On Reducing the Acceleration Time of Electrons in a 1500 MeV Synchrotron

V. V. IVASHIN, G. P. FOMENKO

In electron cyclic accelerators, at high energies of the accelerated electrons, the main part of the power of the accelerating system is expended on compensating radiation losses. The quantum nature of the radiation leads to the buildup of phase and betatron oscillations and to the loss of a fraction of the accelerated electrons. To reduce electron losses and the power of the accelerating system, the rate of rise of the magnetic field at the end of the acceleration cycle can be increased. In the present work, one variant of increasing the rate of rise of the magnetic field at the end of the cycle in the “Sirius” accelerator to 1.5 GeV is considered, and the loss of electrons due to excitation of phase oscillations by quantum fluctuations of the radiation is calculated.

Excitation Scheme of the Guide Field of an Accelerator with a Reduced Acceleration Time

The magnetic field of the electromagnet of the “Sirius” accelerator at 1.5 GeV is produced by discharging, through switching devices (TIRATRONs TR1-85/15), a powerful capacitor bank \(C_1\) into the excitation winding of the electromagnet \(L_1\) [1]. In this case the magnetic field has, in time, the form of a sinusoidal curve, and acceleration to 1.5 GeV must take place in \(37.3 \cdot 10^{-3}\) sec, which corresponds to an angle of \(80^\circ\) on the half-cycle of the electromagnet excitation curve. Calculations show that during the last 0.3 of the acceleration time the energy of the electrons increases by only 16%. During this same part of the acceleration time the intensity of the beam of accelerated particles decreases by 80% at a final value of the accelerating field of 180 kV.

Fig. 1

Figure 1 shows a circuit that makes it possible to substantially reduce the acceleration time at high electron energies.

The main storage capacitance \(C_1\) is discharged into the electromagnet \(L_1\) through the thyratrons \(T_1\). For the current and voltage in the circuit one may write:

\[ i_1=-\frac{U_{C1}e^{-bt}}{\omega L_1}\sin \omega t, \tag{1} \]

\[ u_{C1}=\frac{U_{C1}\cdot e^{-bt}}{\omega\sqrt{L_1C_1}}\sin(\omega t+\psi_0), \tag{2} \]

where \(\omega\) is the angular frequency of the circuit \(C_1L_1\), taking damping into account,

\[ \psi_0=\operatorname{arctg}\frac{\omega}{b}, \qquad b=\frac{r}{2L_1}. \]

At an angle of approximately \(60^\circ\), the thyratron \(T_2\) is opened by the control circuit, and the current is rapidly, under the action of the voltage \(u_{C2}\), transferred from \(T_1\) to \(T_2\). The introduction into the \(L_1C_1\) circuit of the previously charged capacitance \(C_2\), whose voltage is concordant in direction with the voltage \(U^{*}_{C1}\), increases the rate of rise of the current (and field) in the electromagnet \(L_1\).

The current in the inductance \(L_1\) after the capacitance \(C_2\) is introduced into the circuit is described by the equation

\[ i_1=I_k e^{-bt}\left(\cos \omega_2 t-\frac{b}{\omega_2}\sin \omega_2 t\right) -\frac{U_{C1}+U_{C2}}{\omega_2L_1}e^{-bt}\sin \omega_2 t, \tag{3} \]

where

\[ I_k,\ U^{*}_{C1},\ U_{C2} \]

are the current in the circuit and the voltages on the capacitances \(C_1\) and \(C_2\) at the end of the transfer of current from valve \(T_1\) to \(T_2\).

Taking into account that the damping has little effect on the current \(i_1\), since the quality factor of accelerator power-supply systems is comparatively high, one may set \(b=0\) and somewhat simplify the expression for the current:

\[ i_1=I_k\cos \omega_2 t-\frac{U_{C1}+U_{C2}}{\omega_2L_1}\sin \omega_2 t, \tag{4} \]

where

\[ \omega_2 \simeq \sqrt{\frac{C_1+C_2}{C_1C_2L_1}} \]

is the angular frequency of oscillations of the resulting circuit \(L_1C_1C_2\).

After the sign of the voltage on the capacitance \(C_2\) changes, or even after it is recharged to the voltage value \(-U_{C2}\), the thyratron \(T_1\) may again be opened and may intercept the current of valve \(T_2\). Thus, after the particles have been accelerated, the circuit \(L_1C_1\) is restored again, and the energy from the electromagnet on the falling part of the sinusoidal current curve passes into the storage capacitance \(C_1\). It should be noted that if valve \(T_1\) is opened when the sign of the voltage on the capacitance \(C_2\) changes, when the absolute value of the voltage is small, an additionally introduced energy

\[ \frac{1}{2}C_2U_{C2}^{2} \]

is present in the electromagnet.

Calculations by formulas (1) and (4) show that, with an entirely acceptable value of the capacitor bank \(C_2\), equal to approximately 0.1 of the value of the main bank \(C_1\), the nominal energy of 150 MeV can be reached not at an angle of \(80^\circ\), but at an angle of \(70^\circ\) of the frequency \(\omega\). The acceleration time is thereby reduced by \(5\cdot10^{-3}\) sec, and the introduction of the capacitance \(C_2\) into the circuit must be carried out at an angle of \(60^\circ\).

The acceleration time corresponding to angles of \(60\text{--}80^\circ\), when the main electron losses occur, is thus reduced by approximately a factor of two.

Figure 2 gives the excitation-current curves of the electromagnet, which can be constructed from formulas (1) and (4).

Fig. 2.

Curve 1 corresponds to the change in the excitation current of the electromagnet without increasing the rate of rise of the field, while curve 2 corresponds to an increase in the rate of rise of the field in the region of angles \(60\text{--}70^\circ\) of the frequency \(\omega\). The fraction of lost particles was calculated by Kramer’s formula [2]. In calculating the rms amplitude of the phase oscillations excited by quantum fluctuations of the radiation, it was assumed that the amplitude of the accelerating voltage changes during the cycle according to the law shown in Fig. 3.

The jump in the rate of rise of the amplitude of the high-frequency field occurs at the moment when the rate of rise of the magnetic field changes. In the first half of the cycle the accelerating voltage will not vary as shown in Fig. 3; however, since during this time quantum fluctuations of the radiation do not affect the electron losses, the actual fraction of lost electrons will differ only slightly from the calculated one.

Figure 4 shows the change in the number of particles over the acceleration cycle, in relative units, for final values of the amplitude of the accelerating voltage of 220 kV (curves 1) and 180 kV (curves 2), for the shortened (dashed curves) and full acceleration times. The dependence of the fraction of particles remaining in the chamber by the end of acceleration on the magnitude of the amplitude of the high-frequency field is shown in Fig. 5. Curve 1 shows the dependence of the fraction of particles remaining in the chamber for the full acceleration time, and curve 2 for the shortened acceleration time.

Fig. 3

Fig. 4

Fig. 5

It follows from Fig. 5 that, at a final accelerating voltage of 180 kV, reducing the acceleration time makes it possible for 50% of the particles, out of the total number of accelerated particles, to reach the final energy. Without reducing the acceleration time, only 20% of the particles have this possibility.

At a voltage of 220 kV, correspondingly, 90% of the particles will be accelerated instead of 75%.

Thus, reducing the acceleration time by \(5 \cdot 10^{-3}\) s at the expense of the final part makes it possible either to reduce the accelerating voltage without decreasing the number of accelerated particles, or, at the former voltage, to substantially increase the number of accelerated particles.

References

1. V. M. Kuznetsov. Excitation of the electromagnet of a synchrotron with an energy of accelerated electrons of 1500 MeV. Dissertation, Tomsk, Scientific Research Institute of Nuclear Physics, 1963.

2. H. A. Kramers. Physica 7, 285 (1940).