SETUP FOR GENERATING STRONG CENTRIFUGAL FIELDS

In 1946, Beams and co-workers described a setup for generating strong centrifugal fields, as well as some results obtained with its aid\(^{1,2}\). In developing the method, the authors relied on the fact that rupture of a homogeneous elastic rotor occurs upon reaching a certain peripheral velocity \(v_{\mathrm{crit}}\) (for the given material and shape of the rotor), independently of the magnitude of the centrifugal

forces. Therefore the largest centrifugal field attainable with a given rotor is determined by the condition:

\[ (\omega^2 r)_{\text{critical}}=\frac{v^2_{\text{critical}}}{r}\sim \frac{1}{r}, \]

where \(\omega\) is the angular velocity of rotation of the rotor and \(r\) is its radius. Consequently, in order to obtain the strongest possible centrifugal fields it is necessary to proceed by reducing the diameter of the rotor. This conclusion, known from turbine-construction practice, was confirmed by the authors by direct experiments: for steel balls (from ball bearings) the critical peripheral speed proved to be approximately equal to \(1\ \text{km/sec}\). The greatest intensity of the centrifugal field reached by the authors in 1946 was \(2.4 \cdot 10^9\ \text{m/sec}^2\), i.e. approximately 240 million times greater than the acceleration of gravity. The radius of the ball corresponding to this case was \(\sim 0.4\ \text{mm}\). Further reduction of the rotor dimensions proved impossible for technical reasons.

Bims has now constructed an apparatus in which these obstacles have been partially eliminated, as a result of which centrifugal fields have been attained with intensities exceeding the acceleration of gravity by more than half a billion times. The method employed by Bims is distinctive and is of undoubted interest.

In its main features the apparatus (see the figure) has not undergone substantial change. The rotor \(P\), consisting of a solid steel ball, is placed in a vertical glass tube \(T\), evacuated to a high vacuum (\(\sim 10^{-6}\ \text{mm Hg}\)), and is suspended in it by the axial magnetic field of the solenoid \(C\). The rotor is then spun up by a rotating magnetic field produced by coils \(K\) placed outside the vacuum tube. The spinning-up process continues for several hours, after which (as measurements show, the method of which is described in ²) the rotor begins to rotate synchronously with the magnetic field. Horizontal stabilization of the rotor is provided by the axial field of the solenoid \(C\). Random horizontal motions of the rotor are damped by a thin iron needle \(I\), placed along the continuation of the axis of the solenoid \(C\) (outside the vacuum tube) and immersed in a liquid. Such a magnetic suspension of the rotor proves to be very stable, while the resistance to rotation is less than friction against air, even under high-vacuum conditions.

The greatest difficulties are presented by the vertical stabilization of the rotor, carried out by automatic regulation of the current flowing around the solenoid \(C\). In the first version¹, for this purpose the dependence of the impedance of a certain auxiliary coil, placed below the rotor, on the position of the latter was used. However, for rotors whose diameter is less than \(0.5\ \text{mm}\), this mechanism proved insensitive, and further reduction of the rotor size was impossible. In the second work³ the author used optical stabilization. A beam of light from the illuminator \(O\) (see the figure), cut off by the diaphragm \(D\), is focused by the lens \(L_1\) on the axis of the vacuum tube directly above the rotor \(P\), so that a certain amount of light is scattered by the rotor and, through the prism \(\Pi\) and the lens \(L_2\), falls on the photomultiplier \(\Phi\), connected to the circuit \(U\), which controls the current flowing around the solenoid \(C\). The slightest displacement of the rotor upward or downward causes a corresponding change in the intensity of the scattered light falling on the photomultiplier, and causes a compensating change in the magnetic field of the solenoid \(C\). In the circuit of the control device (given by the author) special measures have been taken to suppress possible vertical oscillations. As a result, attain-

a very high degree of stabilization is achieved—in observation with a microscope of a suspended steel rotor of radius 0.18 mm over the course of several hours no noticeable vertical displacements were noted.

The smallest rotor tested by the authors in the described apparatus had a radius of 0.05 mm. However, with such small rotor sizes difficulties arise with horizontal stabilization. The greatest rotational speed attained by the author with a rotor of radius 0.2 mm was \(8 \cdot 10^5\) revolutions per second.

The author notes that the limiting peripheral velocity \((v_{\text{crit}})\) at small rotor diameters apparently does not remain constant, but increases as the diameter decreases. As a possible explanation he points out that, with decreasing diameter, the probability of cracks or defects being present in the zone where the maximum velocities occur also decreases.

In the process of pumping air out of the working tube, a slight lowering of the rotor was regularly observed, which could be explained by a change in the density of the air in which the rotor is immersed. Special measurements showed that for a rotor of volume \(3.36 \cdot 10^{-5}\ \text{cm}^3\) and weight \(2.6 \cdot 10^{-4}\ \text{g}\), a change in weight of \(10^{-8}\)—\(10^{-9}\ \text{g}\) is easily observable. The author emphasizes that the sensitivity of the apparatus to changes in the weight of the rotor can be considerably increased and, thus, the apparatus can be used as a microbalance.

R. G.

References

1. J. W. Beams, J. L. Joung and J. W. Moore. J. Appl. Phys. 17, 886 (1946).
2. E. V. Shpol’skii, UFN 32, 134 (1947).
3. I. W. Beams, Rev. of Scient. Instr. 21, 182 (1950).