MAGNETIC SYSTEM OF AN AUTORESONANCE ACCELERATOR

A. P. ISHKOV

(Presented by the scientific seminar of NIIYaFEA)

A new autoresonance method for accelerating charged particles by an electromagnetic wave [1] presupposes the use of a constant magnetic field in the region of interaction of the charged particle with the electromagnetic wave. The direction of the magnetic field must coincide with the direction of propagation of the electromagnetic wave. The magnetic field must be uniform when the phase velocity of propagation of the electromagnetic wave is equal to the speed of light, and its magnitude is determined by the cyclotron frequency of rotation of the particle in the magnetic field, which in the particular case is equal to the frequency of the electromagnetic wave.

In the case where acceleration is produced by an electromagnetic wave with a phase velocity greater than the speed of light in a uniform constant magnetic field, the acceleration will be periodic in character. The length of the section over which acceleration occurs is determined by the following relation

\[ l = \frac{\beta \lambda}{2(\beta^2 - 1)}, \tag{1} \]

where \(\beta\) is the relative phase velocity of the electromagnetic wave;
\(\lambda\) is the wavelength of the electromagnetic wave.

The requirements on the uniformity of the magnetic field are not formulated in the theory [1], but experiments conducted by us show that nonuniformities of less than 5% have no substantial effect.

For an experimental investigation of the autoresonance method of electron acceleration, an accelerator is being constructed with a relative phase velocity of the accelerating wave of 1.14 and with a wavelength in free space of about 10 cm.

The purpose of the present work is to create a magnetic system for this accelerator, with the aid of which it is possible to obtain a constant magnetic field of strength of the order of 1000 oersteds in a cylindrical volume 200 mm long, which is determined by formula (1), and 190 mm in diameter, with a distribution uniformity no worse than 5%. The magnetic system must possess high accessibility, since inside it there must be placed a waveguide system into which the electron beam is injected and from which the accelerated electrons are extracted.

Existing methods for obtaining uniform magnetic fields of the order of 1000 oersteds in large volumes using iron magnetic circuits are cumbersome and have limited access to the region of the uniform field. The use of solenoids is also complicated, since do-

access to the region of their uniform field is possible only from the end side.

The noted shortcomings are absent in the magnetic system of Helmholtz coils [2, 3], which are two coaxial identical coils. However, the direct use of Helmholtz coils in our case is difficult, since the extent of the uniform field in them is equal to half the mean diameter of the coil. Therefore the coils will be required to be very large, and a considerable dc power (on the order of several tens of kilowatts) will be needed to feed them. The design of the magnetic system in this case will be complex.

A magnetic system of three coils, synthesized on the basis of Helmholtz coils, has been chosen as acceptable for practical use; its construction is shown in Fig. 1. The coils, made of copper busbar, are connected in series and oriented so that the fields they create in the working volume add together.

Fig. 1.

The magnetic field on the axis of an individual coil is determined by the formula [4]

\[ H(l)=\frac{\pi}{5} i\lambda \left\{ (x-l)\ln \frac{y_2+\sqrt{y_2^2+(x-l)}}{y_1+\sqrt{y_1^2+(x-l)}} + (x+l)\ln \frac{y_2+\sqrt{y_2^2+(x+l)}}{y_1+\sqrt{y_1^2+(x+l)}} \right\}, \tag{2} \]

where
\(l\) is the distance from the center of the coil along the axis,
\(x\) is half the width of the coil,
\(y_1\) is the inner diameter of the coil,
\(y_2\) is the outer diameter of the coil,
\(\lambda\) is the packing-density coefficient of the coil winding,
\(i\) is the current density in amperes per square centimeter.

All dimensions are taken in centimeters, and the magnetic-field intensity is obtained in oersteds.

For given dimensions of the main coils and the distance between them, the geometry of the additional middle coil and the number of ampere-turns in it are chosen so that the sum of all three components in the working volume remains a constant quantity,

\[ H_1(l) + H_2(l) + H_3(l) = \mathrm{const}. \tag{3} \]

Fig. 2

With an accuracy of up to \(1 \div 2\%\), this problem can be readily solved by a graphical-analytical method. The results of the calculations performed are given in the table.

With a current in the windings of \(280\ \mathrm{A}\), the magnetic-field intensity at the center of the system was \(1045\) oersteds. The topography of the magnetic field in the working volume is shown in Fig. 2a. The results of measurement of the magnetic field on the axis of the system are shown in Fig. 2b. The graphs show good agreement of the experimental dashed curve with the calculated solid curve in the central part of the working volume of the magnetic system.

The distribution of the magnetic field along the generatrix of the surface of a cylindrical coaxial cone with a base diameter equal to \(12\ \mathrm{cm}\), in

in the vicinity of which the accelerated electron moves, was obtained as a geodesic section in the direction \(OA\) in Fig. 2a, and is shown in Fig. 2c. The inhomogeneity of the magnetic field is less than 3%.

Table

In conclusion, the author expresses his gratitude to Yu. G. Yushkov for a useful discussion of the work.

REFERENCES

1. A. A. Kolomenskii and A. N. Lebedev. ZhETF, vol. 44, no. 1, 1963.
2. M. F. Peters. J. Opt. Soc. Amer., vol. 13, p. 205, 1926.
3. S. T. Lin and Kaufman. Rev. of Modern Physics, vol. 25, p. 253, 1953.
4. V. G. Karasik. Physics and Technology of Strong Magnetic Fields, 1964.