Optimization method for arc region compression section of energy recovery type linear accelerator

Abstract

The invention provides an optimization method for an arc region compression section of an energy recovery type linear accelerator, and the method comprises the steps: determining the beam length of a beam bunch at an entrance / exit of the arc region compression section and the energy dispersion of the initial projection of the beam bunch, and obtaining an overall transmission matrix; an arc region compression section is divided into a pre-compression section and a second compression section, and a reverse beam line of the second compression section is optimized by taking slice centrifugal offset caused by minimization of a coherent synchrotron radiation effect of the second compression section as an optimization target and by taking establishment of a reverse optimization beam line as a means; establishing constraint conditions 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 an arc region compression section. According to the method provided by the invention, the beam bunches can be compressed while deflecting by a large angle, and the emittance increase caused by the steady-state CSR effect and partial unsteady-state CSR effect can be suppressed, so that the emittance increase is reduced while the non-ideal beam bunches are compressed.

Description

Technical Field

[0001] The present invention belongs to the field of accelerator physics and technology, and in particular relates to an optimization method for an arc compression section of an energy recovery type linear accelerator, which is suitable for beam compression using a 180° arc compression section. Background Art

[0002] Among the high-power laser light source generation schemes, energy recovery linear accelerator (ERL) driven free electron laser (FEL) has become a very promising candidate due to its high efficiency, high brightness, tunability, continuous operation capability, compact design and low radiation. However, in order to meet the demand for high-power BEUV radiation in future lithography technology, 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 increase the radiation power of FEL.

[0003] The ERL device is mainly composed of the following parts: injector (including merger 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 a compression section to compress the bunch while turning. In order to achieve the required kA-level bunch peak flux, the bunch needs to be compressed to an ultrashort pulse below 100fs while maintaining a single bunch charge of 100pC. During the compression process, the coherent synchrotron radiation effect (CSR) is the main reason for limiting the bunch compression effect.

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

[0005] In an energy recovery linear accelerator (ERL), conventional compression methods include but are not limited to: magnetic compression section (chicane compression section), arc compression section (Arc compression section), etc. [1] Arc compression is more common. For example, the 800 MeV accelerator of the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan uses six double bent iron structures (DBAs) as arc segments to deflect the bunch by 180°. At the same time, the term R in the 5th row and 6th column of the transfer matrix of the DBA structure is used. 56 (R ijThe characteristic that the item in the i-th row and j-th column of the transmission matrix is ​​not 0 is used to compress the bunch, and the bunch is compressed to 30 times the original [2] ; and make the phase shift between the bent irons in the DBA structure π, thereby partially suppressing the influence of the coherent synchrotron radiation effect (CSR), but the suppression result is poor, and the horizontal emittance increases by about 3 times. Further, KEK has used the method of combining arc segments and chicane segments for compression, but due to the natural transmission matrix of the arc segment, the item R in the 5th row and 6th column 56 In contrast to the chicane segment, the compression effect is poor. At the same time, ASML has proposed a FODO magnetic focusing structure to deflect and compress the bunch: the FODO segment consists of 18 bent irons, each with a deflection angle of 10°, and a quadrupole magnet is inserted between the bent iron segments to focus the bunch. Compared with previous methods, the FODO compression segment has a compact structure and occupies less space, and the bunch emittance is well maintained. After compressing the bunch to 1000A, the emittance increases by 1.6 times (0.5μ~0.8μ) [3] However, due to its compact structure, it is difficult to insert beam measuring components in practical applications, and in the face of non-ideal bunches, the unadjustable high-order terms make it difficult to compress the bunches to a higher flow intensity.

[0006] The kick-point method is currently commonly used to estimate the coherent synchrotron radiation effect (CSR). By solving the equations based on the kick-point method, the solution obtained can effectively suppress the CSR effect. However, the kick-point method is currently only used for steady-state CSR, and there is a lack of good evaluation methods for non-steady-state CSR. At the same time, the DBA structure designed based on the kick-point method cannot effectively control high-order terms, and the effect of non-ideal bunching needs further study.

[0007] References:

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

[0009] [2]Nakamura N,Kato R,Miyajima T,et al.S2E simulation of an ERL-basedhigh-power EUV-FEL source for lithography[C] / / Journal of Physics:ConferenceSeries.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 of the invention

[0011] The object of the present invention is to provide an optimization method for the arc compression section of an energy recovery type linear accelerator, so as to reduce the emittance growth while compressing the non-ideal bunch.

[0012] In order to achieve the above object, the present invention provides an optimization method for an arc compression section of an energy recovery type linear accelerator, comprising:

[0013] S1: Determine the target bunch length at the exit of the arc compression section The initial projected energy spread of the bunch is σ e and the initial bunch length at the entrance of the arc compression section

[0014] S2: According to the target bunch length at the exit of the arc compression section The initial projected energy spread of the bunch is e and the initial bunch length at the entrance of the arc compression section Obtain the item R in the 5th row and 6th column of the overall transfer matrix of the arc compression segment 56 ;

[0015] S3: The arc compression section is divided into a pre-compression section and a second compression section. The pre-compression section includes two groups of three-bend iron achromatic structures, and the second compression section includes multiple pieces of bent iron. The optimization goal is to minimize the centrifugal deviation of the slice caused by the coherent synchrotron radiation effect of the second compression section, and the reverse beam line of the second compression section is optimized by establishing a reverse optimization beam line.

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

[0017] S5: Obtain a second compression section according to the optimization result of step S3, obtain a pre-compression section according to the optimization result of step S4, and add a transition matching section between the pre-compression section and the compression section to form a total arc zone compression section.

[0018] The step S3 specifically includes:

[0019] S31: Taking the reverse beam of the second compression section as the complete beam of the second reverse optimization beam, establishing the partial beam of the second reverse optimization beam and its constraint conditions according to the remaining bent irons and their matching sections after removing the first bent iron in the second compression section, and optimizing the bent iron and matching section parameters in the partial beam of the second reverse optimization beam according to the constraint conditions;

[0020] S32: establishing a complete beam line of a second reverse optimized beam line and its constraint conditions, and optimizing the parameters of the first bend iron and the transmission matrix of its adjacent matching segments according to the constraint conditions of the complete beam line of the second reverse optimized beam line;

[0021] S33: By adding quadrupole magnets at the locations of all matching segments and optimizing the positions and strengths of the quadrupole irons, the total transmission matrix satisfies the transmission matrices of all matching segments. During the optimization process, the total length of the complete beam line of the second reverse optimization beam line is ensured to meet the optimization result of step S31.

[0022] In the step S31, the constraint conditions of the second reverse optimization beamline part beamline include: minimizing the slice centrifugal deviation caused by the steady-state coherent synchrotron radiation and the downstream coherent synchrotron radiation; and the dispersion function constraint conditions;

[0023] In the step S32, the constraint conditions of the complete beamline of the second inverse optimization beamline include the overall achromatic condition of the complete beamline of the inverse optimization beamline.

[0024] The minimization of the slice centrifugal deviation caused by the downstream coherent synchrotron radiation is achieved by substituting the target bunch length at the exit of the arc compression section into By changing the length of all matching segments of the second reverse optimized beam line and the transmission matrix of all matching segments except the matching segment adjacent to the first bend iron, the relevant amount of the slice centrifugal deviation caused by the downstream CSR corresponding to the second reverse optimized beam line part is tends to 0, so that the downstream CSR effect of the second compression section in the positive direction is suppressed;

[0025] Among them, R 5j,k The item R in the 5th row and jth column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 5j The corresponding value, ρ is the radius of the bending magnet, R 5j It is a constant in the non-bend iron region, k is the bend iron number, j is the column number of the transmission matrix, j = 1, 2; ζ k To inversely optimize the beamline size parameters, σ z,k is the bundle length of the kth bend iron exit of the reverse beam line, σ e is the initial energy dispersion, determined by the accelerator exit, is the target beam length, R56,k The item R in the 5th row and 6th column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 56 The corresponding value; L D,k To reversely optimize the distance between the kth bent iron and the k+1th bent iron in the beam line;

[0026] The minimization of the centrifugal deviation of the slice caused by the steady-state coherent synchrotron radiation is specifically achieved by changing the transmission matrix of all matching sections other than the matching section adjacent to the first bending iron and changing the transmission matrix of all bending irons other than the first bending iron so that they satisfy the following formula:

[0027]

[0028] in, I j is the beamline related parameter; s0 is the entrance of the arc compression section, s f It 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 projection energy spread of the bunch, determined by the machine parameters; R 5j is the entry in the 5th row and jth column of the transfer matrix of the reverse optimized beamline, where j is the column number of the transfer matrix. is the fifth row and sixth column of the overall transfer matrix of the arc compression segment, R 56 (s) is the entry in the 5th row and 6th column of the transfer matrix of the reverse optimized beamline from the exit of the arc compression section to any point s.

[0029] In step S31, the dispersion function constraint condition includes: restricting the dispersion function so that it has the same sign in the global range of the second reverse optimization beamline part, and the dispersion function includes the item R in the first row and sixth column of the transmission matrix 16 and the entry R in row 2 and column 6 of the transfer matrix 26 ;

[0030] In the step S32, the overall achromatic condition of the second reverse optimization beamline complete beamline refers to the item R in the first row and sixth column of the transmission matrix at the exit of the second reverse optimization beamline complete beamline. 16 , the entry R in row 1 and column 6 of the transfer matrix 26 Both are equal to 0.

[0031] The constraints of the pre-compression stage include:

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

[0033] 2) Make the lateral transmission matrix of the entrance of the two groups of three-bend iron achromatic structures tend to -I matrix to achieve the suppression of CSR effect;

[0034] 3) The entry R in the 5th row and 6th column of the transmission matrix of the pre-compression section 56，sec1 Range conditions;

[0035] 4) Overall achromatic conditions of the pre-compression section.

[0036] The entry R in row 5 and column 6 of the transmission matrix of the pre-compression segment is 56，sec1 The scope conditions include:

[0037]

[0038] in, is the expected change in longitudinal length, σ e is the initial projection energy dispersion of the bunch, are the initial bunch length at the entrance of the arc compression section and the target bunch length at the exit of the arc compression section, respectively; R 56，sec1 , R 56,sec2 They are the entries in row 5 and column 6 of the transmission matrix of the pre-compression section and the second compression section respectively.

[0039] The step S5 further includes: adjusting the parameters of the transition matching segment to satisfy the constraint condition of the transition matching segment; wherein the constraint condition of the transition matching segment is: the lateral beta function of all positions of the arc zone compression segment is at most 100.

[0040] The optimization method for the arc compression section of the energy recovery type linear accelerator also includes step S6: adjusting the overall high-order matrix items of the arc compression section by adjusting the strength of all the sixth-level iron and the fourth-level iron in the arc compression section so that the longitudinal cross-section of the bunch at the exit of the arc compression section meets the requirements.

[0041] The method for optimizing the arc compression section of an energy recovery linear accelerator also includes step S7: for the optimized arc compression section, simulating the emittance increase caused by coherent synchrotron radiation while scanning the parameters of the arc compression section entrance, and obtaining the arc compression section with the smallest emittance increase.

[0042] The optimization method of the arc compression section for an energy recovery type linear accelerator of the present invention can compress the bunch while deflecting it at a large angle, and 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 bunch. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a structural diagram of the arc zone compression section obtained by the optimization method of the arc zone compression section for an energy recovery type linear accelerator of the present invention.

[0044] Figure 2It is a structural diagram of a complete beam line of a second reverse optimized beam line of an arc zone compression section obtained by the optimization method of the arc zone compression section of an energy recovery type linear accelerator of the present invention.

[0045] Figure 3A is the entry in row 5 and column 6 of the transfer matrix R 56 The graph of the change with the beam length, Figure 3B is the entry R in row 5 and column 1 of the transmission matrix of the second compression segment Sec2 51 , the entry R in the 5th row and 2nd column of the transfer matrix 52 Variation with beam length.

[0046] Figure 4 This is a graph showing the emittance growth caused by the CSR effect under bunch compression conditions with different charge amounts.

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

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

[0049] The present invention is further described below in conjunction with specific examples. It should be understood that the following examples are only used to illustrate the present invention and are not used to limit the scope of the present invention.

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

[0051] Considering the influence of steady-state CSR effect and downstream CSR effect, when the bunch moves in the bent iron, the electron beam will emit radiation. Due to the existence of path difference (the bunch moves along an arc, and the photons propagate along a straight line), the head particle of the bunch will receive radiation from the tail of the bunch, thereby generating additional energy dispersion. This additional energy dispersion will be coupled with the transmission matrix, causing the bunch of the same slice to produce an additional offset in the lateral phase space, resulting in an offset in the phase space of the bunch. This offset will cause an increase in the distribution area of ​​the phase space and an increase in the projected emittance. The difference between steady-state CSR and downstream CSR is that the head particle is located in the bent iron or at the straight section downstream of the bent iron when receiving the radiation photon.

[0052] From the definition, we know that for any slice u( z is the longitudinal coordinate of the slice, σ z is the bunch length, i.e. the longitudinal root mean square length of the bunch), which is determined by the steady-state coherent synchrotron radiation at the exit of the arc compression section or at the measuring point s f The cumulative shift in phase space caused by can be expressed as:

[0053]

[0054] Where Δx i (u) represents the coherent synchrotron radiation at the exit of the arc compression section s f The deflection in the x direction (i=1) and x' direction (i=2) caused by the deflection in the phase space, the subscripts i=1 and 2 represent the x direction (i=1) and x' direction (i=2) in the transverse phase space, respectively. Similarly, when the deflection plane is in the y direction, i=1 / 2 represents the y and y' directions, respectively. The transmission matrix is ​​from any point s to the exit s of the arc compression section f The transmission matrix is ​​determined by the specific beamline structure, u is the slice, δ(s,u) is the energy dispersion caused by the CSR effect on slice u at any point s, is the increment of energy dispersion caused by CSR effect at any point s in slice u.

[0055] For the steady-state CSR effect, the energy dissipation increment caused by the CSR effect at any point s in slice u is It can be expressed as:

[0056]

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

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

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

[0060] From the above, we can see that for a linear compression process, for any distribution of bunches, the growth of the slice energy dispersion caused by the steady-state coherent synchrotron radiation (CSR) satisfies Among them, dδ1 and dδ2 represent the energy dispersion change of the bunch caused by coherent synchrotron radiation within unit length at any two points, and σ1 and σ2 represent the beam length of the bunch at any two points.

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

[0062] Δxj (u) = k csr (u)I j ,

[0063] Among them, k csr (u) is the parameter related to the longitudinal distribution of the bunch, I j is the beamline related parameter, j is the column number of the transmission matrix, i=1, 2 represent the x direction (i=1) and x' direction (i=2) in the transverse phase space respectively.

[0064] From the above formula, we can see that the deviation caused by the CSR effect can be divided into two parts: the longitudinal distribution parameter k of the bunch csr (u) and beam-related parameters I j , j is the column number of the transmission matrix, when j = 1, 2 and k csr When it is not 0, the corresponding parameters under the condition of i=2,1 are obtained.

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

[0066]

[0067] Among them, I j is a beamline related parameter, which indicates the slice centrifugal deviation related quantity caused by coherent synchrotron radiation. The larger the slice centrifugal deviation related quantity, the larger the slice centrifugal deviation. s0 is the entrance of the arc compression section, s f It is the exit of the arc compression section; is the target bunch length at the exit of the arc compression section, which can be regarded as the compression target length in the present invention and is determined by the designer according to actual needs; σ e is the initial projection energy spread of the bunch, determined by the machine parameters; R 5j is the entry in the 5th row and jth column of the transfer matrix of the reverse optimized beamline, where j is the column number of the transfer matrix. is the fifth row and sixth column of the overall transfer matrix of the arc compression segment, R 56 (s) is the entry in the 5th row and 6th column of the transfer matrix of the reverse optimized beamline from the exit of the arc compression section to any point s.

[0068] In the above simplified process of obtaining formula (3), the present invention applies the symplectic property of the matrix Using the reverse optimization beam line pair R 5i The integral from any point s to the exit s of the arc compression section is replaced by f The entry in the ith row and sixth column of the transfer matrix Specifically, since existing accelerator simulation programs cannot directly provide Therefore, by adopting the optimization "reverse optimization beamline", that is, the arrangement of the components of the optimized reverse optimization beamline is opposite to the arrangement of the components of the beamline in the actual arc compression section, the upper and lower limits of the optimization integral are also transformed into the export index s f to the entry index s0. Then use the optimized reverse beam line to R 5i The points are used to replace the required In the decompression process, the length of the bunch changes. When only linear compression is considered, the change of the length of the bunch in the reverse optimization beamline is opposite to that in the forward optimization. The length σ at any point s in the reverse optimization beamline is z (s) is expressed as in is the exit beam length, is the target length of the compressed beam, and R 56 (s) is the transmission matrix of point s in the reverse beamline (i.e., the position at a distance s from the beamline exit). e is the RMS energy dispersion of the bunch and is the statistics of the bunch at the entrance.

[0069] Therefore, the present invention can use the optimization algorithm to transform the left side of formula (3) As the optimization target, since the column number j of the transmission matrix is ​​1, 2, there are two optimization targets. Making the two optimization targets as close to 0 as possible (ie, the absolute value is minimized) can greatly reduce the lateral offset caused by the steady-state CSR.

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

[0071]

[0072]

[0073] Among them, r e is the classical electron radius, γ is the relativistic factor, and for a fixed arc compression segment, both are constants; R 5j,k The item R in the 5th row and jth column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 5j The corresponding value is, in the arc compression section of the high-energy accelerator (referring to the machine with energy greater than 100MeV), R 5j It is a constant in the non-bent iron region, k is the bent iron number, and j is the column number of the transmission matrix; ζ k To reversely optimize the beam size parameters, Among them, L D,kTo reversely optimize the distance between the kth bend and the k+1th bend in the beam line; φ k To reversely optimize the intermediate parameters of the beam size parameters, Where, σ is the radius of the bending magnet, σ z,k is the beam length of the bunch at the exit of the kth bend iron of the reverse beam line (when the overall energy of the machine is greater than 100MeV, the beam length can be regarded as a constant in the non-bend iron area).

[0074] Similar to the above expression for the offset caused by steady-state CSR, equations (4) and (5) can be further expressed as follows:

[0075]

[0076]

[0077] Among them, k csr,d is a non-zero constant, so if you want to make the offset caused by the downstream CSR effect 0, the sum of the right side of the above two formulas should be 0. Assuming that the radius ρ of all curved iron magnets in the arc compression section is a constant, for any slice u, in order to make the slice centrifugal offset caused by the downstream CSR approach 0, the sum (i.e., the amount related to the slice centrifugal offset caused by the downstream CSR) should satisfy after expansion:

[0078]

[0079] Among them, R 5j,k The item R in the 5th row and jth column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 5j The corresponding value, ρ is the radius of the bending magnet, R 5j It is a constant in the non-bent iron region, k is the bent iron number, and j is the column number of the transmission matrix; ζ k To inversely optimize the beamline size parameters, σ z,k is the bundle length of the kth bend iron exit of the reverse beam line, σ e is the initial energy dispersion, determined by the accelerator exit, is the target beam length, R 56,k The item R in the 5th row and 6th column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 56 The corresponding value; L D,k To reversely optimize the distance between the kth bent iron and the k+1th bent iron in the beam line.

[0080] The optimization method for the arc compression section of the energy recovery type linear accelerator of the present invention can be realized 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 of the present invention includes:

[0082] Step S1: Determine the target bunch length at the exit of the arc compression section by using the free electron laser (FEL) parameters, the acceleration cavity parameters and the injector parameters. The initial projected energy spread of the bunch is e and the initial bunch length at the entrance of the arc compression section

[0083] The free electron laser (FEL) parameters, acceleration cavity parameters and injector parameters are specified in advance.

[0084] Step S2: According to the target bunch length at the exit of the arc compression section The initial projected energy spread of the bunch is e and the initial bunch length at the entrance of the arc compression section Using the formula Obtain the item R in the 5th row and 6th column of the overall transfer matrix of the arc compression segment 56 .

[0085] Step S3: Figure 1 As shown, the arc zone compression section is divided into a pre-compression section Sec1 and a second compression section Sec2, the pre-compression section Sec1 includes two groups of three-bend iron achromatic (TBA) structures 10, and the second compression section Sec2 includes multiple bent irons (four bent irons are taken as an example in the present invention); minimizing the centrifugal deviation of the slice caused by the CSR effect of the second compression section Sec2 is used as the optimization goal, and the reverse optimization beam line of the second compression section Sec2 is optimized by establishing a reverse optimization beam line.

[0086] Since the upstream beam length of the arc compression section is longer, the CSR effect is smaller (steady state Downstream CSR~1 / σ z ). Therefore, if Figure 1 As shown, during the design process, the present invention divides the arc zone compression section into two parts: the pre-compression section Sec1 and the second compression section Sec2. Due to the large change in beam length, the I matrix cannot well control the center offset 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 while only considering the CSR effect of the second compression section Sec2.

[0087] The step S3 specifically includes:

[0088] Step S31: The reverse beam of the second compression section is used as the complete beam of the second reverse optimization beam, and the remaining bent irons and matching sections after removing the first bent iron B1 from the second compression section Sec2 are used to establish the partial beam of the second reverse optimization beam and its constraint conditions, and the bent iron and matching section parameters in the partial beam of the second reverse optimization beam are optimized according to the constraint conditions;

[0089] In this embodiment, if 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, and a matching section located between two adjacent bent irons, including the third matching section M3, the second matching section M2 and the first matching section M1. Figure 2 As shown, it can be seen that the optimization target of the present invention is that along the propagation direction of the actual beam line, in the phase space of the beam, the longitudinal position coordinate z gradually decreases and the energy spread δ gradually increases.

[0090] Therefore, step S31 is Figure 2 The second compression section Sec2 shown in the figure is used to establish the second reverse optimized beam line by removing the remaining bends (i.e., the fourth bend B4 to the second bend B2) after the first bend B1 and all matching sections (i.e., matching sections M1 to M3) of the second compression section Sec2, and then optimize. The bends and matching section parameters in the optimized second reverse optimized beam line section mainly include: the parameters of the second bend B2 to the fourth bend B4, the transmission matrix and length of the first matching section M1 to the second matching section M2, and the length of the third matching section M3 adjacent to the first bend B1.

[0091] The constraints of the second reverse optimization beamline part include: minimizing the centrifugal deviation of the slice caused by the steady-state CSR and the downstream CSR; and the dispersion function constraint.

[0092] The centrifugal deviation of the slice caused by the downstream CSR is minimized by substituting the target bunch length at the exit of the arc compression section into By changing the length of all matching segments (i.e., M1-M3) of the second reverse optimized beam line part and the transmission matrix of all matching segments (i.e., M1-M2) except the matching segment adjacent to the first bend iron, the slice centrifugal deviation correlation amount caused by the downstream CSR corresponding to the second reverse optimized beam line part is reduced. tends to 0, that is, makes formula (6) tend to 0, so that the downstream CSR effect of the second compression section in the positive direction is suppressed.

[0093] Among them, R 5j,k The item R in the 5th row and jth column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 5jThe corresponding value, ρ is the radius of the bending magnet, R 5j It is a constant in the non-bend iron region, k is the bend iron number, j is the column number of the transmission matrix, j = 1, 2; ζ k To inversely optimize the beamline size parameters, σ z,k is the bundle length of the kth bend iron exit of the reverse beam line, σ e is the initial energy dispersion, determined by the accelerator exit, is the target beam length, R 56,k The item R in the 5th row and 6th column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 56 The corresponding value; L D,k To reversely optimize the distance between the kth bent iron and the k+1th bent iron in the beam line.

[0094] In this embodiment, the transmission matrix evolution curve can be derived by changing the beam line arrangement through an accelerator simulation computer program such as ELEGANT, and then substituted into the two cases of j=1 and 2 in formula (6).

[0095] The minimization of the centrifugal deviation of the slice caused by the steady-state coherent synchrotron radiation is specifically achieved by changing the transmission matrix of all matching segments (i.e., M1 to M2) other than the matching segment adjacent to the first bend iron and changing the transmission matrix of all bend irons (i.e., B2 to B4) other than the first bend iron to satisfy formula (3):

[0096]

[0097] Among them, I j is a beamline related parameter, which indicates the slice centrifugal deviation related quantity caused by coherent synchrotron radiation. The larger the slice centrifugal deviation related quantity, the larger the slice centrifugal deviation. s0 is the entrance of the arc compression section, s f It is the exit of the arc compression section; is the target bunch length at the exit of the arc compression section, which can be regarded as the compression target length in the present invention and is determined by the designer according to actual needs; σ e is the initial projection energy spread of the bunch, determined by the machine parameters; R 5j is the entry in the 5th row and jth column of the transfer matrix of the reverse optimized beamline, where j is the column number of the transfer matrix. is the fifth row and sixth column of the overall transfer matrix of the arc compression segment, R 56 (s) is the entry in the 5th row and 6th column of the transfer matrix of the reverse optimized beamline from the exit of the arc compression section to any point s.

[0098] In step S31, the dispersion function constraint condition includes: for the dispersion function (ie, the item R in the first row and sixth column of the transmission matrix 16 , the entry R in row 2 and column 6 of the transfer matrix26 ) is restricted so that it has the same sign in the global range of the second reverse optimized beamline part (always negative or positive, which is related to the reference frame taken), thereby preventing the generation of too short bunches during the compression process and ensuring that the shortest bunch appears at the exit of the arc compression section, which can effectively reduce the impact of downstream CSR. The item R in the first row and sixth column of the transmission matrix in the global range of the second reverse optimized beamline part is 16 , the entry R in row 2 and column 6 of the transfer matrix 26 The .mat output files can be exported using the elegant software.

[0099] Therefore, the present invention optimizes the second reverse optimization wiring part wiring (i.e., the wiring of the remaining bends B1 after removing the first bend B1) in the arc zone compression section. Figure 2 When optimizing B4~B2, M1~M3), emphasis was placed on suppressing the CSR effect.

[0100] Step S32: Establish a complete second reverse optimization beam line by adding the transmission matrix of the first bend iron B1 and its adjacent matching segment M3 downstream of the second reverse optimization beam line partial beam line, establish the constraint conditions of the complete second reverse optimization beam line, and optimize the parameters of the first bend iron B1 and the transmission matrix of its adjacent matching segment M3 according to the constraint conditions of the complete second reverse optimization beam line.

[0101] That is to say, the second reverse optimized complete bundle is a structure obtained by reversely arranging the entire second compression section Sec2, wherein the matching section of the first bend iron B1 is located between the first bend iron B1 and the second bend iron B2. Thus, step S32 optimizes the arrangement of the entire second compression section Sec2.

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

[0103] The overall achromatic condition of the complete beamline of the second reverse optimization beamline refers to the item R in the first row and sixth column of the transmission matrix at the exit of the complete beamline of the second reverse optimization beamline. 16 , the entry R in row 1 and column 6 of the transfer matrix 26 All equal to 0.

[0104] Therefore, the last bent iron B1 and its matching section M3 are used to make the overall transmission matrix of the second compression section Sec2 satisfy R 16 =0,R 26 =0.

[0105] The item R in the 5th row and 1st column of the transmission matrix of the second compression segment Sec2 obtained after optimization is 51, the entry R in the 5th row and 2nd column of the transfer matrix 52 , the entry R in the 5th row and 6th column of the transfer matrix 56 like Figure 3A and Figure 3B shown.

[0106] Step S33: By Figure 2 A quadrupole magnet is added to the location of the matching segments M1 to M3 in the figure, and the position and strength of the quadrupole iron are optimized to make the total transmission matrix meet the requirements of all matching segments (i.e. Figure 2 In the optimization process, the total length of the complete beam line of the second reverse optimization beam line is guaranteed to meet the optimization result of step S31.

[0107] Step S4: establishing constraint conditions for the pre-compression section Sec1 and optimizing the pre-compression section Sec1;

[0108] The pre-compression section Sec1 includes two three-bend iron achromatic (TBA) structures 10. At the same time, a sixth-grade iron (corresponding to the embodiment of the present invention) can be optionally placed. Figure 1 The solid black dots in the middle are used to adjust the overall high-order energy dispersion of the arc compression section.

[0109] The constraints of the pre-compression section Sec1 include:

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

[0111] 2) Make the entrance of two sets of three-bend iron achromatic (TBA) structures (i.e. Figure 1 The lateral transmission matrix of the red marked position in the figure tends to the -I matrix to achieve the suppression of the CSR effect.

[0112] 3) The item R in the 5th row and 6th column of the transmission matrix of the pre-compression segment Sec1 56，sec1 Range conditions;

[0113] 4) Overall achromatic conditions of the pre-compression section.

[0114] like Figure 1 As described above, the pre-compression section Sec1 suppresses the CSR effect by optimizing the lateral transmission matrix corresponding to the entrance of the dual TBA structure to be close to the -I matrix. That is, through the beam optical optimization program such as elegant, the lateral transmission matrices at the entrances of the two three-bend iron achromatic structures 10 are all -I matrices, where the -I matrix is ​​a 4×4 matrix with a diagonal element of -1 and other elements of 0; since the beam length of the magnetic structure changes little, the I matrix can greatly suppress the lateral deviation caused by the CSR effect.

[0115] Among them, the item R in the 5th row and 6th column of the transmission matrix of the pre-compression segment Sec1 is 56，sec1 The scope conditions include:

[0116]

[0117] in is the expected change in longitudinal length, σ e is the initial projection energy dispersion of the bunch, are the initial bunch length at the entrance of the arc compression section and the target bunch length at the exit of the arc compression section, both of which are determined by the accelerator's own parameters and are known quantities; R 56，sec1 , R 56,sec2 They are the entries in the 5th row and the 6th column of the transmission matrix of the pre-compression section Sec1 and the second compression section Sec2 respectively.

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

[0119] The step S5 further includes: adjusting the parameters of the transition matching segment to meet the constraints of the transition matching segment; wherein the constraints of the transition matching segment are: the lateral beta function β of all positions of the arc zone compression segment xf The maximum value is 100, so that the overall lateral dimension of the arc zone compression section is kept in a small range.

[0120] Step S6: By adjusting the strength of all the sixth-level iron and fourth-level iron in the arc zone compression section, the overall high-order matrix items (such as T 166 ,R 566 etc.) to make the longitudinal cross-section of the bunch at the exit of the arc zone compression section meet the requirements, thereby optimizing the strength of grade VI and grade IV iron.

[0121] Among them, the overall high-order matrix terms of the arc compression segment (such as T 166 ,R 566 The value of (, etc.) is related to the design purpose. For example, some machines require high peak flux, while others require Gaussian-like beam.

[0122] Step S7: For the optimized arc compression segment, the emittance increase caused by coherent synchrotron radiation (CSR) is simulated while scanning the parameters (lateral radius, lateral divergence angle) of the arc compression segment entrance to obtain the arc compression segment with the smallest emittance increase.

[0123] Therefore, CSR simulation is performed by scanning the parameters (lateral radius, lateral divergence angle) of the entrance of the arc compression section.

[0124] In this embodiment, by using optimization algorithm + simulation software, taking elegant as an example, by changing the twist optical function (including the lateral beta function β xf , the horizontal alpha function α xf ), after simulation, export the "enx" data in the ".sig" file to compare the size of the emittance growth, find the minimum value of the emittance growth, and obtain the arc compression segment with the minimum emittance growth.

[0125] Experimental results:

[0126] In one of the experimental examples, the parameters of the bent iron and matching section in the complete beam line of the second reverse optimization beam line obtained in step S3, that is, the structural parameters of the second compression section are shown in Table 1.

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

[0128] The simulation effect of the second compression section Sec2 is: the final beam length Initial beam length Energy dispersion e =0.005, the simulation results show that the emittance increase is less than 0.01μmrad.

[0129] For the design of the compression section, the lateral displacement caused by the CSR effect is effectively controlled while the bunch is compressed, thereby controlling the emittance growth of the bunch. As a test, we set the bunch compression target length to 50fs and the compression factor to 20, and scanned bunches with different bunch charges. The emittance growth results caused by the CSR effect under the compression of bunches with different charge amounts are shown in the figure below: Figure 4 As shown, the simulation results considering all CSR effects show that the emittance increase is less than 5%, which meets the design requirements. For the actual bunch, combined with the double TBA pre-compression structure, the emittance change of the actual bunch in the arc compression section can be found in Figure 5 , where ε x,y is the transverse emittance, s is the beam path. The longitudinal phase space and flux distribution of the bunch at the entrance and exit of the arc compression section can be found in Fig. 6A and Figure 6B , Fig. 6A The entrance of the arc compression section is shown. Figure 6B The arc zone compression section outlet is shown. In the figure, βγ is the energy coefficient, which is related to the particle energy. z is the longitudinal coordinate of the particle. pk The beam compression ratio is 40 (length) / 70 (peak current) for the slice current. The relative increase in emittance is less than 5%, and the absolute increase is less than 0.1 μmrad.

[0130] 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 the arc compression section of an energy recovery linear accelerator, characterized in that: include: Step S1: Determine the target bunch length at the exit of the arc compression section The initial projected energy spread of the bunch is σ e and the initial bunch length at the entrance of the arc compression section Step S2: According to the target bunch length at the exit of the arc compression section The initial projected energy spread of the bunch is σ e and the initial bunch length at the entrance of the arc compression section Obtain the item R in the 5th row and 6th column of the overall transfer matrix of the arc compression segment 56 ; Step S3: Divide the arc zone compression section into a pre-compression section and a second compression section, the pre-compression section includes two groups of three-bent iron achromatic structures, and the second compression section includes multiple bent irons; minimize the slice centrifugal deviation caused by the coherent synchrotron radiation effect of the second compression section as the optimization target, and establish a reverse optimization beam line as a means to optimize the reverse beam line of the second compression section; Step S4: establishing constraints for the pre-compression section and optimizing the pre-compression section; Step S5: Obtain the second compression section according to the optimization result of step S3, obtain the pre-compression section according to the optimization result of step S4, and add a transition matching section between the pre-compression section and the compression section to form a total arc zone compression section.

2. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The step S3 specifically includes: Step S31: Taking the reverse beam of the second compression section as the complete beam of the second reverse optimization beam, establishing the partial beam of the second reverse optimization beam and its constraint conditions according to the remaining bent irons and their matching sections after removing the first bent iron in the second compression section, and optimizing the bent iron and matching section parameters in the partial beam of the second reverse optimization beam according to the constraint conditions; Step S32: establishing a complete beam line of a second reverse optimized beam line and its constraint conditions, and optimizing the parameters of the first bend iron and the transmission matrix of its adjacent matching segments according to the constraint conditions of the complete beam line of the second reverse optimized beam line; Step S33: By adding quadrupole magnets at the locations of all matching segments and optimizing the position and strength of the quadrupole iron, the total transmission matrix satisfies the transmission matrices of all matching segments. During the optimization process, the total length of the complete beam line of the second reverse optimization beam line is ensured to meet the optimization result of step S31.

3. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 2, characterized in that: In the step S31, the constraint conditions of the second reverse optimization beamline part beamline include: minimizing the slice centrifugal deviation caused by the steady-state coherent synchrotron radiation and the downstream coherent synchrotron radiation; and the dispersion function constraint conditions; In the step S32, the constraint conditions of the complete beamline of the second inverse optimization beamline include the overall achromatic condition of the complete beamline of the inverse optimization beamline.

4. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 3, characterized in that: The minimization of the slice centrifugal deviation caused by the downstream coherent synchrotron radiation is achieved by substituting the target bunch length at the exit of the arc compression section into By changing the length of all matching segments of the second reverse optimized beam line and the transmission matrix of all matching segments except the matching segment adjacent to the first bend iron, the relevant amount of the slice centrifugal deviation caused by the downstream CSR corresponding to the second reverse optimized beam line part is tends to 0, so that the downstream CSR effect of the second compression section in the positive direction is suppressed; Among them, R 5j,k The item R in the 5th row and jth column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 5j The corresponding value, ρ is the radius of the bending magnet, R 5j It is a constant in the non-bend iron region, k is the bend iron number, j is the column number of the transmission matrix, j = 1, 2; To inversely optimize the beamline size parameters, σ z,k is the bundle length of the kth bend iron exit of the reverse beam line, σ e is the initial energy dispersion, determined by the accelerator exit, is the target beam length, R 56,k The item R in the 5th row and 6th column of the transmission matrix downstream of the kth bend in the reverse optimization beam line is 56 The corresponding value; L D,k To reversely optimize the distance between the kth bent iron and the k+1th bent iron in the beam line; The minimization of the centrifugal deviation of the slice caused by the steady-state coherent synchrotron radiation is specifically achieved by changing the transmission matrix of all matching sections other than the matching section adjacent to the first bending iron and changing the transmission matrix of all bending irons other than the first bending iron so that they satisfy the following formula: Among them, I j are beamline related parameters; s0 is the entrance of the arc compression section, s f It 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 projection energy spread of the bunch, determined by the machine parameters; R 5j is the entry in the 5th row and jth column of the transfer matrix of the reverse optimized beamline, where j is the column number of the transfer matrix. is the fifth row and sixth column of the overall transfer matrix of the arc compression segment, R 56 (s) is the entry in the 5th row and 6th column of the transfer matrix of the reverse optimized beamline from the exit of the arc compression section to any point s.

5. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 3, characterized in that: In step S31, the dispersion function constraint condition includes: restricting the dispersion function so that it has the same sign in the global range of the second reverse optimization beamline part, and the dispersion function includes the item R in the first row and sixth column of the transmission matrix 16 and the entry R in row 2 and column 6 of the transfer matrix 26 ; In the step S32, the overall achromatic condition of the second reverse optimization beamline complete beamline refers to the item R in the first row and sixth column of the transmission matrix at the exit of the second reverse optimization beamline complete beamline. 16 , the entry R in row 1 and column 6 of the transfer matrix 26 Both are equal to 0.

6. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The constraints of the pre-compression stage include: 1) The sum of the deflection angles of the pre-compression section and the second compression section is 180°; 2) making the lateral transmission matrix of the entrance of the two sets of three-bend iron achromatic structures approach the -I matrix to achieve the suppression of CSR effect; and 3) The entry R in the 5th row and 6th column of the transmission matrix of the pre-compression section 56，sec1 Range conditions; 4) Overall achromatic conditions of the pre-compression section; Among them, the item R in the 5th row and 6th column of the transmission matrix of the pre-compression section is 56，sec1 The scope conditions include: in, is the expected change in longitudinal length, σ e is the initial projection energy dispersion of the bunch, are the initial bunch length at the entrance of the arc compression section and the target bunch length at the exit of the arc compression section, respectively; R 56，sec1 , R 56,sec2 They are the entries in row 5 and column 6 of the transmission matrix of the pre-compression section and the second compression section respectively.

7. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The step S5 further includes: adjusting the parameters of the transition matching segment to satisfy the constraint condition of the transition matching segment; wherein the constraint condition of the transition matching segment is: the lateral beta function of all positions of the arc zone compression segment is at most 100.

8. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The method further includes step S6: adjusting the strength of all the sixth-grade iron and fourth-grade iron in the arc zone compression section to adjust the overall high-order matrix items of the arc zone compression section so that the longitudinal cross section of the bunch at the outlet of the arc zone compression section meets the requirements.

9. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The method further comprises step S7: for the optimized arc compression section, simulating the emittance increase caused by coherent synchrotron radiation while scanning the parameters of the arc compression section entrance, and obtaining the arc compression section with the minimum emittance increase.

10. The method for optimizing the arc compression section of an energy recovery linear accelerator according to claim 1, characterized in that: The number of bent irons in the second compression section is 4.

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