A method for determining the electron temperature of xenon plasma based on a radiative collision model

Abstract

The present disclosure provides a method for determining the electron temperature of xenon plasma based on a radiation collision model, comprising: determining the rate equation of atomic energy levels in a steady-state approximation state; determining the dominant particle reaction type in the xenon plasma in a Z-pinch fusion; determining the rate balance equation of the xenon plasma according to the dominant particle reaction type in the xenon plasma and the rate equation of atomic energy levels in the steady-state approximation state; determining the population density ratio of adjacent energy levels; determining the simplified rate balance equation of the xenon plasma according to the population density ratio of adjacent energy levels; determining the spectral line intensity ratio; and determining the electron temperature of the xenon plasma according to the simplified rate balance equation of the xenon plasma, the spectral line intensity ratio, and a preset Boltzmann equation. By the present disclosure, the electron temperature of the xenon plasma under the Z-pinch condition is calculated simply by the relative light intensity line ratio method, the data processing amount is reduced, and the data accuracy is improved.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of plasma, in particular, to a method for determining electron temperature of xenon plasma based on radiation collision model. BACKGROUND

[0002] Z-pinch technology means that by instantaneously discharging a large current to a target gas, the target gas is ionized into high-valence state plasma, and under the action of electromagnetic field, a pinch plasma column is formed at the center of the electrode, and in this process, a light source is formed by outward radiation. Its main working principle is as follows: the working chamber is filled with xenon gas (Xe), and a discharge is induced by applying a high voltage electric field to form a plasma at the center of the electrode, in which xenon atoms are ionized into positively charged ions and free electrons. The pseudo spark preheats the xenon plasma and produces seed electrons. The main pulse then heats the xenon plasma to a higher temperature, resulting in further ionization and excitation, thereby producing a higher density, higher temperature plasma with a wider electron energy distribution. In the process of high-energy electron collision with target ions, EUV radiation is generated. The radiation intensity is a very important indicator for the light source, and the collision radiation model establishes the relationship between the light intensity ratio of the radiation spectrum line and the electron temperature, and the key lies in the determination and simplification of the reaction particles and the reaction type. The relative light intensity line ratio method can be applied to plasma diagnosis under various reaction conditions and in a wide range of electron density, and is also the core of determining electron temperature.

[0003] The study of high-temperature and high-density plasma state has always been one of the research focuses in the field of plasma. Spectroscopic diagnosis as a method for studying plasma state has been very active in the field of diagnosis, and the corresponding theoretical model has become more and more sophisticated and complex. In recent years, there is no clear calculation method for the electron temperature of xenon plasma under non-thermal equilibrium conditions based on the radiation collision model. With the development of z-pinch technology, high-temperature and high-density plasma can be produced in the laboratory, which provides strong evidence support for the establishment and verification of the theoretical model for calculating the electron temperature of plasma. SUMMARY

[0004] In view of the defects in the prior art, the purpose of the present disclosure is to provide a method for determining electron temperature of xenon plasma based on radiation collision model.

[0005] According to one aspect of the present disclosure, a method for determining electron temperature of xenon plasma based on radiation collision model is provided, comprising:

[0006] Using a preset radiation collision model of a steady-state approximation state, the rate equation of the atomic energy level of the steady-state approximation state is determined;

[0007] Determine the dominant particle reaction type in the xenon plasma in Z-pinch fusion;

[0008] determining rate balance equations of the xenon plasma according to rate equations of particle reaction types occupying a dominant position in the xenon plasma and the atomic energy levels in the steady-state approximation;

[0009] transforming the rate balance equations of the xenon plasma to determine population density ratios of adjacent energy levels;

[0010] simplifying the rate balance equations of the xenon plasma according to the population density ratios of adjacent energy levels to determine simplified rate balance equations of the xenon plasma;

[0011] determining a spectral line intensity ratio based on the Z-pinch fusion;

[0012] determining a xenon plasma electron temperature according to the simplified rate balance equations of the xenon plasma, the spectral line intensity ratio, and a preset Boltzmann equation.

[0013] Optionally, the particle reaction types occupying a dominant position in the xenon plasma include:

[0014] (1) spontaneous radiation:

[0015]

[0016] wherein, Xe represents the xenon plasma in an atomic energy level j, and hν represents a first photon; i +q Xe represents the xenon plasma in an atomic energy level i, and hν represents a first photon;

[0017] (3) stimulated radiation:

[0018]

[0019] wherein, hv1 represents a second photon, and hv2 represents a third photon;

[0020] (3) photoionization and radiative recombination:

[0021]

[0022] wherein, e represents an electron.

[0023] Optionally, the determining of the rate balance equations of the xenon plasma according to the rate equations of particle reaction types occupying a dominant position in the xenon plasma and the atomic energy levels in the steady-state approximation includes:

[0024] The rate balance equation of the xenon plasma is determined by substituting the dominant particle reaction type in the xenon plasma into the rate equation of the atomic energy level in the steady-state approximation.

[0025] Optionally, the rate balance equation of the xenon plasma is:

[0026]

[0027] wherein n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j, β ji represents the photoionization rate of the xenon plasma from the atomic energy level j to the atomic energy level i, A ij represents the spontaneous emission rate of the xenon plasma from the atomic energy level i to the atomic energy level j, B ji represents the stimulated emission rate of the xenon plasma from the atomic energy level j to the atomic energy level i, C represents the average frequency of the transition radiation field intensity, ω represents the radiation recombination rate of the xenon plasma from the atomic energy level i to the atomic energy level j, n e represents the electron density of the xenon plasma.

[0028] Optionally, the population density ratio of the adjacent energy levels is:

[0029]

[0030] wherein n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j,

[0031] Optionally, the rate balance equation of the xenon plasma is simplified according to the population density ratio of the adjacent energy levels, and a simplified rate balance equation of the xenon plasma is determined, including:

[0032] The rate coefficient in the population density ratio of the adjacent energy levels is redefined to determine a defined rate coefficient.

[0033] The defined rate coefficient is substituted into the population density ratio of the adjacent energy levels to determine the simplified rate balance equation of the xenon plasma.

[0034] Optionally, the simplified rate balance equation of the xenon plasma is:

[0035]

[0036] wherein k1 = ∑A ij , k4 =∑β ii ; k1 represents a spontaneous emission rate coefficient of the xenon plasma from an atomic energy level i to an atomic energy level j, k2 represents an induced emission rate coefficient of the xenon plasma from the atomic energy level j to the atomic energy level i, k3 represents a radiative recombination rate coefficient of the xenon plasma from the atomic energy level i to the atomic energy level j, and k4 represents a photoionization rate coefficient of the xenon plasma from the atomic energy level j to the atomic energy level i.

[0037] Optionally, the spectral line intensity ratio is:

[0038]

[0039] wherein I i represents a spectral line intensity of a transition from an atomic energy level i, I j represents a spectral line intensity of a transition from an atomic energy level j, A i represents an Einstein transition coefficient of the atomic energy level i, A j represents an Einstein transition coefficient of the atomic energy level j, hv i represents a photon transition energy of a transition from the atomic energy level i, hv j represents a photon transition energy of a transition from the atomic energy level j.

[0040] Optionally, the determining the xenon plasma electron temperature according to the simplified rate balance equation of the xenon plasma, the spectral line intensity ratio, and a preset Boltzmann equation comprises:

[0041] substituting the simplified rate balance equation of the xenon plasma into the spectral line intensity ratio to determine a first equation;

[0042] determining a second equation according to the preset Boltzmann equation and the spectral line intensity ratio;

[0043] solving the first equation and the second equation to determine the xenon plasma electron temperature.

[0044] Optionally, the solving the first equation and the second equation to determine the xenon plasma electron temperature comprises:

[0045]

[0046] wherein, represents the first equation, represents the second equation, g i represents a degeneracy of the atomic energy level i, g j represents a degeneracy of the atomic energy level j, E idenotes the energy at the atomic energy level i j denotes the energy at the atomic energy level j, k denotes the preset Boltzmann equation constant, and T e denotes the xenon plasma electron temperature.

[0047] Compared with the prior art, the embodiments of the present disclosure have at least one of the following beneficial effects:

[0048] Through the above technical solution, for the atomic energy level rate equation of the steady-state approximation state under the Z-pinch fusion condition, a non-thermodynamic equilibrium model is adopted, which can improve the accuracy, increase the calculation speed and accuracy of the spectral line intensity, reduce the calculation amount of the atomic energy level, save the calculation resources, reduce the difficulty of solving the atomic energy level rate equation, improve the solving speed and accuracy of the rate coefficient, and realize the simple calculation of the plasma electron temperature. BRIEF DESCRIPTION OF DRAWINGS

[0049] Other features, objects, and advantages of the present disclosure will become more apparent from the following detailed description of non-limiting embodiments, made with reference to the accompanying drawings:

[0050] Figure 1 is a flowchart of a xenon plasma electron temperature determination method based on a radiation collision model according to an example embodiment. DETAILED DESCRIPTION

[0051] The present disclosure will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present disclosure, but do not limit the present disclosure in any form. It should be noted that, for those skilled in the art, without departing from the concept of the present disclosure, a number of modifications and improvements can be made. These all belong to the protection scope of the present disclosure.

[0052] Fusion plasma simulation needs to obtain plasma state information, i.e. the temperature of the plasma and the ion population distribution of different ionization degrees of various elements, average ionization degree, etc. Before diagnosing the fusion plasma simulation, the model of the plasma and a large number of various atomic process parameters need to be obtained. Under laboratory conditions, the plasma does not conform to the local thermodynamic equilibrium state (LTE), and the present disclosure adopts a non-local thermodynamic equilibrium state (NLTE) model to simulate atomic physical processes.

[0053] Figure 1 is a flowchart of a xenon plasma electron temperature determination method based on a radiation collision model according to an example embodiment.

[0054] As Figure 1As shown, the present disclosure provides a method for determining the electron temperature of xenon plasma based on a radiation collision model, comprising S11 to S17.

[0055] S11, using a preset radiation collision model of a steady-state approximation state, determining the rate equation of the atomic energy level of the steady-state approximation state.

[0056] wherein the rate equation of the atomic energy level is determined based on a multi-level collision radiation (CR) rate equation:

[0057]

[0058] wherein n i represents the population density of atomic energy level i, i.e. ionization degree, n j represents the population density of atomic energy level j, i.e. ionization degree, W ij represents the rate coefficient of atomic process from atomic energy level i to atomic energy level j, W ji represents the rate coefficient of atomic process from atomic energy level j to atomic energy level i.

[0059] W ij The atomic process from atomic energy level i to atomic energy level j includes stimulated absorption, collisional excitation, collisional ionization, photoionization.

[0060] W ji The atomic process from atomic energy level j to atomic energy level i includes spontaneous emission, stimulated emission, collisional de-excitation, two-electron recombination, radiative recombination, collisional recombination.

[0061] According to the preset radiation collision model of the steady-state approximation state, it is assumed that the population of each energy state of the plasma reaches a steady state or an approximate steady state within a preset time, and no longer changes with time. The rate equation of the atomic energy level of the steady-state approximation state is:

[0062]

[0063] S12, determining the particle reaction type that dominates in the xenon plasma in Z-pinch fusion.

[0064] wherein the particle reaction type that dominates in the xenon plasma includes:

[0065] (1) Spontaneous emission:

[0066]

[0067] wherein, represents the xenon plasma of atomic energy level j, represents the xenon plasma of atomic energy level i, and hν represents the first photon;

[0068] (4) Stimulated emission:

[0069]

[0070] wherein hv1 represents the second photon, and hv2 represents the third photon;

[0071] (3) photoionization and radiative recombination:

[0072]

[0073] wherein e represents an electron.

[0074] S13, according to the rate equation of the particle reaction type and the atomic energy level of the steady-state approximation state that occupies the dominant position in the xenon plasma, determines the rate balance equation of the xenon plasma.

[0075] In the radiative collision model, the plasma forms a high-temperature dense condition due to the action of external force, and the radiation process is much larger than the collision process. According to the particle reaction type that occupies the dominant position in the xenon plasma, the atomic process can be simplified, thereby simplifying the rate balance equation of the xenon plasma.

[0076] In a possible embodiment, according to the rate equation of the particle reaction type and the atomic energy level of the steady-state approximation state that occupies the dominant position in the xenon plasma, the rate balance equation of the xenon plasma can include:

[0077] The rate balance equation of the xenon plasma is determined by substituting the particle reaction type that occupies the dominant position in the xenon plasma into the rate equation of the atomic energy level of the steady-state approximation state.

[0078] For example, according to the particle reaction type that occupies the dominant position in the xenon plasma, the rate balance equation of the xenon plasma is listed, that is, the above-mentioned formula (3) to formula (5) are substituted into the above-mentioned formula (2), and the rate balance equation of the xenon plasma is determined as:

[0079]

[0080] wherein n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j, β ji represents the photoionization rate of the xenon plasma from the atomic energy level j to the atomic energy level i, A ij represents the spontaneous radiation rate of the xenon plasma from the atomic energy level i to the atomic energy level j, B ji represents the stimulated radiation rate of the xenon plasma from the atomic energy level j to the atomic energy level i, represents the average frequency of the transition radiation field intensity, represents the radiative recombination rate of the xenon plasma from the atomic energy level i to the atomic energy level j, ne represents the electron density of the xenon plasma.

[0081] In the present disclosure, the energy level of the atomic energy level j is higher than the atomic energy level i.

[0082] S14, the rate balance equation of the xenon plasma is transformed to determine the population density ratio of adjacent energy levels.

[0083] wherein the population density ratio of adjacent energy levels is:

[0084]

[0085] wherein n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j.

[0086] S15, according to the population density ratio of adjacent energy levels, the rate balance equation of the xenon plasma is simplified to determine the simplified rate balance equation of the xenon plasma.

[0087] In one possible embodiment, S15 can include S21 to S22.

[0088] S21, the rate coefficient in the population density ratio of adjacent energy levels is redefined to determine the defined rate coefficient.

[0089] wherein the redefinition of the rate coefficient includes:

[0090] k1 = ∑A ij ; (8)

[0091]

[0092] k4 = ∑β ji ; (11)

[0093] ∑A ij is redefined as k1, ∑B is redefined as k2, ∑C is redefined as k3, and ∑β ji is redefined as k4, and k1, k2, k3, k4 are taken as redefined rate coefficients.

[0094] S22, the defined rate coefficient is substituted into the population density ratio of adjacent energy levels to determine the simplified rate balance equation of the xenon plasma.

[0095] As an example, the above formula (8) to formula (11) are substituted into the above formula (7) to determine the simplified rate balance equation of the xenon plasma as:

[0096]

[0097] wherein, k1 =∑A ij , k4 =∑β ii ; k1 represents a spontaneous emission rate coefficient of the xenon plasma from an atomic energy level i to an atomic energy level j, k2 represents an induced emission rate coefficient of the xenon plasma from the atomic energy level j to the atomic energy level i, k3 represents a radiative recombination rate coefficient of the xenon plasma from the atomic energy level i to the atomic energy level j, and k4 represents a photoionization rate coefficient of the xenon plasma from the atomic energy level j to the atomic energy level i.

[0098] S16, determining the spectral line intensity ratio based on the Z-pinch fusion.

[0099] In a possible embodiment, the plasma is set to be optically thin based on the Z-pinch fusion, and the medium attenuation coefficient of the plasma is small, so that the spectral line intensity ratio is:

[0100]

[0101] wherein, I i represents the spectral line intensity of the transition from the atomic energy level i, I j represents the spectral line intensity of the transition from the atomic energy level j, A i represents the Einstein transition coefficient of the atomic energy level i, A j represents the Einstein transition coefficient of the atomic energy level j, hv i represents the photon transition energy of the transition from the atomic energy level i, hv j represents the photon transition energy of the transition from the atomic energy level j.

[0102] S17, determining the xenon plasma electron temperature according to the simplified rate balance equation of the xenon plasma, the spectral line intensity ratio, and a preset Boltzmann equation.

[0103] wherein, the preset Boltzmann equation is a Boltzmann transport equation (BTE).

[0104] In a possible embodiment, S17 can include S31 to S33.

[0105] S31, substituting the simplified rate balance equation of the xenon plasma into the spectral line intensity ratio to determine a first equation.

[0106] In the above example, substituting the above formula (12) into the above formula (13) to determine the first equation:

[0107]

[0108] S32, determining the second equation according to the preset Boltzmann equation and the spectral line intensity ratio.

[0109] According to the above example, the second equation is:

[0110]

[0111] wherein g i represents the degeneracy of the atomic energy level i, g j represents the degeneracy of the atomic energy level j, E i represents the energy of the atomic energy level i, E j represents the energy of the atomic energy level j, k represents the preset Boltzmann equation constant, and T e represents the xenon plasma electron temperature.

[0112] The degeneracy of the atomic energy level is not greater than 2 in a one-dimensional system, the degeneracy of the atomic energy level ranges from 1 to 4 in a two-dimensional system, and the degeneracy of the atomic energy level is not less than 3 in a three-dimensional system.

[0113] S33, determining the xenon plasma electron temperature by combining the first equation and the second equation.

[0114] According to the above example, the first equation and the second equation are combined as follows:

[0115]

[0116] The electron temperature of the xenon plasma is determined as follows:

[0117]

[0118] According to the above technical solution, for the atomic energy level rate equation of the steady-state approximation state adopted under the Z-pinch fusion condition, the non-thermal equilibrium model can improve the accuracy, the calculation speed and the calculation accuracy of the spectral line intensity, reduce the calculation amount of the atomic energy level, save the calculation resources, reduce the difficulty of solving the atomic energy level rate equation, improve the solving speed and the accuracy of the rate coefficient, and realize the simple calculation of the plasma electron temperature.

[0119] The specific embodiments of the present disclosure are described above. It should be understood that the present disclosure is not limited to the above specific embodiments, and various modifications or changes can be made by those skilled in the art within the scope of the claims, which does not affect the essential content of the present disclosure. The above preferred features can be combined in any manner without conflict.

Claims

1. A method for determining the electron temperature of a xenon plasma based on a radiative collisional model, characterized in that, The method comprises the following steps: determining the rate equation of the atomic energy level of the steady-state approximation state by using a preset radiation collision model of the steady-state approximation state; determining the particle reaction type that occupies a dominant position in the xenon plasma in the Z-pinch fusion; determining the rate balance equation of the xenon plasma according to the particle reaction type that occupies a dominant position in the xenon plasma and the rate equation of the atomic energy level of the steady-state approximation state; determining the population density ratio of adjacent energy levels by performing deformation processing on the rate balance equation of the xenon plasma; determining the simplified rate balance equation of the xenon plasma by performing simplification processing on the rate balance equation of the xenon plasma according to the population density ratio of adjacent energy levels; determining the spectral line intensity ratio value based on the Z-pinch fusion; determining the xenon plasma electron temperature according to the simplified rate balance equation of the xenon plasma, the spectral line intensity ratio value and a preset Boltzmann equation.

2. The method of claim 1, wherein, The particle reaction type that occupies a dominant position in the xenon plasma comprises: (1) spontaneous radiation: wherein said xenon plasma representing an atomic level j, said xenon plasma representing an atomic level i, h v represents a first photon; (2) stimulated radiation: wherein hv1 represents a second photon and hv2 represents a third photon; (3) photoionization and radiation recombination: wherein e represents an electron.

3. The method of claim 2, wherein, The method for determining the rate balance equation of the xenon plasma according to the particle reaction type that occupies a dominant position in the xenon plasma and the rate equation of the atomic energy level of the steady-state approximation state comprises: substituting the particle reaction type that occupies a dominant position in the xenon plasma into the rate equation of the atomic energy level of the steady-state approximation state to determine the rate balance equation of the xenon plasma.

4. The method of claim 3, wherein, The rate balance equation of the xenon plasma is: wherein n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j, β ji represents the photoionization rate of the xenon plasma from the atomic energy level j to the atomic energy level i, A ij represents the spontaneous emission rate of the xenon plasma from the atomic energy level i to the atomic energy level j, B ji represents the stimulated emission rate of the xenon plasma from the atomic energy level j to the atomic energy level i, B represents the average frequency of the transition radiation field intensity, B represents the radiative recombination rate of the xenon plasma from the atomic energy level i to the atomic energy level j, n e represents the electron density of the xenon plasma.

5. The method of claim 1, wherein, The population density ratio of adjacent energy levels is: where n i represents the population density of the atomic energy level i, n j represents the population density of the atomic energy level j.

6. The method of claim 1, wherein, The method for determining the simplified rate balance equation of the xenon plasma by performing simplification processing on the rate balance equation of the xenon plasma according to the population density ratio of adjacent energy levels comprises: redefining the rate coefficient in the population density ratio of adjacent energy levels to determine a defined rate coefficient; substituting the defined rate coefficient into the population density ratio of adjacent energy levels to determine the simplified rate balance equation of the xenon plasma.

7. The method of claim 6, wherein, The simplified rate balance equation of the xenon plasma is: wherein k1 =∑A ij , k4 =∑β ii ; k1 denotes the spontaneous emission rate coefficient of the xenon plasma from an atomic level i to an atomic level j, k2 denotes the stimulated emission rate coefficient of the xenon plasma from the atomic level j to the atomic level i, k3 denotes the radiative recombination rate coefficient of the xenon plasma from the atomic level i to the atomic level j, and k4 denotes the photoionization rate coefficient of the xenon plasma from the atomic level j to the atomic level i.

8. The method of claim 1, wherein, The spectral line intensity ratio value is: where I i represents the spectral line intensity of the transition from the atomic energy level i, I j represents the spectral line intensity of the transition from the atomic energy level j, A i represents the Einstein transition coefficient of the atomic energy level i, A j represents the Einstein transition coefficient of the atomic energy level j, hv i represents the photon transition energy of the transition from the atomic energy level i, hv j represents the photon transition energy of the transition from the atomic energy level j.

9. The method of claim 1, wherein, The method for determining the xenon plasma electron temperature according to the simplified rate balance equation of the xenon plasma, the spectral line intensity ratio value and a preset Boltzmann equation comprises: substituting the simplified rate balance equation of the xenon plasma into the spectral line intensity ratio value to determine a first equation; determining a second equation according to the preset Boltzmann equation and the spectral line intensity ratio value; determining the xenon plasma electron temperature by simultaneously solving the first equation and the second equation.

10. The method of claim 9, wherein, The method for determining the xenon plasma electron temperature by simultaneously solving the first equation and the second equation comprises: wherein, represents the first equation, represents the second equation, g i represents the degeneracy of the atomic energy level i, g j represents the degeneracy of the atomic energy level j, E i represents the energy at the atomic energy level i, E j represents the energy at the atomic energy level j, k represents the pre-set Boltzmann equation constant, T e represents the xenon plasma electron temperature.

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