AUTOMATIC OPTIMIZATION OF THE INJECTION BEAMLINE OF A SYNCHROTRON AT AN ENERGY OF 1.5 GeV

P. A. DYUGAI, V. P. IVANCHENKOV, V. A. KOCHEGUROV

(Presented by the scientific seminar of the AVTA, Research Institute of Nuclear Physics, Electronics, and Automation)

This article presents the results of studies of the injection beamline of a synchrotron at an energy of 1.5 GeV by the method of mathematical modeling, and selects its optimal parameters and structure. The synchrotron has multi-turn injection. The synchrotron injection system consists of a 5.5 MeV injector microtron and an electron transport beamline. Beam focusing during transport is carried out by two pairs of quadrupole lenses.

The electron beam at the exit of the microtron occupies, in the phase space \(X, X', Z, Z'\), a certain region bounded by a closed curve. Experimental studies of the synchrotron have shown that the envelope curve can be represented in the form of an ellipse, whose equation in normalized form is written as [2]

\[ \gamma(y)X^2 + 2\alpha(y)XX' + \beta(y)X'^2 = \varepsilon, \tag{1} \]

where

\[ \varepsilon = \frac{F}{\pi} \]

is the beam emittance,

\(F\) is the area of the phase ellipse,

\(\alpha, \beta, \gamma\) are the coefficients of the phase ellipse,

\(Y\) is the distance along the transport beamline of charged particles.

The experimental values of the horizontal and vertical emittances at the entrance of the injection beamline are equal to

\[ \varepsilon_x = 29 \cdot 10^{-3}\ \text{mm rad}; \qquad \varepsilon_z = 8.56 \cdot 10^{-3}\ \text{mm rad}. \]

In the synchrotron, during acceleration, only those particles are captured which have a definite angle and deviation from the optical axis of the beamline. The vertical admittance of the synchrotron is described by the equation of an ellipse and is a constant quantity during the injection process.

The horizontal (radial) admittance of the synchrotron has a more complex character, since the region satisfying the capture conditions in the \(\rho, \nu\) plane during injection does not remain constant and depends on the injection time \(\tau_j\) [3]. Entry of a particle into the chamber of the main accelerator is carried out by an electrostatic inflector. The plates of the inflector limit the possible deviation of electrons from

of the optical axis of the injection beamline, which leads to the loss of particles on the inflector plates. The inflector plates in the phase planes \(X, X'\) and \(Z, Z'\) are represented in the form of a parallelogram [2].

The choice of the optimal coefficients of the quadrupole lenses of the transport beamline must be made from the conditions for matching the beam emittance at the beamline exit with the synchrotron admittance (Fig. 1) in the horizontal and vertical planes, taking into account the “constraints” introduced by the plates of the deflecting device during beam transport. The “constraints” introduced by the outer plates of the inflector are taken into account by superimposing the image of the plates on the corresponding admittance of the accelerator; i.e., matching of the beam emittance at the beamline exit is performed with the region in the phase plane obtained as a result of superimposing the image of the inflector plates on the corresponding admittance of the accelerator (Fig. 1).

Determination of the optimal parameters and structure of the forming system was carried out on an MNB-1 analog computer using a correlation-extremal system developed by us [1, 2]. In calculating the radial admittance of the synchrotron, it was specified for several discrete values of the injection time \(\tau_j\). For each admittance value corresponding to the time instant \(\tau_j\), a search was made for the best set of parameters \(K_i\). As a result of the calculation, the optimal variant was taken to be that for which the average particle losses were smallest. The calculation of the average particle losses for the horizontal plane was carried out according to the following expression:

Fig. 1. Diagrams explaining the conditions for determining the optimal parameters of the synchrotron injection beamline

\[ S_{\mathrm{cp},x}= \frac{S_{\tau_1}+S_{\tau_2}+\cdots+S_{\tau_j}}{n_{\mathrm{ne}x}}, \tag{2} \]

where

\[ S_{\tau_j} \]
— particle losses at the injection time \(\tau_j\),

\[ n \]
— number of averaging intervals.

Table 1 gives the optimal variants of the values of the quadrupole-lens parameters \(K_i\), obtained in the course of the calculation, for several arrangements along the injection beamline. The first arrangement of lenses

corresponds to the currently adopted arrangement of quadrupole lenses along the synchrotron injection beamline. Figure 3 gives oscillograms showing the change in the characteristics of the beam phase ellipse in the horizontal plane of symmetry of the forming system during its transport from the injector into the accelerator chamber. For the optimal variant of the quadrupole-lens coefficients with the first arrangement of lenses, particle losses during injection in the horizontal plane amount to 45%. In the vertical plane there are no particle losses, i.e., the vertical emittance of the microtron after transformation is completely contained within the vertical admittance of the synchrotron. In order to reduce particle losses during injection, the arrangement of lenses along the beamline was changed (variants 3–5, Table 1). The calculations performed showed that the selected arrangements of lenses along the

Table 1

beamline do not lead to a significant improvement in the matching of the beam emittance at the beamline exit with the synchrotron admittance. In the calculation, a transport line consisting of three quadrupole lenses along the injection beamline was also investigated (variants 6, 7 in Table 1). It is seen from Table 1 that transport of the beam from the injector to the accelerator can be accomplished by a system of three lenses, on average with the same effect as by a system consisting of four quadrupole lenses. At the same time, the use of an electron-optical system consisting of three quadrupole lenses makes it possible to free space on the synchrotron injection beamline for the placement of additional experimental apparatus. Measurements of current transmission along the injection beamline and through the inflector showed that, with the parameters of the quadrupole lenses given in Table 1 (variants 1, 2), it is possible to obtain the maximum current at the inflector exit. The measurements were carried out using Faraday cylinders at the microtron exit and downstream of the inflector. The emittance of the microtron in the horizontal plane has dimensions considerably larger than in the vertical plane; at the same time, the region satisfying the capture conditions in the vertical plane exceeds by a factor of 2–3 in area the region satisfying the conditions for particle capture into acceleration in the horizontal plane. In this connection, the supposition was made that it would be expedient to rotate the beam emittance by 90°. Such a rotation can be effected by rotating the plane of the injector magnet by 90° relative to the plane of the synchrotron or by means of an axially symmetric magnetic field of a short lens.

The calculations performed confirmed the correctness of the assumption made (Table 1, variants 8–10).

Variants 8–9 were obtained with the emittance rotated at the entrance of the beamline, and variant 10 at the exit of the beamline (Fig. 1). Oscillograms of the beam emittances at the exit of the beamline in the horizontal and vertical planes of symmetry for the optimal parameters of the quadrupole lenses (variants 8, 9—rotation of the beam emittance at the entrance of the beamline by \(90^\circ\)) are shown in Fig. 4. Taking into account the energy spread of the injected beam, rotation of the beam emittances by \(90^\circ\) at the entrance of the beamline (variants 8, 9) makes it possible to increase the capture coefficient at the first stage of injection by a factor of 1.5–2.

Fig. 2. Dependence of the change in average particle losses for different parameters of the forming system on the injection time

At present, a system for rotating the emittances by \(90^\circ\) is being developed for the synchrotron. Figure 2 shows the calculated dependences \(S_{\mathrm{cp}} = f(\tau)\) for the obtained optimal variants of the coefficients of quadrupole lenses 1, 6, 8, 9 (Table 1). It follows from Fig. 2 that the greatest particle losses occur at the beginning and at the end of the first stage of injection. In the injection-time interval \(\tau_j = 1 \div 2.3\ \mu\text{s}\), the particle losses remain constant. Experience from the study of the synchrotron injection beamline has shown that the correlation-extremal system developed makes it possible to reduce, by a factor of 30–40, the time required for the analysis and synthesis of the best structure of the transport beamline, and to select optimal parameters with an accuracy sufficient for engineering practice.

Fig. 3. Variation of the parameters of the phase ellipse of the beam as it moves along the injection channel: 1 — horizontal emittance at the entrance to the injection channel; 2 — emittance at the entrance to the 1st quadrupole lens; 3 — emittance at the exit of the 1st quadrupole lens; 10 — emittance at the exit of the injection channel.

Visible panel labels:

1. \(\beta_x = 19;\ \beta'_x = -7\)
2. \(\beta_x = 25;\ \beta'_x = 9\)
3. \(\beta_x = 86;\ \beta'_x = -4\)
4. \(\beta_x = 62;\ \beta'_x = 37\)
5. \(\beta_x = 64;\ \beta'_x = 42\)
6. \(\beta_x = 86;\ \beta'_x = 5\)
7. \(\beta_x = 35;\ \beta'_x = 39\)
8. \(\beta_x = 72;\ \beta'_x = 35\)
9. \(\beta_x = 21;\ \beta'_x = 11\)
10. \(\beta_x = 52;\ \beta'_x = 0.3\)

Fig. 4. Oscillograms of the beam emittances at the exit of the beamline when it is rotated by \(90^\circ\): \(a, в\) — horizontal and vertical emittances for the optimal set of parameters of a shaping system consisting of two pairs of lenses; \(б, г\) — horizontal and vertical emittances for the optimal set of parameters of a shaping system consisting of 3 lenses.

REFERENCES

1. V. P. Ivanchenkov, V. A. Kochegurov. Development and application of extremal systems in problems of electron optics. Abstracts of papers of the Fourth All-Union Symposium on Extremal Problems, Kaunas, 1969.

2. N. V. Tikhanova, V. A. Kochegurov. Calculation on an analog computer of electron-optical systems taking account of the phase volume of the beam. Elektronnaya tekhnika, series 1, no. 1, 1967.

3. M. P. Shanin. Problems in the development, creation, and study of the injection system of a synchrotron at 1.5 GeV. Dissertation for the degree of Candidate of Technical Sciences, TPI, 1966.