PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV,
ORDER OF THE OCTOBER REVOLUTION AND ORDER OF THE RED BANNER OF LABOR

Vol. 232　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1975

EXPERIMENTAL STUDY OF PIN ACCELERATING STRUCTURES

R. G. KAMINSKAYA, V. V. BARABOSHKIN

(Presented at the seminar of the RF and AI sector of the Nuclear Physics Research Institute.)

In waveguide synchrotrons, smooth or diaphragm-loaded curved waveguides were used as the accelerating structure [1, 2]. However, as shown in [3], pin structures can also be used as accelerating systems for high-energy synchrotrons. But these structures have not yet been sufficiently studied.

This article presents the results of an experimental study of the electrodynamic characteristics of single-row and double-row pin combs (Fig. 1) by the method of small perturbing bodies.

Figure 2 presents the calculated and experimental dispersion characteristics. To calculate the dispersion curves, the expressions given in [4] were used. The large discrepancy between the experimental and calculated data for the $\pi$-mode of oscillation is explained by the fact that the dispersion was calculated under the assumption of field uniformity between the pins.

Fig. 1. Pin slow-wave systems: 1 — single-row, 2 — double-row.

Fig. 2. Dispersion dependences of a pin system: 1 — single-row, 2 — double-row.

Figures 3 and 4 present the dependences of the coupling impedance and the ratio of shunt impedance to quality factor, \(R_{\mathrm{sh}}/Q\), which characterizes the effectiveness of the chosen system and depends only on the geometrical dimensions expressed in wavelengths of the generator.

The dependences \(R_{\mathrm{c}}\) and \(R_{\mathrm{sh}}/Q\) are given for the \(\pi/2\)-mode of oscillation, since near this type of oscillation the maximum shunt impedance is observed [5]. As follows from the figure, the coupling impedance and \(R_{\mathrm{sh}}/Q\) for a single-row comb depend strongly on the distance between the side wall and the pin, and for a two-row comb on the distance between pins, \(a/\lambda\), and depend much less on the other geometrical dimensions.

Fig. 3. Dependence of \(R_{\mathrm{c}}\) and \(R_{\mathrm{sh}}/Q\) on geometrical dimensions for a single-row pin structure.

With an increase in the gap above the pins, both in the single-row and in the two-row structure, in the case \(b<h\) a very weak dependence is observed; in the case \(b \ge h\), however, the effectiveness of the structure decreases, and the pins have no noticeable influence on the slowing of the wave, while the structure behaves like a smooth waveguide with additional losses.

As is seen from the dispersion curves, pin structures possess a large bandwidth, which makes it possible to use them for accelerating particles over a wide frequency range without retuning. But increasing the bandwidth leads to an increase in the group velocity \(\beta_{\mathrm{gr}}\), which becomes considerably greater than for circular diaphragm-loaded waveguides used in accelerators.

The dependences of the group velocity \(\beta_{\mathrm{gr}}\) for single-row and two-row combs are shown in Fig. 5. For comparison, the same figure includes the dependence of \(\beta_{\mathrm{gr}}\) for a circular diaphragm-loaded waveguide on the dimensions of the interaction space, constructed from the data of [6].

Since the coupling impedance and \(R_{\mathrm{sh}}/Q\) are related by the relation \(R_{\mathrm{sh}}/Q = \dfrac{2\pi}{\lambda} R_{\mathrm{c}}\beta_{\mathrm{gr}}\), then, for identical \(R_{\mathrm{sh}}/Q\) for pin combs and a circular diaphragm-loaded waveguide, the coupling impedance \(R_{\mathrm{c}}\) for pin combs is always smaller than for a circular diaphragm-loaded waveguide.

The group velocity and attenuation in the waveguide are related by

\[ \alpha=\frac{\pi}{\lambda \beta_{\mathrm{gr}} Q}. \]

Therefore, an increase in the group velocity corresponds to a decrease in attenuation. This, in turn, will lead to a decrease in the particle energy gain while passing through the waveguide, which, as is known, is determined by the formula

\[ V=\sqrt{2\alpha R_{\mathrm{sh}}P_0} \]

and, taking into account beam loading,

\[ V=\sqrt{\frac{2R_{\mathrm{sh}}P_0}{\alpha}\left(1-e^{-\alpha L}\right)-IR_{\mathrm{sh}}L\left(1-\frac{1-e^{-\alpha L}}{\alpha L}\right)}, \]

where \(P_0\) is the applied high-frequency power, and \(I\) is the particle current.

Now let us consider how an increase in \(\beta_{\mathrm{gr}}\) affects the energy gain in a waveguide system that has a feedback loop. In this case the particle energy gain is expressed, according to [7], by the expression

Fig. 4. Dependence of \(R_{\mathrm{sv}}\) and \(R_{\mathrm{sh}}/Q\) on the geometric dimensions for a two-row pin structure

Fig. 5. Dependence of the group velocity \(\beta_{\mathrm{gr}}\) on the geometric dimensions: 1 — single-row, 2 — two-row, 3 — circular diaphragm-loaded waveguide.

\[ V=\sqrt{\frac{2R_{\mathrm{sh}}P_0}{\alpha}(1-e^{-\alpha})}\, \frac{k}{1-\sqrt{1-k^2}\,e^{-\tau}} -\frac{IR_{\mathrm{sh}}}{\tau} \left[ \frac{(1-e^{-\tau})^2 e^{-\tau}\sqrt{1-k^2}} {1-\sqrt{1-k^2}\,e^{-\tau}} +\alpha-1-e^{-\alpha} \right], \]

where \(\tau=\alpha+\gamma\) is the total attenuation in the accelerating waveguide \(\alpha\) and in the feedback system \(\gamma\), and \(k\) is the coupling coefficient.

For the case \(\alpha\ll1\) and \(\tau\ll1\), we have

\[ V= \frac{\sqrt{2\alpha R_{\mathrm{sh}}P_0}\,k -IR_{\mathrm{sh}}\alpha\sqrt{1-k^2}} {1-\sqrt{1-k^2}(1-\tau)}. \]

The first term in this expression describes the particle energy gain during flight through the accelerating waveguide; the second, the field induced by the beam.

It follows from this expression that a decrease in the attenuation $\alpha$ with increasing $\beta_{\mathrm{gr}}$ leads to a decrease in the energy gain, which is proportional to $\sqrt{\alpha}$. At the same time, the field induced by the beam decreases by a factor of $\alpha$. Consequently, systems with a large group velocity can be effectively used in feedback systems for high-current accelerators.

Thus, the results obtained in the experimental study of the electrodynamic characteristics of single-row and double-row pin combs have shown that pin structures have lower attenuation and a considerably broader bandwidth than circular diaphragm-loaded waveguides. They can be effectively used as accelerating systems with feedback for high-current accelerators.

REFERENCES

1. A. A. Vorob'ev [et al.]. Proceedings of the IV Interuniversity Conference on Electron Accelerators. Moscow, “Vysshaya shkola,” 1964.

2. A. A. Vorob'ev [et al.]. In: Electron Accelerators, Proceedings of the VII Interuniversity Conference on Electron Accelerators. Moscow, Gosatomizdat, 1970.

3. A. A. Vorob'ev, A. N. Didenko. Atomnaya energiya, 12, 242, 1962.

4. L. N. Bezmaternykh. Dissertation. Tomsk, 1964.

5. P. I. Gos'kov. Izv. vuzov, “Radiotekhnika,” VII, 5, 398, 1964.

6. O. A. Val'dner, N. P. Sobenin, V. V. Zverev, I. S. Shchedrin. Handbook on Diaphragm-Loaded Waveguides. Moscow, Atomizdat, 1969.

7. A. P. Didenko, G. P. Fomenko. Radiotekhnika i elektronika, XVI, 6, 1017, 1971.