A method and system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions

Abstract

The application discloses a kind of nuclear fusion product energy spectrum calculation method and system under neutral beam injection condition, as follows: according to the velocity distribution function of first reactant, second reactant, N Monte Carlo samples are randomly generated, the velocity and weight of each Monte Carlo sample are obtained;According to the relative velocity of two kinds of reactants, and the mass center velocity of two kinds of reactants, the first relative motion kinetic energy of the system composed of two kinds of reactants is calculated;According to the first relative motion kinetic energy obtained, the first kinetic energy of nuclear fusion product is calculated;By introducing Dirac function and parameterized reaction cross section based on R matrix, the reaction rate coefficient of nuclear fusion product under the first kinetic energy is calculated, and the final reaction rate result is obtained by introducing the reaction rate calculation formula;According to energy box, data statistics is arranged, and the energy spectrum of nuclear fusion product is calculated.The application can accurately calculate the energy spectrum of nuclear fusion product obtained by various nuclear fusion research devices under different operation modes.

Description

A method and system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions. Technical Field

[0001] This invention relates to the fields of nuclear engineering and nuclear technology, and more specifically, to a method and system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions. Background Technology

[0002] Nuclear fusion energy, as a highly valuable future energy source, boasts numerous advantages, including high energy density, abundant raw material reserves, and excellent safety. In modern society, with its ever-increasing energy consumption and the advancement of science and technology, humanity's demand for energy is growing. At the same time, the environmental damage caused by traditional fossil fuels is receiving increasing attention.

[0003] For the reasons mentioned above, it is essential for humanity to conduct relevant scientific research on nuclear fusion energy to promote its commercialization. In current nuclear fusion research, tokamak devices, considered highly feasible magnetic confinement thermonuclear fusion experimental devices, are being widely used. In tokamak devices, deuterium-tritium fusion produces high-energy neutrons and alpha particles as products of the fusion reaction. Both fusion reaction products possess enormous energy, which can be converted into heat and then further into electricity, realizing the complete process of nuclear fusion power generation. Therefore, calculating the energy spectrum of the fusion reaction products is crucial. The initial stage of the tokamak device heating process typically employs ohmic heating. However, ohmic heating has drawbacks such as decreased heating efficiency above a certain temperature, low heating efficiency for ions during the heating process, and unsuitability for the pulsed operation of a fusion reactor in steady-state operation. Therefore, in addition to ohmic heating, neutral beam injection is also required as an auxiliary heating method. Traditional calculation methods lack research on the energy spectrum of fusion products under neutral beam injection conditions, and due to limitations in experimental conditions, there are few research results on the energy spectrum of deuterium-tritium fusion under neutral beam injection conditions. Therefore, it is essential to develop a new calculation method applicable to the energy spectrum of fusion products under neutral beam injection conditions.

[0004] The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions has significant research value and broad future research prospects. It provides important reference and practical value for subsequent research on nuclear fusion-related topics based on tokamak devices. The calculation results of the energy spectrum of nuclear fusion products under neutral beam injection conditions obtained based on this method can serve as an important reference for improving reaction conditions and achieving steady-state operation in tokamak devices. Summary of the Invention

[0005] In order to address the shortcomings and defects of the existing technology, this invention provides a method and system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions.

[0006] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0007] A method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions, the method comprising the following steps:

[0008] Based on the velocity distribution functions of the first reactant and the second reactant, N Monte Carlo samples are randomly generated for each reactant, and the velocity and weight of each Monte Carlo sample for each reactant are obtained.

[0009] Calculate the first relative kinetic energy of the system composed of the two reactants in the center-of-mass frame based on the relative velocities of the two reactants.

[0010] The two reactants undergo nuclear fusion to produce nuclear fusion products. Assuming that the direction of motion of the nuclear fusion products is along any given direction, the first kinetic energy of the nuclear fusion products is calculated based on the obtained first relative kinetic energy.

[0011] By introducing the Dirac function and a parameterized reaction cross section based on the R matrix, the reaction rate coefficient of nuclear fusion products at the first kinetic energy is calculated, and then substituted into the reaction rate calculation formula to obtain the final reaction rate result.

[0012] Data was statistically analyzed and organized according to the energy boxes, and the energy spectrum of the nuclear fusion products was calculated.

[0013] Preferably, the first reactant and the second reactant undergo nuclear fusion under neutral beam injection conditions, wherein the neutral beam injection conditions assume that no nuclear fusion reaction occurs between neutral beam particles inside the neutral beam, and nuclear fusion reaction occurs only between background reactants.

[0014] Furthermore, the background reactant is the background plasma in the tokamak device, which follows a Maxwell-Boltzmann distribution, while assuming that the plasma in the tokamak device is isotropic.

[0015] Furthermore, the neutral beam particles are monoenergetic particle beams or particle beams with a given velocity distribution.

[0016] Preferably, the first kinetic energy of the nuclear fusion products is calculated as follows:

[0017] Based on the mass deficit between the two reactants and the nuclear fusion products, the increase in the second kinetic energy of the system after the reaction is calculated.

[0018] Based on the law of conservation of momentum, calculate the second relative kinetic energy of the system composed of two nuclear fusion products in the center-of-mass frame;

[0019] The second relative motion kinetic energy is distributed according to the mass ratio of the two nuclear fusion products to obtain the first kinetic energy of the two nuclear fusion products in the center of mass system.

[0020] Preferably, the normalized velocity distribution function of the two reactants in the laboratory reference frame is obtained based on the distribution law of reactant particles;

[0021] Substituting the probability density function of particle kinetic energy and the standard expression of the Maxwell-Boltzmann distribution of microscopic particle velocity into the reaction rate expression, and performing substitution calculations under certain conditions, the final energy spectrum calculation formula is obtained. The reaction rate calculation formula is obtained by integrating the energy spectrum calculation formula.

[0022] Furthermore, the Dirac function is introduced into the reaction rate calculation formula to avoid repeated counting when the same type of particles react.

[0023] Furthermore, the parameterized reaction cross section based on the R matrix is ​​specifically achieved by introducing the Gamow constant. and polynomial The differential cross section of the reaction is calculated, and the reaction rate coefficient is calculated based on the differential cross section of the reaction.

[0024] A system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions, comprising:

[0025] The random sampling module randomly generates N Monte Carlo samples based on the velocity distribution functions of the first reactant and the second reactant, and obtains the velocity and weight of each Monte Carlo sample corresponding to each reactant.

[0026] The first relative motion kinetic energy calculation module is used to calculate the first relative motion kinetic energy of the system composed of the two reactants in the center-of-mass frame, based on the relative velocity of the two reactants and the velocity of their center of mass.

[0027] The first kinetic energy calculation module is used to calculate the first kinetic energy of the nuclear fusion products based on the obtained first relative motion kinetic energy.

[0028] The reaction rate calculation module is used to calculate the reaction rate coefficient of nuclear fusion products at the first kinetic energy by introducing the Dirac function and the parameterized reaction cross section based on the R matrix, and then substituting it into the reaction rate calculation formula to obtain the final reaction rate result.

[0029] The energy spectrum calculation module is used to perform statistical processing of data according to energy boxes and calculate the energy spectrum of nuclear fusion products.

[0030] Preferably, it also includes a graphing and analysis module, which collects and statistically analyzes the data according to the energy spectrum distribution of the obtained nuclear fusion products, and constructs a visual histogram.

[0031] The beneficial effects of this invention are as follows:

[0032] This invention calculates the broadening of the energy spectrum of nuclear fusion products at a standard value determined by the mass defect by analyzing the kinetic energy of reactants in a nuclear fusion reaction. This is achieved by introducing the Dirac function. To avoid duplicate counting when the same type of particle undergoes nuclear fusion reaction, parameterized reaction cross-section data based on the R-matrix are used for numerical calculation of the energy spectrum of nuclear fusion products under neutral beam injection conditions.

[0033] The calculation method described in this invention can accurately calculate the energy spectrum of nuclear fusion products obtained by various nuclear fusion research devices under different operating modes, and obtain the basic characteristics of the energy spectrum of nuclear fusion products under neutral beam injection by establishing a simplified calculation model of the neutral beam injection device. Attached Figure Description

[0034] Figure 1 is a flowchart of the steps of the method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to the present invention.

[0035] Figure 2 is a schematic diagram of the velocity distribution of deuterium particles randomly generated at the center of the plasma cross section according to the Maxwell-Boltzmann distribution.

[0036] Figure 3 is a schematic diagram of the velocity distribution of tritium particles randomly generated at the center of the plasma cross section according to the Maxwell-Boltzmann distribution.

[0037] Figure 4. Neutron normalized energy spectrum at 40 keV in neutral beam particle injection mode at the center of plasma cross section.

[0038] Figure 5. Neutron normalized energy spectrum at 60 keV in neutral beam particle injection mode at the center of the plasma cross section.

[0039] Figure 6 shows the neutron normalized energy spectrum at the center of the plasma cross section in the neutral beam particle injection mode with an energy of 120 keV.

[0040] Figure 7 is a schematic diagram of the calculation system for the energy spectrum of nuclear fusion products under neutral beam injection conditions. Detailed Implementation

[0041] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0042] Example 1

[0043] As shown in Figure 1, a method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions is described, and the method includes the following steps:

[0044] Based on the velocity distribution functions of the first reactant and the second reactant, N Monte Carlo samples are randomly generated for each reactant, and the velocity and weight of each Monte Carlo sample for each reactant are obtained.

[0045] Calculate the first relative kinetic energy of the system composed of the two reactants in the center-of-mass frame based on the relative velocities of the two reactants.

[0046] The two reactants undergo nuclear fusion to produce nuclear fusion products. Assuming that the direction of motion of the nuclear fusion products is along any given direction, the first kinetic energy of the nuclear fusion products is calculated based on the obtained first relative kinetic energy.

[0047] By introducing the Dirac function and a parameterized reaction cross section based on the R matrix, the reaction rate coefficient of nuclear fusion products at the first kinetic energy is calculated, and then substituted into the reaction rate calculation formula to obtain the final reaction rate result.

[0048] Data was statistically analyzed and organized according to the energy boxes, and the energy spectrum of the nuclear fusion products was calculated.

[0049] In one specific embodiment, the present invention considers the two-body reaction theory, which is applicable to reaction types in which a first reactant and a second reactant react to generate a first nuclear fusion product and a second nuclear fusion product.

[0050] The first and second reactants undergo nuclear fusion under neutral beam injection conditions, which assume that no nuclear fusion reaction occurs between neutral beam particles inside the neutral beam, and nuclear fusion reaction only occurs between background reactants.

[0051] In this embodiment, the background reactant is the background plasma in the tokamak device, which follows a Maxwell-Boltzmann distribution, and it is assumed that the plasma in the tokamak device is isotropic.

[0052] In this embodiment, the neutral beam particles are monoenergetic particle beams or particle beams with a given velocity distribution.

[0053] In one specific embodiment, the two-body reaction theory applies to reaction types where two reactants produce two other nuclear fusion products. The rates of the first reactant and the first reactant are randomly sampled, and the production rates are... and To make it satisfy the set velocity distribution function and Meanwhile, the weight of each reactant particle is set as follows: and .

[0054] Based on the velocity of each Monte Carlo sample corresponding to each reactant and the mass of the reactant, the relative velocity of the two reactants and their center-of-mass velocities are calculated as follows:

[0055] First, the relative rates of the two reactants are given. and the centroid velocities of the two reactants :

[0056]

[0057]

[0058] in, , The mass of the two reactants is... , The values ​​represent the rates of the two reactants in a laboratory reference frame.

[0059] Calculate the first relative kinetic energy of the system composed of the two reactants in the center-of-mass frame:

[0060]

[0061] In the formula, To reduce mass, it is defined as:

[0062]

[0063] In one specific embodiment, the first kinetic energy of the nuclear fusion products is calculated as follows:

[0064] The increase in energy of the system after the reaction is calculated based on the mass deficit between the two reactants and the nuclear fusion products.

[0065]

[0066] in, Represents the speed of light. , Let Q be the mass of the two nuclear fusion products and Q be the energy.

[0067] Based on the law of conservation of momentum, calculate the second relative kinetic energy of the system composed of two nuclear fusion products in the center-of-mass frame:

[0068]

[0069] The second relative motion kinetic energy is distributed according to the mass ratio of the two nuclear fusion products to obtain the first kinetic energy of the two nuclear fusion products in the center of mass system.

[0070] This embodiment takes the first nuclear fusion product as an example to obtain the kinetic energy of the first nuclear fusion product in the center-of-mass system:

[0071]

[0072] in,

[0073]

[0074]

[0075] In the formula, The velocity of the first nuclear fusion products in the center-of-mass frame. The velocity of the first nuclear fusion products in a laboratory reference frame. This indicates the mass of the first nuclear fusion product. Indicates the mass of the second nuclear fusion product, It is the velocity of the center of mass in the laboratory reference system.

[0076] In one specific embodiment, the normalized velocity distribution function of the two reactants in the laboratory reference frame is obtained based on the distribution law of reactant particles;

[0077] Substituting the probability density function of particle kinetic energy and the standard expression of the Maxwell-Boltzmann distribution of microscopic particle velocity into the reaction rate expression, and performing substitution calculations under certain conditions, the final energy spectrum calculation formula is obtained. The reaction rate calculation formula is obtained by integrating the energy spectrum calculation formula.

[0078] In this embodiment, the Dirac function is introduced into the reaction rate calculation formula to avoid repeated counting when the same type of particles react.

[0079] In this embodiment, the parameterized reaction cross section based on the R matrix is ​​specifically achieved by introducing the Gamow constant. and polynomial The differential cross section of the reaction is calculated, and the reaction rate coefficient is calculated based on the differential cross section of the reaction.

[0080] Normalized rate distribution functions of the two reactants in the laboratory reference frame:

[0081]

[0082] By introducing the Dirac function To avoid duplicate counting when the same type of particles react:

[0083]

[0084] in, , This indicates the type of reactant.

[0085] The reaction rate R represents the number of times the two reactants react per unit volume per unit time.

[0086]

[0087] In the formula, , It is the number density of the two reactants. For the reaction rate coefficient:

[0088]

[0089] in, The cross section of the nuclear reaction, its properties, and the relative velocity of the two nuclei ( )related.

[0090] Therefore, reaction rate It can be represented as:

[0091]

[0092] Subsequent calculations are performed by introducing a parameterized reaction cross section based on the R-matrix:

[0093]

[0094] In the formula, It is Gamow's constant. for Polynomial:

[0095]

[0096] In the formula, , , , , , , , , All are constants, and their values ​​are shown in the table below:

[0097]

[0098] The expression for the velocity of a microscopic particle at temperature T under the Maxwell-Boltzmann distribution is:

[0099]

[0100] In the formula, It is the particle mass. The velocity of the microscopic particles.

[0101] The formula for calculating the energy spectrum is derived through substitution:

[0102]

[0103] The reaction rate R is:

[0104]

[0105] In this embodiment, the velocity of the center of mass in the two-body system is The velocity of the first nuclear fusion product in the laboratory reference frame is:

[0106]

[0107] The kinetic energy of the first nuclear fusion product in the laboratory reference frame is:

[0108]

[0109] For a given velocity and The reaction rate of the reactant particles per unit time, per unit volume, and per unit solid angle is:

[0110]

[0111] The effect of each Monte Carlo event on the reaction rate is:

[0112]

[0113] After N iterations, a series of results can be obtained. and The value of the energy spectrum of the first nuclear fusion product is given by... The value is obtained by placing it into the energy range.

[0114] Energy range to Number of ions in Given by the average reaction rate:

[0115]

[0116] in, The sum of the weights of each reactant particle For the Dirac function, variance Depend on variance Decide:

[0117]

[0118] in:

[0119]

[0120] The relative error for each energy range can be expressed as:

[0121] .

[0122] This embodiment calculates the kinetic energy of reactants in a nuclear fusion reaction to obtain the broadening of the energy spectrum of nuclear fusion products at a standard value determined by the mass defect. This is achieved by introducing the Dirac function. To avoid duplicate counting when the same type of particle undergoes nuclear fusion reaction, parameterized reaction cross-section data based on the R-matrix are used for numerical calculation of the energy spectrum of nuclear fusion products under neutral beam injection conditions.

[0123] The calculation method described in this embodiment can accurately calculate the energy spectrum of nuclear fusion products obtained by various nuclear fusion research devices under different operating modes, and obtain the basic characteristics of the energy spectrum of nuclear fusion products under neutral beam injection by establishing a simplified calculation model of the neutral beam injection device.

[0124] This embodiment extends the application of the nuclear fusion two-body reaction theory applicable to nuclear fusion research devices, enabling accurate calculation of the energy spectrum and reaction rate data of two nuclear fusion products.

[0125] This embodiment uses the Monte Carlo method to establish a calculation method by random sampling under a normalized distribution function, which can meet the needs of calculating the energy spectrum of nuclear fusion reaction products under various velocity distributions and has a wider range of applicability.

[0126] This embodiment establishes simplified models for different neutral beam injection devices, enabling effective calculation of the energy spectrum of nuclear fusion reaction products under neutral beam injection conditions. It accurately reflects the differences in the influence of different neutral beam injection devices on the energy spectrum of nuclear fusion products, further meeting the needs of scientific research related to nuclear fusion.

[0127] This embodiment calculates the temperature of the reactants to obtain a clear product energy spectrum broadening, making the energy distribution of the product energy spectrum clearer and more explicit.

[0128] Example 2

[0129] Based on the calculation method of the energy spectrum of nuclear fusion products under neutral beam injection conditions shown in Example 1, this example provides an application example as follows:

[0130] The energy spectra of deuterium-tritium fusion reaction products of a tokamak nuclear fusion research device were calculated under neutral beam injection conditions (Beam-Thermal mode, BT mode) and steady-state operation conditions (Thermal-Thermal mode, TT mode), and the calculation results were compared. A simplified model of the neutral beam injection device was established, in which the injected particles were deuterium particles.

[0131] This embodiment considers the reaction of hot ions with beam ions at all locations. The first reactant represents hot tritium ions, following a Maxwell-Boltzmann distribution. The second reactant represents neutral beam deuterium particles, with the energy distribution of the beam particles injected by the neutral beam injection device being: 63% beam particles with an energy of 120 keV; 21% beam particles with an energy of 60 keV; and 16% beam particles with an energy of 40 keV.

[0132] This embodiment assumes that the neutral beams of both devices have a certain emission direction. The broadening of the neutral beam, and the distribution that the broadening of the neutral beam in the emission direction follows, are defined as follows:

[0133]

[0134] This embodiment studies the energy spectrum of fusion products under the influence of neutral beam particles of different energies. It uses the case where both reactants have a Maxwell-Boltzmann distribution, and calculates the normalized energy spectrum of neutrons at the center of the plasma cross-section under two modes. The normalized radius represents the temperature at the center of the plasma cross-section, i.e. .

[0135] (1) Randomly sample the rates of the first reactant and the second reactant to generate and So that it satisfies the corresponding distribution function and Meanwhile, the weight corresponding to each reactant particle is... and .

[0136] 1.1) Two types of reactant particles are randomly generated according to the Maxwell-Boltzmann distribution, i.e., 10 6 A deuterium particle and a tritium particle.

[0137] 1.2) The velocity distributions of the two reactant particles are shown in Figures 2 and 3. As can be seen from Figures 2 and 3, the particle distribution generated by random sampling is very close to the actual Maxwell-Boltzmann distribution, so the sampling process can be considered accurate.

[0138] 1.3) Simultaneously, let the weights of deuterium particles and tritium particles be respectively... and .

[0139] (2) Calculate the kinetic energy E3 of the neutrons in the fusion products.

[0140] 2.1) First, based on the masses of the two reactants and their velocities in the laboratory reference frame, the first relative kinetic energy of the system composed of the two reactants in the center-of-mass frame is obtained.

[0141] 2.2) Based on the mass defect between reactants and products, the increase in the second kinetic energy of the system after the reaction is calculated.

[0142] 2.3) According to the law of conservation of momentum, the second relative kinetic energy of the system composed of two nuclear fusion products under the center of mass is obtained.

[0143] 2.4) Based on neutrons and The mass ratio of the two fusion reaction products of the particle determines the first kinetic energy of the neutron in the center-of-mass system.

[0144] (3) Calculate the differential cross section of the reaction and then calculate the reaction rate.

[0145] 3.1) A parameterized reaction cross section based on the R-matrix is ​​introduced for subsequent calculations.

[0146] 3.2) By introducing the Gamow constant and polynomial The differential cross section of the reaction was calculated.

[0147] 3.3) Based on the differential cross section of the reaction, the reaction rate coefficient is further calculated.

[0148] 3.4) Substitute the reaction rate coefficient into the reaction rate calculation formula to obtain the final reaction rate result.

[0149] (4) Calculation of the energy spectrum of fusion products.

[0150] The data from the energy boxes were statistically analyzed and the energy spectrum of the fusion products was calculated.

[0151] (5) Collect data, perform statistics, and create a histogram.

[0152] The normalized energy spectra of the products (neutrons) obtained by nuclear fusion at the center of the plasma cross section are shown in Figures 4, 5, and 6.

[0153] Example 3

[0154] As shown in Figure 4, a system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions includes:

[0155] The random sampling module randomly generates N Monte Carlo samples based on the velocity distribution functions of the first reactant and the second reactant, and obtains the velocity and weight of each Monte Carlo sample corresponding to each reactant.

[0156] The first relative motion kinetic energy calculation module is used to calculate the first relative motion kinetic energy of the system composed of the two reactants in the center-of-mass frame, based on the relative velocity of the two reactants and the velocity of their center of mass.

[0157] The first kinetic energy calculation module is used to calculate the first kinetic energy of the nuclear fusion products based on the obtained first relative motion kinetic energy.

[0158] The reaction rate calculation module is used to calculate the reaction rate coefficient of nuclear fusion products at the first kinetic energy by introducing the Dirac function and the parameterized reaction cross section based on the R matrix, and then substituting it into the reaction rate calculation formula to obtain the final reaction rate result.

[0159] The energy spectrum calculation module is used to perform statistical processing of data according to energy boxes and calculate the energy spectrum of nuclear fusion products.

[0160] This embodiment also includes a graphing and analysis module, which collects and statistically analyzes the data according to the energy spectrum distribution of the obtained nuclear fusion products, and constructs a visual histogram.

[0161] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions, characterized in that: The method includes the following steps: Based on the velocity distribution functions of the first reactant and the second reactant, N Monte Carlo samples are randomly generated for each reactant to obtain the velocity and weight of each Monte Carlo sample corresponding to each reactant; based on the relative velocities of the two reactants and their center-of-mass velocities, the first relative kinetic energy of the system composed of the two reactants in the center-of-mass frame is calculated; after the two reactants undergo nuclear fusion, nuclear fusion products are obtained. Assuming the direction of motion of the nuclear fusion products is along any given direction, the first kinetic energy of the nuclear fusion products is calculated based on the obtained first relative kinetic energy. By introducing the Dirac function and a parameterized reaction cross section based on the R matrix, the reaction rate coefficient of nuclear fusion products at the first kinetic energy is calculated, and the result is obtained by substituting it into the reaction rate calculation formula. The data is statistically processed according to the energy level, and the energy spectrum of the nuclear fusion products is calculated.

2. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 1, characterized in that: The first reactant and the second reactant undergo nuclear fusion under neutral beam injection conditions, which assume that nuclear fusion reactions do not occur between neutral beam particles inside the neutral beam, but only between the neutral beam particles and the background reactants.

3. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 2, characterized in that: The background reactant is the background plasma in the tokamak device, which follows a Maxwell-Boltzmann distribution, and it is assumed that the plasma in the tokamak device is isotropic.

4. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 2, characterized in that: The neutral beam particles are monoenergetic particle beams or particle beams with a given velocity distribution.

5. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 1, characterized in that: The first kinetic energy of the nuclear fusion products is calculated as follows: Based on the mass deficit between the two reactants and the nuclear fusion products, the increase in the second kinetic energy of the system after the reaction is calculated; based on the law of conservation of momentum, the second relative kinetic energy of the system composed of the two nuclear fusion products is calculated in the center-of-mass frame; the second relative kinetic energy is distributed according to the mass ratio of the two nuclear fusion products to obtain the first kinetic energy of the two nuclear fusion products in the center-of-mass frame.

6. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 1, characterized in that: Based on the distribution law of reactant particles, the normalized velocity distribution functions of the two reactants in the laboratory reference frame are obtained; the probability density function of particle kinetic energy and the standard expression of the Maxwell-Boltzmann distribution of microscopic particle velocity are substituted into the reaction rate expression, and the final energy spectrum calculation formula is obtained by substitution calculation under certain conditions. The reaction rate calculation formula is obtained by integrating the energy spectrum calculation formula.

7. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 6, characterized in that: The Dirac function is introduced into the reaction rate calculation formula to avoid repeated counting when the same type of particles react.

8. The method for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 6, characterized in that: The parameterized reaction cross section is based on the R matrix, specifically by introducing the Gamow constant. and polynomial The differential cross section of the reaction is calculated, and the reaction rate coefficient is calculated based on the differential cross section of the reaction.

9. A system for calculating the energy spectrum of nuclear fusion products under neutral beam injection conditions, characterized in that: include: The random sampling module randomly generates N Monte Carlo samples based on the velocity distribution functions of the first and second reactants, obtaining the velocity and weight of each Monte Carlo sample corresponding to each reactant. The first relative motion kinetic energy calculation module is used to calculate the first relative motion kinetic energy of the system composed of the two reactants in the center-of-mass frame based on the relative velocities of the two reactants and their center-of-mass velocities. The first kinetic energy calculation module is used to calculate the first kinetic energy of the nuclear fusion products based on the obtained first relative motion kinetic energy. The reaction rate calculation module is used to calculate the reaction rate coefficient of the nuclear fusion products at the first kinetic energy by introducing the Dirac function and the parameterized reaction cross section based on the R matrix, and then substitute it into the reaction rate calculation formula to obtain the final reaction rate result. The energy spectrum calculation module is used to perform statistical processing of data according to energy boxes and calculate the energy spectrum of nuclear fusion products.

10. The calculation system for the energy spectrum of nuclear fusion products under neutral beam injection conditions according to claim 9, characterized in that: It also includes a graphing and analysis module, which collects and statistically analyzes the data according to the energy spectrum distribution of the nuclear fusion products, and constructs a visual histogram.

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