An optimization method for an injector of an energy recovery linear accelerator

Abstract

The application provides an optimization method for an injector of an energy recovery type linear accelerator, comprising the following steps: estimating the beam group parameters at the outlet of an injection part and the distance from the outlet to the inlet of a main accelerator through an existing design; determining the transformation of the caused phase space nonlinear modulation amount in the unit length caused by the transverse space charge force; simultaneously, estimating the phase space nonlinear modulation amount caused by the transverse space charge force in the matching section and the merging section of the injector; adding an emittance optimization function in the original constraint condition of the injection part in the process of optimizing the injection part of the injector device; and then, making the emittance optimization function tend to 0. The optimization method of the application optimizes or screens the beam group of the injection part of the injector device on the basis of considering the transverse space charge effect of the subsequent low-energy region, reduces the influence of the transverse charge force on the beam group in the subsequent transmission, and can effectively improve the power of the subsequent radiation section.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of accelerator physics and technology, and particularly relates to an optimization method for an injector of an energy recovery type accelerator. BACKGROUND

[0002] Compared with a linear accelerator, an energy recovery type linear accelerator (ERL) can ensure beam quality and achieve a higher repetition frequency, thereby improving the average power of the whole machine. Currently, the repetition frequency of the mainstream energy recovery type accelerator internationally is as high as 100-1300 MHz, which is more than 100 times the repetition frequency of the Shanghai hard X-ray free electron laser.

[0003] The beam quality of the whole accelerator is determined by the injector device, and the beam quality of the injector device determines the beam quality of the whole machine. Figure 1 is a layout diagram of a typical injector device of an energy recovery type accelerator, the beam transmission direction is from left to right: injection part 100→matching section 200→merging section 300→subsequent beam line. As shown in Figure 1 Unlike the injector device of a conventional linear accelerator, the injector device of an energy recovery type linear accelerator mainly includes two parts: the injection part 100, the matching section 200 and the merging section 300. The injection part is similar to the injection part of a conventional accelerator, but in order to improve the energy recycling efficiency, the energy of the injection part of the ERL is smaller, and the energy at the outlet of the conventional injection part is less than 15 MeV. Further, since the ERL is a ring device, the merging section is needed to deflect the beam from the injection part to the main circulating line. A typical injector device of an ERL is shown in Figure 1 The injection part usually consists of an electron gun 101, a solenoid 102, a buncher 103, a solenoid 102 and an acceleration module 104 arranged in sequence. The electron gun 101, the solenoid 102, the buncher 103 and the acceleration module 104 are respectively used to generate an electron beam, compensate the emittance of the beam, produce energy chirp of the beam to compress the beam and pre-accelerate the beam. The matching section 200 consists of several quadrupole magnets 201, and the merging section 300 consists of dipole magnets 301 and quadrupole magnets 302, which are respectively used to bunch and deflect the beam, and transfer the beam from the injector device to the main accelerator section.

[0004] In addition to the cathode material properties and laser performance in the electron gun, a key factor affecting the beam performance in the injector is the space charge effect, i.e. the influence of the Coulomb repulsion between individual electrons within the electron beam on the electron distribution of the beam. The space charge effect exists throughout the machine and decreases with increasing energy. In accelerator physics, the space charge effect exists in two ways: transverse space charge and longitudinal space charge. The transverse space charge is directed radially outward. Generally, the transverse space charge force is nonlinearly distributed, and the nonlinear space charge force enhances the nonlinear distribution of the beam in the transverse phase space, which in turn increases the beam emittance in the transverse slice. A common method is to use a solenoid to rotate the beam to reduce the coupling term in the x-y direction to reduce the emittance size in a single dimension, which is widely used in the optimization process of conventional injectors. The conventional optimization work is often at the exit of the injection section. For conventional accelerators, the beam at the exit of the injection section will be further accelerated to the high-energy region, and the subsequent beam line is less affected by the space charge.

[0005] Unlike conventional injectors, the injector device of the ERL includes an additional matching section 200 and merging section 300 in addition to the injection section 100, which functions as follows: the injection section 100 accelerates the electrons generated by the electron gun to about 10 MeV, mitigating the impact of the space charge on the beam; the matching section 200 is used to adjust the beam envelope to prevent excessive dispersion of the beam, which can cause the beam to be too large in the transverse dimension; and the merging section 300 is used to deflect the beam to the main circulating line, so that the beam can be further accelerated. Due to this additional matching section 200 and merging section 300, the injector device of the ERL has a longer space charge working region. However, the existing optimization scheme is only the best result for the injection section, and the matching section 200 and merging section 300 after the injector device are not considered, so the current optimization scheme may cause the slice emittance to increase in the subsequent process, resulting in poor beam quality. For longitudinal space charge, the longitudinal space charge changes the energy spread. In the non-dispersive region, the longitudinal space charge does not directly affect the emittance; in the dispersive region such as the merging section 300, the additional energy spread caused by the longitudinal space charge force will couple with the dispersion term, thereby affecting the transverse emittance.

[0006] The conventional optimization methods include the R-matrix method and the beam dispersion function optimization. For the former method, the existing model cannot accurately reflect the non-uniform energy spread changes caused by the longitudinal space charge; and the beam dispersion optimization needs to be combined with the finite element method, which is slow in optimization speed and poor in universality, and has its own limitations.

[0007] Therefore, it is necessary to propose a new optimization method to mitigate the influence of the transverse space charge force on the downstream structure of the injection section (i.e. the matching section and the merging section), and to maintain the attenuation of the emittance through the design of the merging section to improve the brightness of the beam. Summary of the Invention

[0008] The purpose of this invention is to provide an injector design for low-energy beam injection in an energy recovery linear accelerator, wherein a pre-modulation method is used to counteract the transverse space charge force of the subsequent beamline, which can effectively reduce the impact of the transverse space charge force on the quality of the injected beam and improve the overall performance of the device.

[0009] To achieve this objective, the present invention provides an optimization method for an injector in an energy recovery linear accelerator, comprising:

[0010] S1: Based on the existing design, estimate the bundle parameters at the exit of the injection section and the distance from the exit to the main accelerator inlet;

[0011] S2: Determine the transformation of the phase space nonlinear modulation per unit length caused by the transverse space charge force. At the same time, based on To predict the phase space nonlinear modulation ΔA caused by the transverse space charge force in the matching and merging sections of the injector. ε ;

[0012] S3: During the optimization of the injection section of the injector device, the phase space nonlinear modulation amount ΔA caused by the obtained transverse space charge force in the matching and merging sections of the injector is considered. ε In the original constraints of the injection part, an emission optimization function f is added. obj Subsequently, based on the reactivity optimization function f obj The optimization result is obtained by considering the constraints approaching 0 and the original constraints, or based on the emission optimization function f. obj The optimization results obtained under the original constraints are filtered to ensure that the emittance optimization function f obj Approaching 0;

[0013] The emission optimization function f obj for:

[0014] f obj =ΔW ε +ΔA ε ,

[0015] Where, ΔA ε ΔW represents the phase-space nonlinear modulation caused by the transverse space charge force in the matching and merging sections of the injector; ε It is the phase space premodulation quantity, which is obtained from the bundle at the exit of the statistical injection section.

[0016] The bunch parameters at the exit of the injection section include at least one of a transverse dimension and / or a radial dimension of the bunch at the exit of the injection section, a bunch energy, and a charge amount of the bunch.

[0017] The transformation of the transverse phase space non-linear modulation amount caused by the transverse space charge force in the unit length is:

[0018]

[0019] wherein N e is the number of point particles in a single bunch; r e is a classical electron radius; γ is a relativistic factor, σ z is a bunch longitudinal root mean square length at the exit of the injection section.

[0020] The phase space pre-modulation amount ΔW ε is obtained by statistics as follows:

[0021]

[0022] wherein W ij is an area of a parallelogram formed by connecting the positions of any two particles i and j with the origin O, <> ij is a statistical index for i and j, r i , r j respectively represent phase space coordinates of any particles i and j.

[0023] The original constraint conditions of the injection section include: taking a laser coefficient of an electron gun of the injection section, a solenoid position and intensity, positions, phases, and peak electric fields of an acceleration cavity and an acceleration module as non-optimized variables, and taking a bunch length and a transverse emittance at the exit of the injection section as optimization targets.

[0024] The optimization method for the injector of the energy recovery type linear accelerator further includes:

[0025] S4: obtaining a bunch longitudinal root mean square length σ z and a bunch projected energy spread σ e at the exit of the injection section according to the exit parameters of the injector device;

[0026] S5: in the process of optimizing the merging section of the injector device, obtaining a second emittance optimization function according to the transverse phase space displacement in the x and x' directions caused by the longitudinal space charge effect; then, obtaining an optimization result according to a constraint condition that the second emittance optimization function tends to 0 and the existing constraint conditions, or screening the optimization result obtained in step S3 based on the second emittance optimization function so that the second emittance optimization function tends to 0.

[0027] According to the transverse phase space displacement in the x and x' directions caused by the longitudinal space charge effect, a second emittance optimization function is obtained, specifically including:

[0028] Taking the outlet of the merging section of the injector device as an observation point, according to the transverse phase space displacement Δx f (z) and Δx' LSC (z) in the x and x' directions at the observation point s LSC , a second emittance optimization function is obtained, including:

[0029]

[0030]

[0031] wherein, is the item of the 6th row of the i-th column of the transfer matrix from any point s to the observation point s f in the merging section from the outlet of the j-th bending magnet to the inlet of the j+1-th bending magnet, i=1, 2, R 56,j is the item of the 6th row of the 5th column of the transfer matrix from the outlet of the i-th bending magnet to the i+1-th bending magnet in the merging section, L j is the distance between the j-th bending magnet and the j+1-th bending magnet in the merging section, and h is the initial energy chirp of the beam.

[0032] The step S5 further includes adding a constraint condition, and the added constraint condition includes: a color dispersion condition of the merging section; and / or wherein, σ z is the longitudinal root mean square length of the beam at the outlet of the injection part, σ e is the projection energy spread of the beam at the outlet of the injection part, R 56 is the item of the 6th row of the 5th column of the transfer matrix of the structure as a whole of the injector device.

[0033] Compared with the existing optimization method, the optimization method for the injector of the energy recovery type linear accelerator of the present application considers the transverse space charge effect of the subsequent low-energy region, optimizes or screens the beam of the injection part of the injector device, reduces the influence of the transverse charge force of the beam in the subsequent transmission, and can effectively improve the power of the subsequent radiation section. Furthermore, the present application designs the merging section on the basis of considering the influence of the beam length change, can reduce the slice center deviation caused by the longitudinal space charge effect, reduces the transverse emittance of the beam and improves the peak power of the FEL process, therefore, the design of the merging section is faster in optimization speed, simpler in form, does not need to be specifically optimized for different beams, has strong applicability, and the result is closer to the real situation. In summary, the optimization method for the injector of the energy recovery type linear accelerator of the present application reduces the slice center deviation, and can reduce the beam loss phenomenon in the undulator. Attached Figure Description

[0034] Figure 1 This is a typical injector layout diagram for an energy recovery accelerator.

[0035] Figure 2 This is a flowchart of the optimization method for the injector of the present invention for an energy recovery linear accelerator.

[0036] Figure 3A and Figure 3B This is a schematic diagram illustrating the phase space distribution variation upon which the optimization method for the injector in an energy-recovery linear accelerator of this invention is based. Figure 3A This is a schematic diagram illustrating the principle by which transverse space charge forces cause a nonlinear distribution in the phase space of the cluster. Figure 3B How to use ΔA ε The principle diagram of opposite phase space distributions canceling each other out is shown in... Figure 3A and Figure 3B In the middle, the two large images on either side show the spatial distribution of the image before and after being affected by a nonlinear force (in this invention, the space charge force); the small image in the middle shows the distribution of the space charge force.

[0037] Figure 4 It is a comparison of the calculation results (curve) and the BMAD simulation results (data points) of the formula (3) for the transformation of the phase space nonlinear modulation amount caused within a unit length.

[0038] Figure 5 This is a schematic diagram illustrating the principle that different slice centers of a bundle cause an increase in emissivity.

[0039] Figure 6 This is a simulation result diagram showing the relationship between the normalized extra energy dissipation generated by the longitudinal space charge force per unit length and the beam length.

[0040] Figure 7A and Figure 7B The lateral displacement coefficient ζ of the beamline in the x-direction is given in this invention. sc The lateral displacement coefficient ζ′ of the bundle in the x′ direction sc The graph compares the function values ​​with the simulation results, where... Figure 7A The lateral displacement coefficient ζ of the beamline in the x-direction is shown. sc , Figure 7B The lateral displacement coefficient ζ′ of the beamline in the x′ direction is shown. sc .

[0041] Figure 8A This is a slice of emittance along the x-direction and the longitudinal beam cross-section of the beam cluster at the injection point exit. Figure 8B This is a diagram showing the longitudinal beam cross-section and x-direction slice emittance distribution of the beam cluster at the exit of the merged section. DETAILED DESCRIPTION

[0042] The preferred embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0043] The optimization method for the injector of the energy recovery type linear accelerator of the present application also adopts the same layout as the typical injector layout of the energy recovery type accelerator shown in Figure 1 The optimization method for the injector of the energy recovery type linear accelerator of the present application is mainly based on the following principles:

[0044] In general, the distribution of the beam bunch is close to a Gaussian distribution, and the transverse space charge force is nonlinearly distributed in the transverse longitudinal direction, which acts on the beam bunch and changes the distribution of the slice phase space. This nonlinear distribution increases the slice emittance compared to the original phase space distribution. In order to facilitate understanding, the emittance ε at this time is rewritten as:

[0045]

[0046] where n is the total number of particles, W ij is the area of the parallelogram formed by the connection line between the positions of any two particles i and j and the origin O, W ij = R i SR j , where R i , R j represent the phase space coordinates of any particles i, j respectively. S is a symplectic form, and in the accelerator, its form is:

[0047]

[0048] Therefore, W ij is the area of the parallelogram formed by the connection line between the positions of any two particles i and j and the origin O, which is 0 when the phase space is straight, and the emittance tends to 0; when the transverse space charge force makes the phase space a curve, the area of this parallelogram is not 0, and the emittance increases.

[0049] On this basis, the optimization method for the injector of the energy recovery type linear accelerator of the present application proposes a pre-modulation method to balance the subsequent transverse space charge force. The principle of the phase space distribution change based on the optimization method for the injector of the energy recovery type linear accelerator of the present application is shown in Figure 3A As shown in Figure 3A , for a linear phase space, the transverse space charge force will cause a nonlinear distribution of the phase space and thus increase the emittance. As shown in Figure 3B , an opposite nonlinear distribution can offset this effect. In the optimization process of the injection part, this nonlinear modulation amount can be included in the objective function, so that the phase space of the injection part produces an opposite nonlinear distribution.

[0050] And this pre-modulation of the quantitative description can be analyzed by the following way.

[0051] In the present application, A ε is used to represent the phase space nonlinear modulation caused by different external forces, and the transformation of the phase space nonlinear modulation caused by different external forces in unit length ds is The calculation formula is:

[0052] Where λ(r i ,z i ) is the density of the beam at (r i ,z i ), P r , P z are the momentum components of the particles in the transverse and longitudinal directions, r1, r2 represent the transverse coordinates of different particles, z1, z2 represent the longitudinal coordinates of different particles, represent the change of the normalized momentum of different particles.

[0053] Where, when only considering the transverse space charge force, the change of the normalized momentum is:

[0054]

[0055] Where e is the charge amount of a unit charged particle (in this embodiment, the charged particle is an electron, and hereinafter the electron is used instead of the charged particle), which is a constant, γ is the relativistic factor, which can be calculated by the exit energy of the injection part 100, m e is the rest mass of the electron, which is a constant, c is the speed of light in a vacuum, which is a constant, and E r is the radial electric field distribution caused by the transverse space charge force.

[0056] In the optimization process of the injector device of the energy recovery type linear accelerator (ERL), in most cases, the beam distribution at the exit of the injection part 100 in the injector device is a Gaussian-like distribution, and satisfies γσ z >>σ r , where σ r is the beam radial root mean square length at the exit of the injection part, σ z is the beam longitudinal root mean square length at the exit of the injection part, and γ is the relativistic factor.

[0057] Then, after the calculation of formula (2), the transformation of the phase space nonlinear modulation caused by different external forces in unit length ds is :

[0058]

[0059] Where Ne N is the number of particles per bunch, which is determined by the design parameters of the injector device; r e is the classical electron radius, and γ is the relativistic factor, σ z is the longitudinal root-mean-square bunch length at the exit of the injection section.

[0060] For a Gaussian bunch and a quasi-Gaussian bunch, the transformation of the phase space non-linear modulation quantity caused by the space charge force per unit length can be expressed by the above formula (3). Further, the symbol A' ε will be used instead of to represent the transformation of the phase space non-linear modulation quantity per unit length (for example, in Figure 4 ).

[0061] Figure 4 is the numerical result (curve) of the transformation of the phase space non-linear modulation quantity per unit length calculated by formula (3) , and the calculation result (data points) of the BMAD software simulation varies with the longitudinal root-mean-square bunch length σ z at the exit of the injection section, and the two have good consistency, verifying the accuracy.

[0062] Further, by estimating the total length ΔL of the matching section and the merging section in the injector device, the phase space non-linear modulation quantity ΔA ε caused by the transverse space charge force in the matching section and the merging section is estimated by the following formula:

[0063]

[0064] where ΔL is the total length of the matching section and the merging section in the injector device, represents the transformation of the phase space non-linear modulation quantity per unit length of different external forces (the space charge force in the present application).

[0065] Therefore, in the optimization process, the phase space of the bunch at the exit of the injection section can have an opposite phase space pre-modulation quantity ΔW ε , and this phase space pre-modulation quantity needs to satisfy the relationship: ΔW ε = -ΔA ε .

[0066] At this time, the phase space pre-modulation quantity ΔW ε can be offset by the non-linear modulation caused by the transverse space charge force in the matching section 200 and the merging section 300, so as to reduce the influence of the transverse space charge force on the transverse emittance in the downstream structure (i.e., the matching section 200 and the merging section 300) of the injection section.

[0067] For the particle cluster at the exit of the injected portion, the phase space premodulation amount ΔW ε It can be obtained statistically by the following formula:

[0068]

[0069] Among them, W ij Let O be the area of ​​the parallelogram formed by the lines connecting the positions of any two particles i and j to the origin O. ij To perform statistical analysis on indicators i and j, r i r j and represent the phase space coordinates of arbitrary particles i and j, respectively.

[0070] This inverse phase space premodulation amount ΔW ε The longitudinal gradient originates from the solenoid and is related to the solenoid's design.

[0071] Based on the above principles, in order to counteract the effects of transverse space charge in the matching and merging sections of the injector in an energy recovery linear accelerator (ERL), such as... Figure 2 As shown, the optimization method for the injector of the present invention for an energy recovery linear accelerator includes the following steps:

[0072] Step S1: Based on the existing design, estimate the bundle parameters at the exit of the injection section and the distance from the exit to the main accelerator inlet. The bundle parameters at the exit of the injection section include the lateral and / or radial dimensions of the bundle at the exit of the injection section, energy, bundle charge, etc.

[0073] Among them, the existing design can be, for example, the design goals in references [1]-[4] and the design goals of the machine itself. For energy recovery accelerator devices used for free electron lasers, the transverse and radial dimensions of the exit bundle parameters of the injection section are approximately: the root mean square length of the bundle radial direction at the exit of the injection section σ r ~The root mean square length σ of the bundle at the outlet of the injection section z ~1mm, energy approximately 5~10MeV (relativistic factor γ approximately 10~20). Based on the existing design, the distance from the injection section outlet to the main accelerator inlet is estimated, while also considering factors such as spatial arrangement. The total length of the conventional matching section 200 and merging section 300 is approximately 10m.

[0074] During injector optimization, most of the output bunch parameters are distributed as Gaussian (or near-Gaussian) or uniform. Uniform distributions do not introduce nonlinear modulation. However, uniform distributions are more ideal, so this paper calculates a Gaussian distribution. Since this invention considers a near-Gaussian distribution, the bunch parameters at the injection exit that need to be estimated include the bunch charge, energy, and the root mean square length σ of the bunch longitudinal direction at the injection exit.z .

[0075] Step S2: Determine the transformation of the phase space nonlinear modulation per unit length caused by the transverse space charge force. At the same time, based on To predict the phase space nonlinear modulation ΔA caused by the transverse space charge force in the matching and merging sections of the injector. ε ;

[0076] The transformation of the phase space nonlinear modulation caused by the transverse space charge force per unit length is calculated using formula (3) above. That is, the transformation of the phase space nonlinear modulation amount per unit length caused by the transverse space charge force. for:

[0077]

[0078] Where, N e The number of charged particles in a single cluster is determined by the design specifications of the injector device; r e σ is the classical electron radius, γ is a constant; γ is the relativistic factor, σ z The root mean square length of the bundle at the outlet of the injection section.

[0079] Step S3: During the process of optimizing the injection section of the injector device, the phase space nonlinear modulation amount ΔA caused by the obtained transverse space charge force in the matching and merging sections of the injector is calculated. ε In the original constraints of the injection part, an emission optimization function f is added. obj Subsequently, based on the reactivity optimization function f obj The optimization result is obtained by considering the constraints approaching 0 and the original constraints, or based on the emission optimization function f. obj The optimization results obtained under the original constraints are filtered to ensure that the emittance optimization function f obj It approaches 0.

[0080] The original constraints of the injection section include: taking the electron gun laser coefficient, solenoid position and intensity, acceleration cavity and acceleration module position, phase and peak electric field of the injection section as unoptimized variables, and taking the beam length and transverse emittance at the exit of the injection section as optimization targets.

[0081] Emittance optimization function f obj for:

[0082] f obj =ΔW ε +ΔA ε ,

[0083] wherein, ΔA ε represents the amount of nonlinear modulation in phase space caused by the transverse space charge force in the matching section and merging section of the injector, which is estimated by step S2 and is a constant; ΔW ε is the amount of pre-modulation in phase space, which is obtained from the beam bunch at the exit of the statistical injection section. Specifically, ΔW ε is obtained statistically using the formula (4) above.

[0084] In addition, the present application can further comprise the following steps to further optimize the emittance:

[0085] Step S4: obtaining the beam bunch longitudinal root mean square length σ z and the beam bunch projected energy spread σ e at the exit of the injection section according to the exit parameters of the injector device.

[0086] wherein, the beam bunch longitudinal root mean square length σ z and the beam bunch projected energy spread σ e at the exit of the injection section can be directly derived using a conventional accelerator.

[0087] Step S5: obtaining a second emittance optimization function according to the transverse phase space displacement in the x and x' directions caused by the longitudinal space charge effect in the process of optimizing the merging section of the injector device; then, obtaining the optimization result according to the constraint condition that the second emittance optimization function tends to 0 and the existing constraint conditions, or screening the optimization result obtained in step S3 based on the second emittance optimization function so that the second emittance optimization function tends to 0.

[0088] In addition, the step S5 further comprises: adding a new constraint condition, and the new constraint condition comprises: a merging section achromatic condition; and / or wherein, σ z is the beam bunch longitudinal root mean square length at the exit of the injection section, σ e is the beam bunch projected energy spread at the exit of the injection section, R 56 is the item in the 5th column and the 6th row of the transfer matrix of the structure as a whole of the injector device, R 56 has symmetry, and the calculation results of the reverse beam line and the beam line are the same. Specifically, since the deflection angle of the merging section is large (generally in the range of [10° to 20°]), it is easy to cause excessive compression of the beam bunch due to R 56 being too large, and therefore, R 56 needs to be additionally limited, and the limitation condition is:

[0089] wherein, the second emittance optimization function is obtained according to the transverse phase space displacement in the x and x' directions caused by the longitudinal space charge effect, and specifically comprises:

[0090] Using the outlet of the merging section 300 of the injector device as the observation point, based on the observation point s f Transverse phase space displacement Δx in the x and x′ directions caused by the longitudinal space charge effect LSC (z), Δx′ LSC The second emittance optimization function is obtained, including:

[0091]

[0092]

[0093] in, Let any point s between the exit of the j-th curved iron block and the entrance of the (j+1)-th curved iron block in the merged section be the observation point s. f The item in the 6th row of the i-th column of the transfer matrix, R 56,j L is the item in the 5th column and 6th row of the transmission matrix from the outlet of the i-th bent iron to the (i+1)-th bent iron in the merged section. j Let h be the distance between the j-th bent iron block and the (j+1)-th bent iron block in the merging segment, and let h be the initial energy chirp of the cluster, defined as...

[0094] For the merged section 300 of the injector device, the physical process causing bunch mass decay is as follows: the longitudinal space charge force alters the bunch energy (energy dissipation) during bunch motion. This additional energy dissipation is coupled with the bundle transfer matrix; therefore, an additional step is added to the emittance optimization function at observation point s. f Transverse phase space displacement in the x and x′ directions caused by longitudinal space charge effect and in, Represents the distance from any point s to the observation point s f The term in the 6th row of the i-th column of the transmission matrix is ​​given. The transmission matrix is ​​calculated using the method presented in the textbook and is a 6×6 matrix; s is an arbitrary point. f The observation point can be either the beamline exit of the accelerator or a measurement point, Δδ LSC (s) represents the extra energy dissipation caused by the longitudinal space charge force at any point s within a unit length.

[0095] For non-dispersive regions such as linear nodes, the distance from any point s to the observation point s f The item in the 6th row of the i-th column of the transfer matrix At any point s, it equals 0. Therefore, the phase space premodulation amount ΔW εAs the bundle moves through the dispersive regions (such as the merging section 300 in the injector device and the arc section downstream of the injector device), the total displacement is obtained by summing all displacements. For different slices, the additional energy dispersion produced at the same location is different, thus causing different displacements, which results in each slice in the bundle having a different center position at the measurement point. For example... Figure 5 As shown, different bundle slice centers will cause the projected area of ​​the transverse phase space, which in turn will increase the overall emissivity of the bundle (also known as projected emissivity).

[0096] Quantitatively calculate the additional energy dissipation Δδ caused by the longitudinal space charge force at any point s within a unit length. LSC (s) is complex, but when the bundle satisfies γσ z >>σ r At any point s, the additional energy dissipation Δδ caused by the longitudinal space charge force per unit length is... LSC (s) will be related to 1 / σ z (s) 2 Proportional, σ z (s) represents the root-mean-square length of the bundle at any point s. For example... Figure 6 The figure shows the BMAD software simulation results of the relationship between normalized extra energy dissipation and bundle length under different lateral dimensions, with the bundle energy set to 10 MeV. It can be seen that the extra energy dissipation Δδ caused by the longitudinal space charge force at any point s per unit length is significant. LSC (s) is indeed related to 1 / σ z (s) 2 Proportional, σ z (s) represents the root mean square length of the bundle at any point s.

[0097] Therefore, for any two points s1 and s2 in the bundle, the following relation holds:

[0098]

[0099] Δδ LSC (s1), Δδ LSC (s2) represents the extra energy dissipation caused by the longitudinal space charge force at any two points s1 and s2 within a unit length, σ z (s1), σ Z (s2) represents the root mean square length of the bundle longitudinally at any two points s1 and s2.

[0100] Therefore, in this invention, the additional energy dissipation Δδ caused by the longitudinal spatial charge force at any point s within a unit length is... LSC (s) is represented as:

[0101]

[0102] where k sc is the constant of energy spread, which is constant for the whole beam line, and σ z (z) is the longitudinal root-mean-square (RMS) length of the beam at slice z.

[0103] At this time, for any slice z, the transverse phase space displacement Δx f (z) and Δx′ LSC (z) in x and x' directions at observation point s LSC caused by the longitudinal space charge effect are:

[0104]

[0105]

[0106] where σ (z) and σ 56 (z) are the longitudinal RMS length and the projected energy spread of the beam at the exit of the injection section, respectively, and R (z) is the value of the 5th column and 6th row of the transport matrix at any point s z (z) is the longitudinal RMS length of the beam at any point s sc (z); k (z) is the constant of energy spread, and ζ f (z) is the value of the i-th column and 6th row of the transport matrix from any point s sc (z) is the transverse displacement coefficient of the beam line in x direction, and ζ' sc (z) is the transverse displacement coefficient of the beam line in x' direction.

[0107] That is, in Eqs. (5) and (6), the displacement caused by the longitudinal space charge effect is divided into two parts: the constant of energy spread k sc : this parameter is only related to the specific distribution of the beam, such as the amount of charge, the three-dimensional distribution in real space, etc.; the transverse displacement coefficients of the beam line in x direction ζ sc and x' direction ζ' sc : only related to the transport matrix of the beam line and the longitudinal RMS length σ z (z) and the projected energy spread σ e (z) of the beam at the exit of the injection section, especially the ratio σ e (z) / σ z (z).

[0108] Further, we assume that the bending iron region in the merging section is much smaller than the straight line region, and the change of the beam length in the non-bending iron region is ignored. In order to make the transverse displacement of the slice to be 0, according to Eqs. (5)-(6), the merging section needs to satisfy:

[0109]

[0110]

[0111] wherein, R f is the item of the 6th row of the i-th column of the transfer matrix from any point s to the observation point s in the merging section between the exit of the j-th block of the bending magnet and the entrance of the j+1-th block of the bending magnet, 56,j R 56,i is the item of the 6th row of the 5th column of the transfer matrix from the exit of the i-th block of the bending magnet to the i+1-th block of the bending magnet, R j is the distance between the j-th block of the bending magnet and the j+1-th block of the bending magnet in the merging section.

[0112] Experimental results:

[0113] The conditions of the formulas (7) and (8) are irrelevant to the beam parameters k sc , and are theoretically valid for any beam. In order to verify the correctness of the theory, the simulation results of the transverse phase space displacement caused by the longitudinal space charge effect and are introduced as the beam line transverse displacement coefficient ζ sc in the x direction and the beam line transverse displacement coefficient ζ′ sc in the x′ direction. The zigzag merging section is proposed in the document [5], and is currently recognized as the best merging section. Figure 7A and Figure 7B The comparison chart of the function values of the beam line transverse displacement coefficient ζ sc in the x direction and the beam line transverse displacement coefficient ζ′ sc in the x′ direction in the present application and the simulation results is given, wherein Figure 7A the beam line transverse displacement coefficient ζ sc in the x direction is shown, Figure 7B the beam line transverse displacement coefficient ζ′ sc in the x′ direction is shown. Figure 7A and Figure 7B The function values and the simulation results show good consistency.

[0114] Taking the FV injector as an example, wherein the exit beam selection of the injector adopts the emittance optimization function f obj = ΔW ij + ΔA ε to select the beam so that the emittance optimization function f obj tends to 0. The selection results are as follows: Figure 8A and Figure 8BThe longitudinal beam cross section is shown as a curve with two slightly higher portions on the sides, and the slice emittance distribution is a curve with a higher middle portion. Figure 8A The longitudinal beam cross section at the injection section exit of the FV injector and the x-direction slice emittance distribution are Figure 8B The longitudinal beam cross section at the injection section exit of the FV injector and the x-direction slice emittance distribution are Figure 8A , Figure 8B The beam is further compressed, and the slice emittance growth is negligible, less than the ideal beam. In multiple iterations, it was found that multiple sets of slice emittance reduction results were not displayed due to other parameters not meeting the requirements.

[0115] For the merging section, taking the injection section exit of the FV injector as an example, the slice emittance growth of the merging section 300 optimized by the optimization method of the present application is less than that of other existing merging sections, and the beam brightness is increased by 1.5 times under the same optical parameters.

[0116] It should be noted that the optimization method of the present application is an improvement on the existing optimization method by adding constraints, so the remaining steps are consistent with the optimization method of the existing injector device.

[0117] Compared with the previous optimization method, the optimization method of the injector for the energy recovery type linear accelerator of the present application optimizes or screens the injection section of the injector device on the basis of considering the transverse space charge effect of the subsequent low-energy region, so that the beam reduces the influence of the transverse charge force in the subsequent transmission, and the power of the subsequent radiation section can be effectively improved. Furthermore, the present application designs the merging section on the basis of considering the influence of the beam length change, which can reduce the slice center offset caused by the longitudinal space charge effect, reduce the transverse emittance of the beam, and thus improve the peak power of the FEL process. Therefore, the design of the merging section is faster, simpler, and does not need to be specifically optimized for different beams, has strong applicability, and the results are closer to the real situation. In summary, the optimization method of the injector for the energy recovery type linear accelerator of the present application reduces the slice center offset, and can reduce the beam loss phenomenon in the undulator.

[0118] The references are as follows:

[0119] [1] Bazarov, I. V., and C. K. Sinclair. "High brightness, high current injector design for the Cornell ERL prototype." Proceedings of the 2003 Particle Accelerator Conference. Vol. 3. IEEE, 2003.

[0120] [2] Jiao, Yi, and Ou-Zheng Xiao. "Beam dynamics studies of the photo- injector in low-charge operation mode for the ERL test facility at IHEP." Chinese Physics C 38.6 (2014): 067003.

[0121] [3] Kuske, B., et al. "The injector layout of BERLinPro." Proc. 4th Int. Particle Accelerator Conf. (IPAC'13). 2013.

[0122] [4] Tanaka, O. A., N. Higashi, and T. Miyajima. "Injector Optimization for the IR-FEL Operation at the Compact ERL at KEK." Proc. IPAC'21 (2021): 4531-4534.

[0123] [5] Litvinenko, Vladimir N., Ryoichi Hajima, and Dmitry Kayran. "Merger designs for ERLs." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 557.1 (2006): 165-175.

[0124] The above description is only the preferred embodiment of the present application, not to limit the scope of the present application, the above embodiment of the present application can be made various changes. Any simple, equivalent changes and modifications made according to the content of the claims and the description of the present application, all fall within the scope of the present application. The present application is not described in detail, all are conventional technical content.

Claims

1. An optimization method for an injector in an energy recovery linear accelerator, characterized in that, include: Step S1: Based on the existing design, estimate the bundle parameters at the exit of the injection section and the distance from the exit to the main accelerator inlet; Step S2: Determine the transformation of the phase space nonlinear modulation per unit length caused by the transverse space charge force. At the same time, based on To predict the phase space nonlinear modulation caused by the transverse space charge force in the matching and merging sections of the injector. ; The total length of the matching and merging segments in the injector device; Step S3: During the process of optimizing the injection section of the injector device, the phase space nonlinear modulation amount caused by the obtained transverse space charge force in the matching and merging sections of the injector is determined. Add an emittance optimization function to the original constraints of the injection part. Subsequently, based on the reactivity optimization function... The optimization result is obtained by considering constraints approaching 0 and the original constraints, or based on the emission optimization function. The optimization results obtained under the original constraints are filtered to make the emittance optimization function... Approaching 0; The emission optimization function for: = ， in, This represents the phase-space nonlinear modulation caused by the transverse space charge force in the matching and merging sections of the injector; It is the phase space premodulation quantity, which is obtained from the bundle at the exit of the statistical injection section; The transformation of the phase space nonlinear modulation per unit length caused by the transverse space charge force is expressed as: ， Where, N e The number of charged particles in a single cluster; The classical electron radius; Relativistic factor The root mean square length of the bundle at the outlet of the injected portion; The phase space premodulation amount The results are obtained from the following formula: ， in, Let the positions of any two particles i and j be relative to the origin. The area of ​​the parallelogram formed by the connecting lines. To perform statistical analysis on indicators i and j, and represent the phase space coordinates of arbitrary particles i and j, respectively.

2. The optimization method for the injector of an energy recovery linear accelerator according to claim 1, characterized in that, In step S1, the bundle parameters at the outlet of the injection portion include at least one of the following: the lateral and / or radial dimensions of the bundle at the outlet of the injection portion, the bundle energy, and the amount of charge in the bundle.

3. The optimization method for the injector of an energy recovery linear accelerator according to claim 1, characterized in that, The original constraints of the injection section include: taking the electron gun laser coefficient, solenoid position and intensity, acceleration cavity and acceleration module position, phase and peak electric field of the injection section as unoptimized variables, and taking the beam length and transverse emittance at the exit of the injection section as optimization targets.

4. The optimization method for the injector of an energy recovery linear accelerator according to claim 1, characterized in that, Also includes: Step S4: Based on the outlet parameters of the injector device, obtain the root mean square length of the bundle at the outlet of the injection section. Bundle projection energy dispersion ; Step S5: During the optimization of the merging section of the injector device, based on the longitudinal space charge effect... and The lateral phase space displacement in the direction is used to obtain the second emittance optimization function; Subsequently, the optimization result is obtained based on the constraint that the second emission optimization function tends to 0 and the existing constraints, or the optimization result obtained in step S3 is filtered based on the second emission optimization function so that the second emission optimization function tends to 0.

5. The optimization method for the injector in an energy recovery linear accelerator according to claim 4, characterized in that, Caused by the longitudinal space charge effect and The lateral phase space displacement in the direction yields the second emittance optimization function, which specifically includes: Using the outlet of the combined section of the injector device as the observation point, based on the observation point Caused by longitudinal space charge effect and Lateral phase space displacement in the direction , The second emittance optimization function is obtained, including: ， ， in, For any point s between the exit of the j-th curved iron block and the entrance of the (j+1)-th curved iron block in the merged section, the observation point is considered. The item in the 6th row of the i-th column of the transfer matrix, , This refers to the item in the 5th column and 6th row of the transmission matrix from the outlet of the i-th bent iron block to the (i+1)-th bent iron block in the merged section. For the merger of Section 1 The bent iron block and the first +1 is the spacing between the bent iron pieces, and h is the initial energy chirp of the cluster.

6. The optimization method for the injector in an energy recovery linear accelerator according to claim 4, characterized in that, Step S5 further includes: adding new constraints, including: a merger segment anti-dispersion condition; and / or ,in, The root mean square length of the bundle at the outlet of the injection section is the longitudinal direction. The bundle projection energy dispersion at the outlet of the injected portion, This is the item in the 5th column and 6th row of the overall transfer matrix of the injector device.

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