Optimization method for arc-compression section of energy-recovery linear accelerator

Abstract

The application provides an optimization method for an arc compression section of an energy recovery linear accelerator, comprising the following steps: determining the bunch length and the initial projection emittance of the bunch at the entrance and exit of the arc compression section, and obtaining an overall transmission matrix; dividing the arc compression section into a pre-compression section and a second compression section, taking the slice centrifugal deviation caused by the coherent synchrotron radiation effect of the second compression section as an optimization target, establishing a reverse optimization beam line as a means to optimize the reverse beam line of the second compression section; establishing a constraint condition of the pre-compression section, and optimizing the pre-compression section; and adding a transition matching section between the pre-compression section and the compression section to obtain the arc compression section. The method can make the bunch deflect a large angle while compressing the bunch, and can suppress the emittance growth caused by the steady-state CSR effect and part of the non-steady-state CSR effect, so that the emittance growth is reduced while the non-ideal bunch is compressed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of accelerator physics and technology, and particularly relates to an optimization method for an arc compression section of an energy recovery linear accelerator, which is suitable for beam compression using a 180° arc compression section. BACKGROUND

[0002] In the generation scheme of high-power laser light sources, the energy recovery linear accelerator (ERL) driven free electron laser (FEL) has become a promising candidate due to its high efficiency, high brightness, tunability, continuous operation capability, compact design, and low radiation, etc. However, in order to meet the demand of high-power BEUV radiation for future lithography technology, the energy recovery linear accelerator driven free electron laser (ERL-FEL) faces the challenge of further improving the radiation power. In the ERL-FEL system, beam compression is one of the key technologies to improve the radiation power of the FEL.

[0003] An ERL device mainly consists of the following parts: injector (including merging section), acceleration cavity, arc section, compression section, insertion section (i.e. FEL radiation section), decompression section, and return arc section. In general design, the arc section is often used as the compression section to compress the beam while the beam turns. In order to achieve the required kA-level beam peak current, the beam needs to be compressed to an ultra-short pulse below 100 fs while maintaining a single beam charge of 100 pC. During the compression process, the coherent synchrotron radiation effect (CSR) is the main reason limiting the beam compression effect.

[0004] The physical process of the coherent synchrotron radiation effect (CSR) can be briefly described as follows: during deflection, due to the change of particle velocity (direction), the charged particles radiate photons outward. Although in the high-energy case, the electron beam moves at the speed of light, but due to the difference in the movement path of the beam and the photon (the beam moves along a curve, and the photon moves along a straight line). This path difference will cause the beam tail electrons to radiate photons and interact with the beam head electrons, causing the energy spread to change, and affecting other dimensions of the phase space through the transfer matrix.

[0005] In the energy recovery linear accelerator (ERL), conventional compression methods include but are not limited to: magnetic compression compression section (chicane compression section), arc compression section (Arc compression section), etc. [1] Among them, Arc compression is more common, for example, the 800 MeV of the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan uses six double-bend-iron-group structures (DBA) as arc sections to deflect the beam by 180°, and at the same time uses the item R 56 (R ijThe feature that the item in the i-th row and j-th column of the transfer matrix is not zero compresses the beam bundle to 30 times the original size [2] ; and the phase shift between the chicane segments in the DBA structure is π, which partially suppresses the effect of coherent synchrotron radiation (CSR), but the suppression result is poor, and the horizontal emittance increases by about 3 times the original. Further, KEK has used a combination of arc segments and chicane segments for compression, but due to the natural item R 56 in the 5th row and 6th column of the transfer matrix of the arc segment, the compression effect is poor compared to the chicane segment. Meanwhile, ASML (ASML) has proposed a FODO magnetic focusing structure to deflect and compress the beam bundle: the FODO segment is composed of 18 bending magnets, each with a deflection angle of 10°, and a quadrupole magnet is inserted between the bending magnet segments to focus the beam bundle. Compared to the previous method, the FODO compression segment structure is compact and occupies less space, and the beam bundle emittance is maintained well, and the beam bundle is compressed to 1000A after the emittance increases by 1.6 times the original (0.5μ~0.8μ) [3] . However, due to its compact structure, it is difficult to insert beam measurement elements in practical applications, and in the face of non-ideal beam bundles, the non-adjustable high-order terms make it difficult to compress the beam bundle to a higher current.

[0006] Kick-point method is currently commonly used to estimate the effect of coherent synchrotron radiation (CSR). By solving the equation based on the kick-point method, the solution can better suppress the CSR effect. However, the current kick-point method is only for steady-state CSR, and lacks a good evaluation method for non-steady-state CSR. Meanwhile, the DBA structure designed based on the kick-point method cannot well control the high-order terms, and the effect on non-ideal beam bundles needs to be further studied.

[0007] References:

[0008] [1] Simone Di MITRI, Bunch compressor. CERN accelerator school: FEL and ERL. 2016.

[0009] [2] Nakamura N, Kato R, Miyajima T, et al. S2E simulation of an ERL-based high-power EUV-FEL source for lithography [C] / / Journal of Physics: Conference Series. IOP Publishing, 2017, 874(1): 012013.

[0010] [3]Akkermans J AG,Di Mitri S,Douglas D,et al.Compact compressive arcand beam switchyard for energy recovery linac-driven ultraviolet freeelectron lasers[J].Physical Review Accelerators and Beams,2017,20(8):080705. SUMMARY

[0011] The present application aims to provide an optimization method for the arc compression section of an energy recovery linear accelerator, to reduce the emittance growth while compressing non-ideal beamlets.

[0012] To achieve the above-mentioned purpose, the present application provides an optimization method for the arc compression section of an energy recovery linear accelerator, comprising:

[0013] S1: determining the target beamlet bunch length at the outlet of the arc compression section the initial projection energy spread σ of the beamlet e and the initial beamlet bunch length at the inlet of the arc compression section

[0014] S2: according to the target beamlet bunch length at the outlet of the arc compression section the initial projection energy spread σ of the beamlet e and the initial beamlet bunch length at the inlet of the arc compression section obtaining the item R of the 5th row and the 6th column of the overall transmission matrix of the arc compression section 56 ;

[0015] S3: dividing the arc compression section into a pre-compression section and a second compression section, the pre-compression section comprising two sets of three-bend iron achromatic dispersion structures, and the second compression section comprising multiple pieces of bend iron; taking the minimization of the slice centrifugal deviation caused by the coherent synchrotron radiation effect of the second compression section as the optimization target, and taking the establishment of the reverse optimization beam line as the means to optimize the reverse beam line of the second compression section;

[0016] S4: establishing the constraint conditions of the pre-compression section, and optimizing the pre-compression section;

[0017] S5: obtaining the second compression section according to the optimization result of step S3, obtaining the pre-compression section according to the optimization result of step S4, and adding a transition matching section between the pre-compression section and the compression section to form the overall arc compression section.

[0018] The step S3 specifically comprises:

[0019] S31: establishing a second reverse optimization beam line partial beam line and its constraint condition according to the remaining bending magnets and their matching sections of the second compression section after removing the first bending magnet, and optimizing the parameters of the bending magnets and the matching sections in the second reverse optimization beam line partial beam line according to the constraint condition;

[0020] S32: establishing a second reverse optimization beam line complete beam line and its constraint condition, and optimizing the parameters of the first bending magnet and the transmission matrix of the matching section adjacent to the first bending magnet according to the constraint condition of the second reverse optimization beam line complete beam line;

[0021] S33: adding quadrupole magnets at positions of all the matching sections, and optimizing the positions and intensities of the quadrupole magnets so that the total transmission matrix satisfies the transmission matrices of all the matching sections, and ensuring that the total length of the second reverse optimization beam line complete beam line meets the optimization result of step S31 in the optimization process.

[0022] In the step S31, the constraint condition of the second reverse optimization beam line partial beam line includes: minimizing the slice centroidal offset caused by the stable coherent synchrotron radiation and the downstream coherent synchrotron radiation; and a dispersion function constraint condition;

[0023] In the step S32, the constraint condition of the second reverse optimization beam line complete beam line includes an overall achromatic condition of the reverse optimization beam line complete beam line.

[0024] The slice centroidal offset caused by the downstream coherent synchrotron radiation is minimized by: substituting the target bunch length at the outlet of the arc region compression section The slice centroidal offset related quantity corresponding to the second reverse optimization beam line partial beam line is made to tend to 0 by changing the lengths of all the matching sections of the second reverse optimization beam line partial beam line and the transmission matrices of all the matching sections except the matching section adjacent to the first bending magnet, so that the downstream CSR effect of the forward second compression section is suppressed;

[0025] Wherein, R 5j,k is the corresponding value of the item R 5j , ρ is the radius of the bending magnet, R 5j is a constant in the non-bending magnet region, k is the bending magnet serial number, j is the column serial number of the transmission matrix, j = 1, 2; ζ k is a size parameter of the reverse optimization beam line, σ z,k is the bunch length of the beam at the outlet of the k-th bending magnet of the reverse beam line, σ e is the initial emittance determined by the outlet of the accelerator, is the target bunch length, and R​56,k Rk-5 is the item of the 5th row and the 6th column of the transfer matrix of the kth bending magnet in the beamline 56 corresponding value; L D,k dk is the distance between the kth bending magnet and the k+1th bending magnet in the beamline;

[0026] minimizing the slice centripetal shift caused by the steady-state coherent synchrotron radiation by changing the transfer matrix of all matching sections except the matching sections adjacent to the first bending magnet and changing the transfer matrix of all bending magnets except the first bending magnet to satisfy the following formula:

[0027]

[0028] wherein, I j is a beamline-related parameter; s0 is the entrance of the arc-compression section, s f is the exit of the arc-compression section; is the target bunch length at the exit of the arc-compression section; σ e is the initial projected emittance of the bunch, which is determined by machine parameters; R 5j Rk-5 is the item of the 5th row and the jth column of the transfer matrix of the beamline, j is the column number of the transfer matrix, R is the item of the 5th row and the 6th column of the transfer matrix of the arc-compression section as a whole, R 56 (s) is the item of the 5th row and the 6th column of the transfer matrix of the beamline from the exit of the arc-compression section to an arbitrary point s.

[0029] In the step S31, the dispersion function constraint condition comprises: limiting the dispersion function to be of the same sign in the global range of the second reverse-optimized beamline part, the dispersion function comprising the item R 16 of the 1st row and the 6th column of the transfer matrix and the item R 26 of the 2nd row and the 6th column of the transfer matrix.

[0030] In the step S32, the overall achromatic condition of the second reverse-optimized beamline complete beamline refers to the item R 16 of the 1st row and the 6th column of the transfer matrix at the exit of the second reverse-optimized beamline complete beamline, and the item R 26 of the 1st row and the 6th column of the transfer matrix are both equal to 0.

[0031] The constraint condition of the pre-compression section comprises:

[0032] 1) the deflection angles of the pre-compression section and the second compression section are 180°;

[0033] 2) the transverse transfer matrix of the entrance of the two sets of three-bending magnet achromatic structures tends to be an -I matrix to achieve the suppression of the CSR effect;

[0034] 3) the item R of the 5th row and the 6th column of the transfer matrix of the pre-compression section 56，sec1 the range condition of R

[0035] 4) the overall achromatic condition of the pre-compression section.

[0036] the item R of the 5th row and the 6th column of the transfer matrix of the pre-compression section 56，sec1 the range condition of R includes:

[0037]

[0038] wherein, is the predicted longitudinal length variation, and σ e is the initial projected emittance of the beam, are respectively the initial beam length at the entrance of the arc-compression section and the target beam length at the exit of the arc-compression section; and R 56，sec1 , R 56,sec2 are respectively the items of the 5th row and the 6th column of the transfer matrix of the pre-compression section and the second compression section.

[0039] The step S5 further comprises: satisfying the constraint condition of the transition matching section by adjusting the parameters of the transition matching section; wherein the constraint condition of the transition matching section is that the transverse beta function of all positions of the arc-compression section is at most 100.

[0040] The optimization method for the arc-compression section of the energy recovery type linear accelerator further comprises a step S6: adjusting the overall high-order matrix item of the arc-compression section by adjusting the strength of all six-level iron and four-level iron in the arc-compression section, so that the beam longitudinal cross section at the exit of the arc-compression section meets the requirements.

[0041] The optimization method for the arc-compression section of the energy recovery type linear accelerator further comprises a step S7: for the optimized arc-compression section, simulating the emittance growth caused by coherent synchrotron radiation by scanning the parameters of the entrance of the arc-compression section, to obtain the arc-compression section with the minimum emittance growth.

[0042] The optimization method for the arc-compression section of the energy recovery type linear accelerator can make the beam deflect a large angle while compressing the beam, and at the same time, suppress the emittance growth caused by the steady-state CSR effect and part of the non-steady-state CSR effect, thereby reducing the emittance growth while compressing the non-ideal beam. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is the structure diagram of the arc-compression section obtained by the optimization method for the arc-compression section of the energy recovery type linear accelerator.

[0044] Figure 2is the structure diagram of the second reverse optimization beam line complete beam line of the arc section compression section of the energy recovery type linear accelerator obtained by the optimization method of the arc section compression section of the energy recovery type linear accelerator of the present application.

[0045] Figure 3A is the item R of the 5th row and the 6th column of the transfer matrix 56 is the diagram of the change with the beam line length, Figure 3B is the item R of the 5th row and the 1st column of the transfer matrix of the second compression section Sec2 51 , the item R of the 5th row and the 2nd column of the transfer matrix 52 is the diagram of the change with the beam line length.

[0046] Figure 4 is the diagram of the growth of the emittance caused by the CSR effect under the compression of the beam bunches of different charge amounts.

[0047] Figure 5 is the emittance change diagram of the emittance change of the actual beam bunch in the arc section compression section.

[0048] Figure 6A and Figure 6B is the beam bunch longitudinal phase space and the flow intensity distribution diagram of the entrance and exit of the arc section compression section. DETAILED DESCRIPTION

[0049] The present application is further described below in connection with specific embodiments. It should be understood that the following embodiments are used to illustrate but not to limit the scope of the present application.

[0050] The optimization method of the arc section compression section of the energy recovery type linear accelerator of the present application is mainly based on the following principles:

[0051] When the beam bunch moves in the bending iron, the electron beam will emit radiation, and due to the path difference (the beam bunch moves along the arc line, and the photon propagates along the straight line), the head particles of the beam bunch will receive the radiation from the tail of the beam bunch, and further generate additional energy dispersion. This additional energy dispersion will be coupled with the transfer matrix, so that the beam bunch in the same slice will produce an additional offset in the transverse phase space, causing the phase space to be offset, which will cause the growth of the distribution area of the phase space and the growth of the projected emittance. The difference between the steady-state CSR and the downstream CSR is that the head particles are located in the bending iron or the straight section downstream of the bending iron when receiving the radiation photons.

[0052] It can be known from the definition that for any slice u( z is the longitudinal coordinate of the slice, σ z is the beam length of the beam bunch, i.e. the longitudinal root mean square length of the beam bunch), the cumulative offset in the phase space caused by the steady-state coherent synchrotron radiation at the outlet of the arc section compression section or the measurement point s f can be expressed as:

[0053]

[0054] where Δx i (u) represents the shift in the x direction (i = 1) and x' direction (i = 2) in the phase space at the exit of the arc compression section s f caused by the coherent synchrotron radiation, where the subscript i = 1, 2 represents the x direction (i = 1) and x' direction (i = 2) in the transverse phase space, and similarly, when the deflection plane is in the y direction, i = 1 / 2 represents the y and y' direction, respectively, is the transport matrix from any point s to the exit of the arc compression section s f , which is determined by the specific beamline structure, u is the slice, and δ(s, u) is the energy spread at any point s caused by the CSR effect on the slice u, is the increment of the energy spread at any point s caused by the CSR effect on the slice u.

[0055] For the steady-state CSR effect, the increment of the energy spread at any point s caused by the CSR effect on the slice u can be expressed as:

[0056]

[0057] where ρ is the bending magnet radius, λ(u) is the bunch longitudinal distribution, which is related to the specific bunch distribution; u0 is the slice at the tail of the bunch, and σ z is the bunch length, represents the effect of any slice u' of the bunch on the slice u.

[0058] It should be noted that the steady-state coherent synchrotron radiation (CSR) needs to satisfy the following condition: the bunch length ρ is the bending magnet radius, and φ is the angle of the bending magnet.

[0059] By solving the above formula (2) and substituting it into formula (1), the cumulative shift in the phase space caused by the coherent synchrotron radiation can be obtained.

[0060] As can be seen from the above, for a linear compression process, for any distribution of the bunch, the growth of the slice energy spread caused by the steady-state coherent synchrotron radiation (CSR) satisfies where dδ1 and dδ2 represent the energy spread change of the bunch caused by the coherent synchrotron radiation per unit length at any two points, and σ1 and σ2 represent the bunch length at any two points.

[0061] For any distribution of the bunch, the shift of the coherent synchrotron radiation (CSR) effect at the exit of the beamline can be expressed as:

[0062] Δxj (u)=k csr (u)I j ,

[0063] Where, k csr (u) represents the parameters related to the longitudinal distribution of the bundle, I j Here are the bundle-related parameters, j is the column number of the transmission matrix, and i = 1 and 2 represent the x-direction (i = 1) and x'-direction (i = 2) in the transverse phase space, respectively.

[0064] As can be seen from the above equation, the migration caused by the CSR effect can be divided into two parts: the bundle longitudinal distribution correlation parameter k csr (u) and related parameters of the harness I j Let j be the column number of the transmission matrix. When j = 1, 2 and k csr The parameters are obtained under the condition that i = 2, 1 when the value is not 0.

[0065] Therefore, in order to eliminate the effects of steady-state CSR, the compression or decompression section needs to satisfy the following relationship:

[0066]

[0067] Among them, I j Here, is a beamline correlation parameter, representing the correlation amount of slice centrifugal shift caused by coherent synchrotron radiation. The larger the correlation amount of slice centrifugal shift, the greater the slice centrifugal shift; s0 is the entrance of the arc-compression section, s f This is the outlet of the arc-shaped compression section; σ represents the target bundle length at the exit of the arc compression section. In this invention, it can be considered as the compression target length, determined by the designer based on actual needs; e The initial projected energy dispersion of the bundle is determined by machine parameters; R 5j This refers to the item in the 5th row and jth column of the transmission matrix for the reverse optimization bundle, where j is the column number of the transmission matrix. It is the item in the 5th row and 6th column of the overall transfer matrix of the arc-compressed section, R. 56 (s) is the item in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline from the exit of the arc compression section to any point s.

[0068] In the process of simplifying the above to obtain formula (3), the present invention applies the symplectic property of matrices. Using reverse optimization beamlines to pair R 5i The integral is used to replace the integral from any point s to the outlet s of the arc compression section. f The item in the i-th row and 6-th column of the transfer matrix Specifically, because existing accelerator simulation programs cannot directly provide information about... of the calculation result. Therefore, by using the optimized "reverse optimization beam line", i.e. the element arrangement of the optimized reverse optimization beam line is opposite to the element arrangement of the actual arc compression section, and the upper and lower limits of the optimization integral are also changed to the exit index s f to the entrance index s0. Then the integral of the optimized reverse beam line R 5i is used to replace the required integral of R . Meanwhile, in the decompression process, the bunch length is changing, and in the case of only considering linear compression, the change of the bunch length of the bunch in the reverse optimization beam line is opposite to the forward direction, and the bunch length σ z (s) at any point s in the reverse optimization beam line is expressed as wherein σ is the exit bunch length, σ 56 is the target length of the compressed bunch, R e (s) is the transport matrix of the point s in the reverse beam line (i.e. the position at a distance s from the exit of the beam line). σ z is the RMS emittance of the bunch, and σ

[0069] Therefore, the present application can use the optimization algorithm to take the left part of formula (3) as the optimization target, and since the column ordinal number j = 1, 2 of the transport matrix, there are two optimization targets, and the two optimization targets are made as close to 0 (i.e. the absolute value is minimized) as possible, so that the transverse deviation caused by the steady-state CSR can be greatly reduced.

[0070] For the downstream CSR effect, it is difficult to analytically solve the emittance growth, and currently the present application needs to use an approximate formula to solve, and in the small-angle approximation (and the longitudinal position z of the bunch slice << σ z ), the deviation of the bunch slice caused by the downstream CSR can be expressed as:

[0071]

[0072]

[0073] wherein r e is the classical electron radius, and γ is the relativistic factor, both of which are constants for a fixed arc compression section; R 5j,k is the corresponding value of the item R 5j of the 5th row and the jth column of the transport matrix downstream of the kth block of bending magnets in the reverse optimization beam line, and in the arc compression section of the high-energy accelerator (referring to the machine with an energy greater than 100 MeV), R 5j is a constant in the non-bending magnet area, k is the ordinal number of the bending magnet, and j is the column ordinal number of the transport matrix; ζ k is the size parameter of the reverse optimization beam line, wherein L D,kTo optimize the spacing between the k-th and (k+1)-th bent iron pieces in the beam; φ k Intermediate parameters for reverse optimization of the bundle dimensions. Where σ is the radius of the bent magnet, σ z,k The bundle length is the length of the bundle at the exit of the kth bent iron of the reverse bundle (when the overall energy of the machine is greater than 100MeV, the bundle length can be regarded as constant in the non-bent iron region).

[0074] Similar to the expression for the offset caused by steady-state CSR mentioned above, formulas (4) and (5) can be further expressed in the following forms:

[0075]

[0076]

[0077] Where, k csr,d Since ρ is a non-zero constant, to make the offset caused by the downstream CSR effect zero, the summation term on the right side of the above two formulas should be zero. Assuming the radius ρ of all bent magnets in the arc compression section is constant, for any slice u, to make the slice centrifugal offset caused by the downstream CSR approach zero, the summation term (i.e., the correlation quantity of the slice centrifugal offset caused by the downstream CSR) should satisfy the following after expansion:

[0078]

[0079] Among them, R 5j,k To optimize the transmission matrix downstream of the k-th bent section in the beam, the term R in the 5th row and j-th column is... 5j The corresponding values ​​are ρ, which is the radius of the bent magnet, and R. 5j In the non-bending iron region, this is a constant, where k is the bending iron ordinal number and j is the column ordinal number of the transmission matrix; ζ k To reverse-optimize the dimensional parameters of the bundle, σ z,k Let be the bundle length at the exit of the kth bent iron section of the reverse bundle. σ e The initial energy dissipation is determined by the accelerator exit. For the target beam length, R 56,k To optimize the transfer matrix downstream of the k-th bent iron in the reverse optimization bundle, the term R in the 5th row and 6th column is... 56 The corresponding value; L D,k To optimize the spacing between the k-th and (k+1)-th bent iron blocks in the beam.

[0080] The optimization method for the arc compression section of an energy recovery linear accelerator according to the present invention can be achieved by optimizing the results of accelerator simulation computer programs such as ELEGANT.

[0081] Based on the above principle, the optimization method for the arc compression section of the energy recovery type linear accelerator comprises the following steps:

[0082] Step S1: determining the target bunch length at the outlet of the arc compression section by free electron laser (FEL) parameters, accelerating cavity parameters and injector parameters Bunch initial projection energy dispersion sigma e and the initial bunch length at the inlet of the arc compression section

[0083] The free electron laser (FEL) parameters, the accelerating cavity parameters and the injector parameters are predefined.

[0084] Step S2: according to the target bunch length at the outlet of the arc compression section Bunch initial projection energy dispersion sigma e and the initial bunch length at the inlet of the arc compression section The item R of the 5th row and the 6th column of the overall transmission matrix of the arc compression section is obtained by using the formula . 56 .

[0085] Step S3: as shown in the formula Figure 1 , the arc compression section is divided into a pre-compression section Sec1 and a second compression section Sec2, the pre-compression section Sec1 comprises two sets of three-bend iron achromatic dispersion (TBA) structures 10, and the second compression section Sec2 comprises a plurality of bend irons (four bend irons are taken as an example in the present application); the optimization of the reverse optimization beam line of the second compression section Sec2 is performed by taking the minimization of the slice centrifugal deviation caused by the CSR effect of the second compression section Sec2 as an optimization target and taking the establishment of the reverse optimization beam line as a means.

[0086] Since the upstream bunch length of the arc compression section is long, the CSR effect is small (steady Downstream CSR ~ 1 / sigma z ) Therefore, as shown in the formula Figure 1 , in the design process, the arc compression section is divided into two parts: a pre-compression section Sec1 and a second compression section Sec2, and since the bunch length changes greatly, the I matrix cannot well control the central deviation caused by the CSR effect at the second compression section Sec2, therefore, only the CSR effect of the second compression section Sec2 is considered, and the second compression section Sec2 is optimized only by considering the CSR effect of the second compression section Sec2.

[0087] The step S3 specifically comprises the following steps:

[0088] Step S31: Using the reverse bundle of the second compression section as the complete bundle of the second reverse optimization bundle, establish the second reverse optimization bundle part bundle and its constraints based on the remaining bent iron and matching segment after removing the first bent iron B1 from the second compression section Sec2, and optimize the parameters of the bent iron and matching segment in the second reverse optimization bundle part bundle according to the constraints.

[0089] In this embodiment, as Figure 1 and Figure 2 As shown, the second compression section Sec2 has a total of 4 bent irons (10° / piece), namely the first bent iron B1, the second bent iron B2, the third bent iron B3, and the fourth bent iron B4, as well as matching sections located between adjacent bent irons, including the third matching section M3, the second matching section M2, and the first matching section M1. Figure 2 As shown, the optimization objective of this invention is that, along the propagation direction of the actual beamline, the longitudinal position coordinate z in the phase space of the beam gradually decreases, while the energy dispersion δ gradually increases.

[0090] Therefore, step S31 is for Figure 2 The second reverse-optimized bundle section is constructed using the remaining bends (i.e., fourth bend B4 to second bend B2) of the second compression segment Sec2 (excluding the first bend B1) and all matching segments (i.e., matching segments M1 to M3) of the second compression segment Sec2, and then optimized. The bend and matching segment parameters in the optimized second reverse-optimized bundle section mainly include: the parameters of the second bend B2 to the fourth bend B4, the transmission matrix and length of the first matching segment M1 to the second matching segment M2, and the length of the third matching segment M3 adjacent to the first bend B1.

[0091] Among them, the constraints of the second reverse optimization bundle part include: minimizing the slice centrifugal offset caused by steady-state CSR and downstream CSR; and dispersion function constraints.

[0092] To minimize the slice centrifugal shift caused by downstream CSR, the following method is used: Substitute the target bundle length at the exit of the arc-region compression section. By changing the lengths of all matching segments (M1 to M3) of the second reverse-optimized bundle section and the transfer matrix of all matching segments (M1 to M2) except for the matching segment adjacent to the first bend, the correlation amount of slice centrifugal offset caused by the downstream CSR corresponding to the second reverse-optimized bundle section is reduced. The formula (6) approaches 0, which means that the downstream CSR effect of the positive second compression segment is suppressed.

[0093] Among them, R 5j,k To optimize the transmission matrix downstream of the k-th bent section in the beam, the term R in the 5th row and j-th column is... 5jcorresponding value, p is the radius of the bending magnet, R 5j is a constant in the non-bending magnet region, k is the bending magnet number, j is the column number of the transfer matrix, j = 1, 2; ζ k is the size parameter of the reverse optimization beam line, σ z,k is the beam length of the beam group at the exit of the kth bending magnet in the reverse beam line, σ e is the initial energy dispersion determined by the exit of the accelerator, is the target beam length, R 56,k is the item R in the 5th row and the 6th column of the transfer matrix downstream of the kth bending magnet in the reverse optimization beam line. 56 corresponding value; L D,k is the spacing between the kth bending magnet and the k+1th bending magnet in the reverse optimization beam line.

[0094] In the embodiment, the accelerator simulation computer program such as ELEGANT can be used to change the beam line arrangement and derive the transfer matrix evolution curve, and j = 1, 2 in formula (6) is substituted.

[0095] The slice centrifugal deviation caused by the stable coherent synchrotron radiation is minimized by changing the transfer matrix of all matching sections (M1-M2) adjacent to the first bending magnet and changing the transfer matrix of all bending magnets (B2-B4) other than the first bending magnet to satisfy formula (3):

[0096]

[0097] wherein, I j is a beam line related parameter, represents a slice centrifugal deviation related quantity caused by the coherent synchrotron radiation, and the greater the slice centrifugal deviation related quantity, the greater the slice centrifugal deviation; s0 is the entrance of the arc compression section, s f is the exit of the arc compression section; is the target beam length at the exit of the arc compression section, which can be regarded as a compression target length in the present application and is determined by the designer according to actual requirements; σ e is the initial projection energy dispersion of the beam group, which is determined by the machine parameters; R 5j is the item in the 5th row and the jth column of the transfer matrix of the reverse optimization beam line, j is the column number of the transfer matrix, is the item R in the 5th row and the 6th column of the transfer matrix of the arc compression section as a whole. 56 (s) is the item R in the 5th row and the 6th column of the transfer matrix of the reverse optimization beam line from the exit of the arc compression section to an arbitrary point s.

[0098] In the step S31, the dispersion function constraint condition includes: the dispersion function (i.e. the item R 16 in the 1st row and the 6th column of the transfer matrix, the item R26 ) is limited to be the same sign (always negative or positive, which is related to the reference system taken) in the global range of the second reverse optimization beamline part, so that the over-short bunch is prevented from being generated in the compression process, and the shortest bunch is ensured to appear at the outlet of the arc compression section, which can effectively reduce the influence of the downstream CSR. The item R 16 , the item R 26 of the 6th column of the 2nd row of the transmission matrix of the second reverse optimization beamline part can be exported by using the.mat output file of the elegant software.

[0099] Therefore, when the second reverse optimization beamline part corresponding to the remaining bending magnets except the first bending magnet B1 of the arc compression section (i.e., B4-B2 and M1-M3 in Figure 2 ) is optimized, the suppression of the CSR effect is focused on.

[0100] Step S32: The first bending magnet B1 and the transmission matrix of the matching section M3 adjacent to the first bending magnet B1 are added downstream of the second reverse optimization beamline part to establish a second reverse optimization beamline complete beamline, constraint conditions of the second reverse optimization beamline complete beamline are established, and the parameters of the first bending magnet B1 and the transmission matrix of the matching section M3 adjacent to the first bending magnet B1 are optimized according to the constraint conditions of the second reverse optimization beamline complete beamline.

[0101] That is, the second reverse optimization beamline complete beamline is the structure obtained after the entire second compression section Sec2 is reversely arranged, and the matching section of the first bending magnet B1 is located between the first bending magnet B1 and the second bending magnet B2. Therefore, the arrangement mode of the entire second compression section Sec2 is obtained by the step S32.

[0102] The constraint conditions of the second reverse optimization beamline complete beamline include the overall achromatic condition of the second reverse optimization beamline complete beamline.

[0103] The overall achromatic condition of the second reverse optimization beamline complete beamline refers to that the items R 16 and R 26 of the 6th column of the 1st row of the transmission matrix of the second reverse optimization beamline complete beamline are both equal to 0.

[0104] Therefore, the transmission matrix of the entire second compression section Sec2 is made to satisfy R 16 = 0 and R 26 = 0 by using the last bending magnet B1 and the matching section M3 thereof.

[0105] The item R 51the item R 52 the item R 56 As Figure 3A and Figure 3B shown.

[0106] Step S33: adding quadrupole magnets at positions where all the matching sections (i.e., the matching sections M1-M3 in Figure 2 ) are located, and optimizing the positions and strengths of the quadrupole magnets so that the total transmission matrix satisfies the transmission matrices of all the matching sections (i.e., the matching sections M1-M3 in Figure 2 ), while ensuring that the total length of the second reverse-optimized beam line satisfies the optimization result of step S31.

[0107] Step S4: establishing a constraint condition for the pre-compression section Sec1, and optimizing the pre-compression section Sec1.

[0108] The pre-compression section Sec1 includes two triple-bend-iron achromatic (TBA) structures 10. Meanwhile, six-bend-iron structures (corresponding to the black solid points in Figure 1 in the example of the present application) can be selected and added to adjust the overall high-order dispersion of the arc compression section.

[0109] The constraint condition for the pre-compression section Sec1 includes:

[0110] 1) the deflection angles of the pre-compression section Sec1 and the second compression section Sec2 are 180°;

[0111] 2) the transverse transmission matrices of the entrances of the two sets of triple-bend-iron achromatic (TBA) structures (i.e., the red marked positions in Figure 1 ) tend to be -I matrices, so as to achieve suppression of the CSR effect;

[0112] 3) the range condition of the item R 56，sec1 of the 5th row and the 6th column of the transmission matrix of the pre-compression section Sec1;

[0113] 4) the overall achromatic condition of the pre-compression section.

[0114] As Figure 1 described, the pre-compression section Sec1 achieves suppression of the CSR effect by optimizing the transverse transmission matrices of the entrances of the two triple-bend-iron achromatic structures to tend to be -I matrices. That is, the transverse transmission matrices of the entrances of the two triple-bend-iron achromatic structures 10 are -I matrices through the elegant beam optics optimization program, where the -I matrix is a 4x4 matrix and is a matrix with diagonal elements being -1 and other elements being 0. Since the beam length of the magnetic structure changes little, the I matrix can greatly suppress the transverse displacement caused by the CSR effect.

[0115] R 56，sec1 The range condition includes:

[0116]

[0117] wherein is the predicted longitudinal length variation, σ e is the initial projected emittance of the beam, are the initial beam length at the entrance of the arc compression section and the target beam length at the exit of the arc compression section, respectively, which are determined by the parameters of the accelerator itself and are known quantities; R 56，sec1 , R 56,sec2 are the 5th row and 6th column entries of the transfer matrix of the pre-compression section Sec1 and the second compression section Sec2, respectively.

[0118] Step S5: obtaining the second compression section Sec2 according to the optimization result of step S3, obtaining the pre-compression section Sec1 according to the optimization result of step S4, and adding a transition matching section between the pre-compression section and the compression section to obtain the arc compression section.

[0119] The step S5 further includes: satisfying the constraint condition of the transition matching section by adjusting the parameters of the transition matching section; wherein the constraint condition of the transition matching section is that the transverse beta function β xf of all positions of the arc compression section is at most 100, so that the overall transverse size of the arc compression section is kept within a small range.

[0120] Step S6: adjusting the overall high-order matrix entries (such as T 166 , R 566 , etc.) of the arc compression section by adjusting the strengths of all six-level and four-level magnets in the arc compression section, so that the longitudinal cross section of the beam at the exit of the arc compression section meets the requirements, thereby optimizing the strengths of the six-level and four-level magnets.

[0121] wherein the values of the overall high-order matrix entries (such as T 166 , R 566 , etc.) of the arc compression section are related to the design purpose, such as some machines requiring high peak current and some machines requiring quasi-Gaussian beam.

[0122] Step S7: for the optimized arc compression section, simulating the emittance growth caused by coherent synchrotron radiation (CSR) under the condition of scanning the parameters (transverse radius, transverse angular spread) of the entrance of the arc compression section to obtain the arc compression section with the minimum emittance growth.

[0123] Thus, the CSR simulation is performed by scanning the parameters (transverse radius, transverse angular spread) of the entrance of the arc compression section.

[0124] In the embodiment, the optimization algorithm + simulation software, for example, elegant, can be used to change the twiss optical function (including the transverse beta function β xf , the transverse alpha function α xf ) of the inlet of the arc compression section, and the “enx” data in the “.sig” file is derived after simulation to compare the size of the emittance growth, find the minimum value of the emittance growth, and obtain the arc compression section with the minimum emittance growth.

[0125] Experimental results:

[0126] In one of the experimental examples, the parameters of the bending iron and the matching section in the complete beam line obtained according to step S3, i.e., the structure parameters of the second compression section, are shown in Table 1.

[0127] Table 1: Structure parameters of the second compression section

[0128]

[0129] The simulation effect of the second compression section Sec2 is: the final beam length The initial beam length The energy dispersion σ e = 0.005, and the simulation result shows that the emittance growth is less than 0.01 μmrad.

[0130] For the design of the compression section, the CSR effect caused transverse deviation is effectively controlled while the beam bunch is compressed, thereby controlling the emittance growth of the beam bunch. As a test, we set the beam bunch compression target length to 50 fs and the compression coefficient to 20, and scanned the beam bunches with different beam bunch charges. The emittance growth caused by the CSR effect under the compression of the beam bunches with different charges is shown in Figure 4 , and the simulation result considering all the CSR effects shows that the emittance growth is less than 5%, which meets the design requirement. For the actual beam bunch, in combination with the double-TBA pre-compression structure, the emittance change of the actual beam bunch in the arc compression section is shown in Figure 5 , where ε x,y is the transverse emittance, and s is the beam line path. The beam bunch longitudinal phase space and the current distribution at the inlet and outlet of the arc compression section are shown in Figure 6A and Figure 6B , Figure 6A , which shows the inlet of the arc compression section, Figure 6B , which shows the outlet of the arc compression section, and βγ is the energy coefficient, which is related to the particle energy, z is the longitudinal coordinate of the particle, and I pk is the slice current. The beam bunch compression ratio is 40 (length) / 70 (peak current). The relative emittance growth is less than 5%, and the absolute growth is less than 0.1 μmrad.

[0131] The above merely describes preferred embodiments of the present application, and is not intended to limit the scope of the present application. The above-described embodiments of the present application can be variously changed. Any simple, equivalent changes and modifications made according to the content of the claims and the specification of the present application are intended to fall within the scope of the present application. The present application is not limited by the above-described embodiments.

Claims

1. An optimization method for the arc compression section of an energy recovery linear accelerator, characterized in that, The method comprises the following steps: Step S1 : determining a target bunch length at the exit of the arc-compression section , the initial projected emittance of the bunch , and the initial bunch length at the entrance of the arc-compression section ; Step S2: Based on the target bundle length at the exit of the arc compression section Initial projection energy dispersion of the bundle Initial bundle length at the entrance of the arc compression section The term in the 5th row and 6th column of the overall transmission matrix of the arc-compressed section is obtained. ; Step S3: dividing the arc section compression section into a pre-compression section and a second compression section, the pre-compression section comprising two sets of three-bend iron dispersion structures, and the second compression section comprising a plurality of bend irons; taking minimizing the slice centrifugal deviation caused by the coherent synchrotron radiation effect of the second compression section as an optimization target, and taking establishing a reverse optimization beam line as a means to optimize the reverse beam line of the second compression section; Step S4: establishing a constraint condition of the pre-compression section, and optimizing the pre-compression section; Step S5: obtaining the second compression section according to the optimization result of step S3, obtaining the pre-compression section according to the optimization result of step S4, and adding a transition matching section between the pre-compression section and the compression section to form a total arc section compression section.

2. The optimization method for an arc-compression section of an energy-recovery linear accelerator according to claim 1, characterized by, The step S3 specifically comprises: Step S31: taking the reverse beam line of the second compression section as a second reverse optimization beam line complete beam line, establishing a second reverse optimization beam line partial beam line and a constraint condition thereof according to the remaining bend irons and matching sections of the second compression section after removing the first bend iron, and optimizing the bend irons and matching sections in the second reverse optimization beam line partial beam line according to the constraint condition; Step S32: establishing a second reverse optimization beam line complete beam line and a constraint condition thereof, and optimizing the parameters of the first bend iron and the transmission matrix of the matching section adjacent to the first bend iron according to the constraint condition of the second reverse optimization beam line complete beam line; Step S33: adding quadrupole magnets at positions of all the matching sections, optimizing the positions and intensities of the quadrupole magnets, and making the total transmission matrix meet the transmission matrices of all the matching sections, and in the optimization process, ensuring that the total length of the second reverse optimization beam line complete beam line meets the optimization result of step S31.

3. The optimization method for an arc-compression section of an energy-recovery linear accelerator according to claim 2, characterized by, In the step S31, the constraint condition of the second reverse optimization beam line partial beam line comprises: minimizing the slice centrifugal deviation caused by the steady-state coherent synchrotron radiation and downstream coherent synchrotron radiation; and a dispersion function constraint condition; In the step S32, the constraint condition of the second reverse optimization beam line complete beam line comprises an overall dispersion elimination condition of the reverse optimization beam line complete beam line.

4. The optimization method for an arc compression section of an energy-recovery type linear accelerator according to claim 3, characterized by, Minimizing slice centripetal excursion caused by downstream coherent synchrotron radiation, in particular by imposing a target bunch length at the exit of the arc compression section tending to zero by changing the length of all matching sections of the second reverse optimization beamline section and the transfer matrix of all matching sections except the one adjacent to the first dipole, the slice centripetal excursion related quantity corresponding to the second reverse optimization beamline section tends to zero, so that the downstream CSR effect of the second compression section in forward direction is suppressed wherein, is the term of the 5th row and jth column of the transfer matrix downstream of the kth bending magnet of the reverse optimization beam line corresponding value, is the radius of the bending magnet, is a constant in the non-bending magnet region, k is the bending magnet number, j is the column number of the transfer matrix, ; is the size parameter of the reverse optimization beam line, is the bunch length of the beam at the exit of the kth bending magnet of the reverse beam line, , is the initial emittance determined by the exit of the accelerator, is the target bunch length, is the term of the 5th row and 6th column of the transfer matrix downstream of the kth bending magnet of the reverse optimization beam line corresponding value; is the spacing between the kth bending magnet and the k+1th bending magnet of the reverse optimization beam line; The slice centrifugal deviation caused by the steady-state coherent synchrotron radiation is minimized by changing the transmission matrices of all the matching sections except the matching section adjacent to the first bend iron and changing the transmission matrices of all the bend irons except the first bend iron to meet the following formula: ， wherein, is the beam line related parameter; s0is the entrance of the arc-compression section, f is the exit of the arc-compression section; is the target bunch length at the exit of the arc-compression section; is the initial projected emittance of the bunch, determined by the machine parameters; R 5j is the item of the 5th row and the jth column of the transfer matrix of the inverse-optimized beam line, j is the column ordinal of the transfer matrix, is the item of the 5th row and the 6th column of the transfer matrix of the inverse-optimized beam line from the exit of the arc-compression section to an arbitrary point s.

5. The optimization method for an arc compression section of an energy-recovery type linear accelerator according to claim 3, characterized by, In the step S31, the dispersion function constraint condition comprises: limiting the dispersion function to be same sign in the global range of the second reverse optimization beamline part beamline, the dispersion function comprises the item of the 1st row and the 6th column of the transmission matrix and the item of the 2nd row and the 6th column of the transmission matrix ; In the step S32, the second reverse optimization beamline completely optimizes the overall achromatic condition of the beamline, which means that the item in the 1st row and the 6th column of the transmission matrix at the exit of the second reverse optimization beamline is equal to 0. , the item in the 1st row and the 6th column of the transmission matrix is equal to 0. , the item in the 1st row and the 6th column of the transmission matrix is equal to 0.

6. The optimization method for an arc compression section of an energy-recovery linear accelerator according to claim 1, characterized by, The constraint condition of the pre-compression section comprises: 1) the deflection angles of the pre-compression section and the second compression section are 180°; 2) the transverse transmission matrix of the inlet of the two sets of three-bend iron dispersion structures tends to an -I matrix to realize CSR effect suppression; and 3) the term of the 5th row and 6th column of the transfer matrix of the pre-compression section the range condition; 4) an overall dispersion elimination condition of the pre-compression section; wherein the term in the 5th row and 6th column of the transfer matrix of the pre-compression section The range condition includes: ， wherein, is the predicted longitudinal length variation, is the initial projected emittance of the beam, are the initial beam length at the entrance of the arc compression section and the target beam length at the exit of the arc compression section, respectively; , are the 5th row, 6th column entries of the transfer matrices of the pre-compression section and the second compression section, respectively.

7. The optimization method for an arc compression section of an energy-recovery linear accelerator according to claim 1, characterized by, The step S5 further comprises: adjusting the parameters of the transition matching section to meet the constraint condition of the transition matching section; wherein the constraint condition of the transition matching section is that the transverse beta function of all positions of the arc section compression section is at most 100.

8. The optimization method for an arc compression section of an energy-recovery linear accelerator according to claim 1, characterized by, The method further comprises step S6: adjusting the overall high-order matrix term of the arc section compression section by adjusting the intensities of all the sextupole magnets and quadrupole magnets in the arc section compression section, so that the bunch longitudinal cross section at the outlet of the arc section compression section meets the requirements.

9. The optimization method for an arc compression section of an energy-recovery type linear accelerator according to claim 1, characterized by, Further comprising a step S7: simulating the increase of emittance caused by the coherent synchrotron radiation for the optimized arc-compression section to obtain the arc-compression section with the minimum increase of emittance under the condition of scanning the parameters at the entrance of the arc-compression section.

10. The optimization method for an arc compression section of an energy-recovery type linear accelerator according to claim 1, characterized by, The number of the bending magnets in the second compression section is 4.

Images