Optimization method for magnetic compressor decompression device in energy recovery accelerator

Abstract

This invention provides an optimization method for a magnetic compressor decompression device in an energy recovery accelerator, comprising: sequentially setting first to sixth bends along the beam direction to establish a chicane-structured magnetic compressor decompression device; determining the structure of the reverse-optimized beamline based on the decompression device; establishing constraints for a total deflection angle of 0, an anti-dispersion constraint, and a transfer matrix constraint, and solving the constraint conditions; establishing corresponding criteria with minimizing the slice center shift caused by coherent synchrotron radiation as the optimization objective; optimizing the variables of the reverse-optimized beamline based on the constraints and criteria; and reversing the placement of the reverse-optimized beamline to obtain the decompression device. This invention retains the advantages of conventional chicanes, such as a smaller deflection angle, which prevents over-compression, effectively reducing peak current intensity and helping to suppress slice center shift caused by CSR effects, thereby achieving lower emittance.

Description

Technical Field

[0001] This invention belongs to the field of accelerator physics and technology, and specifically relates to an optimization method for a magnetic compressor decompression device used in an energy recovery accelerator. Background Technology

[0002] Moore's Law states that the number of transistors in integrated circuits roughly doubles every two years, guiding the semiconductor industry for half a century. To maintain this trend, lithography technology has continuously advanced, with the wavelength of light sources gradually shortening. Currently, EUV lithography uses a 13.5nm wavelength, matching the reflectivity of Mo / Si multilayer mirrors. High-volume manufacturing uses a 500W laser-plasma (LPP) light source, but this suffers from issues such as contamination and stochastic effects. Future nodes require higher EUV power; the 3nm node is estimated to require over 1.5kW, and the 2nm node 2.8kW. After EUV, the 6.x nm wavelength (BEUV) is considered the best choice for improving resolution. The transition from EUV to BEUV is relatively straightforward because EUV technology is already well-suited for mass production. In this context, free-electron lasers (FELs) have emerged as strong contenders for generating high-power BEUV radiation. In particular, FELs driven by energy-recovery linear accelerators (ERLs) exhibit unique advantages:

[0003] 1. High efficiency: ERL can recover electron beam energy, which greatly improves system efficiency.

[0004] 2. High brightness: The electron beam generated by ERL is of high quality, which is conducive to generating high-quality BEUV light.

[0005] 3. Tunable: The wavelength of ERL-FEL is adjustable to adapt to future changes in lithography requirements.

[0006] 4. Continuous operation: ERL supports high repetition frequency operation, which is beneficial to improving lithography capacity.

[0007] 5. Compact design: Compared to traditional accelerators, ERLs can be designed to be more compact, making them easier to use in industrial applications.

[0008] 6. Low radiation: Energy recovery reduces the need for radiation protection, making it safer and more environmentally friendly.

[0009] These advantages make ERL-FEL an ideal choice for future high-power BEUV light sources, which is expected to drive the continued development of lithography technology and extend Moore's Law.

[0010] In ERL-FEL, to further enhance the radiation power of the FEL, the required peak current of the bundle is in the kA range. With a single bundle charge of 100 pC, the bundle needs to be compressed to below 100 fs. However, during machine operation, ultrashort bundles will affect bundle quality, such as the wake field effect and coherent synchrotron radiation (CSR) effect. The intensity of the wake field effect is related to... It is inversely proportional, where σ z Let RMS (root mean square) length be the bundle length. The CSR effect occurs during bundle deflection. Due to the path difference between particle motion and photon motion, the head particle will receive radiation from the tail particle, causing additional energy dissipation. This energy dissipation will couple with the bundle line transmission matrix, causing additional offset at the decompression device exit. The lateral offset of the bundle caused by this effect will increase the lateral size of the bundle, thus affecting the magnitude of the overall threshold current (Ithreshold current) of the machine. th ∝1 / σ r A lower threshold current limits the repetition rate and single-bundle charge of the machine, which significantly reduces the radiated power of the FEL. Therefore, reducing the overall lateral dimensions of the machine and the longitudinal dimensions outside the radiating section is crucial. Given a fixed overall beam envelope function, the lateral dimension σ of the bundle... x , σ y The additional growth is determined by the change in emissivity, so preventing further growth in the lateral dimension is equivalent to suppressing the growth in emissivity.

[0011] In most cases, high-current machines require further compression of the initial spool. In this situation, the increase in emittance primarily arises from the compression and decompression sections. The compression section compresses the spool length, reducing it from a long spool to a shorter spool; conversely, the decompression section decompresses the compressed short spool back into a longer spool. To counteract the emittance increase caused by coherent synchrotron radiation in the compression section, various international solutions have been developed. [1][2] Therefore, compared to the compression section, the increase in emittance caused by coherent synchrotron radiation in the decompression section of the existing scheme is more severe. [3] .

[0012] In conventional ERL devices, the first arc segment is often used as the compression segment to compress the bundle. Due to the natural R of the first arc segment... 56 <0, where R ij Let R be the item in the i-th row and j-th column of the transfer matrix in the accelerator, where the transfer matrix is ​​a 6×6 matrix, and let R be the item in the 5-th row and 6-th column of the transfer matrix. 56 This is used to evaluate the effect of bunch energy dispersion on the bunch longitudinal position. Continuing to use the second arc segment for decompression leads to over-compression of the bunch, causing further degradation of bunch quality, even though the arc segment can adjust the term R in the 5th row and 6th column of the transfer matrix. 56The positive and negative values ​​are not directly related, but excessively large bending angles can still lead to further compression of the ultrashort bundle. The term R in the 5th row and 6th column of the natural transfer matrix of the chicane (double-bend) structure... 56 In contrast to the arc section, and with a relatively small first bend angle, the effects of excessive compression can be effectively avoided. However, conventional chicane structures have poor ability to suppress lateral offset caused by coherent synchrotron radiation (CSR), which will still cause a significant increase in additional emissivity, thus affecting the overall lateral dimensions of the machine.

[0013] References:

[0014] [1] Khan, Donish Z., and Tor O. Raubenheimer. "Novel compressor bunchchicane: The five-bend chicane." Physical Review Accelerators and Beams 25.9(2022):090701.

[0015] [2] Di Mitri, S., M. Cornacchia, and S. Spampinati. "Cancellation of coherent synchrotron radiation kicks with optics balance." Physical Review Letters 110.1 (2013): 014801.

[0016] [3]Nakamura, Norio, et al. "S2E simulation of an ERL-based high-powerEUV-FEL source for lithography." Journal of Physics:ConferenceSeries.Vol.874.No.1.IOP Publishing, 2017. Summary of the Invention

[0017] The purpose of this invention is to provide an optimization method for the decompression device of a magnetic compressor in an energy recovery accelerator. It is based on a non-standard chicane, which retains the advantages of conventional chicanes, such as a small deflection angle that can prevent over-compression, while also effectively suppressing the slice center shift caused by the CSR effect, thereby further suppressing the increase in emittance.

[0018] To achieve the above objectives, an optimization method for a magnetic compressor decompression device in an energy recovery accelerator includes:

[0019] S1: The actual magnetic compressor decompression device is established by sequentially setting the first to sixth bends along the direction of the beam to create a chicane structure. The incident and exit angles of the first to sixth bends are (0,θ1), (-θ1,0), (0,-θ2), (θ2,0), (0,θ3), and (-θ3,0), respectively. The structure of the reverse optimized beamline is determined based on the actual magnetic compressor decompression device.

[0020] S2: Establish constraints for the reverse optimization beamline, including the constraint that the total deflection angle is 0, the anisochromatic constraint, and the term R in the 5th row and 6th column of the transfer matrix. 56 The constraints are determined by using the reverse optimization of the beamline's transfer matrix to solve for the constraints.

[0021] S3: Establish corresponding criteria with the optimization objective of minimizing the center offset correlation of the slice caused by coherent synchrotron radiation, and optimize the free variables of the inverse optimization beamline according to the constraints and criteria.

[0022] S4: After obtaining the optimization result that satisfies the optimization objective, the reverse optimization beam corresponding to the optimization result is placed in reverse to obtain the required magnetic compressor decompression device.

[0023] The distance between the second and third bent irons of the magnetic compressor decompression device is 0, and the distance between the fourth and fifth bent irons is 0.

[0024] The achromatic condition of the reverse-optimized beamline is the term R in the 1st row and 6th column of the transfer matrix of the reverse-optimized beamline. 16 =0.

[0025] The term R in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline 56 The constraints include the term R in the 5th row and 6th column of the transfer matrix. 56 The size range is determined based on the bundle length range at the outlet of the actual magnetic compressor decompression device.

[0026] The term R in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline 56 The size range is:

[0027]

[0028] in, The length of the bundle before compression. σ is the bundle length of the bundle before decompression. e The energy of the bundle is dispersed.

[0029] The criterion for minimizing the center shift correlation of the slice caused by coherent synchrotron radiation includes: making the absolute values ​​of the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation approach 0, where the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation are:

[0030]

[0031] Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, s0 is the inlet of the decompression device, and s f For the outlet of the decompression device, 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. The length of the bundle before decompression. It is the item in the 5th row and 6th column of the overall transfer matrix of the decompression structure, R 56 (s) is the term in the 5th row and 6th column of the transfer matrix of the reverse optimized bundle from the decompression device outlet to any point s, σ e The energy of the bundle is dispersed.

[0032] During the optimization process, under the constraint conditions of the reverse optimization bundle, multiple free variables are optimized based on the optimization objective. The free variables include the deflection angle θ1 of the first bend, the deflection angle θ2 of the fourth bend, the deflection angle θ3 of the fifth bend, the distance between the first bend B1 and the second bend B2, the distance between the third bend B3 and the fourth bend B4, and the distance between the fifth bend B5 and the sixth bend B6.

[0033] In step S3, the deflection angle θ1 of the first bent iron is less than 0.05 rad.

[0034] Following step S4, the method further includes:

[0035] S5: For the magnetic compressor decompression device obtained in step S4, the following formula is used to evaluate the increase in emissivity caused by the coherent synchrotron radiation in the steady state:

[0036]

[0037] Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, and β xf ,α xf ,γ xf All are Twiss optical functions at the outlet of the decompression device;

[0038] S6: The Twiss optical function β at the outlet of the decompression device xf ,α xf ,γxf Using as the independent variable, find the minimum value of the emissivity increase caused by steady-state coherent synchrotron radiation.

[0039] The Twiss optical function β at the outlet of the decompression device xf ,α xf ,γ xf Using the independent variable, the minimum emissivity increase caused by steady-state coherent synchrotron radiation is obtained. Specifically, this includes: performing steady-state and unsteady-state coherent synchrotron radiation simulations, using the Twiss optical function at the decompression device outlet as the optimization variable by scanning or using optimization algorithms, and using the emissivity change as the optimization objective to find the optimal solution for the optimization variable.

[0040] The magnetic compressor decompression device for energy recovery accelerators of this invention is based on a non-standard chicane. On the one hand, it retains the advantages of conventional chicanes, such as smaller deflection angles to prevent over-compression. On the other hand, it effectively reduces the peak current intensity of the bundle in the energy recovery linear accelerator, i.e., the maximum current intensity of a single bundle. This elongates the ultra-short bundle at the undulator exit, reducing its susceptibility to collective effects such as coherent synchrotron radiation (CSR). This helps suppress slice center shift caused by CSR, resulting in a smaller emittance at the bundle exit of the decompression device, thus ensuring stable and safe bundle transmission in the return beamline. Furthermore, the smaller emittance reduces the lateral dimension of the bundle when it passes through the accelerator module a second time. This reduces the interaction between the bundle and higher-order modes in the accelerator, thereby increasing the threshold current of the entire machine and enabling it to accept a higher average current intensity, thus increasing the repetition rate of the radiated laser.

[0041] The optimized method for the magnetic compressor decompression device of an energy recovery accelerator of the present invention establishes a magnetic compressor decompression device with a non-circular chicane structure. Compared with arc segment decompression, the ultrashort particle bundle deflection angle is smaller, the decompression process is faster, and the structure is simple and easy to design and modify; and it has the opposite natural R 56 This prevents energy modulation caused by ultrashort bundles due to excessive bundle compression. Furthermore, compared to traditional chicanes, the irregular chicane structure better suppresses the additional offset caused by the CSR effect, reducing the emission increase caused by CSR. Moreover, the optimization method for the magnetic compressor decompression device of the present invention utilizes inverse optimization, allowing calculations to be performed by deriving the transfer matrix evolution curve using conventional accelerator software, simplifying additional calculations and improving design efficiency. Attached Figure Description

[0042] Figure 1 This is a schematic diagram illustrating the additional emissivity increase caused by the slice center offset in the existing magnetic compressor decompression device.

[0043] Figure 2 This is a schematic diagram of the structure of a magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention.

[0044] Figure 3A and Figure 3B The R of the magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention is... 51 R 52 Example diagram of the possible values.

[0045] Figure 4 This is an example diagram showing the variation of bundle length at various points in the magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention.

[0046] Figure 5 This is an example diagram showing the variation of the lateral emittance of the bundle at various points in the magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention. Detailed Implementation

[0047] The preferred embodiments of the present invention are given below with reference to the accompanying drawings and described in detail.

[0048] The optimization method for the decompression device of the magnetic compressor for energy recovery accelerator of the present invention also adopts the irregular chicane structure. The irregular chicane is used for decompression for the first time, so it is different from the previous traditional chicane structure.

[0049] The optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention is mainly based on the following principles:

[0050] Considering the steady-state CSR effect: When the cluster moves in the curved iron, the electron beam emits radiation. Due to the path difference (the cluster moves along an arc, while photons propagate in a straight line), particles at the cluster head will receive radiation from the cluster tail, resulting in additional energy dissipation. This additional energy dissipation will couple with the transfer matrix, causing an additional offset in the transverse phase space of the cluster within the same slice. This offset will lead to an increase in the phase space distribution area and the projected emissivity, as shown below. Figure 1 As shown.

[0051] As defined, for any slice u( z is the vertical coordinate of the slice, σ z The bundle length (i.e., the root mean square length of the bundle's longitudinal direction) is determined by steady-state coherent synchrotron radiation at the outlet s of the decompression device.f The cumulative shift in phase space caused by this point can be expressed as:

[0052]

[0053] Where, Δx i (u) represents coherent synchrotron radiation at the outlet s of the decompression device. f The offset in the x-direction (i=1) and x′-direction (i=2) in phase space caused by the location, s0 is the inlet of the decompression device, s f For the outlet of the decompression device, From any point s to the outlet s of the decompression device f The term in the i-th row and 6-th column of the transfer matrix, δ(s,u) is the energy dispersion of slice u at any point s. Let represent the energy dissipation change of slice u at any point s caused by coherent synchrotron radiation, and let i be the row number of the transfer matrix.

[0054] The energy dissipation change of slice u at any point s caused by coherent synchrotron radiation can be expressed as:

[0055]

[0056] Where ρ is the radius of the bent magnet, λ(u) is the longitudinal distribution of the bundle, which is related to the specific bundle distribution; u0 is the slice at the very end of the bundle, σ z For the length of the bundle, This represents the effect of any bundle slice u' on slice u.

[0057] It is important to note that steady-state coherent synchrotron radiation (CSR) requires the following condition to be met: bundle length Where ρ is the radius of the bent magnet and φ is the angle of the bent iron.

[0058] By solving the above formula (2) and substituting it into formula (1), the cumulative shift in phase space caused by coherent synchrotron radiation can be obtained.

[0059] As shown above, for a linear compression process, for an arbitrarily distributed bundle, the energy dissipation growth caused by steady-state coherent synchrotron radiation satisfies the following... Where dδ1 and dδ2 represent the energy dissipation changes of the bundle caused by coherent synchrotron radiation at any two points within a unit length, and σ1 and σ2 represent the bundle lengths at any two points.

[0060] Since the influence of coherent synchrotron radiation (CSR) on bundles increases with decreasing bundle length, bundles that do not meet the steady-state CSR conditions are less affected by this effect, and the center shift correlation caused by CSR can still be approximated by formula (2). Therefore, for any bundle distribution, simplified from formula (2), to eliminate the influence of steady-state CSR, the compression or decompression section needs to meet the following criteria:

[0061]

[0062] Among them, I j The correlation between the center shift of the slice caused by coherent synchrotron radiation and s0 is the inlet of the decompression device. f For the outlet of the decompression device, 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. The length of the bundle before decompression. It is the item in the 5th row and 6th column of the overall transfer matrix of the decompression device, R 56 (s) is the term in the 5th row and 6th column of the transfer matrix of the reverse optimized bundle from the decompression device outlet to any point s, σ e The energy of the bundle is dispersed.

[0063] In the simplification process, this invention applies the symplectic property of matrices. The transfer matrix of the reverse-optimized beamline is used to replace the path from any point s to the decompression device outlet s. f The item in the i-th row and 6-th column of the transfer matrix Because existing accelerator simulation programs cannot directly provide information about... The calculation results show that by employing "reverse optimization of the bundle," where the arrangement of the optimized bundle elements is opposite to the actual arrangement of the bundle elements in the magnetic compressor decompression device, the upper and lower limits of the optimization integral are transformed by the outlet s of the actual magnetic compressor decompression device. f To the decompression device inlet s0. Then use the term R in the 5th row and jth column of the reverse optimized bundle's transfer matrix. 5j The integral is used to replace any point s from the outlet s of the decompression device. f The item in the i-th row and 6-th column of the transfer matrix The integral. Therefore, similar to formula (2), after substituting the symplectic matrix property into formula (3), the column numbers j = 1 and 2 of the transmission matrix correspond to the criteria for eliminating the influence of coherent synchrotron radiation in the x′ and x directions, respectively. At the same time, during the decompression process, the bundle length changes. Considering only linear compression, the bundle length change in the reverse optimization bundleline is opposite to that in the forward direction. The bundle length σ at any point s is... z(s) is represented as:

[0064]

[0065] in, R is the bundle length of the bundle before decompression. 56 (s) is the 5th row and 6th column of the transmission matrix of the reverse optimized bundle line from the decompression device outlet to any point s (i.e., the position at a distance s from the decompression device outlet), σ e The energy dissipation of the clusters is obtained by performing cluster statistics at the inlet of the decompression device. It is the item in the 5th row and 6th column of the overall transfer matrix of the decompression structure.

[0066] Therefore, the present invention can use an optimization algorithm to optimize the left-hand side of formula (3). As optimization objectives, since column numbers j = 1 and 2, there are two optimization objectives. The goal is to make the two optimization objectives as close to 0 as possible (i.e., minimize the absolute value), which can greatly reduce the lateral offset caused by steady-state CSR.

[0067] Based on the above principles, the optimization method for the magnetic compressor decompression device of the present invention for an energy recovery accelerator includes:

[0068] Step S1: Sequentially arrange the first to sixth bends along the beam direction to establish the actual magnetic compressor decompression device with an irregular chicane structure. The incident and exit angles of the first to sixth bends are (0, θ1), (-θ1, 0), (0, -θ2), (θ2, 0), (0, θ3), and (-θ3, 0), respectively. The incident and exit angles are written in the form of (incident angle, exit angle). The angles without parentheses represent the deflection angles of the bends, such as the deflection angle θ1 of the first bend, θ2 of the fourth bend, and θ3 of the fifth bend. The deflection angles are automatically determined based on the exit or incident angles. Determine the structure of the reverse optimized beamline based on the actual magnetic compressor decompression device.

[0069] In this case, the radii of the first to sixth bends are set to be the same based on the actual energy of the bundle.

[0070] In this embodiment, the distance between the second and third curved irons is 0, and the distance between the fourth and fifth curved irons is 0. In other embodiments, the distance between the second and third curved irons and the distance between the fourth and fifth curved irons are not 0, so as to appropriately retain the interval for suppressing the downstream CSR effect.

[0071] Figure 2This is a schematic diagram of the actual magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for energy recovery accelerators of the present invention.

[0072] It is important to note that, as described in the principle section above, this optimization process is a reverse optimization. That is, the inlet of the designed reverse-optimized beamline serves as the outlet of the actual magnetic compressor decompression device, and the outlet of the designed reverse-optimized beamline serves as the inlet of the actual magnetic compressor decompression device. In this invention, the deflection angle of the last bent iron piece of the reverse-optimized beamline (i.e., the first bent iron piece at the inlet of the actual decompression device) is θ1, not -θ3.

[0073] Step S2: Establish constraints for the reverse optimization beamline, including the constraint that the total deflection angle is 0, the achromatic constraint, and the term R in the 5th row and 6th column of the transfer matrix. 56 The constraints are determined by using the reverse optimization of the beamline's transfer matrix.

[0074] The dedispersion condition for the inverse optimization beamline is the term R in the 1st row and 6th column of the transmission matrix of the inverse optimization beamline. 16 =0.

[0075] The term R in the 5th row and 6th column of the transfer matrix of the reverse optimized bundle. 56 The constraints include the term R in the 5th row and 6th column of the transfer matrix. 56 The size range. Among them, the item R in the 5th row and 6th column of the transfer matrix. 56 The size range is determined by the length range of the bundle at the outlet of the actual magnetic compressor decompression device.

[0076] Under normal circumstances, the length of the bundle after decompression is often the same as the length of the bundle before compression. Similarly, related to the overall design of the accelerator, assuming an acceptable offset range of 20%, the term R in the 5th row and 6th column of the transfer matrix of the reverse-optimized beamline... 56 The size range is:

[0077]

[0078] in, The length of the bundle before compression. σ is the bundle length of the bundle before decompression. e The energy of the bundle is dispersed.

[0079] In addition, step S2 also includes: adding additional constraints according to the layout requirements, such as spatial placement constraints (limiting the total length of the structure), and applying magnetic field strength constraints (limiting the deflection radius of the magnets).

[0080] Step S3: Establish the corresponding criteria with the optimization objective of minimizing the center offset correlation of the slice caused by coherent synchrotron radiation, and optimize the free variables of the inverse optimization beamline according to the constraints and criteria.

[0081] The criterion for minimizing the center shift correlation of the slice caused by coherent synchrotron radiation includes: making the absolute values ​​of the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation approach 0, where the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation are:

[0082]

[0083] Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, s0 is the inlet of the decompression device, and s f For the outlet of the decompression device, 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. The length of the bundle before decompression. It is the item in the 5th row and 6th column of the overall transfer matrix of the decompression structure, R 56 (s) is the term in the 5th row and 6th column of the transfer matrix of the reverse optimized bundle from the decompression device outlet to any point s, σ e The energy of the bundle is dispersed.

[0084] I1 and I2 correspond to two different lateral directions.

[0085] In step S3, during the optimization process, under the constraint conditions of the reverse optimization beamline (excluding spatial constraints), based on two optimization objectives (the correlation of the center shift of the slice caused by coherent synchrotron radiation in two directions), the free variables are written in and the evolution curve of the transfer matrix is ​​exported through conventional accelerator software (e.g., for the ELEGANT simulation program, the corresponding matrix terms are exported from the default .mat file), and then the correlation of the center shift of the slice caused by coherent synchrotron radiation is calculated, so as to optimize the six free variables through continuous iteration.

[0086] The free variables include the deflection angle θ1 of the first bend, the deflection angle θ2 of the fourth bend, the deflection angle θ3 of the fifth bend, the distance between the first bend B1 and the second bend B2, the distance between the third bend B3 and the fourth bend B4, and the distance between the fifth bend B5 and the sixth bend B6. These six free variables are used as optimization variables.

[0087] In step S3, taking the commonly used accelerator simulation software ELEGANT as an example, the variables are written into the .lte file as input beamlines, and after running, the R output file in the .mat file is read. 51 ,R52 ,R 56 The curve, while setting the bundle length before decompression. and the energy dispersion σ of the bundle e Among them, the bundle length before decompression The energy dispersion σ of the bundle is determined by actual machine parameters. e The values ​​of I1 and I2, which are related to the center offset of the slice caused by coherent synchrotron radiation, are obtained by performing bundle statistics at the inlet of the decompression device. Then, the values ​​are iteratively optimized so that the values ​​of I1 and I2 are close to 0 under the condition of satisfying the constraints.

[0088] During optimization, the deflection angle of the last bent iron in the reverse optimization beam (i.e., the deflection angle θ1 of the first bent iron at the inlet of the actual magnetic compressor decompression device) should not be too large. Specifically, the deflection angle θ1 of the first bent iron should be at most (6σ). z / ρσ e ) 1 / 3 , σ z For the bundle length, σ e Let δ represent the energy dissipation of the bundle, and δ be the radius of the bent magnet. Preferably, the deflection angle θ1 of the first bent magnet should be less than 0.05 rad.

[0089] Step S4: After obtaining the optimization result that satisfies the optimization objective, reverse the reverse optimization beam corresponding to the optimization result to obtain the required magnetic compressor decompression device.

[0090] The structure of the required magnetic compressor decompression device is as follows: Figure 2 As shown.

[0091] Furthermore, after step S4, the present invention may further include:

[0092] Step S5: For the magnetic compressor decompression device obtained in step S4, evaluate the emissivity increase caused by the steady-state coherent synchrotron radiation (CSR).

[0093] In step S5, the following formula is used to evaluate the increase in emissivity caused by obtaining steady-state coherent synchrotron radiation:

[0094] Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, and β xf ,α xf ,γ xf These are all Twiss optical functions at the exit of the decompression device, also known as Twiss functions. In accelerator physics, Twiss functions are usually used to describe the transverse phase space distribution.

[0095] Step S6: Using the Twiss optical function β at the outlet of the decompression device xf ,α xf ,γ xf Using as the independent variable, find the minimum value of the emissivity increase caused by steady-state coherent synchrotron radiation.

[0096] In this invention, the Twiss function (i.e., the Twiss optical function β at the outlet of the decompression device) is used. xf ,α xf ,γ xf Using as the independent variable, find the minimum value of the emissivity increase caused by steady-state coherent synchrotron radiation, specifically including:

[0097] Perform steady-state and unsteady-state coherent synchrotron radiation simulations. By scanning or using optimization algorithms, the Twiss optical function at the decompression device outlet is used as the optimization variable, and the change in emissivity is used as the optimization objective to find the optimal solution for the optimization variable (the range of the optimization variable is set according to the actual situation).

[0098] When the optimization variable reaches its optimal solution, the objective value is the minimum value of the emission change. Ideally, the offset direction caused by the emission change effect is the same as the phase space offset direction, at which point the emission increase reaches its minimum. Figure 1 As shown, phase space shift causes emissivity increase. Therefore, this invention evaluates whether the degree of phase space shift is basically the same as the shift direction caused by the emissivity change effect by directly assessing the emissivity increase.

[0099] Therefore, the physical process of the decompression process of the magnetic compressor decompression device optimized by the optimization method of the present invention is as follows: the bundle passes through the first bent iron, due to the local R of the first bent iron... 56 Value and total R of chicane 56 Conversely, the bundle will be further compressed, so the deflection angle of the first bend (i.e., the angle of the last bend in the reverse-optimized bundle) should not exceed (6σ). z / ρσ e ) 1 / 3 Since the CSR effect is inversely proportional to the -4 / 3 power of the beam length, excessive compression leading to an ultrashort bundle will cause a dramatic increase in the coherent synchrotron radiation effect. A small angle (radians < 0.05 rad) in the first bend can prevent the additional coherent synchrotron radiation effect caused by excessive compression. Here, ρ is the radius of the bend.

[0100] The bundle then passes through the first drift segment (i.e., the first bent iron) and enters the second and third bent irons. Since the distance between the second and third bent irons is 0, in actual operation, the absolute value of the total deflection angle of the second and third bent irons is θ1 + θ2, and the bending direction is opposite to that of the first magnet. The overall edge angle of the second and third bent irons is (-θ1, -θ2). In this invention, the second and third bent irons are referred to as the second group, and similarly, the fourth and fifth bent irons are referred to as the third group. Because the term R in the 5th row and 6th column of the local transmission matrix of the second and third groups of bent irons... 56 The term R in the 5th row and 6th column of the total transfer matrix of the inverted optimized bundle (i.e., chicane structure) is approximately equal to this. 56 In the second set of bends, the bundle is decompressed, but the decompression ratio is lower because the angle of the second set of bends is smaller than that of the third set. The bundle then passes through the second drift segment and enters the third set of bends composed of the fourth and fifth bends (the total deflection angle of the third set of bends is θ2+θ3, the deflection direction is the same as that of the first bend, and the edge angle is (θ2,θ3)). The bundle length is further stretched. Because the angle of the third set of bends is greater than that of the second set, the item R in the 5th row and 6th column of the local transmission matrix of the third set of bends... 56 The beam length is relatively large, and the decompression ratio is relatively large. At this point, the beam length is approximately equal to the target beam length. The bundle then passes through the third drift segment and enters the fourth set of bends (angle -θ3, deflection angle opposite to the first bend, edge angle (-θ3, 0)). Within this local bend, the local R... 56 The term R in the 5th row and 6th column of the total transfer matrix of the inverse optimized bundle (i.e., chicane structure) 56 The signs are reversed. The bundle is compressed within this bend, but since the bundle length is much greater than the inlet bundle length, the compression ratio can be ignored. At this point, the bundle length is stretched to its original length before compression. In this embodiment, the included angles of the various bends satisfy θ2>θ3>θ1, but this may not hold for smaller compression ratios. Therefore, this invention only restricts the size of θ1.

[0101] The optimization method of this invention provides the following process for suppressing the CSR effect in the magnetic compressor decompression device: It is assumed that the deflection surface occurs in the horizontal direction (xs plane), and the offset direction generated by the bundle within the first magnet is defined as positive. Similarly, using... Figure 2Taking the irregular chicane structure as an example, the ultrashort bundle before compression experiences a large CSR kick after passing through the first bend, causing a positive offset (Δx1, Δx1′) at the exit of the chicane structure. Afterward, the bundle passes through the first drift section and enters the second set of bends. The second set of bends initially produces a positive offset, followed by a negative offset. As the bundle length increases, the CSR effect per unit length weakens, resulting in a total offset of (Δx2, Δx2′). The bundle then enters the third set of bends, where the bundle length further increases. The offset process is reversed compared to the second set of bends, initially producing a negative offset at the exit of the chicane structure, followed by a positive offset, resulting in a total offset of (Δx3, Δx3′). Finally, it enters the fourth bend. Due to the longer bundle length, the impact on the exit offset is small, denoted as a positive offset of (Δx4, Δx4′). By optimizing the chicane structure to satisfy formula (3), the offset caused by steady-state CSR at the exit of the chicane structure is 0.

[0102] Experimental results:

[0103] For example Figure 2 Taking the decompression device with the chicane structure shown as an example, the term R of the transfer matrix of the chicane structure is... 51 and R 52 like Figure 3A and Figure 3B As shown, the changes in bundle length and the increase in emittance at the exit are respectively as follows: Figure 4 and Figure 5 As shown, for non-ideal bundles, the bundle length is decompressed from 18 μm to 700 μm. The decompression factor is approximately 40. The emittance increase is approximately 0.4 μm-rad, roughly double the emittance at the inlet. Compared to other similar designs internationally, such as KEK EUV-ERL (decompression factor 30, emittance increase of 5 μm-rad, approximately 2.5 times that at the inlet), the emittance increase is only 1 / 10, and the increase ratio is 1 / 2.5.

[0104] The magnetic compressor decompression device for energy recovery accelerators of this invention is based on a non-standard chicane. On the one hand, it retains the advantages of conventional chicanes, such as smaller deflection angles to prevent over-compression. On the other hand, it effectively reduces the peak current intensity of the bundle in the energy recovery linear accelerator, i.e., the maximum current intensity of a single bundle. This elongates the ultra-short bundle at the undulator exit, reducing its susceptibility to collective effects such as coherent synchrotron radiation (CSR). This helps suppress slice center shift caused by CSR, resulting in a smaller emittance at the bundle exit of the decompression device, thus ensuring stable and safe bundle transmission in the return beamline. Furthermore, the smaller emittance reduces the lateral dimension of the bundle when it passes through the accelerator module a second time. This reduces the interaction between the bundle and higher-order modes in the accelerator, thereby increasing the threshold current of the entire machine and enabling it to accept a higher average current intensity, thus increasing the repetition rate of the radiated laser.

[0105] The optimized method for the magnetic compressor decompression device of an energy recovery accelerator of the present invention establishes a magnetic compressor decompression device with a non-circular chicane structure. Compared with arc segment decompression, the ultrashort particle bundle deflection angle is smaller, the decompression process is faster, and the structure is simple and easy to design and modify; and it has the opposite natural R 56 This prevents energy modulation caused by ultrashort bundles due to excessive bundle compression. Furthermore, compared to traditional chicanes, the irregular chicane structure better suppresses the additional offset caused by the CSR effect, reducing the emission increase caused by CSR. Moreover, the optimization method for the magnetic compressor decompression device of the present invention utilizes inverse optimization, allowing calculations to be performed by deriving the transfer matrix evolution curve using conventional accelerator software, simplifying additional calculations and improving design efficiency.

[0106] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. All simple and equivalent changes and modifications made in accordance with the claims and description of this application fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. An optimization method for a magnetic compressor decompression device in an energy recovery accelerator, characterized in that, include: Step S1: Sequentially set the first to sixth bends along the beam direction to establish the actual magnetic compressor decompression device with an irregular chicane structure, wherein the incident angles and exit angles of the first to sixth bends are (0,θ1), (-θ1,0), (0,-θ2), (θ2,0), (0,θ3), and (-θ3,0), respectively; determine the structure of the reverse optimized beamline based on the actual magnetic compressor decompression device; Step S2: Establish constraints for the reverse optimization beamline, including the constraint that the total deflection angle is 0, the achromatic constraint, and the term R in the 5th row and 6th column of the transfer matrix. 56 The constraints are determined by using the reverse optimization of the beamline's transfer matrix to solve for the constraints. Step S3: Establish the corresponding criteria with the optimization objective of minimizing the center offset correlation of the slice caused by coherent synchrotron radiation, and optimize the free variables of the inverse optimization beamline according to the constraints and criteria. Step S4: After obtaining the optimization result that satisfies the optimization objective, reverse the reverse optimization beam corresponding to the optimization result to obtain the required magnetic compressor decompression device.

2. The optimization method for the magnetic compressor decompression device for an energy recovery accelerator according to claim 1, characterized in that, The distance between the second and third bent irons of the magnetic compressor decompression device is 0, and the distance between the fourth and fifth bent irons is 0.

3. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 1, characterized in that, The achromatic condition of the reverse-optimized beamline is the term R in the 1st row and 6th column of the transfer matrix of the reverse-optimized beamline. 16 =0.

4. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 1, characterized in that, The term R in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline 56 The constraints include the term R in the 5th row and 6th column of the transfer matrix. 56 The size range is determined based on the bundle length range at the outlet of the actual magnetic compressor decompression device.

5. The optimization method for the magnetic compressor decompression device for an energy recovery accelerator according to claim 3, characterized in that, The term R in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline 56 The size range is: in, The length of the bundle before compression. σ is the bundle length of the bundle before decompression. e The energy of the bundle is dispersed.

6. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 1, characterized in that, The criterion for minimizing the center shift correlation of the slice caused by coherent synchrotron radiation includes: making the absolute values ​​of the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation approach 0, where the center shift correlation I1 and I2 of the slice caused by coherent synchrotron radiation are: Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, s0 is the inlet of the decompression device, and s f For the outlet of the decompression device, 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. The length of the bundle before decompression. It is the item in the 5th row and 6th column of the overall transfer matrix of the decompression structure, R 56 (s) is the term in the 5th row and 6th column of the transfer matrix of the reverse optimized bundle from the decompression device outlet to any point s, σ e The energy of the bundle is dispersed.

7. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 1, characterized in that, During the optimization process, under the constraint of the reverse optimization beamline, the free variables are written in and the transmission matrix evolution curve is exported through conventional accelerator software to calculate the center offset correlation of the slice caused by coherent synchrotron radiation, so as to optimize the six free variables through continuous iteration; wherein, the free variables include the deflection angle θ1 of the first bend, the deflection angle θ2 of the fourth bend, the deflection angle θ3 of the fifth bend, the distance between the first bend B1 and the second bend B2, the distance between the third bend B3 and the fourth bend B4, and the distance between the fifth bend B5 and the sixth bend B6.

8. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 1, characterized in that, In step S3, the deflection angle θ1 of the first bent iron is less than 0.05 rad.

9. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 6, characterized in that, Following step S4, the method further includes: Step S5: For the magnetic compressor decompression device obtained in step S4, the following formula is used to evaluate the increase in emissivity caused by the obtained steady-state coherent synchrotron radiation: Where I1 and I2 are the center shift correlation quantities of the slice caused by coherent synchrotron radiation, and β xf ,α xf ,γ xf All are Twiss optical functions at the outlet of the decompression device; Step S6: Using the Twiss optical function β at the outlet of the decompression device xf ,α xf ,γ xf Using as the independent variable, find the minimum value of the emissivity increase caused by steady-state coherent synchrotron radiation.

10. The optimization method for the decompression device of a magnetic compressor for an energy recovery accelerator according to claim 9, characterized in that, The Twiss optical function β at the outlet of the decompression device xf ,α xf ,γ xf Using [variable name] as the independent variable, find the minimum value of the emissivity increase caused by steady-state coherent synchrotron radiation, specifically including: We perform steady-state and unsteady-state coherent synchrotron radiation simulations. By scanning or using optimization algorithms, we take the Twiss optical function at the decompression device outlet as the optimization variable and the change in emissivity as the optimization objective to find the optimal solution for the optimization variable.

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