JPH0765997A - Control method of electron synchrotron - Google Patents

Abstract

PURPOSE:To suppress instability in the transverse direction bunch coupling of incident electrons when electrons are made incident to an electron synchrotron with a low energy. CONSTITUTION:When electrons are made incident with a low energy as shown by a frequency component 11, the bunch becomes long. In this case, the value F'11 of a shape factor can be decreased greatly by shifting the position f1 of the component 11 a little in the negative direction, which permits avoiding the instability in the transverse direction bunch coupling.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a particle accelerator technique such as a synchrotron radiation generator, and more particularly, to reduce the cost of electron incident energy in order to reduce the cost of an electron synchrotron that accelerates or accumulates electrons. The present invention relates to a control method of an electron synchrotron that secures the stability of an electron beam while reducing it, and enables accelerated storage of a large current.

[0002]

2. Description of the Related Art In recent years, research and development utilizing radiated light (electromagnetic waves) emitted in the traveling direction until now when electrons accelerated to almost the speed of light are deflected by a magnetic field have been activated. Therefore, it is desired to develop a small and inexpensive radiation source that can obtain this radiation. To get this emitted light,
It is common to use an electron synchrotron that accumulates high-energy electrons or positrons by orbiting on an orbit. The electron synchrotron uses a deflection magnet to form an orbit of an electron, and an orbital frequency f _{0 of the} electron.
A high-frequency accelerating cavity that applies a high-frequency frequency f _RF for acceleration, which is an integer multiple of the above, accelerates orbiting electrons and replenishes electrons with a constant energy to orbit (accumulate) electrons. Is.

FIG. 2 is a plan view showing a schematic structure of this electron synchrotron. 1 is an orbit around which the electrons of the electron synchrotron orbit, 2 is a deflection magnet that changes the moving direction of the orbiting electrons to orbit the electrons on the orbit 1 and 3 is an electron around the orbit 1. 4 is a converging-type 4-pole magnet for suppressing the horizontal vibration of the magnet, 4 is a non-converging-type 4-pole magnet for suppressing the vertical vibration of the electrons orbiting the orbit 1, and 5 is for obtaining an achromatic condition. Is a convergent quadrupole magnet (QFC). Further, 6 is a high-frequency acceleration cavity for applying a high-frequency frequency f _RF for acceleration to orbiting electrons, 7 is a 6-pole magnet for adjusting chromaticity, 8 is a linear accelerator that supplies electrons, and 9 is a linear accelerator 8
Is an incident deflector for placing the electrons emitted from the on the orbit 1.

The electron accelerated by the linear accelerator 8 to a predetermined speed is changed in its moving direction by the incident deflector 9 and taken into the orbit 1 and deflected at the deflecting magnet 2. To move on the orbit 1 Electrons that have started to orbit 1 orbit 1
The high-frequency acceleration cavity 6 receives a high-frequency frequency f _RF for acceleration that is an integer multiple of the orbital frequency f ₀ obtained by dividing the circumference length by the velocity of electrons, and replenishes kinetic energy. The electrons orbit while oscillating in each of the horizontal and vertical directions, and the number of vibrations during one round of the orbit 1 of the electron is called a betatron frequency. Thus, the electrons orbit while oscillating, but if the amplitude of this oscillation becomes too large, the electrons will disappear from the orbit 1.

In the case of accelerating or accumulating electrons in the electron synchrotron, it is necessary to satisfy the stability of the one-particle system that is established regardless of the number of orbiting electrons. Here, regarding the stability of the one-particle system explain. The stability of one particle system is classified into orbital stability and phase stability, as shown below. In an actual electron synchrotron, there is a magnetic field (error magnetic field) that does not appear in the design due to individual differences of electromagnets installed on the orbit 1 and production errors.

Here, the betatron frequency is the resonance condition k.
When ν _x + lν _y = m (k, l, and m are integers),
The oscillation cycle affected by the above-mentioned error magnetic field and the oscillation cycle when the electron orbits are coincident with each other, the amplitude of the oscillation of the orbiting electron increases, and this electron is lost. For this reason, it is necessary to suppress the amplitude of the circulating electrons to avoid such a resonance condition and perform the operation, and the converging type quadrupole magnet 3 and the non-converging type quadrupole magnet 4 cause horizontal and vertical vibrations. It can be suppressed.

The orbital stability means that the orbiting electrons of the electron synchrotron as described above continue to orbit stably even if they deviate from the orbital orbit 1 by the action of the quadrupole magnet. Note that k + 1 is called the resonance order, but it is generally sufficient to consider the resonance of the fourth order or lower.

On the other hand, the phase stability means the stability when replenishing the energy of electrons with a high frequency or accelerating the electrons. The electrons orbiting the orbit 1 of the electron synchrotron receive a high frequency for acceleration f _RF in the high frequency acceleration cavity 6 which is an integral multiple of the orbital frequency f ₀ of the electron to replenish energy and accelerate the energy. By the way, the electrons with different energies have a deviation of the orbital frequency (a deviation of the position in the traveling direction). Electrons with excessive energy have a low orbital frequency, and electrons with insufficient energy have a high orbital frequency.

Here, these electrons are generated by the high frequency acceleration cavity 6
When passing through, electrons with insufficient energy will be supplemented, and electrons with excessive energy will be supplemented less. As a result, by passing through the high-frequency accelerating cavity 6, the electron deviated from the central energy which is the designed value comes close to this central energy, and as a result, the electron continues to move stably near the central energy. It will be.

Such a region satisfying the phase stability of the orbiting electrons exists at h points (h = f _RF / f ₀ ) in the orbit of the electron synchrotron, and the electrons are present at these h points. It solidifies on average and orbits the orbit. For example,
On the orbit 1 of the electron synchrotron in which the high-frequency acceleration cavity 6 applies the acceleration high-frequency frequency f _RF that is four times the orbital frequency f ₀ of the electrons, the electrons are evenly concentrated at four locations to form bunches, and each is evenly formed. Orbit at regular intervals.

By the way, the electrons change their respective velocities in the bunch, but when this is seen in the bunch, the electrons seem to vibrate in the bunch. The energy of electrons in the bunch and the vibration in the traveling direction, which are generated by the principle of phase stability, are called synchrotron vibration. Regarding the stability of the one-particle system in the electron synchrotron described above, for example, the literature (M. Sands, THE
PHYSICS OF ELECTRON STORA
NGE RINGS AN INTRODUTION,
SLAC-121, 1970).

When accelerating or accumulating electrons in an electron synchrotron, it is important to avoid the collective beam instability that occurs when a large number of electrons orbit at the same time as the stability of one particle system described above. . This collective electron beam instability means that the electrons that orbit the electron synchrotron affect the electrons themselves by generating an electromagnetic field due to the interaction with the surrounding environment such as a vacuum duct and a high-frequency acceleration cavity. This is a phenomenon in which the motion becomes unstable when the electrons orbit. The typical collective beam instability is the lateral bunch coupling instability.

In an electron synchrotron intended to utilize the synchrotron radiation emitted when an electron orbiting on the orbit 1 changes its flight direction, a high frequency acceleration is applied in order to compensate for the energy loss of the electron due to the emission of the synchrotron radiation. The cavity 6 is designed so that a sufficient acceleration voltage can be obtained with a power as low as possible.
However, in such a high frequency accelerating cavity 6, in addition to the accelerating high frequency frequency for giving energy to the electrons, it is usual to emit the higher order resonance frequency.

The induction electromagnetic field generated by the electrons passing through the high-frequency accelerating cavity 6 emitting the resonance frequency of the higher-order mode (higher-order mode frequency) thus lasts for a relatively long time. Therefore, the induction electromagnetic field excited by the bunch that has passed through the high-frequency acceleration cavity 6 affects the subsequent bunch. Then, this occurs in sequence to the next bunch, causing resonance, and betatron oscillations of orbiting electrons may diverge, and electrons may be lost.

This phenomenon is called lateral bunch coupling instability, and higher order mode frequency f _HOM and betatron frequency f
During the fractional part of the _{beta (Δν),} the equations shown in Equation 1 below occurs when substantially satisfied.

F _HOM ≈f _beta = nhf ₀ − (m + Δν) f ₀ ...
(1) Here, n and m are arbitrary integers.

The strength of the lateral bunch bond instability is expressed by the following equation 2 which is the growth rate of the instability.

Τinst = (eIf ₀ βZF ′) / (2E ₀ ) ... (2) where e is the electron charge, I is the beam current, and β is the value of the betatron function at the position of the high frequency acceleration cavity, Z is f
The real part of the lateral coupling impedance of the higher-order mode in _beta , E ₀ is the electron energy, and F ′ is a quantity called a form factor, which is a term that reflects the shape of the bunch as described later.

Therefore, β in equation (2) should be reduced, or Z
If the value of F is smaller or the value of F ′ is smaller, the growth rate τinst of the lateral bunch instability becomes smaller, and the lateral bunch coupling instability can be avoided. Here, Z in equation (2) is made smaller by adjusting the betatron frequency or by adjusting the higher-order mode frequency or impedance of the high-frequency accelerating cavity. It is also possible to give a spread to the number and suppress it by the effect of Landau damping.

Regarding the above technique, for example, reference can be made to the literature (H. Kobayaka, Y. Yamazaki,
Y. Kamiya and M.K. Kihara, Jp
n. J. Appl. Phys. , 25 (1986) 86.
4) or literature (Y. Yamazaki, K. Taka.
ta, and S. Tokumoto, IEEE Tr
ans. Nucl. Ssi. , NS-28 (1981)
2915) and the like.

In order to introduce the electrons into the orbit 1 of the electron synchrotron, as described above, the electrons pre-accelerated by the linear accelerator 8 are taken into the deflector 9 for injection, and the direction is changed here to orbit. Incident on 1. The incident electrons can be accelerated to a target energy by the high-frequency acceleration cavity 6, but considering the stability of the orbiting electrons of the electron synchrotron, the incident electrons are sufficiently accelerated, and the electron synchrotron does not have much energy. It is customary not to accelerate.

[0022]

Since the conventional structure is as described above, there is a problem in that it is not possible to use an electron injection device in consideration of economy. That is, in consideration of economy, it is necessary to downsize the electron incident device and reduce the energy of emitted electrons. In this case, the electrons are accelerated to the final energy in the electron synchrotron. Here, the method for avoiding the transverse bunch coupling instability described above is adopted in the system of the final energy injection method in which electrons with high energy are injected in advance, and is established in the electron synchrotron of the low energy injection method. There is no way to avoid the lateral bunch coupling instability created.

In an electron synchrotron in which electrons are injected with high energy, a multiple injection method is usually used.
This is to reduce the number of electrons that are injected at one time, the amplitude of the betatron oscillation of the injected electrons is attenuated with the emission of synchrotron radiation, and then the next electron is injected. is there. When the electrons are incident on the circular orbit 1, the circular orbit 1 is slightly moved to approach the incident deflector 9. For this reason, when electrons already exist on the orbit 1 and the amplitude of betatron oscillation of the electrons is large, the electrons collide with the incident deflector 9 and disappear.

Here, as the electrons orbiting on the orbit 1 pass through the high frequency acceleration cavity 6, the amplitude of the betatron oscillation gradually decreases. As a result, many electrons can be injected by repeating the operation of re-injecting after the amplitude of the betatron oscillation of the electrons that have already entered and are orbiting the orbit 1 has become sufficiently small. it can.

However, since the decay time of the amplitude is inversely proportional to the cube of the energy of the incident electron, if the incident energy is set to be sufficiently low, the time required for the decay of the amplitude becomes long. Now, while waiting for the amplitude to decrease,
The electrons have a long life, and the electrons that have already entered disappear, so that many electrons cannot enter even if they enter many times. In this way, when it is desired to make the incident energy sufficiently low, there is no choice but to adopt a method in which the number of electrons required for one injection is incident on the electron synchrotron and the electron synchrotron is accelerated as it is.

In order to reduce the cost of the synchrotron radiation generation system by the low energy incidence method, the efficiency of incidence on the electron synchrotron is improved so that a sufficient current can be secured by a single incidence, and at the same time in the low energy region. Satisfaction with stability is essential. However, since the strength of the lateral bunch coupling instability is proportional to the reciprocal of energy, it becomes difficult to secure this stability when the incident energy is lowered. Further, low-energy electrons are easily affected by error magnetic fields such as geomagnetism and residual magnetic field and cause strong resonance, so that the selection range of the betatron frequency is greatly restricted. Therefore, the method of avoiding the lateral bunch coupling instability by adjusting the betatron frequency often cannot obtain a sufficient effect.

Further, in the low energy injection method, it is inevitable to adopt the single injection method, but when a strong non-linear magnetic field is introduced by the 8-pole magnet, the dynamic aperture (a region where the betatron oscillation is stable) is limited, The incidence efficiency is reduced. On the other hand, the method of adjusting the higher-order mode frequency by modifying the high-frequency accelerating cavity is difficult to predict with high accuracy, is not efficient with a process of trial and error, and is strong against low-energy electrons. Since it is often not sufficient to suppress instability, it is difficult to use it at low energy incidence.

As described above, it is difficult to directly apply the method conventionally used as the means for avoiding the lateral bunch coupling instability to the electron synchrotron with low energy incidence. In order to realize the low energy injection method, how to suppress strong lateral bunch coupling to low energy electrons while ensuring sufficient injection efficiency within a narrow selection range of betatron frequencies is important. It becomes a problem.

The present invention has been made to solve the above problems, and suppresses the lateral bunch coupling instability of an incident electron when the electron is incident on the electron synchrotron with low energy. The purpose is to

[0030]

A method of controlling an electron synchrotron according to the present invention comprises an electron orbital frequency f ₀ , a higher-order mode frequency f _HOM generated by a high-frequency accelerating cavity, a chromaticity ξ, and a momentum compaction factor α. It is characterized by controlling the chromaticity ξ or the momentum compaction factor α in the direction of increasing Δf = | ξ / αf ₀ + f _HOM |

[0031]

[Function] By moving the chromaticity ξ or the momentum compaction factor α, the frequency of vibration of the bunch, which is a group of orbiting electrons, changes.

[0032]

The present invention will be described below. The present invention is for avoiding the lateral bunch coupling instability in the low energy injection method. Therefore, for this purpose, attention is paid to the term of F ′ in the above-mentioned formula (2), which represents the strength of the lateral bunch coupling instability. This F ′ term reflects the frequency component of the bunch and depends on the shape (length) of the bunch, and is therefore called a shape factor.

Here, the energy dependence of the betatron frequency of the electrons forming the bunch is called chromaticity (ξ). The difference in electron energy is Δ
e and the deviation of the betatron frequency is Δν, this chromaticity ξ is defined by ξ = Δν / ΔE / E ₀ . Here, the energy E ₀ of the electron and the betatron frequency ν ₀ are determined by the amount of excitation of the electromagnet controlling the orbit of the electron orbiting on the orbit. Since an actual electron has an energy distribution that spreads to some extent, the energy E of one electron, the betatron frequency ν, and E ₀ , ν ₀
The deviations from and are ΔE and Δν respectively.

If this chromaticity ξ is not zero,
By combining synchrotron and betatron vibrations,
The shape of the bunch vibrates. The frequency f _{1 of} this vibration is given by the momentum compaction factor α.
It is given by f ₁ = ξf ₀ / α. Here, the momentum compaction factor α is Δl = 1-l ₀ , where l _{0 is} the circumference of the orbit of an electron having a central energy E ₀ , and l is the circumference of the orbit drawn by an electron whose energy is deviated by ΔE.
Then, α = (Δl / l ₀ ) / (ΔE / E ₀ ).

On the other hand, since the bunch is finite in the direction of travel and the individual electrons that make up the bunch are performing betatron oscillation, the electromagnetic waves emitted by the bunch are observed on the stationary system monitor as the bunch passes. If so, δ-sig
nal = P (t) e ^{a + b} Signal should be observed. Here, a = j2πf ₁ t and b = j2πkν. Where e ^a Represents the bunch-shaped vibration described above, and e ^b The term represents the effect of betatron oscillation.
It should be noted that k indicates the number of rounds of the bunch that the obtained signal is. Further, p (t) is a term of a standing wave that represents the effect of a finite bunch length, and its Fourier component has a frequency distribution h (f) that is in contrast to the sign inversion of the frequency.

Here, the negative frequencies are waves (exp (jωt)) and exp which are included in the standing wave and travel in mutually opposite directions.
This is a concept introduced to distinguish the traveling direction of (-jωt) component, and formally one of the frequencies (ω
If / 2π) is defined as positive, the other becomes negative. When the bunch length is δl, the spread (δf) of h (f) is about δf = c / δl where c is the speed of light. E ^{a of the} signal observed on the stationary system monitor Due to the term of (a = j2πf ₁ t), the frequency distribution shifts by f _1, so the δ-signal actually observed The frequency component h ′ (f) of
It will be centered on ₁ . When the bunch with this frequency component passes through the high-frequency accelerating cavity, it induces an electromagnetic wave and affects the betatron oscillation of the subsequent electron.

Here, when the lateral coupling impedance of the high frequency accelerating cavity is Z (f), the amplitude of the betatron oscillation is attenuated or grown by the real part of Z (f). The electromagnetic wave induced by the positive frequency component of It is known that the electromagnetic wave induced by the negative frequency component of A contributes to the growth. Therefore, the real part of Z (f) is f = ± f
_{Since HOM} has a very sharp peak, h '(-f _HOM )
The size of γ determines the growth rate of the betatron oscillation, that is, the strength of the lateral bunch coupling instability.
This h '(-f _HOM ) is the form factor _F'itself of the above-mentioned formula (2).

For the above, refer to the document (F. Sacher).
er, Proc. 9th Int. Conf. on H
high Energy Accelerators,
Stanford; 1974: 347). When the bunch length is sufficiently long, the spread of the frequency component of the bunch is small, and by changing the centrality of this frequency distribution by adjusting the chromaticity ξ or the momentum compaction factor α, F ′ changes greatly. Therefore, when the bunch length is long, F'is reduced by adjusting ξ or α (direction in which the center of the bunch frequency component is from the higher mode frequency).
It can be seen that the method is effective to avoid the lateral bunch coupling instability.

FIG. 1 illustrates this method. In FIG. 1, 11 is a frequency component when the bunch length is long (up to 60 cm), and 12 is a frequency component when the bunch length is short (up to 6 cm). The vertical axis indicating the form factor F ′ is a value relating to the strength of the lateral bunch coupling instability as described above, and the smaller the vertical axis, the smaller the lateral bunch coupling instability. The values F ′ ₁₁ , F ′ ₁₂ corresponding to the negative higher-order mode frequency −f _HOM of the high-frequency acceleration cavity are the form factors in each case,
In the case of the frequency component 11, the shape factor value F ′ ₁₁ is greatly reduced and the lateral bunch coupling instability can be avoided only by slightly changing the position of f _{1 in} the negative direction.

When a continuous electron beam is incident on an electron synchrotron of a low energy incidence type from an injector such as a linear accelerator, the bunch length is hardly attenuated by the emission of synchrotron radiation. Saved by the bunch chief. In this case, it is effective to avoid the lateral bunch coupling instability by the above method. On the contrary, when the energy becomes higher, the bunch length is attenuated by the emission of synchrotron light, and the bunch length becomes considerably shorter than that at the time of incidence. As a result, since the bunch has a wide frequency distribution, the frequency component 1 in FIG.
It is varied center frequency f ₁ as shown in 2, F _'12
Is difficult to reduce.

Therefore, in the conventional electron synchrotron adopting the high energy injection method, the lateral coupling instability, that is, the beam instability is not avoided by the above-described method. Then, in order to suppress the beam instability by the above-mentioned method, it is a necessary condition that the electron synchrotron has a function of adjusting the chromaticity ξ or the momentum compaction factor α.

By the way, as described above, in the converging quadrupole magnet 3 and the non-converging quadrupole magnet 4 (FIG. 2), the amplitude of the vibration of the circulating electrons is suppressed, but the energy is reduced. If the electron is deviated in the excessive direction, the betatron frequency is corrected in the direction of decreasing the frequency of the electron whose energy is not deviated, that is, the negative chromaticity ξ is generated. Here, the orbit drawn by an electron with a certain energy deviation can be represented by an energy dispersion function, but by installing a 6-pole magnet in a place where this energy dispersion function is not zero, the chromaticity can be adjusted and the bunch's It is possible to avoid lateral coupling instability.

On the other hand, in the achromatic electron synchrotron designed so that the energy dispersion function becomes zero in the straight line portion because the insertion light source is installed, the momentum compaction factor α can be changed by shifting from the achromatic condition. It is possible. Here, it is necessary to avoid the lateral bunch instability in the low-energy state especially when the electron is incident on the orbit, but at this time, it is not necessary to satisfy the achromatic condition. That is, an achromatic state in which there are no electrons that have deviated from the designed orbit is necessary when extracting emitted light, but it is not necessary to be achromatic in this manner when making electrons incident. Therefore, it is possible to avoid instability only by changing the control method without adding extra hardware.

When controlling the chromaticity ξ and the momentum compaction factor α, if the higher order mode frequency which is a problem is f _HOM (> 0), −
Since the frequency component of the bunch in f _{HO M} leads to instability, it is necessary to adjust ξ or α in the direction of expanding Δf = | ξ / αf ₀ + f _HOM |. However, ξ shall be considered including the sign. The frequency component of the bunch immediately after incidence is the high frequency frequency f for acceleration.
Since only has several times the spread of _RF, is sufficient expansion value of the Δf even several times the f _RF.

An embodiment of the present invention will be described below with reference to the drawings. FIG. 2 shows an example of an electron synchrotron adopting low energy incidence according to the present invention. In the figure, 1 is a circular orbit with a circumference of 52.8 m around which the electrons of this electron synchrotron orbit, and 2 is a rectangle (re
(Ctangular type) Deflection magnet that changes the moving direction of orbiting electrons and orbits the electrons on the orbit 1
Is a converging quadrupole magnet (QF) for suppressing the horizontal vibration of the electrons that orbit the orbit 1 and 4 is non-convergence for suppressing the vertical vibration of the electrons that orbit the orbit 1. The quadrupole magnets (QD) and 5 are converging quadrupole magnets (QFC) installed on the short straight line portion of the orbit 1 to obtain an achromatic condition.

Further, 6 is a high-frequency accelerating cavity for applying a high-frequency frequency of 125 MHz (f _RF ) for acceleration to orbiting electrons, and 7 is a 6-pole magnet for adjusting the chromaticity,
Reference numeral 8 is a linear accelerator that pre-accelerates and supplies electrons up to 15 MeV, and 9 is an incident deflector for placing the electrons emitted from the linear accelerator 8 on the orbit 1. The electrons pre-accelerated by the linear accelerator 8 are orbited into 22 bunches, which are accelerated to 800 MeV by the electron synchrotron.
The orbital radius of electrons in the deflection magnet 2 is 1.8 m,
The magnetic field strength of this deflecting magnet is the electron energy of 15 Me.
It changes proportionally from 0.027T corresponding to V to 1.44T corresponding to 800 MeV.

A typical operating condition of the electron synchrotron in this embodiment is that the combination of betatron frequencies in the horizontal and vertical directions of the operating point is (3.25, 1.25).
In addition, the energy dispersion function is zero in the long straight line portion where the converging quadrupole magnet 3 is arranged, that is, the long straight line portion is in an achromatic state. Here, the strength of the quadrupole magnet is defined as K = (B'l _QUAD ) / (3.33E ₀ ). However, B '(T / m) is a value obtained by differentiating the horizontal magnetic field distribution in the quadrupole magnet once with x, l _QUAD (m) is the length of the quadrupole magnet in one orbit of the orbit, and E ₀ (GeV ) Is the energy of the electron.

Here, the strength of the QFC5 required to obtain the achromatic condition is 0.925, and at this time, the combination of the betatron frequencies in the horizontal and vertical directions of the operating point (3.25, QF to set to 1.25)
3 must be 0.521 and QD4 must be -0.282. However, the above value is the strength of each quadrupole magnet. Also, since it depends on l _QUAD , QFC5
The exact value of the strength of must be calculated with this in mind. In the expression representing the strength of QFC5, since the denominator includes E ₀ , its absolute strength B ′ is changed in proportion to energy.

Under the conditions shown above, the momentum compaction factor α is 0.025, and the x-direction chromaticity ξ without correction is about -3. Since the circulating frequency f ₀ is 5.682 MHz, f ₁ is approximately −680 MHz. On the other hand, in the high-frequency accelerating cavity 6 having an accelerating high-frequency frequency of 125 MHz, the existence of a higher-order mode frequency having a strong influence on the betatron oscillation in the x direction is confirmed near f _HOM = 493 MHz.

Although it is difficult to accurately predict the length of the bunch when the electron is incident, it is a quarter of the maximum possible bunch length (2.4 m obtained by dividing the circumference by the number of bunch). Assuming 60 cm, which is about 1, the form factor and f ₁ , f
The relationship of the _HOM is as shown in FIG. 1, as described above. Therefore, for example, by moving f ₁ in the negative direction by 300 MHz, the value of F ′ ₁₁ can be made small, and the strength of the lateral bunch coupling instability can be made sufficiently small.

As a method of moving f ₁ by df ₁ = -300 MHz, when the 6-pole magnet 7 is arranged in each of the four short linear portions as shown in FIG. 2, the amount of excitation required for these is df ₁ = f ₀ ξ _sxt / α = −300 × 10 ⁶ (ξ
_sxt = 4βηG / 4π). Therefore, the value β of the x-direction beta function at the position of the 6-pole magnet 7
By substituting _x = 3 m and the energy dispersion function value η = 1.5 m, the excitation amount G = − per one 6-pole magnet 7
0.92 (m ^-2 ) is obtained.

On the other hand, the chromaticity ξ remains unchanged,
When changing the momentum compaction factor α, f ₁ = f ₀ ξ / α ′ = (− 600−300)
From the formula of × 10 ⁶ , it is necessary to set α ′ = 0.174. To this end, QFC5 may be increased by about 3%, but in order to keep the operating point unchanged, it is necessary to decrease QF3 by 1% and increase the absolute value of QD4 by 1% at the same time. Therefore, when it is desired to change the momentum compaction factor α in this way, it is sufficient to slightly change the amount of excitation of each quadrupole magnet. The above numerical values are merely calculated values, and it is necessary to determine the actual control amount based on the actually measured values.

[0053]

As described above, according to the present invention, it is possible to suppress the lateral inversion bunch coupling instability of an incident electron when the electron is incident on the electron synchrotron with low energy. . Therefore, it becomes possible to secure a sufficient current with one injection while suppressing the lateral bunch coupling instability. Then, the low energy incidence method can be realized, and the cost of the radiation emitting device can be significantly reduced.

[Brief description of drawings]

FIG. 1 is an explanatory diagram showing a relationship between a shape factor and f ₁ and f _HOM .

FIG. 2 is a plan view showing a schematic configuration of an electron synchrotron.

[Explanation of symbols]

 1 Orbit 2 Deflection magnet 3 Convergence type 4 pole magnet (QF) 4 Non-convergence type 4 pole magnet (QD) 5 Convergence type 4 pole magnet (QFC) 6 High frequency accelerating cavity 7 6 pole magnet 8 Linear accelerator 9 Injector deflector 11,12 frequency components

Claims (4)

[Claims] 1. A deflecting magnet for deflecting an electron, a quadrupole magnet for converging the electron on an orbit, and a high-frequency accelerating cavity for supplying energy to the electron are used to orbit the electron while orbiting the orbit. In an electron synchrotron for accelerating or accumulating, the orbital frequency f _{0 of the} electron, the higher-order mode frequency f _HOM generated by the high-frequency accelerating cavity, the chromaticity ξ, and the momentum compaction factor α, Δf = | A method of controlling an electron synchrotron, comprising controlling the chromaticity ξ or the momentum compaction factor α in a direction of increasing ξ / αf ₀ + f _HOM |. 2. The method for controlling an electron synchrotron according to claim 1, wherein the value of Δf is about several times or less of a high frequency frequency for acceleration for supplying energy to the electrons by the high frequency acceleration cavity. A method for controlling an electron synchrotron, which comprises controlling the chromaticity ξ or the momentum compaction factor α. 3. The method for controlling an electron synchrotron according to claim 1 or 2, wherein the chromaticity ξ is controlled by using a 6-pole magnet. 4. The method for controlling an electron synchrotron according to claim 1, wherein the electron synchrotron that satisfies an achromatic condition is used, and the momentum compaction factor α is set by shifting the achromatic condition. A method for controlling an electron synchrotron, which comprises controlling