JPH09115699A - Circular accelerator and beam radiating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To stably produce a small diameter beam and make an accelerator small by installing tow sextapole electromagnetics in 180 deg. rotationally symmetric positions of an encircling orbit, and selecting the resonance point of betatron vibration in 5/3. SOLUTION: A beam incident from the outside with an incident device 9 rotates a vacuum duct 10 after the orbit is bent with a deflection electromagnet 1. A high frequency accelerating cavity 4 gives energy to the orbiting beam, a high frequency electric field applying electrode 7 amplifies the betatron vibration amplitude of the beam, a proton whose amplitude is increased is radiated as a proton beam with a radiating deflector 8. Quadrupole electromagnets 2, 3 adjust the tune of the beam. Sextupole electromagnetic 5, 6 are installed in 180 deg. rotationally symmetric positions each other along the encircling orbit, and the resonance point of betatron vibration is selected in 5/3. Sextupole electromagnetic power sources 12, 13 supply current to the sextupole electromagnets 5, 6 respectively, and excite so that the phase difference of the betatron vibration in the radiation deflector 8 becomes the prescribed relation.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a circular accelerator in which charged particles are circulated and emitted to obtain a beam, and more particularly to a circular accelerator which excites resonance in betatron oscillation of charged particles to extract a beam.

[0002]

2. Description of the Related Art Charged particles in a beam have different tunes depending on the momentum. The momentum dependence of the tune of this charged particle is called chromaticity. Since the size of the stability limit depends on the deviation of the tune from the resonance point, that is, the charged particle has a stability limit that differs depending on the momentum.

However, there are charged particles that are lost during resonance excitation of the emission due to the small stability limit, and charged particles that remain in the accelerator due to the large stability limit. The output efficiency is poor, and
The quality of the emitted beam changed with time. In order to solve this problem, the chromaticity may be corrected to 0 so that the charged particles have the same stability limit regardless of the momentum.

A conventional circular accelerator for extracting a beam by utilizing the third resonance is provided with a pair of sextupole electromagnets for chromaticity correction and a pair of sextupole electromagnets for resonance excitation.

Two hexapole electromagnets for resonance excitation are rotationally symmetric and have a phase difference of betatron oscillation of nπ / 3 (n
Is an odd number) and they are excited in the same strength in opposite directions. The two hexapole electromagnets for resonance excitation are
Excitation of the third resonance without changing the chromaticity.

The two sextupole electromagnets for chromaticity correction are similarly rotationally symmetric, and are arranged at positions where the phase difference of betatron vibration is nπ / 3 (n is an odd number), but both of them are arranged. It is excited by the same strength in the same direction. The two sextupole electromagnets for chromaticity correction have no resonance component and correct chromaticity to zero.

These two pairs of sextupole electromagnets having independent roles correct the chromaticity to 0 so that charged particles have the same stability limit regardless of momentum.
The beam was extracted by the next resonance.

[0008]

However, in the above-mentioned conventional circular accelerator, since at least four hexapole electromagnets for chromaticity correction and resonance excitation are used, a wide installation place is required.

Further, even if each charged particle has the same stability limit, the trajectory of the emitted charged particle on the phase space is different, so that the emitted beam has a large diameter.

An object of the present invention is that the emission efficiency is good, and
It is to provide a circular accelerator having a small outgoing beam diameter.

[0011]

In order to achieve the above object, in the circular accelerator according to claim 1, the phase difference of the betatron oscillation is nπ / 3 (n is an odd number), and the phase difference between the deflector and the outgoing deflector is set. When the phase difference φ of the betatron oscillation is s, the coordinate in the beam traveling direction along the design trajectory is s, the betatron function at the exit deflector position is β, the dispersion function is η, and the derivative of the dispersion function is η ′. ,

[0012]

(Equation 2)

Two hexapoles arranged at positions satisfying (where, θ = (4m ± 1) π / 6, m is an integer satisfying (φ−π / 2) <θ <(φ + π / 2)) The electromagnet excites a magnetic field by supplying a current, and the control device controls the strengths of the magnetic fields excited by the two sextupole electromagnets to different values.

In the circular accelerator according to claim 2, the two hexapole electromagnets according to claim 1 are arranged at positions which are rotationally symmetrical.

In the circular accelerator according to the third aspect, the two hexapole electromagnets according to the second aspect are arranged at positions which are mirror symmetrical.

In the beam emission method of claim 4,
The center of the stability limit of the first charged particles in the beam in the phase space at the exit deflector position when the beam is emitted with the betatron oscillation in the nth resonance state;
A second momentum having a momentum different from the momentum of the first charged particle
The slope of the straight line connecting the center of the stability limit of the charged particle of
It is equal to the inclination of the trajectory drawn by the second charged particle in the phase space every n revolutions.

According to the circular accelerator of claim 1 of the present invention,
The two hexapole electromagnets have a betatron vibration phase difference of nπ /
Since the position is 3 (n is an odd number), the direction of the stability limit is constant regardless of the magnetic field strength of the two sextupole electromagnets, and the two sextupole electromagnets are the control devices. By controlling the strength of the magnetic field to different values, the chromaticity becomes 0, so that all charged particles have the same stability limit regardless of momentum, and the extraction efficiency is good. A stable beam can be obtained. Also,
In the two hexapole electromagnets, the phase difference φ of the betatron vibration with the deflector for emission is the coordinate of the beam traveling direction along the design trajectory as s, and the betatron function at the deflector for emission is β _x , the dispersion Let η _{x be} the function and η _x ′ be the derivative of the dispersion function, then

[0018]

(Equation 3)

(Where θ = (4m ± 1) π / 6, and m is an integer satisfying (φ−π / 2) <θ <(φ + π / 2)), all charges are charged. The exit trajectories of the particles overlap, and an exit beam with a small diameter is obtained. Further, since the control device controls the strength of the magnetic field excited by the two sextupole electromagnets to different values, resonance excitation and correction of chromaticity can be performed by the two sextupole electromagnets. Therefore, since the number of sextupole magnets can be reduced, the circular accelerator can be downsized.

According to the circular accelerator of claim 2 of the present invention,
Since the two hexapole electromagnets are arranged in the arrangement of claim 1 and in positions which are rotationally symmetrical, the same operation as that of the circular accelerator of claim 1 is obtained, and the betatron of the beam in the rotationally symmetrical position is obtained. The vibration parameters are the same, the chromaticity depends on the sum of the magnetic field strengths excited by the two sextupole magnets, and the size of the stability limit is the difference in the magnetic field strengths excited by the two sextupole magnets. Since the correction of the chromaticity and the size of the stability limit need only be controlled by controlling the strength of the magnetic field excited by the two hexapole electromagnets, the control is easy.

According to the circular accelerator of claim 3 of the present invention,
Since the two sextupole electromagnets are arranged in the arrangement of claim 1 and at positions that are mirror-symmetrical, the same operation as the circular accelerator of claim 2 can be obtained.

According to the fourth aspect of the present invention, the first charged particles in the beam in the phase space at the extraction deflector position when the beam is emitted with the betatron oscillation in the nth resonance state. Of the stability limit of the first charged particle and the center of the stability limit of the second charged particle having a momentum different from the momentum of the first charged particle, the slope of the straight line is Since the inclination of the locus drawn in the phase space is equal, the first charged particle and the second charged particle
The distance that the charged particles cross the electrode of the output deflector in the phase space is short, and the diameter of the output beam is small.

[0023]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows a circular accelerator according to this embodiment.

The circular accelerator of this embodiment emits a proton beam by utilizing the third resonance in which the resonance point of betatron oscillation is selected to be 5/3.

The circular accelerator of this embodiment comprises an injector 9 for injecting a beam into the circular accelerator from the outside, a vacuum duct 10 around which the beam circulates, a deflecting electromagnet 1 for bending the beam orbit.
Quadrupole electromagnets 2,3 for adjusting the tune of the beam 2, High-frequency accelerating cavity for energizing the incident beam 4, Six-pole electromagnets 5,6 for correcting the chromaticity and exciting the third resonance, and betatron oscillation of the beam High-frequency electric field applying electrode 7 for increasing the amplitude, betatron oscillation Deflection 8 for emitting protons with increased amplitude as a beam, Hexapole electromagnets 5, 6 for supplying electric current to the hexapole electromagnets 12, 13, 6 The control device 11 is configured to control the strength of the magnetic field generated by the sextupole electromagnets 5 and 6 by changing the currents supplied by the pole electromagnet power supplies 12 and 13.

In the present embodiment, the deflection electromagnet 1 and the quadrupole electromagnets 2 and 3, which are the main electromagnets, are arranged at 90-degree rotational symmetric positions along the vacuum duct 10 around which the beam circulates. Therefore, the circular accelerator of this embodiment has 90
The parameter having the rotational symmetry of degree and the property of the orbiting beam such as the betatron function β and the dispersion function η is 90
It is the same value every degree.

The two hexapole electromagnets 5 and 6 are arranged as follows.

The sextupole electromagnet 5 is arranged at a position where the phase difference φ ₅ (= φ) of the betatron vibration with the deflector 8 for emission satisfies Expression 1.

[0029]

(Equation 4)

Here, θ = (4m ± 1) π / 6, and m is an integer satisfying (φ−π / 2) <θ <(φ + π / 2). Where β _x is the betatron function at the exit deflector position, η _x is the dispersion function at the exit deflector position, and η _x ′ is the derivative of the dispersion function η _x with respect to the beam traveling direction s (η _x ′ = dη _x / ds) and these values are
It is a value determined by the arrangement of each electromagnet and the magnetic field, and can be calculated in advance.

The other sextupole electromagnet 6 is the sextupole electromagnet 5.
And 180 ° rotationally symmetrical position. Since the angle difference with the sextupole electromagnet 5 is 180 degrees, the phase difference φ of the betatron vibration between the sextupole electromagnet 6 and the deflector 8 for emission is φ.
Formula 1 is also satisfied for ₆ (= φ ₅ ± π).

Formula 1 will be described with reference to FIG. Figure 2 shows the proton stability limits A and A'in the phase space.
And trajectories (hereinafter referred to as exit trajectories) Q and Q'followed by protons exceeding the stability limit are shown.

Based on the design trajectory, the horizontal axis is the horizontal direction x
And the vertical axis represents the inclination (orbital gradient) x ′ of the projection of the velocity vector of the particle with respect to the design orbital on the horizontal plane. When the traveling direction of the beam is s, the horizontal trajectory gradient is expressed as x '= dx / ds. This xx 'space is called a phase space. The triangle of this topological space is the particle 3
The stability limit of the second resonance is shown.

The left side of the equation 1 is different from the average momentum, which is the center a of the stability limit A of the proton having the average momentum (which is the central orbit of the orbiting beam in real space) in FIG. 2A. It represents the slope of the line segment aa 'that connects the center a'of the stability limit A'of the proton with momentum. The right side of Expression 1 represents the gradient of the output trajectory Q'of the stability limit A '.
Therefore, Expression 1 indicates that the slope of the straight line connecting the centers of the stability limits of the respective protons is the same as the slope of the output trajectory, and the slope of the output trajectory is the same for all protons.

Further, in the present embodiment, the resonance point of the betatron oscillation is selected to be 5/3, so the phase difference (2π times the tune) of one round of the circular accelerator is 10π / 3, which is 180
The phase difference of the betatron oscillations at positions separated by 5 degrees is 5π / 3.

Therefore, the phase difference of the betatron vibration at the positions of the two sextupole electromagnets 5 and 6 is 5π / 3.

In the sextupole electromagnets 5 and 6, the phase difference φ ₅ and φ _{6 of the} betatron vibration with the deflector 8 for emission satisfy the formula 1, and the phase difference of the betatron vibration is 5π /.
Since it is arranged at the position of 3, the gradient of the center of the stability limit of all protons and the gradient of the emission trajectory are the same, and they are kept constant regardless of the excitation amounts of the sextupole electromagnets 5, 6.

The controller 11 includes a sequence controller 111.
And a magnetic field strength controller 112. Control device 11
Is programmed such that each device is controlled in accordance with a predetermined circular accelerator operation sequence from the start of beam incidence to the end of beam extraction.

The controller 11 controls the sequence controller 111 according to the programmed operation pattern of the circular accelerator.
Then, the beam extraction start signal or the beam extraction end signal is output to the magnetic field strength controller 112. Upon receiving the beam extraction start signal from the sequence controller 111, the magnetic field strength controller 112 outputs control signals A ₁ and A ₂ to the sextupole electromagnet power supplies 12 and 13. The control signals A ₁ and A ₂ are applied to the hexapole electromagnets 5 and 6 in a magnetic field having a predetermined strength.
Is a control signal for exciting each. In addition, when the magnetic field strength controller 112 receives the beam extraction end signal from the sequence controller 111, the hexapole electromagnet power source 12,
The control signal B is output to 13. The control signal B is a control signal for stopping the excitation of the sextupole electromagnets 5, 6.

The power supplies 12 and 13 for the sextupole electromagnets respectively supply currents to the sextupole electromagnets 5 and 6 by the control signals A ₁ and A ₂ , and continue to supply currents until the control signal B is input. The supply of the current is stopped by the control signal B, and the current is not supplied until the next control signals A ₁ and A ₂ are input.

Next, the operating method of this embodiment will be described.

The deflection electromagnet 1 and the quadrupole electromagnets 2 and 3 are excited so that the horizontal tune of the betatron oscillation of the beam circling the circular accelerator is 1.73 and the vertical tune thereof is 0.85. Then, from the beam injection device 9, the energy is 10 MeV and the emittance is 100 π mm.
Inject mrad proton beam into circular accelerator. The incident proton beam is kept in a circular shape by the deflection electromagnet 1 and the quadrupole electromagnets 2 and 3, and circulates in the circular vacuum duct 10 of the accelerator.

The orbiting proton beam is accelerated by applying high-frequency power every time it passes through the high-frequency accelerating cavity 4 while maintaining the tune. The beam energy suitable for beam emission is 200 MeV, and this is the target energy. The emittance of the proton beam when accelerated to the target energy is 21πmm · mrad, and this is referred to as emittance ε.

After accelerating to the target energy, the amount of excitation of the quadrupole electromagnets 2 and 3 is adjusted to set the horizontal tune ν _x of the betatron oscillation of the proton beam to 1.67.

When the beam energy reaches the above-mentioned predetermined value, the sequence controller 111 outputs a beam extraction start signal to the magnetic field intensity controller 112. Magnetic field strength controller
112 is a control signal A ₁ , A _{2 to the} power supplies 12 and 13 for the sextupole electromagnet.
Is output. The control signal A ₁ controls the sextupole electromagnet power supply 12, and controls the current supplied from the sextupole electromagnet power supply 12 to the sextupole electromagnet 5 to a predetermined value. The control signal A ₂ controls the power supply 13 for the sextupole electromagnet, and controls the current supplied from the power supply 13 for the sextupole electromagnet to the sextupole electromagnet 6 to a predetermined value.

The control signal A ₁ is a signal having a magnitude determined corresponding to K ₅ obtained by solving the equations 2 and 3. The control signal A ₂ is a signal having a magnitude determined corresponding to K ₆ similarly obtained by solving the equations 2 and 3. Therefore, the current value supplied to the sextupole electromagnet 5 corresponds to K ₅ , and the current value supplied to the sextupole electromagnet 6 corresponds to K ₆ .

Equations 2 and 3 for obtaining K ₅ and K ₆ will be described in detail below. For the magnetic field excited by the sextupole electromagnet 5, the value obtained by dividing the second derivative in the horizontal direction x by the magnetic rigidity is K ₅ , and for the magnetic field excited by the sextupole electromagnet 6, the second derivative in the horizontal direction x is the magnetic rigidity. The value divided by is K ₆ .
The equation showing the correction of the chromaticity by K ₅ and K ₆ is as follows.

[0048]

(Equation 5)

However, ξ _x is the momentum dependence of the tune at the time of emission when the sextupole electromagnet is not excited (natural chromaticity), β _sx is the betatron function at the positions of the _sextupole electromagnets 5, 6, and η _sx is The dispersion function at the positions of the sextupole electromagnets 5 and 6, ν _x, is a horizontal tune, and these values are values determined by the arrangement of each electromagnet and the magnetic field, and can be calculated in advance. L is the magnetic pole length of the sextupole electromagnets 5 and 6.

Equation 2 shows that when the hexapole electromagnets 5 and 6 are in rotationally symmetric positions, the parameters of the betatron oscillation at the respective positions are equal, and therefore the natural chromaticity is canceled by the sum of K ₅ and K _6. Show.

The equation showing the relationship between K ₅ and K ₆ and the size of the stability limit is as follows.

[0052]

(Equation 6)

However, ε is the emittance of the beam at the end of acceleration, and δ is the deviation from the resonance point of the tune.
67-5 / 3 = 0.00333.

Equation 3 shows that when the sextupole electromagnets 5 and 6 are in rotationally symmetrical positions, the parameters of the betatron oscillation at the respective positions are equal, so the magnitude of the stability limit is determined by the difference between K ₅ and K ₆ , It is equal to emittance ε.

The values of K ₅ and K ₆ are obtained by simultaneous expression 2 and 3. By the strength of the magnetic field excited in the sextupole magnet 5 by the current corresponding to K ₅ and the current corresponding to K ₆ ,
The strength of the magnetic field excited by the sextupole electromagnet 6 is different.

By the control based on the control signals A ₁ and A ₂ ,
Magnetic fields having different strengths are excited in the sextupole electromagnets 5 and 6. For this reason, the
The second resonance is excited and the chromaticity is corrected. The stability limit at the exit deflector position becomes the same as the emittance ε regardless of the momentum of the proton due to the correction of the chromaticity. In addition, the hexapole electromagnet 5,
Since 6 is arranged at a position where the phase difference of betatron oscillation is 5π / 3, the direction of the stability limit is kept constant regardless of K ₅ and K ₆ .

By the way, as for the diameter of the outgoing beam, the electrodes 30i, 30o of the outgoing deflector in the phase space where the protons are in phase space are used.
It is represented by the distance d in the direction of the vertical axis x'that intersects As shown in FIG. 3, even if each of the protons has the same stability limit, the distance d becomes large when the emission trajectories are different,
The diameter of the emitted beam is large.

However, in this embodiment, for all the protons, the gradient of the straight line connecting the central orbits and the gradient of the exit trajectory are the same, and the magnitude of the stability limit is the same, so that FIG. As shown in, the output trajectories in the phase space overlap for all protons, and the range d of the output trajectories becomes small, so the diameter of the output beam is small.

Next, with the excitation of the sextupole electromagnets 5 and 6,
A high frequency electric field is applied in the horizontal direction by the high frequency electric field applying electrode 7 in synchronization with the period of the betatron oscillation of the proton.
Protons receive energy from the high-frequency electric field and gradually increase in amplitude.

Protons exceeding the stability limit resonate and rapidly increase the betatron oscillation amplitude.

The protons entered between the electrodes of the deflector 8 for extraction are taken out of the circular accelerator as a beam. At this time, all protons have different momentums, but since they have the same stability limit, most of the protons that are lost when the stability limit is formed and those that do not reach the stability limit by the end of emission Therefore, the emission efficiency is good. Further, since the stability limit is constant from the start to the end of beam emission, all the protons are emitted under the same conditions, so the quality of the emitted beam is stable.

Further, since the emission loci in the phase space overlap for all protons, an emission beam with a small diameter can be obtained.

When the proton beam circulating in the vacuum duct 10 is emitted for a predetermined time, the sequence control unit 111 outputs a beam extraction completion signal to the magnetic field intensity controller 112. The magnetic field strength controller 112 is a power supply 12 for a sextupole electromagnet,
The control signal B is output to 13. Power supply for sextupole magnet 12,
At 13, the current supply is stopped and the emission of the proton beam is completed.

According to this embodiment, the sextupole electromagnets 5 and 6 arranged at the position where the phase difference of the betatron vibration is 5π / 3 excites magnetic fields of different strength under the control of the controller 11. By doing so, all charged particles have the same direction regardless of the magnetic field and have the same stability limit in size regardless of the momentum, so that the extraction efficiency is good and the beam can be stably obtained. Further, since the emission loci in the phase space overlap for all protons, an emission beam with a small diameter can be obtained.

Further, since the sextupole electromagnets 5 and 6 are arranged at positions which are rotationally symmetric, the chromaticity correction depends on the sum of the magnetic field strengths excited by the sextupole electromagnets 5 and 6,
The size of the stability limit depends on the difference in the strength of the magnetic fields excited by the sextupole electromagnets 5 and 6. Therefore, regarding the correction of chromaticity and the size of the stability limit, the hexapole electromagnets 5, 6
Since it is necessary to control only the strength of the magnetic field excited by, the control is easy.

Further, since the control device controls the strengths of the magnetic fields excited by the sextupole electromagnets 5 and 6 to different values, resonance excitation and correction of chromaticity can be performed by two sextupole electromagnets. . Therefore, since the number of sextupole magnets can be reduced, the circular accelerator can be downsized.

Further, by adjusting the excitation amounts of the quadrupole electromagnets 2 and 3, the horizontal tune ν _x of the betatron oscillation of the proton beam is set to 1.67 and the hexapole electromagnets 5 and 6 are excited. , You may go at the same time.

Further, in a circular accelerator in which a bending electromagnet, which is a main electromagnet, and a quadrupole electromagnet are repeatedly arranged, when the repeating unit has a bilaterally symmetrical arrangement structure,
The circular accelerator is said to have mirror symmetry, and at the position of mirror symmetry, the betatron oscillation parameters are the same as at the position of rotational symmetry. At this time,
Instead of the “180 ° rotational symmetry” in this embodiment, two hexapole electromagnets may be arranged at the “mirror symmetry” position.

[0069]

According to the circular accelerator of claim 1 of the present invention, the phase difference of betatron oscillation is nπ / 3 (n is an odd number).
And the phase difference φ of the betatron oscillation with the output deflector is s, where s is the coordinate in the beam traveling direction along the design trajectory, β is the betatron function at the position of the output deflector, η is the dispersion function, and dispersion When the derivative of the function is η ′,

[0070]

(Equation 7)

(Where, θ = (4m ± 1) π / 6, where m is an integer satisfying (φ−π / 2) <θ <(φ + π / 2)). A polar electromagnet excites a magnetic field of a strength controlled to a different value by the control device, and all charged particles have a constant direction regardless of the magnetic field and have the same stability limit regardless of momentum. And the orbits of all outgoing charged particles overlap,
A beam with a small diameter can be stably obtained with good extraction efficiency, and resonance excitation and correction of chromaticity are performed by two sextupole electromagnets, and the number of sextupole electromagnets can be reduced, so the circular accelerator can be miniaturized. .

According to the circular accelerator of claim 2 of the present invention,
Since the two hexapole electromagnets are arranged in the positions of claim 1 and at positions which are rotationally symmetric, the same effect as the circular accelerator of claim 1 can be obtained by the same operation as that of the circular accelerator of claim 1. And the parameters of the betatron oscillation of the beam at the rotationally symmetric position are the same, the chromaticity depends on the sum of the magnetic field strengths excited by the two sextupole magnets, and the size of the stability limit is two. Since it depends on the difference in the strength of the magnetic field excited by the sextupole electromagnet, for the correction of chromaticity and the size of the stability limit, the sextupole electromagnets 5, 6 are used.
It is sufficient to control only the strength of the magnetic field excited by, and the control is easy.

According to the circular accelerator of claim 3 of the present invention,
Since the two hexapole electromagnets are arranged according to claim 1 and at positions that are mirror-symmetrical to each other, the same operation as that of the circular accelerator according to claim 2 causes the same effect as that of the circular accelerator according to claim 2. Get the effect.

According to the beam extraction method of claim 4, when the betatron oscillation is brought into the nth resonance state and the charged particles are emitted, the first charged particles in the beam in the phase space at the extraction deflector position. Of the stability limit of the first charged particle and the center of the stability limit of the second charged particle having a momentum different from the momentum of the first charged particle, the slope of the straight line is Since the inclination of the trajectory drawn in the phase space is the same, the diameter of the emitted beam becomes small.

[Brief description of the drawings]

FIG. 1 is a diagram showing a circular accelerator according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a stability limit and an output trajectory in a phase space.

FIG. 3 is a diagram showing a stability limit and an output trajectory in a phase space.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Bending electromagnet, 2 ... Focusing quadrupole electromagnet, 3 ... Divergence quadrupole electromagnet, 4 ... High frequency acceleration cavity, 5, 6 ... Hexapole electromagnet,
7 ... Electrode for applying high frequency electric field, 8 ... Deflector for emission,
9 ... Incident device, 10 ... Vacuum duct, 11 ... Control device, 1
2, 13 ... Power supply for sextupole electromagnet, 111 ... Sequence control unit, 112 ... Magnetic field strength controller.

Claims (4)

[Claims] 1. A phase difference of betatron oscillation is nπ / 3 (n
Is the odd number), and the phase difference φ of the betatron oscillation with the deflector for extraction is the coordinate of the beam traveling direction along the design orbit, s is the betatron function at the deflector position for emission, and the dispersion function is If η and the derivative of the dispersion function are η ′, then (However, θ = (4m ± 1) π / 6, and m is (φ−π /
(2) An integer satisfying <θ <(φ + π / 2)), and two 6-pole electromagnets that excite a magnetic field by supplying a current and the two 6-pole electromagnets excite. A circular accelerator comprising: a controller for controlling the strength of the magnetic field to different values. 2. The circular accelerator according to claim 1, wherein the positions where the two hexapole electromagnets are arranged are rotationally symmetrical. 3. The circular accelerator according to claim 2, which has a mirror symmetry instead of the rotational symmetry. 4. A beam radiating the beam which circulates around a circular accelerator is brought close to an integer ± m / n (m / n is an irreducible fraction) to bring the betatron oscillation into an nth resonance state, and the beam is emitted. In the method, a central orbit of a first charged particle in the beam and a central orbit of a second charged particle having a momentum different from the momentum of the first charged particle in the phase space at the exit deflector position are connected. The inclination of the straight line is such that the second charged particle is n
A method of emitting a beam, wherein the inclination is equal to the trajectory drawn in the phase space for each orbit.