On the Application of Double-Row Pin Combs in Iron-Free Waveguide Synchrotrons

P. I. GOSKOV

As shown in [1], as the accelerating system of an iron-free waveguide synchrotron it is most expedient to use a double-row pin slow-wave structure, placing it directly on one of the current-carrying buses; i.e., in this case the pins, together with the bus, will form a single whole (Fig. 1). In this case the slow-wave structure will not be completely shielded: there will be lateral gaps (Fig. 1). Naturally, this fact will to some extent affect the electrodynamic properties of double-row pin combs.

For the purpose of determining the influence of the indicated factor on the electrodynamics of pin combs, the properties of two experimental models were investigated: I — a system consisting of a fully shielded double-row pin comb structure, which, in the notation of [2], had the following geometrical dimensions: \(a = 20\) mm, \(b = 5\) mm, \(v = 65\) mm, \(h = 15\) mm, \(g = 5\) mm, \(p = 40\) mm, \(q = 20\) mm; II — a slow-wave structure with the same dimensions, but not completely shielded, since there was a 40 mm gap between the upper and side walls of the waveguide. The latter variant corresponded to the system shown in Fig. 1. In this case the distance from the pins to the edge of the current-carrying bus was 25 mm, i.e., the width of the buses was 80 mm.

Fig. 1. Accelerating system of an iron-free waveguide synchrotron based on double-row pin combs

The resonant volume in systems I and II was produced by means of solid metallic shorting plates passing in the planes of mirror symmetry midway between two adjacent pins.

From Fig. 2, which presents the experimental dispersion curves of the synchronous wave of both systems, it follows that the presence of lateral

side gaps shifts the passband into the long-wavelength region, and the influence of the gap is somewhat stronger in the modes \(\Psi \to 0\). The passband in this case increased by less than 15%.

For system 1 at \(\Psi=\dfrac{2\pi}{3}\), the value of \(\lambda\) was calculated with the aid of expressions for the end capacitances of double-row pin combs and the corresponding wave conductivities given in [3]. The theoretical value of the wavelength was \(\lambda = 12.2\ \text{cm}\), which differed from experiment by less than 0.2%.

Fig. 2. Dispersion curves of pin combs

Thus, since the shift of \(\lambda\) due to the presence of side gaps is less than 4.5%, the experimental data obtained indicate that the dispersion properties of the accelerating systems of iron-free synchrotrons based on double-row pin combs (Fig. 1) can be quite well calculated using the expressions given in [3], since the discrepancy with experiment will not exceed 5% at

\[ \frac{c}{V_{\phi}} \approx 1 . \]

a)          b)

Fig. 3. Dependences of \(Q\) and \(r_{\text{sh}}\) on \(\Psi\)

Figure 3 presents experimentally determined dependences of the quality factor and shunt resistance of both systems on the operating mode.

It follows from Fig. 3a that the presence of side gaps does not change the character of the dependence \(Q(\Psi)\). The decrease in the \(Q\)-factor due to the side gaps is about 20%. This comparatively small change in the \(Q\)-factor is explained by the fact that, in pin combs, the field is concentrated mainly in the region of the pins.

It follows from Fig. 3b that, both in the case of a completely shielded structure and in the presence of side gaps, the most efficient operating mode will be at \(\Psi = 2\pi/3\). Moreover, in this mode, because of the presence of side gaps, the shunt resistance decreased by 40%.

The most difficult aspect in manufacturing an accelerating system based on double-row pin combs will be ensuring strict parallelism (relative to the beam) of a large number of pins.

In Fig. 4 the results are presented of an experimental study of the influence of nonparallel installation of the pins in a completely shielded double-row comb on its resonant properties.

Fig. 4. Shift of the resonant frequency in the comb structure due to nonparallelism of the pins (relative to the beam).

In the notation of [2], the systems had the following dimensions: a) \(h = 16\) mm, \(g = 14\) mm, \(a = 20\) mm, \(в = 10\) mm, \(w = 10\) mm, \(q = 30\) mm, \(p = 40\) mm, \(\Psi = 2\pi/3\); b) \(h = 16\) mm, \(g = 14\) mm, \(a = 30\) mm, \(w = 15\) mm, \(в = 10\) mm, \(q = 20\) mm, \(p = 40\) mm, \(\Psi = 2\pi/3\). In the case of square pins \((10 \times 10\) mm) (Fig. 4a), the shift of the resonant frequency upon rotation of the pins about their own axis is comparatively small, less than 10 MHz. But for elongated pins with cross section \(10 \times 20\) mm (Fig. 4b), significantly larger shifts of the resonant frequency are observed when all pins are rotated about their own axis. Consequently, in the latter case the accelerating system must be manufactured to a higher accuracy class, i.e., with tighter tolerances.

The shunt resistance in the case of square pins practically did not change, while in the case of elongated pins, when they were rotated by \(90^\circ\) (i.e., it became \(a = 10\) mm, \(в = 20\) mm, \(q = 30\) mm), it changed by 30%.

REFERENCES

1. P. I. Goskov. Izv. TPI, present collection, vol. 156, 166, 1969.
2. P. I. Goskov. Izv. vuzov, “Fizika,” 3, 61, 1965.
3. L. N. Bezmaternykh. Dissertation, TPI, Tomsk, 1964.