A method for analyzing soft X-ray gain phenomena in trapped ions and the cavity type of the X-ray laser.

Abstract

This invention discloses a method for analyzing soft X-ray gain phenomena in trapped ions and the cavity type of the X-ray laser, mainly relating to the field of soft X-ray gain phenomena. The method includes: S1, calculating the small-signal gain coefficient α of the X-ray gain medium to obtain numerical information about the gain coefficient α; S2, the above calculation in S1 requires simulating ion source conditions, selecting different electron densities and incident electron energy points; S3, considering the differences between the ion source and the plasma environment, calculating the small-signal gain coefficient at the center frequency; and S4, analyzing the obtained data. The beneficial effects of this invention are: through the X-ray resonant cavity structure, the output beam can achieve high coherence and good beam quality similar to conventional lasers. It supports high repetition rates and even continuous wave operation, and through continuous collisional excitation and ion reuse in ultra-high vacuum, it eliminates the dependence on driving lasers and target materials, thereby improving peak gain.

Description

Technical Field

[0001] This invention relates to the field of soft X-ray gain phenomena, specifically a method for analyzing soft X-ray gain phenomena in trapped ions and the cavity type of the X-ray laser. Background Technology

[0002] While high harmonic generation (HHG) technology can produce coherent radiation, it relies on a strong laser field and has extremely low conversion efficiency (typically ~). The photon flux is low (< Photons, therefore, are unsuitable for high-brightness applications. In contrast, X-ray free-electron lasers (XFELs) based on large accelerators represent the highest level of current technology, possessing excellent brightness and coherence. However, their scale reaches kilometers, their cost is extremely high, and they are typical large-scale scientific facilities, with only a few institutions worldwide capable of building and operating them, greatly limiting their widespread application. Furthermore, they suffer from poor single-shot stability and complex self-seeding systems. Laser plasma (LPP) X-ray sources have made some progress in miniaturization, reducing the driving energy to the joule level through pre-pulse technology, transient collision excitation, and grazing incidence pumping. However, this technology is still subject to several inherent physical limitations: its gain mechanism mainly relies on amplified spontaneous emission (ASE), and its coherence is generally low (typically...). The residual plasma generated by the previous pulse can interfere with the formation of subsequent plasmas, hindering continuous wave (CW) operation. High-frequency quasi-continuous operation is constrained by two main factors: first, except for capillary discharge XUV lasers, the repetition frequency of driving lasers is mostly limited to the kilohertz level due to the need for cooling and recovery of the gain medium, leaving limited room for improvement; second, the target material needs continuous replacement to avoid laser damage. Solid targets are limited by mechanical movement speed, while liquid or gas targets struggle to maintain density and morphological stability under high-frequency conditions. A deeper problem lies in the fact that hot electrons (following a Maxwell distribution) in the plasma environment pump ions through isotropic collisions. This random process induces significant ion thermal motion and Doppler broadening. This inherent "noise" severely suppresses laser gain, setting an essential upper limit for efficient coherent output, a common limitation of all plasma-based X-ray coherent sources.

[0003] To address the aforementioned issues, a method for analyzing soft X-ray gain phenomena in trapped ions and the design of the cavity type for this X-ray laser are presented. Through the X-ray resonant cavity structure, the output beam achieves high coherence and good beam quality similar to conventional lasers. It supports high repetition rates and even continuous-wave operation. By continuously exciting through collisions in ultra-high vacuum and reusing ions, it eliminates dependence on the driving laser and target material, improving peak gain. Ion trapping and active cooling technologies significantly reduce ion temperature, fundamentally suppressing Doppler broadening, thereby elevating the gain coefficient and energy conversion efficiency to new heights. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing soft X-ray gain phenomena in trapped ions and the design of the cavity type of the X-ray laser. Through the X-ray resonant cavity structure, the output beam can achieve high coherence and good beam quality similar to that of conventional lasers. It supports high repetition rates and even continuous wave operation. By continuously exciting through collisions in ultra-high vacuum and reusing ions, it eliminates the dependence on driving lasers and target materials, improving peak gain. Ion trapping and active cooling technologies significantly reduce ion temperature, fundamentally suppressing Doppler broadening, thereby elevating the gain coefficient and energy conversion efficiency to new heights.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for analyzing soft X-ray gain phenomena in trapped ions includes the following steps:

[0007] S1, calculate the small-signal gain coefficient α of the X-ray gain medium to obtain numerical information about the gain coefficient α;

[0008] S2, the above S1 calculation requires simulating ion source conditions, selecting different electron densities and incident electron energy points, where multiple energy points are set at the first excited state and the highest energy level of interest for each of the four types of neon ions, and the remaining multiple energy points are several multiples of the ionization energy of each type of neon ion.

[0009] S3, Calculate the small-signal gain coefficient at the center frequency, taking into account the differences between the ion source and the plasma environment;

[0010] S4. Analyzing the obtained data, the directional quasi-monoenergetic electron beam can effectively pump neon-like ions in a special ion source, achieving population inversion and generating significant small-signal gain, thus confirming that the system can be used as a high-efficiency gain medium for X-ray lasers.

[0011] In step S1, the small-signal gain coefficient α is defined as follows:

[0012] S11, α can be defined by the transmitted light intensity I after propagation distance z:

[0013] ;

[0014] in, For the incident light intensity, The transmitted light intensity after propagation distance z;

[0015] S12, Calculate the value of the small-signal gain coefficient α:

[0016] ;

[0017] in, (K) represents the ion temperature, which is usually assumed to be equal to the electron temperature in plasma environments for simplified calculations. However, in practice, after adding refrigeration technology... Generally lower ; (g / mol) is the molar mass of the ion; λ is the energy level of the upper energy level ( ) and lower energy level The wavelength of the transition; The spontaneous emission rate from the upper energy level to the lower energy level; ( )and ( ( ) represent the ion number densities of the upper and lower energy levels, respectively; and These are the statistical weights for the corresponding energy levels; / = The relative population of the ions in the lower energy level; / The percentage of ions with a specific degree of ionization; / It is the ratio of the number of ions to the number of electrons. ( () represents electron density;

[0018] S13, in order to determine the relative energy level population = / and = / The requirement is to decouple the rate equations, i.e., under dynamic equilibrium, the number of particles leaving energy level j is equal to the number of particles arriving at that energy level:

[0019] ;

[0020] In the formula, The coefficients are electron collision rate coefficients, with superscripts e and d representing excitation and de-excitation processes, respectively. This equation fully considers the electron collision effects of all accessible energy levels. A is the Einstein A coefficient. Both A and C coefficients can be further calculated from relevant atomic parameters obtained through theoretical calculations or experiments. The relative energy level population satisfies the normalization condition.

[0021] The method for selecting different electron densities and incident electron energy points in step S2 includes the following steps:

[0022] S21, selected 7 electron densities (1× Up to 1× ) and 12 incident electron energy points, of which these 8 energy points are set between the first excited state and the highest energy level of interest for the four types of neon ions respectively. Specifically, Kr and Xe ions correspond to the 75th energy level, and W and U ions correspond to the 61st energy level. Each energy point is increased by 50 eV as the final incident energy point.

[0023] S22, the other four incident energy points are 1.05, 1.5, 5 and 30 times the ionization energy of various neon ions, respectively. These ionization energy data are taken from the NIST database or other precise theoretical calculations.

[0024] S23, considering the differences between the ion source and the plasma environment, calculate the small-signal gain coefficient at the center frequency, and introduce a conversion factor κ into the gain coefficient α in step S12:

[0025] ;

[0026] Where κ is the product of the three factors:

[0027] ;

[0028] = This is temperature-dependent, where β is the ratio of incident electron energy to ion temperature. Ions can be trapped in the ion source by cooling with light elements, making the ion temperature much lower than the incident electron energy. ;

[0029] > 0 reflects two aspects of correction: gain loss caused by ions outside the electron beam's effective range being unable to be excited, and the difference in charge state distribution between the ion source and the plasma.

[0030] >0, reflecting the difference between the ion source and the plasma. The ratios are different.

[0031] In the vicinity of 6.xnm in the X-ray band, the X-ray optical element adopts a curved multilayer film mirror with high reflection efficiency, and the curved multilayer film mirror adopts a composite multilayer film structure such as B, La, and LaN.

[0032] The multilayer film structure is set on a curved substrate, enabling both M1 and M2 mirrors to achieve high reflection and focusing functions simultaneously, forming a stable cavity and avoiding the absorption loss caused by introducing an additional Kirkpatrick-Baez mirror.

[0033] The output is provided through a micro-hole at the center of the M2 mirror.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] First, through the X-ray resonant cavity structure, the output beam can achieve high coherence and good beam quality similar to that of a traditional laser.

[0036] Second, it supports high repetition frequency and even continuous wave operation. Through continuous collision excitation and ion reuse in ultra-high vacuum, it eliminates the dependence on driving lasers and target materials.

[0037] Third, to improve peak gain, ion trapping and active cooling technologies significantly reduce ion temperature, fundamentally suppressing Doppler broadening, thereby raising the gain coefficient and energy conversion efficiency to new heights. Attached Figure Description

[0038] Appendix Figure 1 This is a schematic diagram of the novel soft X-ray laser structure of the present invention, which features a high-reflectivity curved multilayer resonant cavity and a special ion source. (The resonant cavity consists of two high-reflectivity curved multilayer mirrors (M1, M2) and operates in the 6.xnm band; the ion source section is equipped with two deflectors (D) to partially overlap the electron beam path with the X-ray beam path, generating high-charge neon-like ions (⊕) in the overlapping region; the electron beam is compressed by a strong magnetic field generated by a superconducting Helmholtz coil (C); the entire system operates in a vacuum environment).

[0039] Appendix Figure 2These are the energy levels (E, eV) of the neon-like Kr (Z=36), Xe (Z=54), W (Z=74), and U (Z=92) ions in the n≤4 configuration in this invention. The figure lists the lowest energy levels of these four ions, namely 75, 75, 61, and 61. The “Key” column is the energy level number, “Config.” is the electronic configuration, “Term” is the spectral term based on jj coupling (the ground state¹S is represented by LS coupling according to NIST reference), j is the total angular momentum, and π is the parity (0 represents even, 1 represents odd); E(RCI) is the energy calculated using the RCI method in this study, E(Ref.) is the NIST experimental value of Kr, and the values ​​calculated by Vilkas et al. for Xe, W, and U.

[0040] Appendix Figure 3 This is a comparison of the energies (E, eV) and relative populations of the lowest 27 levels of the neon-like Kr plasma environment in this invention. (E(RCI), E(F83), and E(NIST) correspond to the calculated RCI values ​​of this study, the results of Feldman et al., and the experimental values ​​of NIST, respectively; Pop.(F83), Pop.(a), and Pop.(b) represent the populations of Feldman et al., the 27-level model results of this study, and the 75-level model results of this study (the most accurate), respectively. The latter two are all based on the electron temperature 1× K, electron density 1× (Calculation results based on the collision radiation model under the given conditions).

[0041] Appendix Figure 4 This refers to the relative energy level populations (Pop.) of neon-like Kr, Xe, W, and U in the ion source of this invention. (Calculations cover 7 electron densities (1× Up to 1× The four ions considered the lowest energy levels of 75, 75, 61, and 61 for n≤4. Z is the nuclear charge number, and Key is the energy level number (as per the appendix). Figure 2 (Consistent), T(K) is the incident electron energy (expressed in Kelvin); in the figure, a±b represents a×10^±b).

[0042] Appendix Figure 5 It is the small-signal gain coefficient (α) of the neon-like Kr, Xe, W, and U in the ion source of this invention at the center frequency. Only values ​​greater than 0.005 are listed. The results). Calculations covering 7 electron densities (1× Up to 1× The study considered the lowest energy levels of the four ions, namely 75, 75, 61, and 61, and was limited to the X-ray band with wavelength λ < 10 nm. Z represents the nuclear charge number, and j and i are the upper and lower energy level numbers of the laser transition, respectively (see appendix). Figure 2 T(K) is the incident electron energy (Kelvin), ρ( ) represents the electron number density; the notation a±b indicates a×10^±b. Detailed Implementation

[0043] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0044] A method for analyzing soft X-ray gain phenomena in trapped ions includes the following steps:

[0045] S1, calculate the small-signal gain coefficient α of the X-ray gain medium to obtain numerical information about the gain coefficient α; when analyzing traditional X-ray lasers, the core is to explore the mechanism of population inversion and determine the small-signal gain coefficient α of the X-ray gain medium.

[0046] Regarding the derivation method, in step S1, the small-signal gain coefficient α is defined as follows:

[0047] S11, α can be defined by the transmitted light intensity I after propagation distance z:

[0048] ;

[0049] in, For the incident light intensity, The transmitted light intensity after propagation distance z;

[0050] S12, Calculate the value of the small-signal gain coefficient α:

[0051] ;

[0052] in, (K) represents the ion temperature, which is usually assumed to be equal to the electron temperature in plasma environments for simplified calculations. However, in practice, after adding refrigeration technology... Generally lower ; (g / mol) is the molar mass of the ion; λ is the energy level of the upper energy level ( ) and lower energy level The wavelength of the transition; The spontaneous emission rate from the upper energy level to the lower energy level; ( )and ( ( ) represent the ion number densities of the upper and lower energy levels, respectively; and These are the statistical weights for the corresponding energy levels; / = The relative population of the ions in the lower energy level; / The percentage of ions with a specific degree of ionization; / It is the ratio of the number of ions to the number of electrons. ( () represents electron density;

[0053] S13, in order to determine the relative energy level population = / and = / The requirement is to decouple the rate equations, i.e., under dynamic equilibrium, the number of particles leaving energy level j is equal to the number of particles arriving at that energy level:

[0054] ;

[0055] In the formula, The coefficients are electron collision rate coefficients, with superscripts e and d representing excitation and de-excitation processes, respectively. This equation fully considers the electron collision effects of all accessible energy levels. A is the Einstein A coefficient. Both A and C coefficients can be further calculated from relevant atomic parameters obtained through theoretical calculations or experiments. The relative energy level population satisfies the normalization condition.

[0056] S2 simulates ion source conditions, selecting different electron densities and incident electron energy points. Among them, multiple energy points are set at the first excited state and the highest energy level of interest for each of the four types of neon ions, and the remaining multiple energy points are several multiples of the ionization energy of each type of neon ion.

[0057] S3, Calculate the small-signal gain coefficient at the center frequency, taking into account the differences between the ion source and the plasma environment;

[0058] The core difference between a special ion source and a plasma environment lies in the fact that the electron beam in an ion source is directional, has quasi-monoenergetic characteristics, and exhibits a Gaussian distribution, while electrons in a plasma follow a Maxwell distribution and move randomly. Therefore, the methods for selecting different electron densities and incident electron energies in this step include the following steps:

[0059] S21, selected 7 electron densities (1× Up to 1× ) and 12 incident electron energy points, of which these 8 energy points are set between the first excited state and the highest energy level of interest for the four types of neon ions respectively. Specifically, Kr and Xe ions correspond to the 75th energy level, and W and U ions correspond to the 61st energy level. Each energy point is increased by 50 eV as the final incident energy point.

[0060] S22, the other four incident energy points are 1.05, 1.5, 5 and 30 times the ionization energy of various neon ions, respectively. These ionization energy data are taken from the NIST database or other precise theoretical calculations.

[0061] S23, considering the differences between the ion source and the plasma environment, calculate the small-signal gain coefficient at the center frequency, and introduce a conversion factor κ into the gain coefficient α in step S12:

[0062] ;

[0063] Where κ is the product of the three factors:

[0064] ;

[0065] = This is temperature-dependent, where β is the ratio of incident electron energy to ion temperature. Ions can be trapped in the ion source by cooling with light elements, making the ion temperature much lower than the incident electron energy. ;

[0066] > 0 reflects two aspects of correction: gain loss caused by ions outside the electron beam's effective range being unable to be excited, and the difference in charge state distribution between the ion source and the plasma.

[0067] >0, reflecting the difference between the ion source and the plasma. The ratios are different.

[0068] The above calculation process requires the use of the diagram shown in the specification. Figure 4 The relative energy level population table is noteworthy. As a global factor independent of transitions, therefore regardless of its specific value, under the assumption... The high-gain transitions identified under the condition of 1 will still maintain a relative advantage in practical ion sources. For the sake of simplifying the analysis, this study tentatively sets... =1, the calculated small-signal gain coefficient is listed in the appendix of the instruction manual. Figure 5 . Figure 5 All gain coefficients greater than 0.005 were filtered and listed. Furthermore, the transitions with wavelengths less than 10 nm (belonging to the X-ray band) covered a wavelength range from 0.45 nm to 9.88 nm. At an electron density of 1× Up to 1×10²² Under these conditions, the corresponding small-signal gain coefficient is between 0.005. Up to 59 Analysis shows that a directional quasi-monoenergetic electron beam can effectively pump neon-like ions in a special ion source, achieving population inversion and generating significant small-signal gain, thus confirming that this system can serve as a highly efficient gain medium for X-ray lasers.

[0069] S4. Analyzing the obtained data, the directional quasi-monoenergetic electron beam can effectively pump neon-like ions in a special ion source, achieving population inversion and generating significant small-signal gain, thus confirming that the system can be used as a high-efficiency gain medium for X-ray lasers.

[0070] The cavity design of an X-ray laser for analyzing soft X-ray gain phenomena in trapped ions, near 6.x nm in the X-ray band, uses a high-reflection-efficiency curved multilayer mirror as the X-ray optical element, and the curved multilayer mirror adopts a synthetic B\La\LaN multilayer film structure.

[0071] For X-ray optical resonators, priority is given to the 6.x nm range, using high-reflectivity curved multilayer mirrors. Reflectivity: For the 6.x nm band, multilayer structures such as B, La, and LaN can theoretically achieve approximately 80% reflectivity, and experimentally, it has reached approximately 64%. We conservatively adopted the experimental value of 64% in our calculations.

[0072] The multilayer film structure is set on a curved substrate, enabling both M1 and M2 mirrors to achieve high reflection and focusing functions, forming a stable cavity and avoiding the absorption loss caused by introducing an additional Kirkpatrick-Baez mirror.

[0073] Regarding output coupling: Considering the high loss characteristics of the soft X-ray cavity (single-pass reflection loss of approximately 36%), output is achieved through a pinhole at the center of the M2 mirror (output coupling reaches approximately 90%). Based on the above, the gain threshold corresponding to this resonant cavity was calculated, and the results show that the calculated gain coefficient is significantly greater than the gain threshold.

[0074] Therefore, a method for analyzing soft X-ray gain phenomena in trapped ions and the cavity design of the X-ray laser are presented. Through the X-ray resonant cavity structure, the output beam can achieve high coherence and good beam quality similar to that of conventional lasers. It supports high repetition rates and even continuous wave operation. By continuously exciting through collisions in ultra-high vacuum and reusing ions, it eliminates the dependence on driving lasers and target materials, improving peak gain. Ion trapping and active cooling technologies significantly reduce ion temperature, fundamentally suppressing Doppler broadening, thereby elevating the gain coefficient and energy conversion efficiency to new heights.

Claims

1. A method for analyzing soft X-ray gain phenomena in trapped ions, characterized in that: Includes the following steps: S1, calculate the small-signal gain coefficient α of the X-ray gain medium to obtain numerical information about the gain coefficient α; S2, the calculation of S1 requires simulating ion source conditions, selecting different electron densities and incident electron energy points, wherein multiple energy points are respectively set at the first excited state and the highest energy level of interest for various types of neon ions, and the remaining multiple energy points are several multiples of the ionization energy of various types of neon ions. S3, Calculate the small-signal gain coefficient at the center frequency, taking into account the differences between the ion source and the plasma environment; S4. Analyzing the obtained data, the directional quasi-monoenergetic electron beam can effectively pump neon-like ions in a special ion source, achieving population inversion and generating significant small-signal gain, thus confirming that the system can be used as a high-efficiency gain medium for X-ray lasers.

2. The method for analyzing soft X-ray gain phenomena in trapped ions according to claim 1, characterized in that: In step S1, the small-signal gain coefficient α is defined as follows: S11, α can be defined by the transmitted light intensity I after propagation distance z: ； in, For the incident light intensity, The transmitted light intensity after propagation distance z; S12, Calculate the value of the small-signal gain coefficient α: ； in, (K) represents the ion temperature, which is usually assumed to be equal to the electron temperature in plasma environments for simplified calculations. However, in reality, Generally lower ; (g / mol) is the molar mass of the ion; λ is the energy level of the upper energy level ( ) and lower energy level The wavelength of the transition; The spontaneous emission rate from the upper energy level to the lower energy level; ( )and ( ( ) represent the ion number densities of the upper and lower energy levels, respectively; and These are the statistical weights for the corresponding energy levels; / = The relative population of the ions in the lower energy level; / The percentage of ions with a specific degree of ionization; / It is the ratio of the number of ions to the number of electrons. ( () represents electron density; S13, in order to determine the relative energy level population = / and = / The requirement is to decouple the rate equations, i.e., under dynamic equilibrium, the number of particles leaving energy level j is equal to the number of particles arriving at that energy level: ； In the formula, The coefficients are electron collision rate coefficients, with superscripts e and d representing excitation and de-excitation processes, respectively. This equation fully considers the electron collision effects of all accessible energy levels. A is the Einstein A coefficient. Both A and C coefficients can be further calculated from relevant atomic parameters obtained through theoretical calculations or experiments. The relative energy level population satisfies the normalization condition.

3. The method for analyzing soft X-ray gain phenomena in trapped ions according to claim 2, characterized in that: The method for selecting different electron densities and incident electron energy points in step S2 includes the following steps: S21, selected 7 electron densities (1× Up to 1× ) and 12 incident electron energy points, of which these 8 energy points are set between the first excited state and the highest energy level of interest for the four types of neon ions respectively. Specifically, Kr and Xe ions correspond to the 75th energy level, and W and U ions correspond to the 61st energy level. Each energy point is increased by 50 eV as the final incident energy point. S22, the other four incident energy points are 1.05, 1.5, 5 and 30 times the ionization energy of various neon ions, respectively. These ionization energy data are taken from the NIST database or other precise theoretical calculations. S23, considering the differences between the ion source and the plasma environment, calculate the small-signal gain coefficient at the center frequency, and introduce a conversion factor κ into the gain coefficient α in step S12: ； in The product of three factors: ； = This is temperature-dependent, where β is the ratio of incident electron energy to ion temperature. Ions can be trapped in the ion source by cooling with light elements, making the ion temperature much lower than the incident electron energy. ; > 0 reflects two aspects of correction: gain loss caused by ions outside the electron beam's effective range being unable to be excited, and the difference in charge state distribution between the ion source and the plasma. >0, reflecting the difference between the ion source and the plasma. The ratios are different.

4. A cavity type for a soft X-ray laser based on a soft X-ray gain phenomenon analysis method in trapped ions, as described in any one of claims 1-3, characterized in that: In the vicinity of 6.xnm in the X-ray band, the X-ray optical element adopts a high-reflection-efficiency curved multilayer film mirror, and the curved multilayer film mirror adopts a multilayer film structure.

5. The cavity type of the soft X-ray laser based on the soft X-ray gain phenomenon analysis method in trapped ions according to claim 4, characterized in that: The multilayer membrane structure is a synthetic multilayer membrane; The multilayer film structure is set on a curved substrate, enabling both M1 and M2 mirrors to achieve high reflection and focusing functions, forming a stable cavity and avoiding the absorption loss caused by introducing an additional Kirkpatrick-Baez mirror.

6. The cavity type of the soft X-ray laser based on the soft X-ray gain phenomenon analysis method in trapped ions according to claim 1, characterized in that: The output is provided through a micro-hole at the center of the M2 mirror.

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