,}\\ P_a &\text{ is atmospheric pressure,}\\ P_v &\text{ is the pressure in the chamber at which the high-vacuum pumps are switched on,}\\ S_{\mathrm{eff}} &= \frac{S_n}{1+\dfrac{S_n}{u_\phi}} \text{ is the effective pumping speed,}\\ S_n &\text{ is the ultimate pumping speed of the fore-vacuum pumps at atmospheric pressure.} \end{aligned} \]

The pumping time should be no more than 15–20 minutes. Taking this condition into account, the final choice of the type of fore-vacuum pumps is possible.

Technology for Manufacturing the Vacuum Chamber

The technology for manufacturing the accelerator chamber must meet the requirements imposed on vacuum systems. Here we shall consider the technology for manufacturing a sectional accelerator chamber, as the most difficult to manufacture. The manufacture of other chambers will be similar. The technology for manufacturing chambers is divided into a number of operations.

Grinding the Chamber Sectors

The sections of which the chamber consists are laid out on the assembly-table plate laid out according to the chamber dimensions. The table plate is made of gypsum, sheet plastic, or metal, with subsequent machining. The assembled table must have the necessary rigidity and be carefully leveled. The end faces of the sectors intended for gluing are carefully ground to one another. Grinding is carried out on the cast-iron disk of a grinding machine using corundum or carborundum powder of grit size 100–150. Rounding with \(R_c=0.5\ \mathrm{mm}\) is made on the sharp edges of the end faces.

Coating the Sectors with a Conducting Layer

Both metallic and nonmetallic coatings applied by various methods may serve as the conducting layer. The conducting coating must meet the following requirements.

1. Have resistance values close to the calculated ones.
2. Possess sufficient mechanical strength.
3. Be uniform over the surface of the chamber.
4. Not be destroyed under electron bombardment.
5. Be stable over time.
6. Have good vacuum properties.

The following coatings satisfy these requirements to some extent: Aquadag, chemically deposited silver, metallized-

coating by vacuum evaporation and coating with a film of tin dioxide. The greatest use has been made of Aquadag and tin dioxide film. A general requirement necessary for the successful application of any type of coating is the cleanliness of the surface of the sector being coated. The electrical connection of the conducting layers of individual sectors to one another is made by strips of copper foil soldered to the strips of fired silver. The application of conducting coatings by various methods has been well covered in the literature and will not be discussed here [1, 7—10].

Gluing the Chamber

After the sectors of the chamber have been coated with a conducting layer, they are mounted on carriages located on the guide rails of the assembly table. Clamps with turnbuckles for compression during gluing are put on the sections (Fig. 3). The sections are aligned so that the mating is over the entire plane of the end faces, after which they are fastened with screws in the carriages and prepared for application of the glue. Preparation consists in cleaning the end faces with alcohol. BF-4 glue is applied to the end faces of the sections in 10—12 layers. When applying the glue, each layer is dried in air for 10—15 min. The room in which the layer is applied must have low air humidity. After all layers have been applied, the glue is dried for 18—20 hours. The total thickness of the applied glue after drying should be 0.8—1.0 mm. From the inner side the glue is removed over a width of 3—4 mm so that it cannot get onto the inner surface of the chamber. Strips of copper foil 5 mm wide and 0.05 mm thick are soldered with soft solder to the strip of fired silver and are brought out between the end faces being glued along the major axis of the section. After this the end faces to be glued are brought together, and special electric furnaces are put on the seams. For polymerization of the glue, over the course of 50—60 minutes the temperature is raised to 80—90°C. When this temperature is reached, the sections are tightened with turnbuckles to a pressure of 5—6 kg/cm². Further raising of the temperature proceeds at a rate of 26—28°C per hour with simultaneous tightening of the sections. When a temperature of 150—160°C is reached, further increase of temperature is stopped and the seam is held at this temperature for 2.5—3 hours. The temperature is lowered at a rate of 60—70°C per hour down to 60°C, after which the furnaces are removed and the seam is cooled in air. The process of polymerization of the glue lasts altogether 7—8 hours. Duralumin flanges are glued on in the same way. When the specified technology is followed, the seams after gluing, as a rule, do not leak.

Fig. 3. Device for gluing the chamber.

The appearance of a leak may be due to the following causes:

1. Inaccurate grinding of the sections.
2. Poorly dried glue.
3. Weak tightening during gluing.

For the first time, such bonding technology has been used at FIAN. It should also be noted that some sectors of the chamber must have branch pipes needed for placing the sensors and receivers of the indication system, targets, etc. Duralumin flanges are also glued to these branch pipes.

The assembled chamber is tested for overall leakage, and the locations of leaks are also determined. Seams with large leaks are reglued. Small leaks are eliminated by coating the seam with nitro enamel or epoxy resin.

As operating practice has shown, vacuum systems calculated, manufactured, and tested according to the method described above work well and ensure normal operation of electron accelerators.

REFERENCES

1. Vlasov A. G., Izv. TsNI, 87, 1957.

2. F. K. Goward, M. A. T. D. Lawson, B. A. T. T. Wilkins, B. Sc. and R. Carruthers, B. Sc., Associate member, Proc. IEE, 97, 108, 320, 1950.

3. Vlasov A. G., Izv. vuzov, Fizika, No. 1, 1961.

4. Vlasov A. G., “The effect of pressure in the vacuum chamber on the intensity of accelerator radiation,” ZhTF, 31, 613 (1961).

5. Guthrie A. and Wakerling R., Vacuum Equipment and Vacuum Technology, IL, 1957.

6. Jaeckel R., Production and Measurement of Vacuum, IL, 1952.

7. Zhukov V. A. and Evteev F. E., Technology of Radio Equipment, GEI, 1952.

8. Kuznetsov A. Ya., Kruglov A. V., Kryzhanovskii B. P., Zavodskaya laboratoriya, No. 8, 993, 1956.

9. Kuznetsov A. Ya., Zavodskaya laboratoriya, No. 1, 90, 1957.

10. Kryzhanovskii B. P., Kuznetsov A. Ya., PTE, No. 4, 76, 1958.