On the Design of Medium-Energy Electron Synchrotrons with Preliminary Induction Acceleration

G. I. Dimov and V. A. Kochegurov

(Presented by Prof. A. A. Vorob’ev, Doctor of Physical and Mathematical Sciences)

Most of the synchrotrons constructed for energies of 300–400 MeV have a central saturating core, by means of which preliminary induction acceleration is carried out. In this case the main magnetic circuit has a C-shaped cross section with a gap toward the center and with a cut in the median plane (Fig. 1). The upper half of the magnetic circuit is fastened into one piece and is removable. This synchrotron design has one great advantage: the simplicity and reliability of carrying out preliminary acceleration. However, this design has substantial drawbacks:

Fig. 1. Synchrotron electromagnet for 400 MeV with a saturating core.

1. Very poor access to the inter-pole space.
2. The obligatory presence of a cut in the main magnetic circuit; in the presence of the cut, the inhomogeneities of the magnetic field associated with eddy currents increase considerably.

1. Increased horizontal dimensions of the electromagnet in comparison with an electromagnet without preliminary induction acceleration (with a C-shaped cross section of the magnetic core, with the gap on the outside).

For a 400 MeV synchrotron the outside diameter increases from 2.45 to 2.85 m, i.e., by 16%.

We propose several variants of synchrotron designs with preliminary induction acceleration, but with a nonsaturating additional core and with an additional excitation circuit for this core.

First variant (Fig. 2).

The magnetic core has an asymmetric Ш-shaped cross section with a cut in the median plane. The cross section of the outer upright is smaller than that of the inner upright. The main excitation winding of the electromagnet is annular. The magnetic flux excited in the poles by this winding branches and closes through the inner and outer uprights of the magnetic core.

Fig. 2. Electromagnet of a 400 MeV synchrotron with an asymmetric Ш-shaped cross section.

The additional core, by means of which preliminary induction acceleration can be carried out, is here the outer upright of the magnetic core. During the period of induction acceleration, the magnetic fluxes in the poles and in the inner upright pass in one and the same direction and close through the outer upright. The magnetic flux in the inner upright (the central accelerating flux) is matched, in rate of increase, with the magnetic field on the orbit. The indicated distribution of the magnetic flux during the period of induction acceleration is achieved by exciting an additional magnetic flux, which is added to the main magnetic flux.

The additional magnetic flux circulates in a closed contour; in the inner upright its direction coincides with the direction of the main magnetic flux in the poles, while in the outer upright it passes in the opposite direction. The additional magnetic flux does not branch in the poles. This flux is excited by an additional winding consisting of two series-connected parts—the inner and the outer (Fig. 2). Since the magnetic flux excited by the additional winding is not linked with the main winding, i.e., there is no mutual inductance between the main and additional windings, the electrical circuits of the main and additional windings are independent. The condition for independence of the main and additional windings is deter-

is the ratio of the numbers of turns of the inner and outer parts of the additional winding. The ratio of the inner ampere-turns to the outer ones is equal to the ratio of the magnetic resistance of the inner branch of the magnetic circuit to the magnetic resistance of the outer branch. Since the magnetic resistances of the magnetic circuit are not constant, and the ratio of turns in the additional winding may in practice differ somewhat from the ratio of the magnetic resistances, some weak mutual inductance will exist between the main and additional windings. However, a practically small coupling between them is quite permissible.

The absolute value of the ampere-turns of the additional winding during the period of induction acceleration must change at a rate proportional to the rate of increase of the magnetic field on the orbit. The proportionality coefficient is determined by the betatron relation.

The additional winding is supplied by short current pulses whose wavefront steepness corresponds to the rate of rise of the magnetic field on the orbit throughout the entire preliminary induction acceleration. The simplest supply circuit for the additional winding is shown in Fig. 2.

A previously charged capacitor is discharged at the appropriate moment through a thyratron or ignitron into the additional winding; in this case a half-sinusoidal current pulse arises in the winding. During induction acceleration the magnetic field on the orbit changes practically according to a linear law. For induction acceleration only the practically linear part of the front of the half-sinusoidal pulse will be suitable; for a synchrotron of \(300 \div 400\) MeV with an orbit radius of about \(1\) m, approximately \(15^\circ\) of the half-sinusoidal pulse can be used. In this case, by the end of induction acceleration the radius of the betatron orbit will decrease by \(1\%\).

It is possible to supply the additional winding with sawtooth current pulses; in this case the power of its supply circuit will be reduced by a factor of 16 in comparison with the circuit of Fig. 2. However, such a circuit will be more complicated.

The minimum radial size of the outer post is determined by the energy of the preliminary induction acceleration and by the shape of the current pulse in the betatron winding.

The electromagnet of the first variant, in comparison with an electromagnet with a saturating core, has the following advantages:

1. Better access to the inter-pole space, owing to the fact that the radial size of the outer posts is considerably smaller. For a synchrotron of \(400\) MeV this size is \(4\) cm as against \(19\) cm.
2. The fastening of the magnetic circuit is simpler.
3. The dimensions and weight of the electromagnet are reduced.

The outer post, which plays the role of an additional core, not only does not increase the cross section of the main part of the magnetic circuit, but even makes it possible to reduce it, since during synchrotron acceleration this post serves as the return magnetic circuit for part of the main magnetic flux. Therefore the use of preliminary induction acceleration in this variant does not lead to an increase in the weight of the magnetic circuit. For a \(400\) MeV synchrotron the outer diameter of the electromagnet is \(2.54\) m as against \(2.85\) m; the weight of the magnetic circuit is \(14.8\) t as against \(17.3\) t, i.e., \(15\%\) less.

The disadvantage of the proposed electromagnet variant lies in the presence of a special additional supply circuit for the additional winding. However, this circuit has a small power in comparison with the supply circuit of the main winding. For a \(400\) MeV synchrotron with preliminary induction acceleration up to \(5\) MeV, the reactive energy consumed by the additional winding is \(1.42\) kJ as against \(104\) kJ,

consumed by the main winding, i.e., less than \(1.5U_0\). In addition, the supply circuit of the additional winding makes it possible to carry out smooth regulation of the radius of the betatron orbit by regulating the voltage, and therefore there is no need for a special regulation circuit.

Second variant (Fig. 3).

The main magnetic circuit has a C-shaped cross section, with the gap outward, without cuts. On the outside of the main magnetic circuit, along its periphery, U-shaped attached additional cores are installed.

Fig. 3. Electromagnet of a 400 MeV synchrotron with external attached cores.

The main winding, as in the first variant, is annular. In addition to it there is an additional winding, located on the attached cores.

The distribution of magnetic fluxes over the cross section during the period of induction acceleration and during synchrotron acceleration is the same here as in the first variant. However, the required distribution of magnetic fluxes during induction acceleration is achieved here in a somewhat different way.

During induction acceleration the main and additional windings are fed from a common additional circuit. A parallel connection of the windings is recommended, since in this case the ratio of the rates of change of the magnetic fluxes remains unchanged throughout the entire period of induction acceleration, despite changes in the magnetic resistances of individual sections of the magnetic circuit.

With a definite ratio of the numbers of turns of the main and betatron windings, a magnetic flux distributed in the required manner is excited in the magnetic circuit. This ratio of the numbers of turns is determined by the betatron condition. The shape of the voltage (current) pulse feeding the electromagnet windings is arbitrary. The amplitude of the current pulse from the additional circuit is determined by the energy of the preliminary induction acceleration.

At the end of induction acceleration the main winding of the electromagnet is switched over to the main supply circuit, a controlling magnetic field of large amplitude is excited, and synchrotron acceleration is carried out. The ratio between the rates of growth of the magnetic field during induction and synchrotron acceleration is arbitrary (established on techno-economic grounds).

In the variant of the electromagnet under consideration, the main and additional supply circuits are interconnected in voltage. Therefore these circuits must be designed with this circumstance taken into account. The variant considered is suitable only in the case of pulsed operation of the synchro-

...trons. In Fig. 4 we give two possible circuits for feeding the electromagnet during preliminary induction acceleration. In these circuits the decoupling of the circuits with respect to pulsed voltages is accomplished by means of valves.

When the synchrotron operates with the first circuit (Fig. 4), its poles are biased by a direct current, so that a positive static component of the guiding field is produced. The value of this component of the field

Fig. 4. Additional power-supply circuits for an electromagnet with a nonsaturating auxiliary core.

in the orbit corresponds to the energy of the preliminary induction acceleration. The circuit excites a negative half-sinusoidal pulse of the magnetic field. Induction acceleration is carried out on the trailing edge of this pulse. After the end of induction acceleration the electrons circulate in a constant magnetic field. Then the main winding is connected to the main power-supply circuit and synchrotron acceleration takes place. Controlled valve 1 serves for current commutation; valves 2 and 3 serve for decoupling the circuits with respect to pulsed voltages.

The second circuit (Fig. 4) differs from the first by the absence of biasing and by the opposite polarity of the auxiliary power-supply circuit. This circuit excites a positive half-sinusoidal pulse of the magnetic field. Induction acceleration takes place on the leading edge of this pulse. The amplitude of the pulse is determined by the energy of the preliminary acceleration. Synchrotron acceleration begins at the “crest” of this pulse.

In the variant under consideration the total cross section of the add-on cores is determined only by the energy of the preliminary induction acceleration.

The advantages of the second variant of the electromagnet in comparison with the first variant are:

1. Good access to the inter-pole space. In practical cases the add-on cores occupy a small fraction of the outer circumference of the electromagnet. This is explained by the fact that the second variant is equivalent to the first if, in the latter, the additional magnetic flux is excited not by half-sinusoidal but by sawtooth current pulses. The cross section of the add-on cores in the second variant is four times smaller than the minimum cross section of the outer yoke in the first variant. For a 400 MeV synchrotron with preliminary induction acceleration up to 5 MeV, the add-on cores amount, by weight, to 9.5% of ...

of the weight of the magnetic core ($1.63\ t$); with a radial dimension of $5\ \mathrm{cm}$ all the cores occupy $23\%$ of the outer circumference.

1. There is no section cut in the main magnetic core.

2. The power of the auxiliary power-supply circuit is reduced by a factor of 16.

Third variant (Fig. 5).
The electromagnet has straight sections. The cross-section of the magnetic core is C-shaped, with the gap on the outside.

Induction acceleration is carried out with the aid of an additional closed core placed on one of the straight sections. The core embraces the accelerating chamber and, for the period of induction acceleration, is excited by a triangular current pulse.

Fig. 5. Synchrotron electromagnet for $400\ \mathrm{MeV}$ with an induction accelerating gap.

The steepness of the leading edge of the pulse is determined by the rate of rise of the magnetic field on the orbit and by the betatron relation. The amplitude of the current pulse is determined by the energy of induction acceleration.

The dimensions and weight of the closed core are determined by the energy of induction acceleration and are comparatively small. For a $400\ \mathrm{MeV}$ synchrotron, with induction acceleration up to $5\ \mathrm{MeV}$, the weight of the closed core is $0.31\ t$, or $1.8\%$ of the weight of the magnetic core; the reactive energy required to excite the core is about $30\ \mathrm{J}$.

Figure 5 gives a possible power-supply circuit for the additional closed core. The principal feature of this circuit is the presence of a modulator tube. The core is biased by direct current. The advantages of the first and second variants of the electromagnet are here enhanced.

All the variants of the electromagnet presented have been calculated. The auxiliary power-supply circuits for the electromagnet shown may be implemented using thyratrons, ignitrons, gasotrons, and domestically produced modulator tubes.

We have presented the principal variants of a synchrotron with preliminary induction acceleration without a saturating core; other variants are also possible.