Single-Cavity 1 MeV Accelerator for Biological Research

A. N. Didenko, R. G. Kaminskaya, V. V. Osipov, G. A. Uralov,
Yu. G. Yushkov

For a number of biological studies being carried out at the All-Union Scientific Research Institute for the Electrification of Agriculture, it is proposed to use an electron beam with an energy of the order of 1--1.5 MeV. The average current of the accelerated electrons at the output of the installation should be of the order of 100 microamperes, with an energy spread of $\pm 30\%$. The electron energy at the output must be smoothly adjustable in the range 0.1--1 MeV.

For these purposes, in our opinion, an ordinary single-cavity accelerator can be used. In this energy range it will be the cheapest, simplest, and most reliable source of electrons.

Such accelerators are widely used in rebatron devices for generating millimeter and submillimeter waves [1]. In addition, they can be used successfully as a high-voltage injector in betatrons and synchrotrons at 15--300 MeV [2, 3]. Therefore, in calculating the main parameters of the accelerator one may use the results obtained in [1].

In [1] the problem of particle motion in the field of the $E_{010}$ wave of a cylindrical resonator was solved, and it was shown that the solution of the equation of motion can be represented in the form:

\[ \frac{2\pi h}{\lambda} = \int_{\Theta_e}^{\Theta_h} \frac{A\,d\Theta}{\sqrt{1 + A^2}}, \tag{1} \]

where

\[ A = \frac{\beta_e}{\sqrt{1-\beta_e^2}} - \left(\frac{eV_0}{m_0c^2}\right) \left(\frac{\lambda}{2\pi h}\right) (\cos\Theta_e - \cos\Theta_h); \qquad \beta_e = \frac{v_{\text{init}}}{c}, \]

$\Theta_e$ and $\Theta_h$ are the initial and final phases of the electron;

$h$ is the height of the resonator;

$V_0 = E_{z\max}\cdot h$ is the amplitude value of the accelerating voltage;

$\lambda$ is the wavelength of the generator.

The calculation consists in determining, for the specified parameters

\[ \frac{eV_0}{mc^2} \left( \frac{2\pi h}{\lambda} \right), \qquad \Theta_e \quad\text{and}\quad \beta_e, \]

the upper limit of integration of integral (1), at which the integral is equal to

\[ \frac{2\pi h}{\lambda}. \]

In [1] numerical calculations were carried out characterizing the dependence of \(\Theta_h\) and the output energy on \(\Theta_e\) for the case

\[ \frac{2\pi h}{\lambda}=2.332,\qquad \frac{eV_0}{m_0c^2}=4.282\quad (eV_0=2.2\ \text{MeV}) \]

and various \(\beta_e\). It follows from these calculations that, if electrons are injected with \(\beta_e=0.3\), then during one period of the high-frequency field a certain fraction of the incident electrons, equal to 0.37, is accelerated. The number of particles with an energy spread of \(\pm 3\%\) near \(E=1.5\ \text{MeV}\) is 41% of the total number of accelerated particles, and almost all particles have an energy greater than 1 MeV.

Thus, a resonator accelerator with such parameters satisfies the technical conditions formulated above.

Fig. 1. Block diagram of a single-cavity accelerator at 1 MeV. 1—HF generator, 2—ferrite valve, 3—resonator, 4—electron gun

If a high-frequency generator with \(\lambda=11.3\ \text{cm}\) is used for acceleration, the height of the resonator must be \(h=4.2\ \text{cm}\).

Using the formulas widely known in microwave engineering, which characterize the relation between power and voltage, one can obtain that in a resonator of such height the wave \(E_{010}\) will have an intensity \(E_z\simeq0.525\ \text{MV/cm}\), if the input power is \(P=0.7\ \text{MW}\).

Thus, for these purposes an ordinary magnetron generator with a power of \(P_c\simeq1.5\div2\ \text{MW}\) can be used. If the generator produces 50 pulses per second with duration \(\tau=2\ \mu\text{s}\), then to obtain an average current with an energy spread of \(\pm 30\%\), \(I_{\text{av}}=100\ \mu\text{A}\), it is necessary that the pulsed current be \(I_{\text{pulse}}=1\ \text{A}\). With the above capture coefficient it follows from this that the injected current must be not less than \(3\ \text{A}\).

Fig. 2. Accelerating resonator

In terms of volume, this single-cavity accelerator consists of three blocks: 1—a power-supply unit of dimensions \(1\times0.5\times1.5\ \text{m}\); 2—a magnetron ...

generator with the accelerating head ($0.6 \times 1 \times 1.5$ m); 3—the control panel, measuring $0.5 \times 1.5 \times 1.5$ m. The block diagram of the accelerator is shown in Fig. 1.

The accelerating resonator is cylindrical (Fig. 2), 4.1 cm high, and operates in the $TM_{010}$ mode. It is placed in a vacuum chamber and is excited through a coupling aperture measuring $15 \times 25$ mm. The resonator is made of copper, with electropolishing used. The intrinsic quality factor of the resonator is $Q_0 = 9000$.

Fig. 3. Electron gun

Microwave power is supplied through a rectangular waveguide. Between the ferrite valve and the resonator there is a vacuum transition. The standing-wave ratio in the line is 1.5.

The electron gun (Fig. 3) provides an electron-beam current on the order of 10 A at a voltage of 30 kV.

REFERENCES

1. Millimeter and Submillimeter Waves, IL, Moscow, 1959.
2. A. P. Komar, O. P. Korovin, DAN SSSR, 159, 4, 775, 1964.
3. O. P. Korovin, Dissertation. Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad, 1966.