From Current Literature

Giant Cyclotron with a Modulated Section (Phasotron)

In the April issue of Physical Review the first report was published[^1] on the work in Berkeley of a giant 184-inch cyclotron and on the first experiments with deuterons of energy 200 MeV and α-particles of energy 400 MeV. The history of this cyclotron is very instructive. It was designed by Lawrence as an accelerator of the usual type, in which the relativistic increase in the mass of the particles is compensated by a corresponding increase of the electric field on the dees. As is known,[^2] the maximum energy attainable in such a cyclotron is proportional to the square of the amplitude of the voltage on the dees. It was therefore proposed, when putting the accelerator into operation, in order to obtain protons of energy 60 MeV and deuterons of 100 MeV, to raise the amplitude on the dees to 1–2 MeV.[^3] Such a value of the electric field naturally required a large gap in the machine, which also increased the gigantic parameters of the machine even without this. Before the war a giant magnet weighing 4000 t[^4] was completely built, and work was begun on equipping the accelerating part. During the war the construction of the cyclotron was suspended, and the magnet was used for isotope separation.[^5]

In 1945 V. I. Veksler, using the principle of “autophasing” discovered by him as early as 1944[^6] (in the American literature this principle is called the “principle of phase stability”), showed that under certain non-rigid conditions ions can be accelerated to high energies by means of a slow adiabatic change of the frequency supplied to the dees. The total required change in frequency is made up of the change in the mass of the particle during acceleration and of the fall-off of the magnetic field toward the edge, which provides vertical focusing of the beam. The rate of change of frequency is determined by solving Veksler’s equations.[^6] On the one hand, the energy acquired on the average per revolution, \(V_{\mathrm{cp}}\), is determined from the following relation:

\[ V_{\mathrm{cp}}=-\pi \frac{d\omega}{dt}\frac{cH(r)}{K\omega^3(t)}, \]

where

\[ K=1+\frac{N}{1-N}\frac{1}{\beta^2}, \qquad \beta=\frac{v}{c}, \qquad N=-\frac{d\lg H}{d\lg r}; \]

\(H\) is the magnetic field at the dees, \(\omega\) is the angular frequency. On the other hand, the intensity of the ion beam depends on \(\alpha=\dfrac{V_{\mathrm{cp}}}{V_0}\), where \(V_0\) is the amplitude

electric field on the dees. It is maximal¹ at $\alpha$ in the neighborhood of 0.5. This imposes definite requirements on the rate of frequency modulation.

In the autumn of 1945 MacMillan⁷ arrived at analogous conclusions. It was decided to convert the 184-inch cyclotron into a phasotron. But first it was necessary to develop technical methods of frequency modulation and to verify the principle of autophasing on a model.

FREQUENCY MODULATION BY A MECHANICAL METHOD

The method of frequency modulation was developed by Schmidt⁸. We shall briefly set forth the content of his work. Modulation can be carried out in two different ways.

A) Electronic methods of modulation

The essence of these methods is that the frequency of the generator is changed without changing the load of the latter. The frequency can be varied over sufficiently wide limits without using any rotating parts, for example by means of a reactance tube. In order that a change in frequency should not cause a considerable decrease of the amplitude at the accelerating electrodes, the system of these electrodes must have a broad resonance curve and, consequently, a low quality factor. This is a disadvantage of the system, for the higher the quality factor of the latter, the greater the voltage amplitude on the dees.

B) Mechanical modulating systems

The essence of these methods is that the parameters of the system of accelerating electrodes (dees), which constitute the load of the generator, are changed. In this case the generator is strongly coupled with the load, which leads to a change in the generator frequency. However, in contrast to the first method, here the frequency at all times coincides with the natural frequency of the system of accelerating electrodes; consequently the latter may have a narrow resonance curve, i.e. a high quality factor. This is the advantage of mechanical methods of frequency modulation over electronic ones.

Both the capacitance and the inductance of the system of accelerating electrodes can be varied. It is more convenient to vary the capacitance. A variable capacitance, as shown by Schmidt, can be connected to the dees in several ways; some of them are shown in Fig. 1.

a) The variable capacitance is connected directly to the dee.
b) The variable capacitance is at the end of a half-wave coaxial line.
c) Two variable capacitances at the ends of two half-wave coaxial lines. Between them is a quarter-wave section for fastening the dee. (The authors used circuit b.)

The impedance of the transmission line is determined by the following equation:

\[ Z = j Z_0 \operatorname{tg} \frac{\omega \cdot l_d}{c}, \tag{1} \]

where $Z_0$ is the characteristic impedance of the line in ohms $\left(Z_0 = 60 \ln \frac{r_2}{r_1},\ r_1 \text{ and } r_2\right.$ are the radii of the inner and outer cylinders), $\omega$ is the angular frequency, $l_d$ is the distance in cm from the voltage node to the given point, $c$ is the velocity, $j = \sqrt{-1}$ is the imaginary unit.

The resonance conditions require that the sum of the inductive and capacitive impedances be equal to zero. The capacitive impedance in case a is equal to

\[ Z_d=-\frac{j}{\omega(C_d+C_v)}, \]

where \(C_d\) is the capacitance of the duants in farads, and \(C_v\) is the variable capacitance.

Fig. 1. Circuits for connecting a variable capacitor into the duant circuit.

Consequently, from the condition \(Z+Z_d=0\) we obtain:

\[ \frac{1}{\omega(C_d+C_v)}=Z_0 \operatorname{tg}\frac{\omega\cdot l_d}{c}, \tag{2} \]

or, taking \(\frac{\omega\cdot l_d}{c}\ll 1\), which is valid for most practical cases in a cyclotron, we obtain, replacing the tangent by its argument:

\[ \omega=\sqrt{\frac{c}{Z_0 l_d(C_d+C_v)}}. \tag{3} \]

In case b, equality (2) must be replaced by the following two relations:

\[ \frac{1}{\omega C_d}=Z_0 \operatorname{tg}\frac{\omega\cdot l_d}{c} \quad \text{and} \quad \frac{1}{\omega C_v}=Z_0 \operatorname{tg}\frac{\omega l_v}{c}, \tag{4} \]

where \(l_v\) is the distance from the variable capacitor to the voltage node along the transmission line, \(l=l_v+l_d\) is the total length of the transmission line. With the aid of (4) we easily find that

\[ C_v=\frac{1}{Z_0\omega\, \operatorname{tg}\left\{\frac{\omega l}{c}-\operatorname{arctg}\frac{1}{Z_0\omega l_d}\right\}}. \tag{5} \]

In Fig. 2, \(C_v\) is shown as a function of the frequency \(f=\frac{\omega}{2\pi}\) for both cases a and b [case a corresponds to formula (3), case b to formula (5)]. From this figure it is evident that the change in frequency corresponding to a given change in capacitance is greater the smaller this capacitance is. Consequently, from this point of view it is advantageous to take the capacitor \(C_v\) with as small a capacitance as possible (preferably so that \(C_v<C_d\)).

However, it turns out that the voltage arising across the variable capacitor can approximately be expressed by the following formula:

\[ V_v = V_d \frac{C_d}{C_v}, \tag{6} \]

where \(V_d\) is the voltage on the dees. \(V_v\) must not be very large for reasons connected with insulation. Thus, from this point of view, contrary to the preceding consideration, it is desirable that \(C_v\) be greater than \(C_d\).

Fig. 2. Dependence of the frequency on the capacitance of the variable capacitor. The upper curve is for the case in which the capacitor is connected at the end of a half-wave line. The lower curve is for the case of direct connection to the dees.

As a compromise Schmidt chose \(C_{v\max}=C_d\), i.e. the maximum voltage across the capacitor is equal to the voltage on the dees. With the aid of (5) it can be shown that in this case the node is located at the midpoint of the line \((l_v=l_d\) when \(C_v=C_d)\).

From Fig. 2 it is easy to see that a capacitor connected directly to the dee acts more effectively. In addition, \(V_v=V_d\) at all times. However, a capacitor placed at the end of a half-wave line has the advantage that it can be placed in a separate vacuum system. In addition, it will be located outside the magnetic field.

The method of switching on \(c\), as a simple calculation shows, is less advantageous than case \(b\). For example, in order to change the frequency by 15%, it is necessary: for system \(a\),

\[ \frac{C_{v\max}}{C_{v\min}} = 1.64, \]

for system \(b\),

\[ \frac{C_{v\max}}{C_{v\min}} = 1.96, \]

and for system \(c\),

\[ \frac{C_{v\max}}{C_{v\min}} = 2.32. \]

Formulas (4) and (5), as Schmidt points out, are not exact, since they assume that the capacitance of the duants is concentrated; therefore, for an exact determination of the dependence of the frequency on \(C_v\) on models, one can directly

Fig. 3. Photograph of the rotor and stator.

measure the value \(l_v\) as a function of \(C_v\), instead of determining \(l_v\) mathematically by means of the second equation (4). Then the second equation (4) will give the frequency value exactly as a function of \(C_v\) and \(l_v\). Below is given a brief description of the variable capacitor used for the 37-inch cyclotron.

The capacitor consists of a movable disk rotating between two fixed ones. Each disk has blades around its circumference. When the blades of the rotating disk are opposite the blades of the fixed one, the capacitance between them is greatest. The fixed disks are connected to each other and

form one plate of the capacitor; the disk rotating between them is the other plate; by changing the shape of the blades, one can change the dependence of the capacitance, and hence also of the frequency, on time.

The capacitor described has 36 blades around the circumference. For strength, the entire rotor together with the blades is made from a single piece of steel.

Each blade has the shape of a rectangle, whose length is \(3 \tfrac{1}{2}\) inches and width \( \tfrac{3}{4}\) inch. The effective length (i.e., the length of the stator covered by the blades) is 2 inches.

Fig. 4. Capacitor diagram:
\(A\) — rotor; \(B\) — rotor blades; \(C\) — zirconium-porcelain insulator; \(D\) — connecting capacitor; \(E\) — stator ring; \(F\) — stator blades; \(G\) — adjustable stator ring; \(H\) — insulators holding the stator ring; \(I\) — supporting insulating plate; \(J\) — front wall; \(K\) — axle and bearings; \(L\) — “Chevron” vacuum seal; \(M\) — oil-level indicator; \(N\) — drive pulley; \(O\) — shaft of the coupling line; \(P\) — full zirconium-porcelain insulator; \(Q\) — copper strips; \(R\) — vacuum box; \(S\) — axle and insulator for adjusting the stator ring.

It is easy to see that if the rotor blade is rectangular, then the derivative of the curve representing the dependence of capacitance on time is the required shape of the edge of the stator blade, for the capacitance is a linear function of the area of the rotor blades overlapped by the stator blades.

The diameter of the rotor to the end of the blades is 27 inches. It can make up to 3200 revolutions per minute. The thickness of the rotor at the center is 1 inch and decreases to \( \tfrac{1}{8}\) inch at the edge of the blades.

The rotor is mounted on a porcelain insulator, which is a disk 6 inches in diameter and 1 inch thick. This disk prevents leakage of high-frequency current to the shaft and bearings. The high-frequency current is led to ground through a coupling capacitor, one plate of which is the surface of the rotor disk. The other plate, connected to ground, is a special stationary disk without vanes, placed next to the rotor.

The coupling capacitance is 10 times greater than the capacitance of all the plates.

The outside diameter of the stator is 33 inches. The stator disks are fastened to insulators made of disk-shaped porcelain. One of them can be turned through a small angle. In this way the frequency-variable characteristic is adjusted. The stator is connected to the inner conductor of the coaxial line by copper strips.

The entire system is in a vacuum and is driven by a motor at \(1/3\) h.p. The rotating pulley is located outside the vacuum. Despite the fact that the capacitor shaft passes through the wall of the chamber, a vacuum of \(5 \cdot 10^{-5}\) mm is maintained inside the latter for many hours of operation. This was achieved by the use of special bearings and seals.

At a voltage of 15 kV, a current of the order of 175–200 A passed through the capacitor. No strong heating of the disks occurred, despite the absence of water cooling.

Fig. 5. Dependence of capacitance and frequency on time.

In the figure: capacitance in \(\mu\mu\mathrm{F}\); frequency in megacycles; time; \(C_v\); frequency.

The obtained dependence of frequency on time is shown in Fig. 5. This figure also gives the dependence of capacitance on time. Both curves were taken with a distance between rotor and stator of 0.04 inch. The measurements were carried out statically. The main results are summarized in the table.

In the first case, at 6000 revolutions per minute the frequency changed by 13% in 162 microsec, and in the second in 106 microsec. A speed of 3200 revolutions per minute was reached, which corresponds to 1900 modulation cycles per second. In this regime the capacitor could operate continuously for several hours.

MODELING OF THE PHASOTRON ON A 37-INCH CYCLOTRON

To test the principle of “autophasing,” the 37-inch cyclotron at Berkeley was chosen. Since the strength of the magnetic field did not permit deuterons with energy greater than 7 MeV to be obtained and, consequently, the mass of the particles practically did not change, it was decided, by means of shimming, to reduce the field toward the edge of the magnet by 1.3%, thereby artificially creating the conditions arising in the large 184-inch cyclotron. Indeed, at 200 MeV for a deuteron

\[ \frac{\Delta m}{m_0}=10.7\%. \]

2.3% remained for the possible decrease of the magnetic field toward the edge of the magnet in the large machine. Without frequency modulation on such a “spoiled” cyclotron it was possible to obtain only 0.5 MeV (according to Rose’s theory²).

With the aid of frequency modulation by the method described in the preceding section, 600 cycles per second and 3 kV on the single dee, an average ion current of 0.2 μA with deuteron energy of 7 MeV was obtained. The acceleration time was 500 microsec, which corresponds to 5000 deuteron revolutions. The capacitor rotated at a speed of 1000 revolutions per minute. In Fig. 6 the current in microamperes is shown as a function of the modulation frequency. The solid curve was calculated theoretically; the circles are experimental values.

Fig. 6. Beam current of ions at a radius of 17 inches in the 37-inch cyclotron, as a function of modulation speed.

In the absence of modulation, at a radius of 2.5 inches the current intensity was 22 μA. This shows that the efficiency of phasotron capture for the outgoing accelerated particles, as compared with the cyclotron, is 1%, in agreement with theory. In Fig. 7 the current is shown as a function of radius.

Attention was drawn to the fact that 1) the intensity increases by a factor of 10 in going from a voltage of 2 kV to 3 kV, whereas theory predicts an increase by

\[ \sqrt{\frac{3}{2}} \]

times; 2) the intensity increases by a factor of 10 if the dee system is not grounded but is at a constant potential of 1500 V.

The authors believe that this circumstance is connected with an increase in the efficiency of the ion source. The constant field serves as a cleaner of residual ions. In the absence of such a field, residual ionization at small voltages loads the oscillator as much as one hundred times more than the growth of the potential difference on the dee would. In the large machine, for this reason, it was decided to surround the dee with grounded shielding in order to reduce the volume accessible to arc discharge.

The energy amplitude was checked by inducing radioactivity in copper with a half-life of 12.8 hours. Simultaneously with the determination of the current, mea-

the radiation from the cyclotron was measured in an ionization chamber placed in 6 feet of lead from the machine. The radiation from the cyclotron was strictly proportional to the average current.

Fig. 7. Ion-beam current as a function of radius
in the 37-inch cyclotron.

The success of these experiments, as indicated in the work being reported, led to the decision to rebuild the 184-inch cyclotron as a phasotron. At present the 37-inch cyclotron operates on the phasotron principle and is used to obtain protons with an energy of 15 MeV¹.

FIRST REPORT ON THE OPERATION OF THE 184-INCH CYCLOTRON

The cyclotron first began operating in November 1946¹⁰.
Its principal data are as follows:

The magnetic field of the cyclotron fell from the center to the edge almost linearly and, at a radius of 80 inches, amounted to 95.4% of the field at the center. The appropriate form of the field was achieved with the aid of shims placed inside the vacuum chamber. The dimensions of the shims were determined empirically, by measurements on a scale model. To accelerate deuterons up to 200 MeV it was necessary to change the frequency by \(1 \pm 5\% = 16\%\). In practice it proved desirable to carry out a considerably larger change of frequency, in order to make it possible to obtain, with certainty, in the 16% region, a satisfactory form of the frequency–time curve.

Frequency modulation was carried out by a mechanically rotating vacuum capacitor similar in principle to that described above. The frequency modulation reached 2000 cycles per second. The single dees and the capacitor are mounted, as before, at one end of a shielded line forming a resonant system, whose frequency varies between 12.6 and 9 megacycles. The system is excited by a self-excited generator, with a grounded grid, inductively coupled to the resonant circuit. The input power is 18 kW (instead of 250 kW in Lawrence’s original design⁴). The voltage amplitude on the dees (averaged over the modulation cycle) was 15 kV. At the center the magnetic field has an intensity of 15,000 gauss. The magnetic gap is 19 inches, of which 5 inches are available for ions. Under ordinary operating conditions the modulation frequency was 120 cycles per second. But already at 8 kV on the dees and at the corresponding most favorable modulation rate of 48 cycles per second—

duum (which corresponded to 120 revolutions of the capacitor per minute), satisfactory results were obtained.

The target was placed at a radius of 80 inches. Under normal operating conditions the ion, spending 1000 microsec. on the path from the injector to the target, makes approximately 10,000 revolutions. At a radius of 20 inches, an average current of 0.6 μA was measured with the aid of a probe target. This current remains constant up to a radius of 42 inches, which corresponds to 52 MeV. From this point the measured current rapidly decreases; at a radius of 81 inches it is barely measurable (\(\sim 2 \cdot 10^{-10}\) A) and becomes zero at about 82 inches. During the decrease of the current in the probe target, the neutron radiation increases and falls sharply to zero in the vicinity of 82 inches. The authors believe that this decrease of the current is apparent and is explained by the penetration of the beam through the probe target, which tapers toward the end.

Fig. 8. Photograph of the 184-inch cyclotron during construction.

Direct measurement of the neutron radiation and of the radioactivity of the duantum and the probe target shows that at 82 inches the beam is lost because of vertical scattering. Up to the present time all measurements have agreed exactly with theory.

In the near future, as the authors indicate, it is not intended to make attempts to increase the ion current and to extract the beam from the magnetic field.

Experiments have been carried out with the acceleration of \(\alpha\)-particles to an energy of 400 MeV. The yield of the ion current is of approximately the same order as that of deuterons. But as yet too few experiments have been made with \(\alpha\)-particles to permit a comparison with theory.

Measurements of the neutron radiation emitted from the target, both by means of ionization chambers and with the use of a radioactive detector sensitive to fast neutrons, show that most of the radiation is emitted forward in a cone with an angle of \(11^\circ\). The cone is defined so that on its surface the intensity decreases by a factor of 2.

Fission of nuclei under neutron and deuteron bombardment is observed by means of radiochemical studies and by measuring numerous “stars” in a Wilson chamber and in a photographic emulsion. A preliminary estimate of the neutron energy by measuring the tracks of recoil protons in a Wilson chamber with a magnetic field of 10,000 gauss indicates that the neutron energy distribution extends approximately to 100 MeV.

The authors report that these and other experiments will be published as they are completed.

In conclusion, we present a table characterizing the advantage of the frequency-modulation method.

M. Rabinovich

REFERENCES

1. W. M. Brobeck, E. O. Lawrence, Phys. Rev. 71, 449 (1947).
2. M. E. Rose, Phys. Rev. 53, 392 (1938).
3. W. B. Mann, The Cyclotron, 2nd ed. (1944).
4. P. Morrison, J. of Appl. Phys. 11, 339, 1940, UFN XXIV, 529 (1940).
5. Smyth, Atomic Energy for Military Purposes, Gostransizdat, Moscow (1946).
6. V. I. Veksler, J. of Phys. 9, 153 (1945).
7. E. M. McMillan, Phys. Rev. 68, 143 (1945).
8. F. H. Schmidt, Rev. Sci. Instr. 17, 301 (1946).
9. J. R. Richardson et al., Phys. Rev. 69, 669 (1946).
10. Philip Morrison, J. of Appl. Phys. 18, 133 (1947).