ACCELERATING SYSTEM OF AN AUTORESONANCE ACCELERATOR

L. P. Pishkov

(Presented by the scientific seminar of the Sector of Superhigh Frequencies and Accelerator Theory of the Nuclear Physics Research Institute)

The well-known technological difficulties in the creation of linear accelerators have led to the search for new acceleration methods, as a result of which the autoresonance acceleration method was proposed [1, 2]. A distinctive feature of this acceleration method is the use of transverse electromagnetic fields with the superposition of a longitudinal constant magnetic field, whose magnitude is determined by the frequency of oscillations of the electromagnetic field. The trajectory of the particle being accelerated in this case is a conical spiral with an increasing longitudinal pitch.

The direct use of a plane electromagnetic wave propagating in free space is inefficient, because considerable power is required in order to obtain the necessary electric-field strength. Magnetic waves in standard waveguides, of type \(H_{11}\) in a circular guide and \(H_{10}\) in a rectangular guide, make it possible to implement autoresonance acceleration of electrons in a simple way; however, the attainable energy of the accelerated electrons in them is limited [3]. The limitations are introduced by detuning of the resonant interaction of the accelerated electron and the electromagnetic wave, since the phase velocity of the wave in a smooth waveguide is greater than the speed of light. Therefore, in waveguides the acceleration process becomes periodic. For a standard waveguide, the section over which acceleration occurs is several centimeters [3].

To reduce the phase velocity of the \(H_{10}\) wave in a rectangular waveguide, in order to increase the section over which acceleration occurs, it is expedient to use an increase in the transverse cross section of the waveguide. At the same time, favorable conditions are created for increasing the radius of the conical spiral along which the accelerated electron moves.

The purpose of the present article is to investigate the accelerating system of an autoresonance accelerator based on a rectangular waveguide of large cross section. On the basis of practical considerations, as the accelerating system we chose a rectangular waveguide with a cross section of \(120 \times 110\) mm. The phase velocity of the wave in such a waveguide is \(1.15\). The length of the accelerating system is determined by the formula [3]

\[ z = \frac{\lambda \beta_{\phi}}{2(\beta_{\phi}^{2}-1)} , \]

and for our case it is 200 mm. One half of the acceleration period is accommodated in this section.

The matching of the accelerating waveguide with standard waveguides in the original version was carried out with the aid of maximally flat stepped quarter-wave waveguide transformers [4]. The accelerating waveguide was connected to the generator by a standard waveguide of cross section \(72 \times 44\) mm, and to the matched load by a waveguide of cross section \(72 \times 34\) mm (Fig. 1, a). The frequency characteristic of this accelerating system is shown in Fig. 2, a.

The accelerating system simultaneously served as a vacuum chamber, in which a vacuum of \(5 \cdot 10^{-6}\) torr was produced. Electrons were injected along the axis of the accelerating system through an opening in the bend of the waveguide. The accelerated electrons were extracted through an aluminum window 30 μ thick in the end wall of the matching transformer.

Fig. 1.
1 — gun, 2 — vacuum-pump flange, 3 — slots for pumping the waveguide, 4 — input matching transformer, 5 — accelerating waveguide, 6 — point of extraction of the accelerated-electron beam, 7 — output matching transformer, 8 — quartz window, 9 — absorbing load

Investigation of the accelerator in operation showed that the accelerating system makes it possible to accelerate electrons to energies of several MeV. It was established experimentally that the sharp edges of the matching transformer inside the chamber created favorable conditions for field emission. Against the background of field emission, the effect of injecting an electron-current pulse up to 1 ampere was not observed.

This drawback was eliminated by simplifying the working surface of the accelerating system by replacing the stepped transformers with horns. The electrical length of the horns was chosen equal to \(90^\circ\) for mutual compensation of reflections at the bends of the waveguide surface (Fig. 1, b). The reduction in the geometrical length of the matching transformer also facilitates the transport of the injected electron beam from the gun into the accelerating system, which is placed in a magnetic field [5].

The electrical length of the horn can be calculated from the following considerations: the electrical length of a waveguide is determined by the relation

\[ \varphi = 360^\circ \frac{l}{\Lambda}, \tag{1} \]

where \(l\) is the geometrical length of the waveguide,
\(\Lambda\) is the wavelength in the waveguide and is determined by the formula

\[ \Lambda = \frac{\lambda}{\sqrt{1-\left(\frac{\lambda}{\lambda_{\mathrm{cr}}}\right)^2}}. \tag{2} \]

A horn is a waveguide in which \(\lambda\) is a variable quantity, and if its width increases linearly with increasing length, then for it one may write

\[ \lambda_{\mathrm{cr}} = 2(a + cz), \tag{3} \]

where \(z\) is the current coordinate along the horn axis,
\(a\) is the initial width of the horn,
\(c\) is a parameter determining the angle between the narrow walls of the horn.

If (3) and (2) are substituted into (1), then the electrical length of the horn, after the limiting transition, can be represented in the form of the integral

\[ \varphi = \frac{360^\circ}{\lambda} \int_{0}^{l} \sqrt{1-\left[\frac{\lambda}{2(a+cz)}\right]^2}\, dz . \tag{4} \]

Integration of (4) gives the following expression for \(\varphi\):

\[ \varphi = \frac{90^\circ}{\lambda} \left[ \sqrt{4(a+2cl)^2-\lambda^2} - \sqrt{4a^2-\lambda^2} - \lambda \left( \operatorname{arctg} \frac{\sqrt{4(a+2cl)^2-\lambda^2}}{\lambda} - \operatorname{arctg} \frac{\sqrt{4a^2-\lambda^2}}{\lambda} \right) \right]. \tag{5} \]

Putting \(\varphi = 90^\circ\) in (5), it is easy to determine the value of \(l\) by a numerical method.

The frequency characteristic of the accelerating system with horn matching transformers is presented in Fig. 2,b. From the figure it is seen that the VSWR of the accelerating system at the operating frequency is no worse than 1.1. On the mock-up it was experimentally established, by means of probes, that higher wave types were absent in the accelerating system.

Fig. 2.
\(a\) — frequency characteristic of an accelerating system with quarter-wave maximally flat matching transformers; \(b\) — frequency characteristic of an accelerating system with horn matching transformers.

Starting up the accelerator with the use of an accelerating system with a horn matching element showed that the radiation background caused by autoemission electrons decreased by an order of magnitude. The thin walls of the horn, connected to the matched load, were coated with a phosphor in order to observe the intersection points of accelerated electrons moving along a conical helix with the horn. The glow was observed in the form of circular arcs on the walls of the horn, which is in full agreement with theory [1, 2].

LITERATURE

1. A. A. Kolomenskii, A. N. Lebedev. DAN, 145, 1259, 1962.
2. A. A. Kolomenskii, A. N. Lebedev. ZhETF, 44, 261, 1963.
3. A. A. Vorob’ev et al. Atomic Energy, 22, issue 1, p. 3, 1967.
4. A. P. Fel’dshtein et al. Handbook of Elements of Waveguide Technology, 1963.
5. A. P. Ishkov. Izv. TPI, 184, 1970.