Optimization method of magnetic compressor decompression device for energy recovery accelerator

Abstract

The invention provides an optimization method for a magnetic compressor decompression device of an energy recovery type accelerator, which comprises the following steps of: sequentially arranging first to sixth bent irons along a beam flow direction to establish a magnetic compressor decompression device with a special-shaped chicane structure, and determining a structure of a reverse optimization beam line according to the decompression device; establishing a constraint condition that the total deflection angle is 0, an achromatic constraint condition and a constraint condition of a transmission matrix, and solving the constraint conditions; establishing a corresponding criterion by taking the center offset of the slice caused by minimization of coherent synchrotron radiation as an optimization target, and optimizing the variable of the reverse optimization beam line according to the constraint condition and the criterion; and reversely placing the reverse optimized bunch wire to obtain the decompression device. According to the method, the advantages that a conventional chicane is small in deflection angle and capable of preventing excessive compression are reserved, so that the peak flow intensity is effectively reduced, slice center offset caused by the CSR effect can be restrained, and therefore smaller emittance is achieved.

Description

Technical Field

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

[0002] Moore's Law states that the number of transistors on an integrated circuit doubles approximately every two years, and has guided the development of the semiconductor industry for half a century. To maintain this trend, lithography technology has continued to advance and the wavelength of the light source has gradually shortened. Currently, EUV lithography uses a 13.5nm wavelength, which matches the reflectivity of Mo / Si multilayer mirrors. High-volume manufacturing uses a 500W laser plasma (LPP) light source, but there are problems such as contamination and random effects. Future nodes will require higher EUV power, with an estimated 1.5kW for the 3nm node and 2.8kW for the 2nm node. After EUV, 6.x nm wavelength (BEUV) is considered the best choice for improving resolution. The transition from EUV to BEUV is relatively simple because EUV technology has been adapted to high-volume manufacturing. In this context, free electron lasers (FELs) have become a strong contender for producing high-power BEUV radiation. In particular, FELs driven by energy recovery linear accelerators (ERLs) show unique advantages:

[0003] 1. High efficiency: ERL can recycle electron beam energy and greatly improve system efficiency.

[0004] 2. High brightness: The electron beam produced by ERL is of high quality, which is conducive to the generation of 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 rate operation, which is conducive to improving lithography capacity.

[0007] 5. Compact design: Compared with traditional accelerators, ERL can be designed to be more compact and convenient for 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 promote the continued development of lithography technology and continue Moore's Law.

[0010] In ERL-FEL, in order to further increase the radiation power of FEL, the required bunch peak flux is as high as kA level. When the charge of a single bunch is 100pC, the bunch needs to be compressed to less than 100fs. However, during the operation of the machine, the ultra-short bunch will affect the quality of the bunch, such as the tail field effect and the coherent synchrotron radiation (CSR) effect. The strength of the tail field effect is related to is inversely proportional, where σ z is the RMS (longitudinal root mean square) beam length of the bunch. The CSR effect occurs when the bunch is deflected. Due to the path difference between the particle motion and the photon motion, the head particle will receive the radiation of the tail particle, causing additional energy dispersion. At the same time, this energy dispersion will couple with the beam line transmission matrix to cause additional offset at the exit of the decompression device. The lateral offset of the bunch caused by this effect will increase the lateral size of the bunch, thereby affecting the size of the overall threshold current of the machine (I th ∝1 / σ r ). A lower threshold current will limit the repetition frequency of the machine and the charge of a single bunch, which will greatly reduce the radiation power of the FEL. Therefore, it is crucial to reduce the overall lateral size of the machine and the longitudinal size outside the radiation section. When the overall beam envelope function of the machine is determined, the lateral size of the bunch σ x , σ y The additional growth of is determined by the change in emittance, so preventing further growth in the lateral size is equivalent to suppressing the growth of emittance.

[0011] In most cases, in high-intensity machines, the initial bunch needs to be further compressed. In this case, the increase in emittance mainly comes from the compression section and the decompression section. The compression section is used to compress the length of the bunch, from a long bunch to a short bunch; the decompression section is the opposite, used to decompress the compressed short bunch to a long bunch. In response to the increase in emittance caused by the coherent synchrotron radiation effect in the compression section, there are many solutions internationally to offset this effect. [1][2] Therefore, compared with the compression stage, the emittance increase caused by coherent synchrotron radiation in the decompression stage of the existing scheme is more serious [3] .

[0012] In conventional ERL devices, the first arc segment is often used as a compression segment to compress the bunch. 56 <0, where R ij is the item in the i-th row and j-th column of the transmission matrix in the accelerator, where the transmission matrix is ​​a 6×6 matrix, and the item R in the 5th row and 6th column of the transmission matrix 56 It is used to evaluate the influence of bunch energy dispersion on the longitudinal position of the bunch. Continuing to use the second arc segment for decompression will lead to over-compression of the bunch and further degradation of the bunch quality, although the arc segment can adjust the item R in the 5th row and 6th column of the transmission matrix 56However, too large an angle of bending will still lead to further compression of the ultrashort bunch. The chicane (double-bend) structure has a natural transmission matrix of row 5 and column 6, 56 In contrast to the arc section, the first bend angle is relatively small, which can effectively avoid the impact of excessive compression. However, the conventional chicane structure has poor ability to suppress the lateral deviation caused by coherent synchrotron radiation (CSR), which will still cause a large increase in additional emittance, thereby affecting the overall lateral size 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 the present invention is to provide an optimization method for a magnetic compressor decompression device for an energy recovery accelerator, which is implemented based on a special-shaped chicane. It not only retains the advantages of a conventional chicane with a small deflection angle to prevent excessive compression, but also can effectively suppress the slice center offset caused by the CSR effect, thereby further suppressing the increase in emittance.

[0018] In order to achieve the above object, a method for optimizing a magnetic compressor decompression device for an energy recovery accelerator comprises:

[0019] S1: The first to sixth bends are sequentially arranged along the direction of the beam to establish an actual magnetic compressor decompression device of a chicane structure, wherein the incident angles and the exit angles of the first to sixth bends are (0, θ1), (-θ1, 0), (0, -θ2), (θ2, 0), (0, θ3), (-θ3, 0), respectively; the structure of the reverse optimized beam line is determined according to the actual magnetic compressor decompression device;

[0020] S2: Establish the constraints of 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 transmission matrix 56 The constraints are solved by inversely optimizing the transmission matrix of the beam line;

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

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

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

[0024] The achromatic condition of the reverse optimized beamline is the term R in the first row and sixth column of the transmission matrix of the reverse optimized beamline. 16 =0.

[0025] The entry R in the 5th row and 6th column of the transfer matrix of the inverse optimized beamline is 56 The constraints include the entry R in row 5 and column 6 of the transfer matrix 56 The size range is determined according to the beam length range of the bunch at the outlet of the actual magnetic compressor decompression device.

[0026] The entry R in the 5th row and 6th column of the transfer matrix of the inverse optimized beamline is 56 The size range is:

[0027]

[0028] in, is the bundle length before compression, is the bunch length before decompression, σ e For the energy dispersion of the cluster.

[0029] The criterion for minimizing the center offset correlation of the slice caused by the coherent synchrotron radiation as the optimization target includes: making the absolute values ​​of the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation approach 0, wherein the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation are:

[0030]

[0031] Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, s0 is the entrance of the decompression device, s f is the outlet of the decompression device, 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 bundle length before decompression, is the entry in row 5 and column 6 of the overall transfer matrix of the decompressed structure, R 56 (s) is the fifth row and sixth column of the transfer matrix of the reverse optimized beamline from the decompression device outlet to any point s, σ e For the energy dispersion of the cluster.

[0032] During the optimization process, while satisfying the constraints of the reverse optimization beam line, multiple free variables are optimized based on the optimization target, and the free variables include the deflection angle θ1 of the first bend iron, the deflection angle θ2 of the fourth bend iron, the deflection angle θ3 of the fifth bend iron, the spacing between the first bend iron B1 and the second bend iron B2, the spacing between the third bend iron B3 and the fourth bend iron B4, and the spacing between the fifth bend iron B5 and the sixth bend iron B6.

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

[0034] After 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 emittance growth caused by the steady-state coherent synchrotron radiation:

[0036]

[0037] Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, β xf ,α xf ,γ xf All are twist optical functions at the outlet of the decompression device;

[0038] S6: The twist optical function β at the outlet of the decompression device xf ,α xf ,γxf As the independent variable, the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation is obtained.

[0039] The twist optical function β at the outlet of the decompression device xf ,α xf ,γ xf The method takes φ as the independent variable and obtains the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation, specifically comprising: performing steady-state and non-steady-state coherent synchrotron radiation simulations, taking the twist optical function at the outlet of the decompression device as the optimization variable by scanning or using an optimization algorithm, taking the emittance change as the optimization target, and finding the optimal solution of the optimization variable.

[0040] The magnetic compressor decompression device for the energy recovery accelerator of the present invention is implemented based on the special-shaped chicane. On the one hand, it retains the advantages of the conventional chicane with a small deflection angle to prevent over-compression. On the other hand, it can effectively reduce the peak flux of the bunch in the energy recovery linear accelerator, that is, the maximum flux of a single bunch, so that the bunch with an ultra-short beam length at the outlet of the undulator is elongated, so that it is less affected by collective effects such as coherent synchrotron radiation (CSR), which is conducive to suppressing the slice center offset caused by the CSR effect, so that the bunch at the outlet of the decompression device has a smaller emittance, and the stable and safe transmission of the bunch in the return beam line is achieved. Furthermore, by reducing the lateral size of the bunch when it passes through the acceleration module for the second time through a smaller emittance, this will reduce the interaction between the bunch and the high-order mode in the accelerator, thereby increasing the threshold current of the entire machine, so that the machine as a whole can accept a higher average flux, thereby increasing the repetition frequency of the radiated laser.

[0041] The magnetic compressor decompression device established by the optimization method for the magnetic compressor decompression device of the energy recovery accelerator of the present invention adopts a special-shaped chicane structure. Compared with the arc segment decompression, the deflection angle of the ultrashort particle bunch 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 , which can prevent the energy modulation caused by the ultrashort bunch caused by excessive bunch compression; in addition, compared with the traditional chicane, the special-shaped chicane structure can better suppress the additional offset caused by the CSR effect, so that the emittance growth caused by CSR is reduced. Furthermore, the optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention uses the reverse optimization method, and the transfer matrix evolution curve can be derived by conventional accelerator software for calculation, which can simplify the additional calculation process and improve the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0001] Figure 1 It is a schematic diagram of the increase in additional emittance caused by the slice center offset of the existing magnetic compressor decompression device.

[0002] Figure 2 It is a structural schematic diagram of a magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for an energy recovery type accelerator of the present invention.

[0003] 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 the energy recovery type accelerator of the present invention 51 , R 52 Example diagram of the values.

[0004] Figure 4 It is an example diagram of the variation of bunch length at each point of the magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention.

[0005] Figure 5 It is an example diagram of the change of the bunch lateral emittance at each point of the magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention. DETAILED DESCRIPTION

[0006] The preferred embodiments of the present invention are given below in conjunction with the accompanying drawings and described in detail.

[0007] The optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention is also implemented by using a special-shaped chicane structure. The special-shaped chicane is used for decompression for the first time, so the overall structure is different from the previous traditional chicane structure.

[0008] The optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention is mainly based on the following principles:

[0009] Consider the influence of the steady-state CSR effect: when the bunch moves in the bent iron, the electron beam will emit radiation. Due to the existence of the path difference (the bunch moves along an arc, and the photons propagate along a straight line), the particles at the head of the bunch will receive radiation from the tail of the bunch, thereby generating additional energy dispersion. This additional energy dispersion will couple 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, such as Figure 1 shown.

[0010] 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 generated by the steady-state coherent synchrotron radiation at the outlet of the decompression device sf The cumulative shift in phase space caused by can be expressed as:

[0011]

[0012] Where Δx i (u) represents the coherent synchrotron radiation at the exit of the decompression device s f The displacement in the x direction (i=1) and the displacement in the x′ direction (i=2) caused by the position in the phase space, s0 is the entrance of the decompression device, s f For the decompression device outlet, From any point s to the decompression device outlet s f The entry in the ith row and sixth column of the transfer matrix of , δ(s,u) is the energy dispersion of slice u at any point s, is the energy dispersion change of slice u at any point s caused by coherent synchrotron radiation, and i is the row number of the transmission matrix.

[0013] The energy dispersion change of slice u at any point s caused by coherent synchrotron radiation can be expressed as:

[0014]

[0015] 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.

[0016] It should be noted that steady-state coherent synchrotron radiation (CSR) needs to meet the following conditions: the bunch length Among them, ρ is the radius of the bending magnet and φ is the angle of the bending iron.

[0017] 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.

[0018] From the above, we can see that for the linear compression process, for any distribution of bunches, the energy dispersion growth caused by the steady-state coherent synchrotron radiation 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.

[0019] Since the influence of the coherent synchrotron radiation (CSR) effect on the bunch increases with the decrease of the bunch length, the bunch that does not meet the steady-state coherent synchrotron radiation condition is less affected by the coherent synchrotron radiation effect, and the center shift correlation caused by the coherent synchrotron radiation can still be approximately expressed by formula (2). Therefore, for any distributed bunch, formula (2) is simplified to obtain that in order to eliminate the influence of the steady-state coherent synchrotron radiation (CSR), the compression section or decompression section needs to meet the following criteria:

[0020]

[0021] Among them, I j is the center offset correlation of the slice caused by coherent synchrotron radiation, s0 is the entrance of the decompression device, s f is the outlet of the decompression device, 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 bundle length before decompression, is the entry in row 5 and column 6 of the overall transmission matrix of the decompression device, R 56 (s) is the fifth row and sixth column of the transfer matrix of the reverse optimized beamline from the decompression device outlet to any point s, σ e For the energy dispersion of the cluster.

[0022] In the simplification process, the present invention applies the symplectic property of the matrix The transmission matrix of the inversely optimized beamline is used to replace the transmission matrix from any point s to the decompression device outlet s f The entry in the ith row and sixth column of the transfer matrix Since existing accelerator simulation programs cannot directly give Therefore, by adopting the optimization "reverse optimization beam line", that is, the optimized beam line element arrangement is opposite to the beam line element arrangement of the actual magnetic compressor decompression device, the upper and lower limits of the optimization integral are also transformed into the decompression device outlet s of the actual magnetic compressor decompression device. f To the decompression device entrance s0. Then use the 5th row and jth column entry R of the transfer matrix of the inverse optimization beamline 5j The integral is used to replace any point s to the decompression device outlet s f The entry in the ith row and sixth column of the transfer matrix The integral of . Therefore, similar to formula (2), after substituting the properties of the symplectic matrix 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 bunch length changes. When only linear compression is considered, the change of the bunch length in the reverse optimization beamline is opposite to that in the forward direction. The bunch length σ at any point s is z(s) is expressed as:

[0023]

[0024] in, is the bundle length before decompression, R 56 (s) is the item in the 5th row and 6th column of the transmission matrix of the reverse optimized beamline from the decompression device outlet to any point s (i.e., the position at a distance s from the decompression device outlet), σ e is the energy dispersion of the bunch, obtained by counting the bunches at the inlet of the decompression device, It is the entry in row 5 and column 6 of the overall transfer matrix of the decompressed structure.

[0025] 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=1, 2, there are two optimization targets. The two optimization targets are made as close to 0 as possible (ie, the absolute value is minimized), which can greatly reduce the lateral deviation caused by the steady-state CSR.

[0026] Based on the above principles, the optimization method of the magnetic compressor decompression device for an energy recovery accelerator of the present invention includes:

[0027] Step S1: The first to sixth bends are arranged in sequence along the direction of the beam to establish an actual magnetic compressor decompression device of a special-shaped chicane structure, wherein the incident angles and exit angles of the first to sixth bends are respectively (0, θ1), (-θ1, 0), (0, -θ2), (θ2, 0), (0, θ3), (-θ3, 0), wherein the incident angle and the exit angle are written in the form of (incident angle, exit angle), and the angle without brackets represents the deflection angle of the bend, such as the deflection angle θ1 of the first bend, the deflection angle θ2 of the fourth bend, and the deflection angle θ3 of the fifth bend, and the deflection angle is automatically determined according to the exit or incident angle; the structure of the reverse optimized beam line is determined according to the actual magnetic compressor decompression device.

[0028] The radii of the first to sixth bends are set to be the same according to the actual energy of the bunch.

[0029] The spacing between the second bend and the third bend is 0, and the spacing between the fourth bend and the fifth bend is 0. In other embodiments, the spacing between the second bend and the third bend, and the spacing between the fourth bend and the fifth bend are not 0, so that an appropriate spacing is reserved for suppressing the downstream CSR effect.

[0030] Figure 2It is a schematic structural diagram of an actual magnetic compressor decompression device established by the optimization method of the magnetic compressor decompression device for an energy recovery accelerator of the present invention.

[0031] It should be noted that as described in the principle section above, this optimization process is a reverse optimization, that is, the entrance of the designed reverse optimization beam line is used as the decompression device outlet of the magnetic compressor decompression device actually used, and the outlet of the designed reverse optimization beam line is used as the decompression device entrance of the magnetic compressor decompression device actually used. In the present invention, the deflection angle of the last bent iron of the reverse optimization beam line (i.e., the first bent iron at the entrance of the actual decompression device) refers to θ1 instead of -θ3.

[0032] Step S2: Establish the constraints of the reverse optimization beamline, including the constraint that the total deflection angle is 0, the achromatic constraint, and the item R in the 5th row and 6th column of the transmission matrix. 56 constraints; and solving the constraints by inversely optimizing the transmission matrix of the beamline.

[0033] The achromatic condition of the reverse optimized beamline is the term R in the first row and sixth column of the transmission matrix of the reverse optimized beamline. 16 =0.

[0034] The term R in the 5th row and 6th column of the transfer matrix of the inversely optimized beamline is 56 The constraints include the entry R in row 5 and column 6 of the transfer matrix 56 The size range is as follows. Among them, the item R in the 5th row and 6th column of the transmission matrix 56 The size range of is determined by the beam length range of the bunch at the outlet of the actual magnetic compressor decompression device.

[0035] Since in general, the bundle length after decompression is often the same as the bundle length before compression Similar to the overall design of the accelerator, assuming that the acceptable offset range is 20%, the item R in the 5th row and 6th column of the transfer matrix of the inverse optimization beamline is 56 The size range is:

[0036]

[0037] in, is the bundle length before compression, is the bunch length before decompression, σ e For the energy dispersion of the cluster.

[0038] In addition, the 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 applicable magnetic field strength constraints (limiting the magnet deflection radius).

[0039] Step S3: Establish corresponding criteria with the optimization goal of minimizing the center offset correlation of the slice caused by coherent synchrotron radiation, and optimize the free variables of the reverse optimization beamline according to the constraints and criteria.

[0040] The criterion for minimizing the center offset correlation of the slice caused by the coherent synchrotron radiation as the optimization target includes: making the absolute values ​​of the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation approach 0, wherein the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation are:

[0041]

[0042] Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, s0 is the entrance of the decompression device, s f is the outlet of the decompression device, 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 bundle length before decompression, is the entry in row 5 and column 6 of the overall transfer matrix of the decompressed structure, R 56 (s) is the fifth row and sixth column of the transfer matrix of the reverse optimized beamline from the decompression device outlet to any point s, σ e For the energy dispersion of the cluster.

[0043] I1 and I2 correspond to two different lateral directions respectively.

[0044] In step S3, during the optimization process, while satisfying the constraints of the reverse optimization beamline (excluding spatial constraints), based on two optimization objectives (the center offset correlation of the slice caused by coherent synchrotron radiation in two directions), the free variables are written and the transfer matrix evolution curve is exported through conventional accelerator software (such as for the ELEGANT simulation program, the corresponding matrix items are exported from the default .mat file), and then the center offset correlation of the slice caused by coherent synchrotron radiation is calculated, so as to optimize the six free variables through continuous iteration.

[0045] The free variables include the deflection angle θ1 of the first bend iron, the deflection angle θ2 of the fourth bend iron, the deflection angle θ3 of the fifth bend iron, the spacing between the first bend iron B1 and the second bend iron B2, the spacing between the third bend iron B3 and the fourth bend iron B4, and the spacing between the fifth bend iron B5 and the sixth bend iron B6. These six free variables are used as optimization variables.

[0046] In step S3, taking the commonly used accelerator simulation software ELEGANT as an example, the variables are written into .lte as the input beamline, and the R in the .mat output file is read after running. 51 ,R52 ,R 56 The curve of the cluster is set at the same time, and the length of the cluster before decompression is set and the energy dispersion of the bunch σ e , where the bunch length before decompression is Determined by the actual machine parameters, the energy spread of the bunch σ e It is obtained by performing bunch statistics at the entrance of the decompression device; then, these parameters are used to calculate the values ​​of the center offset related quantities I1 and I2 of the slice caused by coherent synchrotron radiation, and the optimized values ​​are continuously iterated so that the two values ​​are close to 0 while satisfying the constraints.

[0047] When optimizing, the deflection angle of the last bend of the reverse optimization beam (i.e., the deflection angle θ1 of the first bend at the entrance of the decompression device of the actual magnetic compressor) should not be too large. The deflection angle θ1 of the first bend is at most (6σ z / ρσ e ) 1 / 3 , σ z is the bunch length, σ e is the energy dispersion of the bunch, and δ is the radius of the bending magnet. Preferably, the radian of the deflection angle θ1 of the first bending iron should be less than 0.05 rad.

[0048] Step S4: After obtaining the optimization result that meets the optimization target, the reverse optimization beam line corresponding to the optimization result is reversely placed to obtain the required magnetic compressor decompression device.

[0049] Among them, the structure of the required magnetic compressor decompression device is as follows Figure 2 shown.

[0050] In addition, after step S4, the present invention may further include:

[0051] Step S5: For the magnetic compressor decompression device obtained in step S4, the emittance growth caused by the steady-state coherent synchrotron radiation (CSR) is evaluated.

[0052] In step S5, the following formula is used to evaluate the emittance growth caused by the steady-state coherent synchrotron radiation:

[0053] Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, β xf ,α xf ,γ xf Both are twist optical functions at the outlet of the decompression device, also known as twist functions. In accelerator physics, twist functions are usually used to describe the transverse phase space distribution.

[0054] Step S6: Decompress the twist optical function β at the outlet of the device xf ,α xf ,γ xf As the independent variable, the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation is obtained.

[0055] In the present invention, the twist function (i.e. the twist optical function β at the outlet of the decompression device) is used. xf ,α xf ,γ xf ) is taken as the independent variable, and the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation is obtained, including:

[0056] Steady-state and non-steady-state coherent synchrotron radiation simulations are performed. The twist optical function at the outlet of the decompression device is used as the optimization variable by scanning or using an optimization algorithm, and the emittance change is used as the optimization target to find the optimal solution of the optimization variable (the range of the optimization variable is set according to the actual situation).

[0057] When the optimization variables reach the optimal solution, the optimization target value is the minimum value of the emittance change. The ideal state is that the offset direction caused by the emittance change effect is the same as the phase space offset direction, and the emittance growth is minimized. Figure 1 As shown, the phase space shift will cause the emittance growth, so the present invention evaluates whether the phase space shift degree is substantially the same as the shift direction caused by the emittance variation effect by directly evaluating the emittance growth.

[0058] 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 bunch passes through the first bent iron, and due to the local R 56 Value and chicane total R 56 On the contrary, the bunch will be further compressed, so the deflection angle of the first bend (i.e. the angle of the last bend of the reverse optimization beam line) should not be greater than (6σ z / ρσ e ) 1 / 3 Since the CSR effect is inversely proportional to the -4 / 3 power of the beam length, the ultrashort bunch caused by excessive compression will cause a sharp increase in the coherent synchrotron radiation effect. A smaller angle (radian < 0.05 rad) of the first bend iron can prevent the additional coherent synchrotron radiation effect caused by excessive compression. Where ρ is the radius of the bend iron.

[0059] After that, the bunch passes through the first drift section (i.e., the first bend iron) and enters the second and third bend irons. Since the spacing between the second and third bend irons is 0, in actual operation, the absolute value of the total deflection angle of the second and third bend 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 bend irons is (-θ1, -θ2). In the present invention, the second and third bend irons are referred to as the second group, and similarly, the fourth and fifth bend irons are referred to as the third group). Since the item R in the 5th row and 6th column of the local transmission matrix of the second and third groups of bend irons is 56 It is approximately equal to the item R in the 5th row and 6th column of the total transmission matrix of the inverse phase optimized beamline (i.e. chicane structure). 56 , in the second group of bends, the bunch is decompressed, but because the angle of the second group of bends is smaller than that of the third group of bends, the decompression ratio is low. After that, the bunch passes through the second drift section and enters the third group of bends composed of the fourth and fifth bends (the total deflection angle of the third group of bends is θ2+θ3, the deflection direction is the same as that of the first bend, and the edge angle is (θ2,θ3)), and the bunch length is further stretched. Since the angle of the third group of bends is larger than that of the second group of bends, the item R in the 5th row and 6th column of the local transmission matrix of the third group of bends is 56 The decompression ratio is large, and the beam length is approximately equal to the target beam length. Then the bunch passes through the third drift section and enters the fourth group of bends (the angle is -θ3, the deflection angle is opposite to the deflection direction of the first bend, and the edge angle is (-θ3,0)). 56 The term R in the 5th row and 6th column of the total transmission matrix of the inverse optimized beamline (i.e. chicane structure) 56 The signs are opposite. The bunch will be compressed in a small range in this bend, but since the bunch length is much larger than the entrance bunch length, the compression ratio can be ignored. At this time, the bunch length is stretched to the length before compression. In this embodiment, the angles of each bend satisfy θ2>θ3>θ1, but for smaller compression multiples, this situation may not hold true, so the present invention only limits the size of θ1.

[0060] The process of suppressing the CSR effect of the magnetic compressor decompression device optimized by the optimization method of the present invention is as follows: Assume that the deflection surface occurs in the horizontal direction (xs plane), and define the offset direction of the bunch generated in the first magnet as the positive direction. Figure 2Taking the special-shaped chicane structure shown in the figure as an example, the ultra-short bunch before compression passes through the first bend and is subjected to a large CSR kick, causing the center of the bunch to produce a positive offset of (Δx1, Δx1′) at the exit of the chicane structure; then the bunch passes through the first drift section and enters the second group of bends. The second group of bends first produces a positive offset and then a negative offset. As the bunch length increases, the CSR effect per unit length weakens, resulting in a total offset of (Δx2, Δx2′). Then the bunch enters the third group of bends, the bunch length further increases, and the offset process is opposite to that of the second group of bends. At the exit of the chicane structure, a negative offset is first produced, followed by a positive offset, resulting in a total offset of (Δx3, Δx3′). Finally, it enters the fourth bend. Due to the long bunch length, the impact on the exit offset is small, recorded as a positive offset of (Δx4, Δx4′). By optimizing the chicane structure to satisfy formula (3), the offset caused by the steady-state CSR at the exit of the chicane structure is 0.

[0061] Experimental results:

[0062] As Figure 2 As an example, the chicane structure decompression device shown in FIG. 1 is used as an example, wherein the item R of the transmission matrix of the chicane structure is 51 and R 52 like Figure 3A and Figure 3B As shown, the bunch length change and emittance growth at the exit are respectively Figure 4 and Figure 5 As shown. For the non-ideal bunch, the bunch length is decompressed from 18μm to 700μm. The decompression factor is about 40. The emittance increases by about 0.4μm-rad, which is about twice the emittance at the entrance. Compared with other similar designs of the same type in the world, KEK EUV-ERL (decompression factor 30, emittance increase of 5μm-rad, which is about 2.5 times the emittance at the entrance), the emittance increase is only 1 / 10 of that, and the growth ratio is 1 / 2.5.

[0063] The magnetic compressor decompression device for the energy recovery accelerator of the present invention is implemented based on the special-shaped chicane. On the one hand, it retains the advantages of the conventional chicane with a small deflection angle to prevent over-compression. On the other hand, it can effectively reduce the peak flux of the bunch in the energy recovery linear accelerator, that is, the maximum flux of a single bunch, so that the bunch with an ultra-short beam length at the outlet of the undulator is elongated, so that it is less affected by collective effects such as coherent synchrotron radiation (CSR), which is conducive to suppressing the slice center offset caused by the CSR effect, so that the bunch at the outlet of the decompression device has a smaller emittance, and the stable and safe transmission of the bunch in the return beam line is achieved. Furthermore, by reducing the lateral size of the bunch when it passes through the acceleration module for the second time through a smaller emittance, this will reduce the interaction between the bunch and the high-order mode in the accelerator, thereby increasing the threshold current of the entire machine, so that the machine as a whole can accept a higher average flux, thereby increasing the repetition frequency of the radiated laser.

[0064] The magnetic compressor decompression device established by the optimization method for the magnetic compressor decompression device of the energy recovery accelerator of the present invention adopts a special-shaped chicane structure. Compared with the arc segment decompression, the deflection angle of the ultrashort particle bunch 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 , which can prevent the energy modulation caused by the ultrashort bunch caused by excessive bunch compression; in addition, compared with the traditional chicane, the special-shaped chicane structure can better suppress the additional offset caused by the CSR effect, so that the emittance growth caused by CSR is reduced. Furthermore, the optimization method of the magnetic compressor decompression device for the energy recovery accelerator of the present invention uses the reverse optimization method, and the transfer matrix evolution curve can be derived by conventional accelerator software for calculation, which can simplify the additional calculation process and improve the design efficiency.

[0065] 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 a magnetic compressor decompression device for an energy recovery accelerator, characterized in that: include: Step S1: sequentially arrange the first to sixth bends along the direction of the beam to establish an actual magnetic compressor decompression device of a special-shaped chicane structure, wherein the incident angles and the exit angles of the first to sixth bends are (0, θ1), (-θ1, 0), (0, -θ2), (θ2, 0), (0, θ3), (-θ3, 0), respectively; determine the structure of the reverse optimized beam line according to the actual magnetic compressor decompression device; Step S2: Establish the constraints of the reverse optimization beamline, including the constraint that the total deflection angle is 0, the achromatic constraint, and the item R in the 5th row and 6th column of the transmission matrix. 56 The constraints are solved by inversely optimizing the transmission matrix of the beam line; Step S3: establishing a corresponding criterion with the optimization goal of minimizing the center offset correlation of the slice caused by the coherent synchrotron radiation, and optimizing the free variables of the reverse optimization beamline according to the constraints and the criterion; Step S4: After obtaining the optimization result that meets the optimization target, the reverse optimization beam line corresponding to the optimization result is reversely placed 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 bent iron and the third bent iron of the magnetic compressor decompression device is 0, and the distance between the fourth bent iron and the fifth bent iron is 0.

3. The optimization method for a magnetic compressor decompression device 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 first row and sixth column of the transmission matrix of the reverse optimized beamline. 16 =0.

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

5. The optimization method for a magnetic compressor decompression device for an energy recovery accelerator according to claim 3, characterized in that: The entry R in the 5th row and 6th column of the transfer matrix of the inverse optimized beamline is 56 The size range is: in, is the bundle length before compression, is the bunch length before decompression, σ e For the energy dispersion of the cluster.

6. The optimization method for a magnetic compressor decompression device for an energy recovery accelerator according to claim 1, characterized in that: The criterion for minimizing the center offset correlation of the slice caused by the coherent synchrotron radiation as the optimization target includes: making the absolute values ​​of the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation approach 0, wherein the center offset correlations I1 and I2 of the slice caused by the coherent synchrotron radiation are: Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, s0 is the entrance of the decompression device, s f is the outlet of the decompression device, 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 bundle length before decompression, is the entry in row 5 and column 6 of the overall transfer matrix of the decompressed structure, R 56 (s) is the fifth row and sixth column of the transfer matrix of the reverse optimized beamline from the decompression device outlet to any point s, σ e For the energy dispersion of the cluster.

7. The optimization method for a magnetic compressor decompression device for an energy recovery accelerator according to claim 1, characterized in that: During the optimization process, while satisfying the constraints of the reverse optimization beamline, the free variables are written and the transfer matrix evolution curve is derived through conventional accelerator software to calculate the center offset related quantities 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 iron, the deflection angle θ2 of the fourth bend iron, the deflection angle θ3 of the fifth bend iron, the spacing between the first bend iron B1 and the second bend iron B2, the spacing between the third bend iron B3 and the fourth bend iron B4, and the spacing between the fifth bend iron B5 and the sixth bend iron B6.

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

9. The optimization method for a magnetic compressor decompression device for an energy recovery accelerator according to claim 6, characterized in that: After 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 emittance growth caused by the steady-state coherent synchrotron radiation: Among them, I1, I2 are the center offset correlation of the slice caused by coherent synchrotron radiation, β xf ,α xf ,γ xf All are twist optical functions at the outlet of the decompression device; Step S6: Decompress the twist optical function β at the outlet of the device xf ,α xf ,γ xf As the independent variable, the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation is obtained.

10. The optimization method for a magnetic compressor decompression device for an energy recovery accelerator according to claim 9, characterized in that: The twist optical function β at the outlet of the decompression device xf ,α xf ,γ xf As the independent variable, the minimum value of the emittance growth caused by the steady-state coherent synchrotron radiation is obtained, including: Steady-state and non-steady-state coherent synchrotron radiation simulations are performed. The twist optical function at the outlet of the decompression device is used as the optimization variable by scanning or using an optimization algorithm, and the emittance change is used as the optimization target to find the optimal solution of the optimization variable.

Images