Optimization method for injector of energy recovery type linear accelerator

Abstract

The invention provides an optimization method for an injector of an energy recovery type linear accelerator, and the method comprises the steps: estimating a beam bunch parameter at an outlet of an injection part and a distance from the outlet to an inlet of a main accelerator through an existing design; determining a transformation of the phase space non-linear modulation amount within a transverse unit length caused by a transverse space charge force; meanwhile, the phase space nonlinear modulation quantity caused by the transverse space charge force in the matching section and the degenerate section of the injector is estimated; in the process of optimizing the injection part of the injector device, newly adding an emittance optimization function in the original constraint condition of the injection part; then, the emittance optimization function tends to 0. According to the optimization method provided by the invention, the beam bunch of the injection part of the injector device is optimized or screened on the basis of considering the transverse space charge effect of a subsequent low-energy region, so that the influence of transverse charge force on the beam bunch in subsequent transmission is reduced, and the power of a subsequent radiation section can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of accelerator physics and technology, and in particular relates to an optimization method for an injector of an energy recovery type accelerator. Background Art

[0002] Compared with linear accelerators, energy recovery linear accelerators (ERLs) can achieve higher repetition rates while ensuring the quality of the bunch, thereby increasing the overall average power of the machine. Currently, the repetition rate of mainstream energy recovery accelerators in the world is as high as 100 to 1300 MHz, which is about 100 times the repetition rate of Shanghai Hard X-ray Free Electron Laser. At the same time, compared with storage rings, ERLs can provide better bunch quality.

[0003] The overall bunch quality of the accelerator is determined by the injector device, and the beam quality of the injector device determines the overall bunch quality of the machine. Figure 1 This is a typical layout diagram of the injector device of an energy recovery accelerator. The direction of bunch transmission is from left to right: injection section 100 → matching section 200 → merger section 300 → subsequent beam line. Figure 1 As shown in FIG. 1 , unlike the injector device of a conventional linear accelerator, the injector device of an energy recovery linear accelerator is mainly divided into two parts: an injection part 100, a matching section 200 and a merging section 300. The injection part is similar to the injection part of a conventional accelerator, but in order to improve the energy circulation efficiency, the energy of the injection part of the ERL is relatively small. The energy at the exit of the conventional injection part is less than 15 MeV. Furthermore, since the ERL is a ring-shaped device, a merging section is required to deflect the bunch from the injection part to the main circulation line. The typical ERL injector device is as follows: Figure 1 As shown, the injection section is usually composed of an electron gun 101, a solenoid 102, a buncher 103, a helical line 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 for the emittance of the bunch, make the bunch generate energy chirp to compress the bunch and pre-accelerate the bunch. The matching section 200 is composed of a plurality of quadrupole magnets 201, and the merging section 300 is composed of a dipole magnet 301 and a quadrupole magnet 302, which are respectively used to bunch and deflect the bunch, and transfer the bunch 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 performance of the bunch in the injector is the space charge effect, that is, the effect of the Coulomb repulsion between the electrons in the electron bunch on the electron distribution in the bunch. The space charge effect exists in the entire range of the machine and weakens with the increase of energy. In accelerator physics, there are two forms of space charge effect: transverse space charge effect and longitudinal space charge. The direction of the transverse space charge is radially outward. Usually, the transverse space charge force is nonlinearly distributed, and the nonlinear space charge force enhances the nonlinear distribution of the transverse phase space of the bunch, and the enhancement of the nonlinear distribution of the transverse phase space increases the transverse slice emittance of the bunch. A common method is to use a solenoid to rotate the bunch to reduce the size of the emittance in a single dimension by reducing the coupling term in the xy direction. This method is widely used in the optimization process of conventional injectors. Conventional optimization work often focuses on the exit of the injection part. For conventional accelerators, the beam at the exit of the injection part will be further accelerated to the high-energy region, and the subsequent beamline will be less affected by the space charge.

[0005] Unlike traditional injectors, the ERL injector device includes an injection section 100 and an additional matching section 200 and a merging section 300, which have the following functions: the injection section 100 accelerates the electrons generated by the electron gun to about 10 MeV to alleviate the influence of space charge on the bunch; the matching section 200 is used to adjust the bunch envelope to prevent the bunch from being over-dispersed and causing beam loss due to excessive lateral size; the merging section 300 is used to deflect the bunch to the main circulation line to further accelerate the bunch. Due to the additional matching section 200 and merging section 300, the ERL injector device has a longer space charge working area. However, the existing optimization scheme is only the best result of the injection part, and the matching section 200 and merging section 300 after the injector device are not taken into account. Therefore, the current optimization scheme may cause the increase of slice emittance in the subsequent process and deteriorate the beam quality. For the longitudinal space charge, the longitudinal space charge changes the energy dispersion. In the non-dispersive region, the longitudinal space charge will not directly affect the emittance; in the dispersive region such as the merging section 300, the additional energy dispersion caused by the longitudinal space charge force will couple with the dispersion term, thereby affecting the transverse emittance.

[0006] Conventional optimization methods include R matrix method, bunch dispersion function optimization, etc. For the former method, the existing model cannot accurately reflect the non-uniform energy dispersion changes caused by longitudinal space charge; while bunch dispersion optimization needs to be combined with finite element method, which has slow optimization speed and poor versatility, and both have their own limitations.

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

[0008] The purpose of the present invention is to provide an injector design for low-energy beam injection in an energy recovery type linear accelerator, in which a pre-modulation method is used to offset the lateral space charge force of the subsequent beam line, which can effectively reduce the influence of the lateral space charge force on the quality of the injected bunch and improve the overall performance of the device.

[0009] In order to achieve the objective, the present invention provides an optimization method for an injector of an energy recovery type linear accelerator, comprising:

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

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

[0012] S3: In the process of optimizing the injection part of the injector device, the phase space nonlinear modulation ΔA caused by the transverse space charge force in the matching section and the merger section of the injector is obtained. ε , add the emittance optimization function f to the original constraints of the injection part obj ; Then, according to the emittance optimization function f obj The constraints tending to 0 and the original constraints are optimized, or based on the emittance optimization function f obj The optimization results obtained by the original constraints are screened so that the emittance optimization function f obj tends to 0;

[0013] The emittance optimization function f obj for:

[0014] f obj =ΔW ε +ΔA ε ,

[0015] Where ΔA ε ΔW represents the nonlinear modulation of the phase space caused by the transverse space charge force in the matching section and the merged section of the injector; ε is the phase space premodulation amount, which is obtained by counting the bunch at the exit of the injection part.

[0016] In the step S1 , the bunch parameters at the outlet of the injection portion include at least one of a lateral size and / or a radial size of the bunch at the outlet of the injection portion, a bunch energy, and a charge amount of the bunch.

[0017] Transformation of the nonlinear modulation in the phase space per unit length caused by the transverse space charge force for:

[0018]

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

[0020] The phase space premodulation amount ΔW ε It is obtained by the following formula:

[0021]

[0022] Among them, W ij is the area of ​​the parallelogram formed by the lines connecting the positions of any two particles i and j and the origin O, <> ij To perform statistics on index i and j, r i , r j Represent the phase space coordinates of arbitrary particles i and j respectively.

[0023] The original constraints of the injection part include: taking the electron gun laser coefficient of the injection part, the solenoid position and strength, the position, phase, and peak electric field of the acceleration cavity and the acceleration module as unoptimized variables, and taking the beam length and lateral emittance at the injection part outlet as optimization targets.

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

[0025] S4: According to the outlet parameters of the injector device, the longitudinal root mean square length σ of the bunch at the outlet of the injection part is obtained z and the bunch projection energy dispersion σ e ;

[0026] S5: In the process of optimizing the merging section of the injector device, a 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; then, the optimization result is obtained according to the constraint condition that the second emittance optimization function tends to 0 and the existing constraint condition, or the optimization result obtained in step S3 is screened 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, the second emittance optimization function is obtained, which specifically includes:

[0028] The outlet of the merging section of the injector device is taken as the observation point. f The transverse phase space displacement Δx in the x and x′ directions caused by the longitudinal space charge effect at LSC (z), Δx′ LSC , the second emittance optimization function is obtained, including:

[0029]

[0030]

[0031] in, From any point s to the observation point s between the exit of the jth curved iron block and the entrance of the j+1th curved iron block in the merged section f The entry in the ith column and sixth row of the transfer matrix, i = 1, 2, R 56,j is the item in the 5th column and the 6th row of the transmission matrix from the exit of the i-th curved iron to the i+1-th curved iron in the merged section, L j is the distance between the jth bent iron and the j+1th bent iron in the merging section, and h is the initial energy chirp of the bunch.

[0032] The step S5 further includes: adding a new constraint condition, the new constraint condition including: a merged segment dispersion elimination condition; and / or Among them, σ z is the longitudinal root mean square length of the bunch at the exit of the injection section, σ e is the projected energy dispersion of the bunch at the exit of the injection part, R 56 It is the entry in the 5th column and the 6th row of the transmission matrix of the overall structure of the injector device.

[0033] Compared with the existing optimization methods, the optimization method of the injector for the energy recovery type linear accelerator of the present invention optimizes or screens the injection part bunch of the injector device on the basis of considering the transverse space charge effect of the subsequent low-energy region, so that the bunch can reduce the influence of the transverse charge force in the subsequent transmission, which can effectively improve the power of the subsequent radiation section. Furthermore, the present invention 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 bunch and thus improve the peak power of the FEL process. Therefore, compared with other methods, the design of the merging section has a faster optimization speed and a simpler form, and does not require specific optimization for different bunches. It has strong applicability and the results are closer to the actual situation. In summary, the optimization method of the injector for the energy recovery type linear accelerator of the present invention reduces the slice center offset and can reduce the beam loss phenomenon of the bunch in the undulator. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0035] Figure 2 It is a flow chart of the optimization method of the injector for energy recovery type linear accelerator of the present invention.

[0036] Figure 3A and Figure 3B is a schematic diagram of the phase space distribution change based on the optimization method of the injector for the energy recovery type linear accelerator of the present invention, Figure 3A This is the principle diagram of the transverse space charge force causing the nonlinear distribution of the bunch phase space. Figure 3B How is ΔA used? ε Schematic diagram of the principle that opposite phase space distributions cancel each other out, in Figure 3A and Figure 3B In the figure, the large figures on both sides are the image space distribution before and after being affected by the nonlinear force (in this invention, the space charge force); the small figure in the middle is the distribution of the space charge force.

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

[0038] Figure 5 It is a schematic diagram of the principle of the increase in emittance caused by different slice centers of the bunch.

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

[0040] Fig. 7A and Figure 7B The beam line lateral displacement coefficient ζ in the x direction of the present invention is given as sc and the beamline lateral displacement coefficient ζ in the x′ direction s ' c The comparison chart of the function value and simulation results, where Fig. 7A The beamline lateral displacement coefficient ζ in the x-direction is shown sc , Figure 7B The beamline lateral displacement coefficient ζ in the x′ direction is shown s ' c .

[0041] Fig. 8A is the longitudinal beam cross section and the x-direction slice emittance distribution diagram of the bunch at the injection part exit, and Figure 8BIt is the longitudinal beam cross section and the x-direction slice emittance distribution diagram of the bunch at the exit of the merging section. DETAILED DESCRIPTION

[0042] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings and described in detail.

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

[0044] Under normal circumstances, the distribution of the bunch is close to Gaussian distribution, and the transverse space charge force is nonlinearly distributed along the transverse and longitudinal directions. When acting on the bunch, it will change the distribution of the slice phase space. This nonlinear distribution will increase the slice emittance compared to the original phase space distribution. For ease of 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 lines connecting 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 arbitrary particles i and j respectively. S is in symplectic form, and its form in the accelerator is:

[0047]

[0048] Therefore, W ij It is the area of ​​the parallelogram formed by the line connecting the positions of any two particles i and j and the origin O. When the phase space is a straight line, the area of ​​the parallelogram is 0 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 invention proposes a pre-modulation method to balance the subsequent transverse space charge force. The principle of phase space distribution change based on the optimization method for the injector of the energy recovery type linear accelerator of the present invention is as follows: Figure 3A As shown. Figure 3A As shown, for linear phase space, the transverse space charge force will cause nonlinear distribution in phase space and increase the emittance. Figure 3BAs shown, 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, thereby causing the phase space of the injection part to produce an opposite nonlinear distribution.

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

[0051] In the present invention, A ε To represent the nonlinear modulation of the phase space caused by different external forces, at the same time, the transformation of the nonlinear modulation of the phase space caused by the unit length ds The calculation formula is:

[0052] Among them, λ(r i ,z i ) is the bunch in (r i ,z i ) density, P r , P z are the horizontal and vertical momentum components of the particle, r1 and r2 represent the horizontal coordinates of different particles, z1 and z2 represent the vertical coordinates of different particles, Represents the change in normalized momentum of different particles.

[0053] Among them, when only the transverse space charge force is considered, the change in normalized momentum is for:

[0054]

[0055] Wherein, e is the charge of a unit charged particle (in this embodiment, the charged particle is an electron, and electrons are used to replace charged particles in the following text), which is a constant, γ is a relativistic factor, which can be calculated by the outlet energy of the injection part 100, and m e is the electron rest mass as a constant, c is the speed of light in a vacuum as a constant, 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 linear accelerator (ERL), in most cases, the bunch distribution at the exit of the injection part 100 in the injector device is a Gaussian distribution and satisfies γσ z >>σ r , where σ r is the radial root mean square length of the bunch at the exit of the injection section, σ z is the longitudinal root mean square length of the bunch at the exit of the injection part, and γ is the relativistic factor.

[0057] Then, after calculation, the transformation of the nonlinear modulation amount in the phase space caused by the unit length ds is for:

[0058]

[0059] Among them, N e is the number of charged particles in a single bunch, obtained from the design index of the injector device; r e is the classical electron radius, which is a constant; γ is the relativistic factor, σ z is the longitudinal root mean square length of the bunch at the outlet of the injection section.

[0060] For Gaussian and quasi-Gaussian bunches, the transformation of the nonlinear modulation of the phase space caused by the space charge force per unit length can be expressed by the above formula (3). Furthermore, the symbol A′ will also be used. ε to replace Represents the transformation of the nonlinear modulation amount in phase space caused by unit length ds (for example, Figure 4 middle).

[0061] Figure 4 is the transformation of the nonlinear modulation amount of phase space caused by unit length calculated by formula (3) The numerical results (curve) and the calculated results (data points) of the BMAD software simulation are plotted with the longitudinal root mean square length σ of the bunch at the outlet of the injection part. z The change relationship diagram shows that the two are in good agreement, which verifies its accuracy.

[0062] Furthermore, by estimating the total length ΔL of the matching section and the merged section in the injector device, the nonlinear modulation amount ΔA of the phase space caused by the transverse space charge force in the matching section and the merged section is estimated by the following formula: ε :

[0063]

[0064] Where ΔL is the total length of the matching section and the merging section in the injector device, It represents the transformation of the nonlinear modulation amount in phase space caused by different external forces (space charge force in the present invention) within unit length.

[0065] Therefore, during the optimization process, the phase space of the bunch at the injection exit can be made to have an opposite phase space premodulation ΔW ε , this phase space premodulation amount needs to satisfy the relationship: ΔW ε =-ΔA ε .

[0066] At this time, the phase space premodulation amount ΔW εThe nonlinear modulation caused by the lateral space charge force in the matching section 200 and the merged section 300 can be offset to reduce the influence of the lateral space charge force on the lateral emittance in the downstream structure of the injection portion (ie, the matching section 200 and the merged section 300).

[0067] For the particle bunch at the exit of the injection part, the phase space premodulation ΔW ε It can be obtained by the following formula:

[0068]

[0069] Among them, W ij is the area of ​​the parallelogram formed by the lines connecting the positions of any two particles i and j and the origin O, <> ij To perform statistics on index i and j, r i , r j Represent the phase space coordinates of arbitrary particles i and j respectively.

[0070] This reverse phase space premodulation ΔW ε The longitudinal gradient from the solenoid is related to the design of the solenoid.

[0071] Based on the above principle, in order to offset the influence of the transverse space charge effect in the matching section and the merging section in the injector of the energy recovery linear accelerator (ERL), as shown in FIG. Figure 2 As shown, the optimization method for the injector of the energy recovery type linear accelerator of the present invention comprises the following steps:

[0072] Step S1: by using the existing design, the bunch parameters at the exit of the injection part and the distance from the exit to the entrance of the main accelerator are estimated, wherein the bunch parameters at the exit of the injection part include the lateral size and / or radial size of the bunch at the exit of the injection part, the energy, the charge amount of the bunch, etc.;

[0073] The existing design may be, for example, the design objectives in references [1]-[4] and the design objectives of the machine itself. For an energy recovery accelerator device for free electron laser, the lateral and radial dimensions of the exit bunch parameters of the injection part are approximately: the radial root mean square length σ of the bunch at the exit of the injection part r The longitudinal root mean square length of the bunch at the exit of the injection part is σ z ~1mm, energy is about 5~10MeV (relativity factor γ is about 10~20). According to the existing design, the distance from the injection part outlet to the main accelerator entrance is estimated, and considering factors such as spatial arrangement, the total length of the conventional matching section 200 and the merging section 300 is about 10m.

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

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

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

[0077]

[0078] Among them, N e is the number of charged particles in a single bunch, obtained from the design index of the injector device; r e is the classical electron radius, which is a constant; γ is the relativistic factor, σ z is the longitudinal root mean square length of the bunch at the outlet of the injection section.

[0079] Step S3: In the process of optimizing the injection part of the injector device, the phase space nonlinear modulation amount ΔA caused by the transverse space charge force in the matching section and the merger section of the injector is obtained. ε , add the emittance optimization function f to the original constraints of the injection part obj ; Then, according to the emittance optimization function f obj The constraints tending to 0 and the original constraints are optimized, or based on the emittance optimization function f obj The optimization results obtained by the original constraints are screened so that the emittance optimization function f obj Tends to 0.

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

[0081] Emittance optimization function f obj for:

[0082] f obj =ΔW ε +ΔA ε ,

[0083] Where ΔA ε represents the nonlinear modulation of the phase space caused by the transverse space charge force in the matching section and the merged section of the injector, which is estimated in step S2 and is a constant; ΔW ε is the phase space premodulation, which is obtained by counting the bunch at the exit of the injection section. Specifically, ΔW ε It is obtained by using the above formula (4).

[0084] In addition, the present invention may further include the following steps to further optimize the emittance:

[0085] Step S4: According to the outlet parameters of the injector device, the longitudinal root mean square length σ of the bunch at the outlet of the injection part is obtained. z and the bunch projection energy dispersion σ e .

[0086] Among them, the longitudinal root mean square length σ of the bunch at the exit of the injection part can be directly derived using a conventional accelerator: z and the bunch projection energy dispersion σ e .

[0087] Step S5: In the process of optimizing the merging section of the injector device, a 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; then, the optimization result is obtained according to the constraint condition that the second emittance optimization function tends to 0 and the existing constraint condition, or the optimization result obtained in step S3 is screened based on the second emittance optimization function so that the second emittance optimization function tends to 0.

[0088] In addition, the step S5 further includes: adding a new constraint condition, the new constraint condition including: a merged segment dispersion elimination condition; and / or Among them, σ z is the longitudinal root mean square length of the bunch at the exit of the injection section, σ e is the projected energy dispersion of the bunch at the exit of the injection part, R 56 is the item in the 5th column and the 6th row of the transmission matrix of the structure of the injector device, R 56 The calculation results of the reverse beamline and the beamline are the same. Specifically, due to the large deflection angle of the merged segment (generally in the range of [10° to 20°]), it is easy to be affected by R 56Too large will lead to excessive compression of the bunch, so R 56 Additional restrictions are imposed, the restrictions are:

[0089] According to the transverse phase space displacement in the x and x′ directions caused by the longitudinal space charge effect, the second emittance optimization function is obtained, which specifically includes:

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

[0091]

[0092]

[0093] in, From any point s to the observation point s between the exit of the jth curved iron block and the entrance of the j+1th curved iron block in the merged section f The entry in the ith column and sixth row of the transfer matrix, R 56,j is the item in the 5th column and the 6th row of the transmission matrix from the exit of the i-th curved iron to the i+1-th curved iron in the merged section, L j is the distance between the jth curved iron and the j+1th curved iron in the merged section, h is the initial energy chirp of the bunch, and is defined as

[0094] For the merging section 300 of the injector device, the physical process of the bunch mass attenuation is: the longitudinal space charge force changes the energy (energy dispersion) of the bunch during the movement of the bunch. This additional energy dispersion is coupled with the beamline transmission matrix. Therefore, a new observation point s is added to the emittance optimization function. f The transverse phase space shift in the x and x′ directions caused by the longitudinal space charge effect and in, Represents any point s to the observation point s f The transfer matrix is ​​calculated in the way that is available in the textbook, which is a 6×6 matrix; s is an arbitrary point, s f is the observation point, which can be the beam line exit or measurement point of the accelerator, Δδ LSC (s) is the additional energy dissipation per unit length caused by the longitudinal space charge force at any point s.

[0095] For non-dispersive regions such as straight sections, any point s to the observation point s f The entry in the ith column and sixth row of the transfer matrix At any point s is equal to 0. Therefore, the phase space premodulation amount ΔW ε As the bunch moves in the dispersion region (such as the merge section 300 in the injector device and the arc section downstream of the injector device), all displacements are accumulated and summed to obtain the total displacement. For different slices, the additional energy dispersion generated at the same position is different, so the displacement caused is also different, which makes each slice in the bunch have a different center position at the measurement point. Figure 5 As shown, different bunch slice centers will cause the projected area of ​​the lateral phase space, which will further lead to an increase in the overall emittance of the bunch (also called projected emittance).

[0096] Quantitative calculation of the additional energy dissipation Δδ caused by the longitudinal space charge force per unit length at any point s LSC (s) is complex, but when the bunch satisfies γσ z >>σ r When the longitudinal space charge force at any point s causes the additional energy dissipation Δδ per unit length LSC (s) will be equal to 1 / σ z (s) 2 Proportional to σ z (s) is the longitudinal root mean square length of the bunch at any point s. Figure 6 The figure shows the BMAD software simulation results of the relationship between the normalized extra energy dispersion and the beam length at different lateral sizes when the bunch energy is set to 10 MeV. It can be seen that the extra energy dispersion Δδ caused by the longitudinal space charge force per unit length at any point s LSC (s) is indeed equal to 1 / σ z (s) 2 Proportional to σ z (s) is the longitudinal root mean square length of the bunch at any point s.

[0097] Therefore, for any two points s1 and s2 in the beam line, the relationship is satisfied:

[0098]

[0099] Δδ LSC (s1), Δδ LSC (s2) represents the additional energy dissipation per unit length caused by the longitudinal space charge force at any two points s1 and s2, σ z (s1),σ z (s2) represents the longitudinal root mean square length of the bunch at any two points s1 and s2.

[0100] Therefore, in the present invention, the additional energy dissipation Δδ caused by the longitudinal space charge force at any point s per unit length is LSC (s) is expressed as:

[0101]

[0102] Among them, k sc is the energy dispersion constant, which is a constant in the entire beamline range and is related to the actual bunch distribution. z (s) is the longitudinal root mean square length of the bunch at any point s.

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

[0104]

[0105]

[0106] in, are the longitudinal root mean square length of the bunch at the exit of the injection part and the projected energy spread of the bunch, R 56 (s) is the value of the entry in the 5th column and the 6th row of the transfer matrix at any point s. Here, the formula is used. To represent the longitudinal root mean square length σ of the bunch at any point s z (s); k sc is the energy dissipation constant, Represents any point s to the observation point s f The entry in the ith column and sixth row of the transfer matrix, ζ sc is the beamline lateral displacement coefficient in the x direction, ζ sc is the beam line lateral displacement coefficient in the x′ direction.

[0107] That is, in equations (5) and (6), the offset caused by the longitudinal space charge effect is divided into two parts: the energy dissipation constant k sc : This parameter is only related to the specific distribution of the bunch, such as the charge, the three-dimensional distribution in real space, etc.; the beam line transverse displacement coefficient ζ in the x direction sc and the beamline lateral displacement coefficient ζ in the x′ direction s ' c : The longitudinal root mean square length σ of the bunch at the exit of the beamline transmission matrix and the injection part z and the bunch projection energy spread σ e related, especially with σ e / σ z related.

[0108] We further assume that the curved area in the merged segment is much smaller than the straight area, and ignore the change of the beam length in the non-curved area. In order to make the lateral offset of the slice 0, according to formulas (5)-(6), the merged segment must satisfy:

[0109]

[0110]

[0111] in, From any point s to the observation point s between the exit of the jth curved iron block and the entrance of the j+1th curved iron block in the merged section f The entry in the ith column and sixth row of the transfer matrix, R 56,j is the item in the 5th column and the 6th row of the transfer matrix from the exit of the i-th curved iron to the i+1-th curved iron in the merged section ( R 56,i It is a constant in the non-bent iron area, so these three items are constants in the area from the exit of the i-th bent iron to the i+1-th bent iron), L j It is the distance between the jth bent iron and the j+1th bent iron in the merged section.

[0112] Experimental results:

[0113] The conditions of formulas (7) and (8) are related to the clustering parameter k sc In order to verify the correctness of the theory, the zigzag merger segment is introduced to obtain the transverse phase space displacement caused by the longitudinal space charge effect. and As the beamline lateral displacement coefficient ζ in the x direction sc and the beamline lateral displacement coefficient ζ in the x′ direction s ' c The zigzag merge segment was proposed in the literature [5] and is currently recognized as the best performing merge segment. Fig. 7A and Figure 7B The beam line lateral displacement coefficient ζ in the x direction of the present invention is given as sc and the beamline lateral displacement coefficient ζ in the x′ direction s ' c The comparison chart of the function value and simulation results, where Fig. 7A The beamline lateral displacement coefficient ζ in the x-direction is shown sc , Figure 7B The beamline lateral displacement coefficient ζ in the x′ direction is shown s ' c . Fig. 7A and Figure 7B It shows a good agreement between the function values ​​and the simulation results.

[0114] Taking the FV injector as an example, the output bunch selection of the injector adopts the emittance optimization function f obj =ΔW ij +ΔA ε Screening is performed to make the bunch satisfy the emittance optimization function f obj Approaching 0. The screening results are as follows Fig. 8A and Figure 8B As shown, the longitudinal beam cross section is a curve with slightly higher parts on both sides, and the slice emittance distribution is a curve with a higher middle part. Fig. 8A is the longitudinal beam cross section of the bunch at the injection part exit and the x-direction slice emittance distribution, and Figure 8B is the longitudinal beam cross section and the x-direction slice emittance distribution of the bunch at the exit of the merger section. Fig. 8A , Figure 8B The bunch is further compressed, and the slice emittance growth is negligible, which is smaller than the ideal bunch. In multiple iterations, the results of multiple groups of slice emittance reduction were found, but they are not shown because other parameters do not meet the standards.

[0115] For the merging section, taking the injection part outlet of the FV injector as an example, the emittance increase of the merging section 300 optimized by the optimization method of the present invention is smaller than that of other existing merging sections, and the bunch brightness is increased by 1.5 times under the same optical parameters.

[0116] It should be noted that the optimization method of the present invention is an improvement on the existing optimization method by adding constraints. Therefore, except for the newly added constraints, the remaining steps are consistent with the optimization method of the existing injector device.

[0117] Compared with previous optimization methods, the optimization method for the injector of the energy recovery type linear accelerator of the present invention optimizes or screens the injection part bunch of the injector device on the basis of considering the transverse space charge effect of the subsequent low-energy region, so that the bunch can reduce the influence of the transverse charge force in the subsequent transmission, which can effectively improve the power of the subsequent radiation section. Furthermore, the present invention 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 bunch and thus improve the peak power of the FEL process. Therefore, compared with other methods, the design of the merging section has a faster optimization speed and a simpler form, and does not require specific optimization for different bunches. It has strong applicability and the results are closer to the actual situation. In summary, the optimization method for the injector of the energy recovery type linear accelerator of the present invention reduces the slice center offset and can reduce the beam loss phenomenon of the bunch in the undulator.

[0118] References are as follows:

[0119] [1]Bazarov,I.V.,and C.K.Sinclair."High brightness,high currentinjector design for the Cornell ERL prototype."Proceedings of the2003Particle 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.4thInt.Particle Accelerator Conf.(IPAC’13).2013.

[0122] [4]Tanaka,O.A.,N.Higashi,and T.Miyajima."Injector Optimization forthe 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."Mergerdesigns for ERLs."Nuclear Instruments and Methods in Physics Research SectionA:Accelerators,Spectrometers,Detectors and Associated Equipment 557.1(2006):165-175.

[0124] The above is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. The above embodiments of the present invention can also be modified in various ways. All simple, equivalent changes and modifications made according to the claims and the description of the present invention fall within the scope of protection of the claims of the present invention. The contents not described in detail in the present invention are all conventional technical contents.

Claims

1. A method for optimizing an injector for an energy recovery linear accelerator, characterized in that: include: Step S1: by using the existing design, estimate the bunch parameters at the exit of the injection part and the distance from the exit to the entrance of the main accelerator; Step S2: Determine the transformation of the nonlinear modulation amount of the phase space per unit length caused by the transverse space charge force At the same time, based on To estimate the phase space nonlinear modulation ΔA caused by the transverse space charge force in the matching section and the merger section of the injector ε ; Step S3: In the process of optimizing the injection part of the injector device, the phase space nonlinear modulation amount ΔA caused by the transverse space charge force in the matching section and the merger section of the injector is obtained. ε , add the emittance optimization function f to the original constraints of the injection part obj ; Then, according to the emittance optimization function f obj The constraints tending to 0 and the original constraints are optimized, or based on the emittance optimization function f obj The optimization results obtained by the original constraints are screened so that the emittance optimization function f obj tends to 0; The emittance optimization function f obj for: f obj =ΔW ε +ΔA ε , Among them, ΔA ε ΔW represents the nonlinear modulation of the phase space caused by the transverse space charge force in the matching section and the merged section of the injector; ε is the phase space premodulation amount, which is obtained by counting the bunch at the exit of the injection part.

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

3. The optimization method for an injector of an energy recovery linear accelerator according to claim 1, characterized in that: Transformation of the nonlinear modulation in the phase space per unit length caused by the transverse space charge force for: Among them, N e is the number of charged particles in a single bunch; r e is the classical electron radius; γ is the relativistic factor, σ z is the longitudinal root mean square length of the bunch at the outlet of the injection section.

4. The optimization method for an injector of an energy recovery linear accelerator according to claim 1, characterized in that: The phase space premodulation amount ΔW ε It is obtained by the following formula: Among them, W ij is the area of ​​the parallelogram formed by the lines connecting the positions of any two particles i and j and the origin O, <> ij To perform statistics on index i and j, r i , r j Represent the phase space coordinates of arbitrary particles i and j respectively.

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

6. The optimization method for an injector of an energy recovery linear accelerator according to claim 1, characterized in that: Also includes: Step S4: According to the outlet parameters of the injector device, the longitudinal root mean square length σ of the bunch at the outlet of the injection part is obtained. z and the bunch projection energy dispersion σ e ; Step S5: in the process of optimizing the merged 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; Subsequently, an optimization result is obtained according to the constraint condition that the second emittance optimization function approaches 0 and the existing constraint condition, or the optimization result obtained in step S3 is screened based on the second emittance optimization function so that the second emittance optimization function approaches 0.

7. The optimization method for an injector of an energy recovery linear accelerator according to claim 6, characterized in that: According to the transverse phase space displacement in the x and x′ directions caused by the longitudinal space charge effect, the second emittance optimization function is obtained, which specifically includes: The outlet of the merging section of the injector device is taken as the observation point. f The transverse phase space displacement Δx in the x and x′ directions caused by the longitudinal space charge effect at LSC (z), Δx′ LSC , the second emittance optimization function is obtained, including: in, From any point s to the observation point s between the exit of the jth curved iron block and the entrance of the j+1th curved iron block in the merged section f The entry in the ith column and sixth row of the transfer matrix, i = 1, 2, R 56,j is the item in the 5th column and the 6th row of the transmission matrix from the exit of the i-th curved iron to the i+1-th curved iron in the merged section, L j is the distance between the jth bent iron and the j+1th bent iron in the merging section, and h is the initial energy chirp of the bunch.

8. The optimization method for an injector of an energy recovery linear accelerator according to claim 6, characterized in that: The step S5 further includes: adding a new constraint condition, the new constraint condition including: a merged segment dispersion elimination condition; and / or Among them, σ z is the longitudinal root mean square length of the bunch at the exit of the injection section, σ e is the projected energy dispersion of the bunch at the exit of the injection part, R 56 It is the entry in the 5th column and the 6th row of the transmission matrix of the overall structure of the injector device.

Images