RESONANT RADIO-FREQUENCY MASS SPECTROMETER

In recent years a number of types of radio-frequency mass spectrometers have been developed, based both on the selection of ions by velocities or by time of flight and on the use of resonance effects in crossed fields. In the note under review*) it is proposed to use, for ion selection, differences in the periods of their free oscillations in an electric field with a parabolic distribution of potential along the ion tube. The scheme of such a mass spectrometer is shown in the figure.

A constant voltage \(V_0\) creates (by means of rings \(G\), separated by resistances \(R\)) a parabolic distribution of potential along the axis of the tube,

\[ V(x)=\frac{1}{2}K^2x^2, \]

shown in the lower part of the figure.

The ions formed in the tube by the electron beam will oscillate in this constant field along the axis of the tube with frequency

\[ \sqrt{\frac{eK^2}{m}} \]

(where \(m\) is the mass of the ion, \(e\) is its charge) and with an amplitude determined by the ion energy. If this energy is less than \(eV_0\), then the ion will never be able to reach the collector \(P\). Suppose now that a radio-frequency electric field is applied between the middle pair of rings. If the period of the ion’s free oscillations \(T_{\text{ion}}\) coincides with the period of the radio-frequency field \(T_{\text{r.f.}}\) (or is an odd integral multiple of it), then the ion will receive energy from the radio-frequency field, as a result of which the amplitude of its oscillations will increase. In this case the ion will be able to reach the collector \(P\).

*) P. Schissel, J. Appl. Phys. 22, 680 (1951).

Thus, the condition for an ion to reach the collector is:

\[ \frac{2\pi}{K}\sqrt{\frac{m}{e}} = (2n - 1)T_{\mathrm{r.f.}}, \]

where \(n\) is an integer, and only those ions whose mass satisfies the condition

\[ m = (2n - 1)^2 \frac{eK^2}{4\pi^2 f^2}, \]

will reach the collector, where \(f\) is the frequency of the alternating field.

The resolving power of the mass spectrometer is

\[ (2n - 1)\pi \frac{V_0}{V_{\mathrm{r.f.}}}, \]

where \(V_{\mathrm{r.f.}}\) is the amplitude of the alternating potential difference between the middle pair of rings.

R. G.