SOME ISSUES IN THE DEVELOPMENT OF HIGH-CURRENT ACCELERATOR TUBES

G. A. KAZYMIN, G. A. KASSIROV, Yu. E. KREGZHEL, T. I. TAITSEVA

In connection with the development of accelerator technology, the problem of increasing the current in the beam of an accelerating electron tube has become urgent. Pulse transformers used to power electron accelerating tubes make it possible to pass practically unlimited discharge currents through the tube. However, not every electrode system of a tube permits large currents in the beam. The limitations are imposed by the emission properties of the cathode and by the possibilities of focusing, which must be ensured by the shape and potentials of the electrodes. We have dealt with questions of the second group, i.e., questions of beam focusing. A substantial obstacle here is the presence of space charge in the beam. Neither classical electron optics nor accelerator technology has until now encountered space-charge limitations, because the currents of high-voltage installations have been too small for this. The use of pulse techniques changes the situation. We investigated the possibility of obtaining substantially larger currents in the beam of a multielectrode accelerating tube of sectionalized type. The problem of obtaining large currents in the beam is solved by the theory and practice of electron guns for electron-beam and microwave devices [1]. Some concepts and technical methods from the field of developing guns with high perveance can be used in accelerator-tube technology. In particular, the use of Pierce-type electron guns [3] as the first sections of accelerating tubes is promising.

Theory of the Problem

The unlimited increase of current is hindered by the beam’s own space charge, whose action appears in two directions.

1. Limitation of the total current. This is expressed in the so-called “three-halves-power law”

\[ I_{tr} = P_{tr} \cdot U_n^{3/2}. \tag{1} \]

provided that the cathode emission is sufficiently large. Here \(I_{tr}\) is the tube current, \(U_n\) is the total tube voltage, and \(P_{tr}\) is a coefficient depending on

geometry of the electrodes, which determines the conductance of the tube and in the theory of electron guns is called “perveance.”

1. An increase in the dimensions of the beam cross section due to internal repulsion [2]. For a beam of circular cross section propagating in an equipotential space, this circumstance is expressed by the relation

\[ 88\,\frac{z_0}{r_0}\sqrt{P} = \frac{1}{2}\int_{1}^{r/r_0}\frac{dy}{\sqrt{\ln y}}, \tag{2} \]

where \(r_0\) is the minimum radius of the beam in the “waist”; \(z_0\) is the distance from the “waist” to the point where the beam has radius \(r\); \(P\) is the beam perveance.

The problem of developing accelerator tubes with a large current amounts to optimally circumventing these limitations under one or another set of specific circumstances.

According to (1), \(P_{tr}\) should be increased while satisfying certain technical requirements. If we are able to determine the optimum \(P_{tr}\), then we can thereby solve the question unambiguously.

In this formulation we have solved this problem for one specific layout of an accelerator tube (Fig. 1). In this layout it is assumed that a Pierce-type electron gun produces a parallel beam which, upon emerging from the aperture in the first anode, acquires divergence according to the well-known Davisson formula:

Fig. 1. Diagram of the electrodes of a sectionalized accelerator tube.

\[ F=\frac{4U_1}{E}, \tag{3} \]

where \(E\) is the field strength at the gun anode, \(U_1\) is the potential of this anode, and \(F\) is the focal distance determining the beam divergence. In the region of the lens the beam acquires convergence [4] according to the relation

\[ p=D_l\,\zeta(\alpha,\beta), \tag{4} \]

where \(D_l\) is the diameter of the lens “aperture,” \(\alpha=U_2/U_1\), \(\beta=Q/D_l\), \(Q\) is the length of the tangent to the beam trajectory in the lens region, but on the exit side, and \(U_2\) is the voltage on the second anode. The function \(\zeta\) “depends” somewhat on the lens geometry, but only slightly.

From relation (2) we obtain for the length of the subtangent \(p\)

\[ p(z_0,x)=\frac{z_0\cdot x}{2f(x)\sqrt{\ln x}}: \tag{5} \]

\[ x=\frac{r}{r_0},\qquad f(x)=\frac{1}{2}\int_{1}^{x}\frac{dy}{\sqrt{\ln y}}. \]

Taken together, equations (1)—(5), under the condition that the beam passes through the aperture of the lens and \(Q < \infty\), give, for the perveance of the tube,

\[ P_{\mathrm{tr}}=\left(\frac{U_1}{U_n}\right)^{3/2} \left[\frac{\delta}{352\sqrt{\ln x}}\right]^2 \frac{1}{\zeta^2(\alpha,\beta)} . \tag{6} \]

Here, \(\delta=\dfrac{2r}{D_l}\), \(\zeta(\alpha,\beta)\) is a function that can be found from the graphs \(p - Q\) [4], and \(r\) is the beam radius in the region of the lens. If the beam radius inside the gun is denoted by \(r_k\), then [5]

\[ x=1.31\,\frac{r}{r_k}. \tag{7} \]

Expression (6) can be rewritten by taking the voltage on the lens as the basic parameter:

\[ U_l=U_2-U_1=(\alpha-1)U_1; \tag{8} \]

\[ U_1=\frac{U_l}{\alpha-1}; \]

\[ P_{\mathrm{tr}}=\left(\frac{U_l}{U_n}\right)^{3/2} \left[\frac{\delta}{352\sqrt{\ln x}}\right]^2 \frac{1}{(\alpha-1)^{3/2}\zeta^2(\alpha,\beta)} . \tag{9} \]

The function

\[ \Phi(\alpha,\beta)=\frac{1}{(\alpha-1)^{3/2}\zeta^2(\alpha,\beta)} \]

has a maximum value at \(\alpha \simeq 5\) and \(\beta \to \infty\), equal to

\[ \Phi(5,\infty)=0.0108 . \tag{10} \]

After substituting (7) and (10) into (9) and calculating the numerical coefficients, we obtain

\[ I_{\mathrm{tr}}=8.7\cdot 10^{-8}\, \frac{\delta^2}{\ln\left(1.31\,\dfrac{r}{r_k}\right)} \,U_l^{3/2}. \tag{11} \]

On the other hand, the current of the tube, if electron losses on the first and subsequent anodes are neglected, will, according to the “\(3/2\)” law, be equal to

\[ I_{\mathrm{tr}}=2.33\cdot 10^{-6}\, \frac{\pi r_k^2}{d^2} \left(\frac{U_l}{\alpha-1}\right)^{3/2}; \tag{12} \]

\(d\) is the cathode—anode 1 distance.

Comparing (11) and (12), we obtain the relation between the basic geometrical parameters of the forming part of the accelerating tube,

\[ d=3.48\,\frac{r_k}{\delta} \sqrt{\ln\left(1.31\,\frac{r}{r_k}\right)} . \tag{13} \]

At the same time, of course, \(\delta<1\), \(\alpha\simeq 5\), \(Q\to\infty\) \((60\div100)\). However, owing to the weak dependence of \(\Phi\) on \(\alpha\), the design will not be critical with respect to the choice of \(\alpha\), if the criterion is the ratio of the current \(I_{\mathrm{tr}}\) to the voltage \(U_l\).

Experimental Studies

$\alpha$-Characteristics

We have called $\alpha$-characteristics the curves of variation of the current to the tube electrodes when $\alpha$ is varied, with the remaining parameters unchanged. Since, when $\alpha$ is varied, not only the shape of the beam changes but also the magnitude of the current from the cathode, one should expect a maximum of the current at the tube output at some $\alpha_{\mathrm{cr}}$.

The study of the $\alpha$-characteristics was carried out on a model of an accelerating tube that had only four electrodes (Fig. 1) [6].

Fig. 2. Comparison of the $\alpha$-characteristics of the output current (2) and cathode current (1) with the voltage on the first anode $U_1$ (3).

The geometry of these electrodes was determined by the design of the insulators and was far from optimal from the standpoint of attaining the maximum current.

Figure 2 compares the $\alpha$-characteristic of the output current $I_{\mathrm{u}}$ and the $\alpha$-characteristic of the cathode current of the gun.

The third curve shows the variation of the voltage $U_1$. It was also established on the model that the useful current of the tube is, to a certain extent, determined by the proper choice of the “cathode–anode 1” distance of the tube.

Tube for 1000 kV

On the basis of studies of the $\alpha$-characteristics, which confirmed the theoretical propositions, a tube [7] was developed and manufactured; its design is shown schematically in Fig. 3. The tube was designed for operation in oil at a voltage of 1000 kV with a current of 0.5 A in a pulse. The tube body consists of 28 ceramic and 27 permalloy rings and has a length of about 60 cm. Ceramic proved to be the best of the materials available to us. This choice was made on the basis of tests of structural assemblies for electric strength under conditions close to operating ones [8]. The tube cathode, in the form of a flat bifilar spiral of 10 mm diameter made of thoriated tungsten, was to provide an emission current of 1 A with a sufficient service life.

The tube was tested at voltages up to 500 kV on an improvised installation.

Fig. 3. Design layout of a 1000 kV accelerator tube.

Fig. 4. Electrical circuit of the electrodes of a 1000 kV accelerator tube.

Fig. 5. Volt–ampere characteristic of a 1000 kV tube.

Fig. 6. Arrangement for winding the wire of the voltage divider.

A GIN was used as the high-voltage source. Instead of the calculated \(170\ \mathrm{mA}\) at a voltage of \(500\ \mathrm{kV}\), \(130\ \mathrm{mA}\) was obtained with a beam diameter of no more than \(1.5\ \mathrm{cm}\) at the output. An attempt was made to measure the fraction of current to the first anode by comparing the charges accumulated in capacitors connected according to the circuit of Fig. 4. It turned out that from 30 to 70% of the electrons leaving the cathode are lost in the tube when voltage is applied to it.

The current–voltage characteristic of the tube (Fig. 5) shows that equation (1) is valid for such a design. An essential part of the circuit is the active voltage divider. The divider must have sufficiently small parasitic capacitances and inductances; a sufficiently large and stable resistance; it must ensure simple connection of taps to the tube electrodes; possess the necessary electrical strength and operational reliability; and fit within the limited dimensions in length and cross section.

We developed two types of such dividers made of nichrome wire: 1—on Plexiglas strips (Fig. 6, \(a\)) with a total resistance of \(40\ \mathrm{k\Omega}\); 2—a fabric divider on a paper base (Fig. 6, \(b\)) with a total resistance of \(250\ \mathrm{k\Omega}\).

Fig. 7. Photographs of the beam: 1. Third layer of photographic paper at \(U_p = 550\ \mathrm{kV}\), \(I_n = 17.5\ \mathrm{A}\). 2. First layer of photographic paper at \(U_p = 550\ \mathrm{kV}\), \(I_n = 18\ \mathrm{A}\), after rotating the tube about its axis by \(90^\circ\). 3. Beam shape immediately behind the magnetic lens at \(I_{m.l.}=0\), \(U_p = 450\ \mathrm{kV}\), \(I_n = 15.4\ \mathrm{A}\). 4. Beam shape immediately behind the magnetic lens at \(I_{m.l.}=2.2\ \mathrm{A}\), \(U_p = 450\ \mathrm{kV}\), \(I_n = 15.4\ \mathrm{A}\). 5. Beam shape at a distance of \(60\ \mathrm{cm}\) from the lens at \(I_{m.l.}=1.2\ \mathrm{A}\), \(U_p = 450\ \mathrm{kV}\), \(I_n = 15.4\ \mathrm{A}\). 6. Beam shape at a distance of \(60\ \mathrm{cm}\) from the lens at \(I_{m.l.}=2\ \mathrm{A}\), \(U_p = 450\ \mathrm{kV}\), \(I_n = 15.4\ \mathrm{A}\).

Both dividers have a bifilar, three-dimensional winding of the high-resistance wire. The principal characteristic of the divider is the maximum value of its resistance per unit length. For divider 1 it is approximately \(600\ \Omega/\mathrm{cm}\), and for divider 2, \(3100\ \Omega/\mathrm{cm}\).

The current consumed by the divider is inversely proportional to this quantity. Figure 7 presents “photographs” of the electron beam at the tube exit. To obtain them, the beam is released into the atmosphere through aluminum foil, behind which is placed a pack with several layers of ordinary photographic paper. In front of the foil, in the vacuum, a thick perforated lead plate is installed; its “pattern” appears in the photograph.

Accelerator tube, 250 kV, 1.5 A

The low voltage on the second anode \((U_2)\) determined the peculiar shape of the forming section (Fig. 8). The lens is brought almost flush with the anode aperture so as to obtain a small value of \(r'/r_k\). The tube is intended for operation in air, which also determines its other design features: water cooling of the cathode assembly and of the first anode, increased length, etc.

The tube body consists of two parts: the cathode assembly and the accelerating column, between which there is a detachable flanged joint. This design facilitates assembly of the internal fittings and bonding of the tube, and also makes it possible to carry out separate testing of its assemblies.

Fig. 8. Design layout of a 250 kV accelerator tube.

Both parts of the tube are bonded from porcelain rings 40 mm thick, with aluminum electrodes 3 mm thick between them. Bonding was carried out with polyethylene in a special fixture. Preliminary experiments on bonding porcelain to aluminum using polyethylene film showed good vacuum, mechanical, and thermal properties of such joints.

The quality of the cathode affects the characteristics of the tube. The spiral tungsten cathode [7] currently used gives a nonuniform current density in the beam, warps with time, has a large magnetic field produced by the heating current, and is not equipotential.

Of great interest is the use of highly efficient indirectly heated cathodes that are free of the listed disadvantages.

Conclusion

As a result of the work carried out, the advantages of a system with electrostatic focusing were identified in the case where, for reasons of electrical strength, it is necessary to section the body of the accelerator tube and, at the same time, the presence of sharp field inhomogeneities is inadmissible. However, the structure of the beam

in a sectioned tube than in an ordinary two-electrode gun. Therefore, in all cases in which conditions permit, it is better to make a simple two-electrode system, which has a higher perveance than a multielectrode system.

REFERENCES

1. N. S. Zinchenko. Course of Lectures on Electron Optics, published by Kharkov State University named after A. M. Gorky, Kharkov, 1958.

2. M. D. Gabovich. UFN, 56, 2, 1956.

3. J. R. Pierce. Journ. Appl. Phys. 11, 548, 1940.

4. Electron-Beam Tubes, Part II, edited by S. A. Obolensky, Sov. Radio Publishing House, 1954.

5. G. S. Kazmin. Review of the USSR Academy of Sciences, Physics, No. 5, 1959.

6. G. S. Kazmin, G. M. Kassirov. Tests of a model accelerator tube at 600 kV in oil. Scientific report, NII TPI, 1960.

7. G. S. Kazmin, G. M. Kassirov. Technical design of an accelerator tube for 1000 kV. Technical report, NII TPI, 1960.

8. G. S. Kazmin, G. M. Kassirov. Results of tests of accelerator-tube housing elements for electrical strength. Technical report, NII TPI, 1960.