A cyclotron as a typical spiral orbit charged particle accelerator was invented by Lowlence in 1930, and the cyclotron includes a magnet 11 for generating magnetic field, accelerating electrodes 12 for generating radio-frequency (RF) voltage to accelerate charged particles, and an ion source 13 for creating charged particles as shown in FIG. 1-(A) and (B). The magnet 11 includes north pole 15 and south pole 16. The particles are accelerated on the spiral orbit 14.
The cyclotron is based on the principle that a period (Tp) of a charged particle circulating in a magnetic field is given by Equation (1):Tp=2πm/eB  (1)where π is the ratio of circle's circumference to its diameter, m is mass of moving particle (kg), e is electric charge (C), and B is magnetic flux density on a beam trajectory (tesla).
The mass m is given by the rest mass of m0 and the particle velocity of v(m/s) as follows:m=m0/(1−(v/c)2)1/2  (2)where c is the velocity of light (approximately 3×108 m/s).
The Equation (1) shows that the revolution period of the particle is constant if the value of m/eB is constant on the beam trajectory. This distribution of magnetic field is called an isochronous magnetic field distribution. Particularly, when the velocity v is much smaller than the light velocity c, the revolution period of the particle is constant in the uniform magnetic flux density B. Thus, the period of the accelerating RF voltage should be constant. FIG. 2 is a view of waveform of the RF voltage showing a relation between phases of the particle and the RF voltage in the isochronous magnetic field. In FIG. 2, the horizontal axis is time and the vertical axis is an RF voltage.
A ratio of the particle revolution period (Tp) to the period (Trf) of accelerating RF voltage is called harmonic number N and given by Equation (3).N=Tp/Trf  (3)
In FIG. 2, a case of N=2 is shown.
A kinetic energy E of a particle moving in a magnetic field is given by Equation (4),E=((ecBR)2+m02c4)1/2−m0c2  (4)where R is a radius of a trajectory curvature.
Equation (4) shows that the magnitude of BR has to be increased to increase particle energy. Thus, the magnetic field or the radius must be increased. However, a proton energy accelerated with a moderate size cyclotron is limited about 200 MeV because technical problems are encountered when the BR increases.
In order to solve the problem, a ring cyclotron as shown in FIG. 3 was developed. The ring cyclotron includes several bending magnets 31 located separately from each other and accelerating RF cavities 32 formed between the magnets 31. A low energy particle beam pre-accelerated is injected at an injection point 33 of the ring cyclotron. The injected particles are accelerated by the RF cavities and bent by the bending magnets. As a result, the accelerated particles pass on the spiral orbit 34 and extracted at an extraction point (not shown). The energy at the injection point is the injection energy and that at the extraction point is extraction energy. The radius of the trajectory curvature at the injection point is the injection radius and that at the extraction point is extraction radius. In the ring cyclotron, accelerated energy in one revolution can reaches higher than 1 MeV because the accelerating cavities and the bending magnets are spatially separated (see Non-Patent Document).
The ring cyclotron also requires the isochronous magnetic field distribution. In other wards, the field averaged on the trajectory must satisfy the condition that Tp of Equation (1) is constant. The particle energy E is also given by Equation (4) using the averaged magnetic field B and the averaged radius R. An energy gain G of the ring cyclotron is given by Equation (5),G=extraction energy/injection energy={((ecB2R2)2+m02c4)1/2−m0c2}/{((ecB1R1)2+m02c4)1/2−m0c2}  (5)where B1 and B2 are averaged magnetic flux densities at injection and extraction points, and R1 and R2 are averaged radiuses of injection and extraction points.
Particularly, when the velocity v is much lower than the light velocity c or in a non-relativistic case, Equation (5) is rewritten as follows:G=(B2R2/B1R1)2  (6)
Thus, the ratio of R2 to R1 is larger as the energy gain G is higher. Consequently, the size of magnets becomes larger as the energy gain becomes higher.
Non-Patent Document 1:
    T. Kamei and H. Kihara, “Accelerator Science”, MARUZEN Co. Ltd., Sep. 20, 1993, p. 210–211