A method and apparatus for thermal safety control of an electron output window of a low-energy electron accelerator

Abstract

The application provides a heat safety control method and device for an electron output window of a low-energy electron accelerator. The method provided by the application comprises the following steps: determining a single-cycle weighted total loss power of the electron output window according to obtained window structure parameters and operation debugging parameters of the low-energy electron accelerator; substituting the single-cycle weighted total loss power as a known heat source term into a heat conduction ideal degeneration model to obtain a reference maximum temperature of a grid rib under ideal uniform heat source distribution; determining an engineering correction factor according to the operation debugging parameters and the window structure parameters, and performing nonlinear compensation on the reference maximum temperature to obtain an actual maximum temperature of the grid rib under actual non-uniform heat source distribution; calculating a transverse maximum temperature difference of a window foil in a transverse gap direction according to the single-cycle weighted total loss power, and superimposing the transverse maximum temperature difference and the actual maximum temperature to obtain an absolute maximum temperature of the electron output window; and adjusting operation parameters of the low-energy electron accelerator according to the absolute maximum temperature.

Description

Technical Field

[0001] This application relates to the field of thermal safety control technology, and in particular to a thermal safety control method and apparatus for an electron output window of a low-energy electron accelerator. Background Technology

[0002] As a key component of low-energy electron accelerators, the electron output window commonly uses titanium as its foil material due to its high specific strength. However, titanium foil has a low thermal conductivity, and the large energy deposition during low-energy electron beam penetration causes the foil to experience a rapid temperature rise. Since the upper limit of titanium's stable operating temperature in air is approximately 350°C, if the electron output window overheats locally, the titanium foil will undergo severe oxidation at high temperatures, leading to cracking and potentially causing major equipment accidents such as vacuum failure. Therefore, strict thermal safety control of the electron output window is crucial.

[0003] While cooling methods such as thermal radiation, gas convection, and water conduction exist, their heat transfer rates are extremely low and often negligible in actual operation. Current thermal safety assessments primarily rely on complex two-dimensional steady-state heat conduction equations to calculate the overall temperature field distribution of the electronic output window. However, this method is extremely cumbersome and time-consuming, failing to meet the urgent needs of industrial production and on-site commissioning for online, real-time thermal safety assessments. More seriously, on-site commissioning personnel can only directly observe parameters such as voltage, current, and the mechanical geometric parameters of the output window. The complex two-dimensional partial differential equations cannot directly and efficiently map these macroscopic commissioning parameters, resulting in a significant technological gap.

[0004] Therefore, there is an urgent need for a method to quickly estimate the maximum temperature of the electron output window, and based on the maximum temperature, to accurately deduce and determine the maximum upper limit of the electron beam current that a low-energy electron accelerator can achieve within the thermal safety boundary, thereby realizing thermal safety control. Summary of the Invention

[0005] In view of this, this application provides a thermal safety control method and apparatus for the electron output window of a low-energy electron accelerator, which can quickly estimate the maximum temperature of the electron output window, and accurately deduce and determine the maximum upper limit of the electron beam current that the low-energy electron accelerator can achieve within the thermal safety boundary based on the maximum temperature, thereby realizing thermal safety control.

[0006] Specifically, this application is implemented through the following technical solution:

[0007] The first aspect of this application provides a thermal safety control method for the electron output window of a low-energy electron accelerator, the method comprising:

[0008] Obtain the window structure parameters and operation and debugging parameters of the low-energy electron accelerator;

[0009] Based on the window structure parameters and the operation and debugging parameters, determine the single-cycle weighted total loss power of the electronic output window;

[0010] The single-cycle weighted total loss power is substituted into the ideal heat conduction degradation model as a known heat source term to calculate the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution.

[0011] Based on the operating and debugging parameters and the window structure parameters, an engineering correction factor is determined. Based on the engineering correction factor, nonlinear compensation is performed on the reference maximum temperature to obtain the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution. The engineering correction factor reflects the electron beam concentration.

[0012] The maximum lateral temperature difference of the window foil in the lateral gap direction is calculated based on the single-cycle weighted total loss power. The maximum lateral temperature difference is then superimposed with the actual highest temperature to obtain the absolute highest temperature of the electronic output window.

[0013] The operating parameters of the low-energy electron accelerator are dynamically adjusted based on the absolute maximum temperature.

[0014] The second aspect of this application provides a thermal safety control device for the electron output window of a low-energy electron accelerator, the device comprising an acquisition module, a determination module, a calculation module, a compensation module, and an adjustment module;

[0015] The acquisition module is used to acquire the window structure parameters and operation and debugging parameters of the low-energy electron accelerator.

[0016] The determining module is used to determine the single-cycle weighted total loss power of the electronic output window based on the window structure parameters and the operation and debugging parameters.

[0017] The calculation module is used to substitute the single-cycle weighted total loss power as a known heat source term into the ideal heat conduction degradation model to calculate the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution.

[0018] The compensation module is used to determine an engineering correction factor based on the operating and debugging parameters and the window structure parameters, and to perform nonlinear compensation on the reference maximum temperature based on the engineering correction factor to obtain the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution; the engineering correction factor reflects the electron beam concentration.

[0019] The calculation module is also used to calculate the maximum lateral temperature difference of the window foil in the lateral gap direction based on the single-cycle weighted total loss power, and to superimpose the maximum lateral temperature difference with the actual highest temperature to obtain the absolute highest temperature of the electronic output window.

[0020] The adjustment module is used to dynamically adjust the operating parameters of the low-energy electron accelerator based on the absolute maximum temperature.

[0021] The thermal safety control method and device for the electron output window of a low-energy electron accelerator provided in this application firstly determines the single-cycle weighted total loss power by collaboratively acquiring window structure parameters and operation and debugging parameters. This breaks through the limitations of traditional modeling that relies solely on static parameters or single empirical current values, laying a full-load data matrix that takes into account both geometric spatial configuration and dynamic beam conditions for subsequent temperature field derivation. Subsequently, this power is substituted as a known heat source term into the ideal degradation model of heat conduction to solve for the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution. By temporarily removing the non-uniform Gaussian aggregation effect mathematically, a low-computational-cost, robust linear temperature base is constructed for the control system, successfully avoiding the risk of slow convergence or system crash caused by the control chip directly solving transcendental equations. Furthermore, an engineering correction factor reflecting the electron beam concentration is used to nonlinearly compensate for the reference maximum temperature, thereby obtaining the actual maximum temperature of the grid ribs under a real non-uniform heat source distribution. This cleverly refines the complex physical field non-uniform aggregation phenomenon into algebraic polynomial compensation, which can not only accurately capture local extreme hot spots caused by beam aggregation, but also make the complex non-uniformity Uniform heat transfer solution can run in real time on a microprocessor with extremely low computational overhead. Next, the maximum lateral temperature difference of the window foil in the lateral gap direction is calculated based on the single-cycle weighted total power loss, and this difference is linearly superimposed with the actual highest temperature of the grid ribs to obtain the absolute maximum temperature. In mathematical modeling, the originally complex two-dimensional temperature field, which is interwoven and deeply coupled, is completely decomposed into two independent one-dimensional feature models. This eliminates the local omissions, undercalculations, and heat loss caused by mutual interference between component temperature fields, and perfectly addresses the secondary spatial temperature rise of the window foil relative to the contact surface. The true physical nature of heat transfer is revealed. Ultimately, at the control closed-loop execution end, based on the absolute maximum temperature that integrates dual physical properties and instantaneous calculation characteristics, the operating parameters of the low-energy electron accelerator are dynamically adjusted. High-precision thermal sensing prediction is directly locked into the control core, realizing intelligent active defense based on the true physical boundary conditions of the window. This allows the low-energy electron accelerator to dynamically maximize its irradiation processing capacity according to the thermal load limit of the window, ensuring the continuous and safe operation of the entire machine while reducing devastating hardware accidents such as window foil rupture and vacuum leakage caused by blind overheating of the window. Attached Figure Description

[0022] Figure 1 A flowchart of a thermal safety control method for the electron output window of a low-energy electron accelerator provided in Embodiment 1 of this application;

[0023] Figure 2 A schematic diagram of the structure of the electronic output window provided in this application;

[0024] Figure 3 This is a schematic diagram of the thermal safety control device for the electron output window of a low-energy electron accelerator provided in Embodiment 2 of this application. Detailed Implementation

[0025] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0026] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0027] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0028] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0029] Figure 1 This is a flowchart illustrating the thermal safety control method for the electron output window of a low-energy electron accelerator provided in Embodiment 1 of this application. Please refer to... Figure 1 The method provided in this embodiment may include:

[0030] S101. Obtain the window structure parameters and operation and debugging parameters of the low-energy electron accelerator.

[0031] The window structure parameters include the grid rib width, grid gap width, grid half length, total length of the electron output window, and window foil thickness; the operation and debugging parameters include the operating voltage of the low-energy electron accelerator, total beam current, reference temperature of the cooling water channel, electron beam current distribution density, and the standard deviation of the normal distribution fitted by the electron beam current distribution density.

[0032] Specifically, Figure 2 A schematic diagram of the electronic output window provided in this application. Please refer to... Figure 2 The window structure parameters refer to the inherent, non-easily altered mechanical geometric dimensions and physical boundary constraints of the electronic output window after manufacturing and assembly. These parameters constitute the geometric boundary conditions and area weighting coefficients in solving the one-dimensional steady-state heat transfer equation. Specifically, they include: grid rib width (the width of the metal grid lines supporting the titanium foil), grid gap width (the lateral width of the "window pane" through which electrons can directly penetrate the foil without metal obstruction), grid half-length (half the longitudinal length of the window pane, belonging to the one-dimensional coordinate boundary of the model solution), total length of the electronic output window (the overall axial dimension of the electronic output window on a macroscopic scale), and foil thickness (the micrometer-level thickness of the titanium foil, which directly determines the energy loss (resistance) when electrons pass through).

[0033] Operational debugging parameters refer to the dynamic electrical, thermal, and beam morphology variables of a low-energy electron accelerator during actual startup, on-site equipment debugging, or dynamic control, which are observed and measured by instruments or directly set by operators. These constitute the dynamic heat source input in the ideal heat conduction degradation model, specifically including: operating voltage and total beam current (the macroscopic power index of the low-energy electron accelerator, which directly determines the total energy input of the electron beam), the reference temperature of the cooling water channel (the basic initial temperature at which external cooling water removes heat, i.e., the reference boundary temperature in the calculation formula), electron beam current distribution density (the actual density of the electron beam in space, generally obtained by measuring with a dose diaphragm placed on-site), and the standard deviation of the normal distribution (since the electron beam is not absolutely uniform in space, but rather denser at the center and sparser at the edges like a mountain peak (conforming to a Gaussian normal distribution), this standard deviation, fitted by mathematical methods using measured density data, is the core control variable used to accurately describe the degree to which the electron beam concentrates towards the center).

[0034] S102. Determine the single-cycle weighted total power loss of the electronic output window based on the window structure parameters and the operation and debugging parameters.

[0035] Specifically, the single-cycle weighted total power loss refers to the equivalent total thermal power converted from energy deposition within a single geometrically repeating unit (one grid cycle) when a high-energy electron beam penetrates the electron output window, after area ratio adjustment. The electron output window of a low-energy electron accelerator is not a smooth flat plate, but rather composed of a periodic topological structure of alternating "metal grid ribs - window foil gaps - metal grid ribs". Here, a single cycle refers to a minimum repeating unit in spatial geometry (i.e., the width of one supporting grid rib plus the width of an adjacent gap). Facing a huge electron output window, global calculations of the entire window would lead to extremely complex partial differential equations. Because the structure is periodically repeating, only the most representative single cycle needs to be analyzed to achieve simplified calculations that reveal the whole from a small detail.

[0036] Secondly, when the electron beam bombards the electron output window, part of it strikes the thick metal grid, while the other part penetrates the thin window foil. Due to differences in material and thickness, these two components exhibit completely different levels of resistance to electrons (energy loss characteristics), and they also occupy different spatial areas. The weighting here refers to the superposition of area weighting and spatial distribution, combining the two distinct power losses into an average value that characterizes the overall heating level of the cycle. Finally, the electron beam possesses high kinetic energy. When it forcibly penetrates the window foil and grid, some of this kinetic energy is lost due to collisions with microscopic particles. According to the law of conservation of energy, this lost electron kinetic energy is 100% converted into the internal energy (i.e., heat energy) of the output window material.

[0037] In specific implementation, the grid rib width and grid gap width in the window structure parameters are extracted as area weighting coefficients for the spatial period. Based on the electron beam current distribution density in the operation and debugging parameters, the first energy loss term of the electron beam on the grid rib and the second energy loss term when passing through the window foil are combined to determine the respective power loss density distribution of the grid rib and the window foil in a single period. Using the area weighting coefficients, the power loss density distribution of the grid rib and the window foil is weighted and superimposed according to their respective spatial proportions in a single grid spatial period. Combined with the total beam current in a single period, spatial dimension integral substitution is performed to establish a quantitative mapping relationship between the operation and debugging parameters and the heat source term of the one-dimensional steady-state heat conduction equation, and the weighted total power loss in a single period is obtained by solving the equation.

[0038] Specifically, the grid ribs are the metal mesh skeleton (or support ribs) used for load-bearing and support in the electronic output window, and are usually made of a metal material with high thermal conductivity (such as copper or copper alloy). The window foil is an extremely thin, sealed metal film that allows electrons to pass through, covering the entire surface of the electronic output window (in engineering, titanium foil with a thickness of only tens of micrometers is usually used, commonly known as "titanium window").

[0039] In practical implementation, firstly, the stored window structure parameters are retrieved, and the two most critical lateral geometric dimensions are extracted: the width of the grid ribs and the width of the grid gaps. Since these two widths directly determine the area proportion occupied by the ribs and foil within a single "repetition cycle" of alternating grids and foil, the width weights of the grid ribs and grid gaps are calculated based on these two width values, serving as area weighting coefficients for subsequent heat generation fusion. The electron beam current distribution density (reflecting the spatial concentration of electrons) is then used. This electron beam current distribution density is multiplied by the first energy loss term of electrons hitting the grid material (i.e., the energy deposition coefficient of a single electron in the grid), generating a power loss density distribution map describing "how much heat is generated at each point on the grid surface." Similarly, the electron beam current distribution density is multiplied by the second energy loss term of electrons penetrating the titanium foil (i.e., the energy loss coefficient of electrons penetrating the foil), generating a power loss density distribution map describing the heat distribution on the foil surface. Within a selected single grid period (one rib + one gap), using predetermined width weights, the heat density distributions of the ribs and the window foil are weighted and superimposed based on their spatial proportions to obtain a hybrid heat spatial distribution function that comprehensively reflects the overall heat trend within this period. Introducing the total beam current of a single period (which can be converted from the total current, etc.), the hybrid heat spatial distribution function is integrally replaced in terms of spatial dimensions within the spatial range of a single geometric period. Through this integration step, the microscopic spatial distribution is eliminated, replaced by a very elegant and clear quantitative mapping relationship. By directly using macroscopic adjustment parameters such as voltage and current, the known heat source term (Q) on the right-hand side of the one-dimensional steady-state heat conduction equation is accurately calculated. Based on the established quantitative mapping relationship, the final scalar result, i.e., the single-period weighted total power loss, is calculated and output.

[0040] For example, in one embodiment, the weighted total power loss per cycle can be expressed as:

[0041] ;

[0042] ;

[0043] ;

[0044] in, This represents the weighted total power loss over a single cycle. This represents the power loss of the grid ribs within a single cycle. The power loss of the window foil within a single cycle; This represents the total beam current of the low-energy electron accelerator. This represents the first energy loss term of the electron beam on the lattice ribs; This is the second energy loss term when the electron beam passes through the window foil; This refers to the width of the grid reinforcement bars; This refers to the grid spacing width; Half the grid length; This is the total length of the electronic output window; Vertical spatial coordinates; The amplitude constant of the normal distribution function; denoted as the standard deviation of the normal distribution of the electron beam spatial distribution.

[0045] make ,but:

[0046] ;

[0047] By analyzing the Gaussian distribution function in the above equation within the vertical effective interval [ , By performing a spatial dimension substitution and introducing a Gaussian error function, the integral expression can be converted into an explicit algebraic expression:

[0048] ;

[0049] in, The periodically weighted composite energy loss coefficient; This is the composite amplitude coefficient of the heat source term.

[0050] S103. Substitute the single-cycle weighted total loss power as a known heat source term into the ideal heat conduction degradation model to calculate the reference maximum temperature of the grid ribs under ideal uniform heat source distribution.

[0051] Specifically, the ideal degradation model of heat conduction refers to a one-dimensional analytical degradation mathematical model established by physically reducing the dimension and weakening the boundaries of the traditional complex two-dimensional steady-state partial differential equations of heat conduction that rely on finite element numerical solutions. Traditional temperature field calculations (such as two-dimensional steady-state partial differential equations) require meshing the entire electron output window surface and multiple rounds of matrix iteration, which is extremely time-consuming. Based on the physical characteristics of the low-energy electron accelerator output window, this application makes two essential degradation treatments: First, it actively eliminates the thermal radiation and gas convection heat transfer terms, which have a very low (usually negligible) contribution to cooling in actual operation, thus degrading the boundary conditions to pure "edge water-cooled conduction"; second, it utilizes the periodic arrangement of the electron output window in its structure to degrade the complex two-dimensional surface heat flow transmission to a one-dimensional line domain heat transmission only along the grid extension direction (vertical).

[0052] An ideal uniform heat source distribution refers to the assumption that, when calculating the reference maximum temperature, the heat generation power deposited by the electron beam within a single grid period is a constant distribution that is absolutely uniform and unchanging along the spatial extension direction. The reference maximum temperature refers to the basic temperature reference value (or temperature origin) obtained directly from elementary algebraic equations under the dual idealized simplification conditions of the above-mentioned idealized degradation model of heat conduction and ideal uniform heat source distribution.

[0053] In specific implementation, the single-cycle weighted total power loss is equivalent to a constant internal heat source uniformly distributed along the entire length of the grid ribs, and substituted into the one-dimensional steady-state heat transfer equation; the reference temperature of the cooling water channel in the operation and debugging parameters is introduced as the temperature boundary condition of the one-dimensional steady-state heat transfer equation at the contact surface on both sides of the grid rib length direction; the one-dimensional steady-state heat transfer equation containing the constant internal heat source and the temperature boundary condition is solved by quadratic integration to obtain a quadratic temperature distribution function expressed by elementary algebra; the maximum value of the quadratic temperature distribution function at the origin of the center of symmetry along the grid rib length direction is extracted, and the maximum value is determined as the reference maximum temperature of the grid rib under an ideal uniform heat source distribution.

[0054] Specifically, first, the single-cycle weighted total power loss calculated in the previous step (S102) is retrieved. Ignoring the actual Gaussian curve fluctuations of the electron beam, the assumption of "heat source uniformity" is directly applied. The total power within this cycle is spread evenly and uniformly across the entire physical length of the grid rib, like spreading butter. In the mathematical model, this evenly distributed heat output directly becomes a spatial constant (internal heat source term), which is then directly substituted into the preset one-dimensional steady-state heat transfer equation. At this point, the partial differential equation degenerates into an ordinary differential equation. The input operating and debugging parameters are retrieved, and the reference temperature of the cooling water channel is directly extracted (e.g., a constant water cooling temperature of 25°C measured on-site). Structurally, the long strips of the grid rib are tightly attached to or submerged in the cooling water at both ends. Therefore, in the algorithm's spatial coordinate system, the temperatures at the left and right endpoints (contact surfaces) along the longitudinal length of the grid ribs are strictly controlled and directly assigned the reference temperature of this cooling channel, thus defining a constant-temperature constraint at both ends for the one-dimensional heat transfer equation. A quadratic integral mathematical operation is then performed on this one-dimensional steady-state heat transfer equation with constant heat source terms and boundary conditions. Integrating the second-order differential equation once yields the temperature gradient (first-order linear), and integrating it again completely eliminates the differential sign. Through these two integrals, and incidentally eliminating the integration constant using the constant temperature at both ends from the second step, a quadratic temperature distribution function, purely expressed using addition, subtraction, multiplication, division, and squaring operations, can be instantly obtained. Mathematically, this function is represented by a standard, downward-opening parabola, describing the temperature distribution at every point along the grid rib from left to right. Because physically the ends are cooled by water cooling while the entire rib heats up uniformly, the temperature increases from the ends towards the middle, and its mathematical maximum must perfectly symmetrically fall at the geometric center along the length direction (the origin of the coordinate system). Substituting the zero point of the coordinate system into the quadratic temperature distribution function obtained in the previous step, we can calculate the maximum temperature at the center using the formula. The calculated temperature at the center vertex is the reference maximum temperature of the grid ribs under ideal uniform heat source distribution.

[0055] For example, in one embodiment, a constant internal heat source can be substituted into the one-dimensional steady-state heat transfer equation as follows:

[0056] ;

[0057] in, It is a quadratic temperature distribution function; This represents the weighted total power loss over a single cycle. The equivalent thermal conductivity of the grid reinforcement material; Half the grid length; Vertical spatial coordinates; is the integration constant.

[0058] Substituting the temperature boundary conditions, i.e. =- , hour, , ,at this time:

[0059] ;

[0060] in, Vertical spatial coordinates; Half the grid length; It is a quadratic temperature distribution function; This is the reference temperature for the cooling water channels; It is the integration constant; This represents the weighted total power loss over a single cycle. The equivalent thermal conductivity of the grid reinforcement material.

[0061] The reference maximum temperature of the grid ribs under an ideal uniform heat source distribution is obtained by solving the problem.

[0062] ;

[0063] in, This is the reference maximum temperature of the grid ribs under an ideal, uniform heat source distribution. This is the reference temperature for the cooling water channels; Half the grid length; This represents the weighted total power loss over a single cycle. The equivalent thermal conductivity of the grid reinforcement material.

[0064] S104. Determine the engineering correction factor based on the operation and debugging parameters and the window structure parameters, and perform nonlinear compensation on the reference maximum temperature based on the engineering correction factor to obtain the actual maximum temperature of the grid rib under the actual non-uniform heat source distribution.

[0065] The engineering correction factor reflects the electron beam concentration.

[0066] Specifically, the engineering correction factor is essentially a nonlinear morphological magnification factor (or concentration compensation function). It serves as a mathematical bridge connecting the "ideal computational model" and the "real physical world," directly reflecting the concentration of the electron beam. In actual engineering, the electron beam is not uniformly spread but rather resembles a "searchlight," with extremely high intensity in the center and gradually weakening at the edges (i.e., a Gaussian distribution). The engineering correction factor is used to quantitatively characterize "how many times more concentrated it is in the center compared to the surrounding areas." In the previous step (S103), to pursue computational speed, the heat source was forced to be "flattened," which leads to a lower calculated temperature (flattening the peak value). The role of the engineering correction factor is to act as a "magnifying glass," precisely "pushing up" the flattened "temperature rise baseline" without complex finite element mesh iterations, thereby restoring the true temperature peak. The actual maximum temperature refers to the absolute highest temperature peak (i.e., the most dangerous hot spot temperature) experienced by the physical surface of the electron output window grid ribs in the actual operation of the low-energy electron accelerator.

[0067] In specific implementation, the engineering correction factor is determined based on the operation and debugging parameters and the window structure parameters, including: extracting the normal distribution standard deviation from the operation and debugging parameters and the grid half-length from the window structure parameters; calculating the ratio of the normal distribution standard deviation to the grid half-length to obtain a dimensionless independent variable to characterize the spatial concentration of the electron beam current density; substituting the dimensionless independent variable into a preset quadratic polynomial fitting curve equation for algebraic calculation, and outputting an engineering correction factor that dynamically matches the spatial concentration.

[0068] Specifically, the algorithm reads data from the system's underlying parameter library, precisely extracting two core physical quantities in different dimensions: the standard deviation of the normal distribution from the runtime parameters (reflecting the beam morphology) and the grid half-length from the window structure parameters (reflecting the physical geometric boundary). The ratio of the normal distribution standard deviation to the grid half-length is calculated. Since the length units of the numerator and denominator cancel each other out in the division, the calculated quotient is directly passed to the next level as a dimensionless independent variable. This value is directly used in the algorithm to characterize the current spatial concentration of the electron beam density. The calculated dimensionless independent variable value is directly substituted into the pre-set and fixed quadratic polynomial fitting curve equation within the system (this equation is usually expressed in the background as an explicit algebraic form of y = Ax^2 + Bx + C). Without any iteration, basic exponentiation, multiplication, and addition algebraic operations are directly performed, outputting an engineering correction factor value that dynamically matches the current spatial concentration.

[0069] For example, in one embodiment, the electron beam is concentrated within the grid area, when 2 ≤ At that time, 95% of the beam was concentrated within the grid area; hour, ; The distribution is as follows:

[0070] ;

[0071] in, This is the actual temperature distribution function along the length of the grid ribs; This is the reference temperature for the cooling water channels; This represents the weighted total power loss over a single cycle. The standard deviation is the normal distribution. The equivalent thermal conductivity of the grid reinforcement material; Half the grid length; Vertical spatial coordinates; Horizontal spatial coordinates; This is the Gaussian error function.

[0072] The highest temperature is:

[0073] ;

[0074] in, This represents the actual highest temperature of the grid ribs under a real non-uniform (Gaussian) heat source distribution.

[0075] It should be noted that the expression for the actual maximum temperature, derived from a real non-uniform (Gaussian) heat source distribution, and the expression for the reference maximum temperature, derived from an ideal uniform heat source distribution, have a high degree of structural correlation. Comparison and analytical analysis of their mathematical configurations reveal that the nonlinear temperature rise deviation of the actual maximum temperature compared to the reference maximum temperature (i.e., the local hotspot peak caused by the Gaussian focusing effect of the electron beam), after removing the linear effects of the basic heat load term and boundary constraints, is mathematically determined solely by the beam morphology characteristics (normal distribution standard deviation). ) and grid physical boundary (grid half length) The relative proportion between these two factors is the sole determinant. In other words, the functional mapping network between the actual non-uniformly distributed maximum temperature and the benchmark maximum temperature under an ideal uniform distribution can be completely decoupled and condensed into an independent functional relationship with only the ratio of the normal distribution standard deviation to the grid half-length (i.e., a dimensionless independent variable) as the independent variable. Since this decoupled mathematical relationship exhibits monotonic and smooth nonlinear evolution characteristics within defined physical boundaries, in practical engineering applications, it is unnecessary to repeatedly execute the Gaussian error function during software runtime. The complex transcendental equations involving exponential terms can be calculated, and a high-precision quadratic polynomial fitting curve equation can be constructed in advance for offline calculation to perfectly approximate the mathematical mapping. Based on this technical principle, this application can extract real-time operation and debugging parameters and window structure parameters to construct a dimensionless independent variable to characterize the spatial concentration of electron beam current density, and directly substitute it into the preset quadratic polynomial fitting curve equation for rapid algebraic calculation, thereby determining the engineering correction factor that dynamically matches the current operating state, and finally achieving instantaneous nonlinear compensation for the highest reference temperature.

[0076] The dimensionless independent variable can be expressed as:

[0077] = / ;

[0078] in, It is a dimensionless independent variable; The standard deviation is the normal distribution. It is half the grid length.

[0079] The engineering correction factor can be expressed as:

[0080] ;

[0081] in, For engineering correction factors; It is a dimensionless independent variable.

[0082] Optionally, nonlinear compensation is performed on the reference maximum temperature based on the engineering correction factor to obtain the actual maximum temperature of the grid rib under the actual non-uniform heat source distribution. This includes: calculating the difference between the reference maximum temperature and the reference temperature of the cooling water channel in the operation and debugging parameters to obtain the reference temperature rise of the grid rib under the ideal uniform heat source distribution; multiplying the reference temperature rise by the engineering correction factor to obtain the actual temperature rise under the actual non-uniform heat source distribution; and adding the actual temperature rise to the reference temperature of the cooling water channel to output the actual maximum temperature of the grid rib under the actual non-uniform heat source distribution.

[0083] Specifically, the difference between the reference maximum temperature and the reference temperature of the cooling water channel obtained from the operation and commissioning parameters is calculated to output the reference temperature rise of the grid ribs under an ideal uniform heat source distribution. The calculated reference temperature rise is then multiplied directly by the engineering correction factor determined in the previous steps to output the actual temperature rise under a real non-uniform heat source distribution (Gaussian distribution). Finally, the calculated actual temperature rise is summed with the reference temperature of the cooling water channel to output the actual maximum temperature of the grid ribs under a real non-uniform heat source distribution.

[0084] For example, in one embodiment, the actual maximum temperature of the grid ribs under actual non-uniform heat source distribution can be expressed as:

[0085] ;

[0086] in, This represents the actual highest temperature of the grid ribs under a real non-uniform heat source distribution. This is the reference temperature for the cooling water channels; This represents the weighted total power loss over a single cycle. The equivalent thermal conductivity of the grid reinforcement material; Half the grid length; This is an engineering correction factor.

[0087] S105. Calculate the maximum lateral temperature difference of the window foil in the lateral gap direction based on the single-cycle weighted total loss power, and superimpose the maximum lateral temperature difference with the actual highest temperature to obtain the absolute highest temperature of the electronic output window.

[0088] Specifically, the lateral gap direction refers to the horizontal dimension perpendicular to the length extension direction of the grid ribs, that is, spanning a single grid gap (window foil overhang) and pointing towards the arrangement direction of adjacent grid ribs. If we define the long axis direction of the grid ribs themselves as the "longitudinal direction" (i.e., the one-dimensional coordinate y-axis established earlier), then the "lateral gap direction" is the horizontal axis perpendicular to it (the spatial periodic arrangement direction). In this direction, the window foil (titanium film) spans between two metal grid ribs. Because the window foil is extremely thin and its ends are fixed to the grid ribs, which act as heat sinks, heat is mainly conducted and dissipated within the window foil along this lateral path, from the central overhang area to the grid ribs on both sides.

[0089] The maximum lateral temperature difference refers to the localized maximum temperature rise difference between the highest temperature at the center of the window foil's suspended area and the temperature at the edge of the contact grid ribs along the lateral gap direction. When a low-energy electron beam bombards the window, the window foil in the unobstructed gap area experiences energy loss (secondary energy loss) due to resistance and generates intense heat. Because the window foil (such as micron-sized titanium foil) has a very small lateral thermal conductivity cross-sectional area and high thermal resistance, heat cannot be conducted away instantaneously, resulting in a localized temperature peak accumulating in the very center of the gap (the position furthest from the grid ribs on both sides). Meanwhile, the temperature is relatively lower at the edges of the window foil that are in close contact with the grid ribs due to the efficient water cooling provided by the ribs.

[0090] In specific implementation, based on the single-cycle weighted total loss power and the standard deviation of the normal distribution in the operation and debugging parameters, the peak heat source intensity at the longitudinal normal distribution center axis position of the actual non-uniform heat source is determined; when the grid gap width in the window structure parameters meets the preset distance threshold, the heat source distribution in the transverse gap direction is simplified to a uniform distribution, and the peak heat source intensity is substituted as a constant internal heat source term into the transverse one-dimensional steady-state heat transfer equation; the contact surfaces of the two sides of the transverse gap in the width direction are used as the first boundary condition with zero relative temperature difference, and the transverse geometric symmetry center line is used as the second boundary condition with zero temperature gradient; the transverse one-dimensional steady-state heat transfer equation is solved analytically by quadratic integration to obtain the maximum temperature difference of the window foil at the transverse geometric symmetry center line relative to the contact surfaces of the two grid ribs, and the maximum temperature difference is determined as the transverse maximum temperature difference.

[0091] Optionally, when the normal distribution standard deviation in the running and debugging parameters is within the range of one-half to one-tenth of the grid half length in the window structure parameters, the function value of the Gaussian error function term introduced by the longitudinal normal distribution integral is directly set to a constant 1.

[0092] Specifically, based on the input single-cycle weighted total power loss and the standard deviation of the normal distribution in the operation and debugging parameters, the peak heat source intensity at the longitudinal normal distribution center axis position of the actual non-uniform heat source is directly calculated. The grid gap width in the window structure parameters is automatically extracted and a condition judgment is performed: when the gap width meets a preset distance threshold, the heat source distribution in the transverse gap direction is automatically simplified to a uniform distribution, and the calculated peak heat source intensity is used as a constant internal heat source term, directly substituted into the constructed transverse one-dimensional steady-state heat transfer equation. Before solving the equation, the following two boundary conditions are forcibly applied to the transverse one-dimensional steady-state heat transfer equation: First boundary condition: the relative temperature difference at the two edge contact surfaces (intersection with the grid ribs) of the transverse gap in the width direction is set to zero. Second boundary condition: the temperature gradient at the transverse geometric symmetry center line position is set to zero. Combining the first and second boundary conditions, a quadratic integral analytical solution is performed on the transverse one-dimensional steady-state heat transfer equation substituted with a constant internal heat source. This directly yields the maximum temperature difference at the transverse geometric symmetry centerline of the window foil relative to the contact surfaces of the grid ribs on both sides, and this maximum value is locked and output as the transverse maximum temperature difference. Throughout the entire calculation process, the system monitors the parameter status in real time: if the normal distribution standard deviation in the running and debugging parameters is detected to be exactly within the range of one-half (1 / 2) to one-tenth (1 / 10) of the grid half-length in the window structure parameters, the calculation of the Gaussian error function is directly terminated. The dynamic function value retrieval method directly forces the function value of the Gaussian error term introduced by the longitudinal normal distribution integral to be set as a constant 1 and substituted into the algebraic equation operation.

[0093] For example, in one embodiment, a one-dimensional steady-state heat transfer equation is established for the window foil in the lateral gap direction:

[0094] ;

[0095] in, The function represents the lateral relative temperature difference distribution of the window foil material within the lateral gap relative to the contact surfaces of the grid ribs on both sides. The heat source for the window foil; The thermal conductivity of the window foil material; represents the horizontal spatial coordinates.

[0096] This application considers that the grid gap width of low-energy electron accelerators is usually within a preset distance threshold (e.g., generally less than 5 mm), so the heat source distribution in its lateral arrangement direction can be equivalently simplified to a uniformly distributed constant internal heat source. In order to accurately capture the most dangerous hot spot, this embodiment extracts the peak beam density of the actual non-uniform heat source at the position of the longitudinal normal distribution center axis (i.e., the longitudinal origin y=0), and determines the corresponding peak heat source intensity of the window foil at the center of the axis within a single cycle, and uses it as a constant internal heat source term. Substituting this into the above one-dimensional steady-state heat transport equation, the substitution mapping relationship is specifically expressed as:

[0097] ;

[0098] in, The heat source for the window foil; This represents the weighted total power loss over a single cycle. The standard deviation is the normal distribution. Half the grid length; The Gaussian error function; This represents the first energy loss term of the electron beam on the lattice ribs; This is the second energy loss term when the electron beam passes through the window foil; This refers to the width of the grid reinforcement bars; This refers to the grid spacing width; denoted as the thermal conductivity of the window foil material.

[0099] The lateral relative temperature difference distribution function can be expressed as:

[0100] ;

[0101] in, The function represents the lateral relative temperature difference distribution of the window foil material within the lateral gap relative to the contact surfaces of the grid ribs on both sides. This represents the weighted total power loss over a single cycle. The thermal conductivity of the window foil material; The standard deviation is the normal distribution. Half the grid length; The Gaussian error function; This represents the first energy loss term of the electron beam on the lattice ribs; This is the second energy loss term when the electron beam passes through the window foil; This refers to the width of the grid reinforcement bars; This refers to the grid spacing width; Vertical spatial coordinates; Temperature gradient constraint at the centerline of spatial geometric symmetry; This is the characteristic temperature term located at the center line of spatial geometric symmetry.

[0102] The first boundary condition is: The second boundary condition is: ,at this time:

[0103] ;

[0104] exist ,

[0105] ;

[0106] It should be noted that, The function is in = to When the function value is approximately 1, therefore:

[0107] ;

[0108] in, The function represents the lateral relative temperature difference distribution of the window foil material within the lateral gap relative to the contact surfaces of the grid ribs on both sides. This represents the weighted total power loss over a single cycle. The thermal conductivity of the window foil material; The standard deviation is the normal distribution. Half the grid length; The Gaussian error function; This represents the first energy loss term of the electron beam on the lattice ribs; This is the second energy loss term when the electron beam passes through the window foil; This refers to the width of the grid reinforcement bars; This refers to the grid spacing width; Vertical spatial coordinates; This represents the absolute highest temperature of the window foil under actual non-uniform heat source distribution. This is the reference temperature for the cooling water channels; The total input electron beam current intensity; For engineering correction factors; It is a comprehensive coefficient of structural characteristics related to window geometry and energy loss constant.

[0109] S106. Dynamically adjust the operating parameters of the low-energy electron accelerator according to the absolute maximum temperature.

[0110] Specifically, operating parameters refer to the core physical and controllable variables that are controlled in real time by the low-energy electron accelerator control system and can directly determine or change the electron beam output energy, current distribution, and window thermal load state. Operating parameters include at least the high-voltage accelerating voltage of the low-energy electron accelerator, the total input beam current intensity, the amplitude of the scanning coil excitation current, and the cooling water flow rate of the window water-cooling system.

[0111] In specific implementation, the absolute maximum temperature is compared with a preset safety control threshold in real time; the safety control threshold includes at least a warning temperature control threshold and a cascading shutdown threshold; when the absolute maximum temperature reaches or exceeds the warning temperature control threshold but is less than the cascading shutdown threshold, a real-time derating control command is generated, and at least one adjustment action is executed according to the real-time derating control command; the adjustment action includes reducing the total beam current, increasing the beam transverse scanning width, and increasing the water flow rate in the cooling channel; when the absolute maximum temperature reaches or exceeds the cascading shutdown threshold, the low-energy electron accelerator is controlled to instantly cut off the operating voltage and shut down the beam output.

[0112] Specifically, the control system periodically or in real-time acquires the calculated absolute maximum temperature and compares it with a pre-set safety control threshold online. When the judgment condition is met: the warning temperature control threshold ≤ absolute maximum temperature < interlocking shutdown threshold, the control system automatically generates a real-time derating control command. Based on this derating command, the control hardware is driven to perform at least one of the following adjustment actions: reduce the total beam current: lower the electron beam current intensity to directly reduce the heat input at the source. Increase the beam lateral scanning width: adjust the scanning parameters to make the electron beam spot diffuse more evenly laterally. Increase the cooling water flow rate: improve heat dissipation efficiency by increasing the circulation flow rate of the cooling medium. When the judgment condition is met: the absolute maximum temperature ≥ interlocking shutdown threshold, the system forcibly interrupts the accelerator operation and performs the following interlocking actions: the control hardware instantly cuts off the operating voltage of the low-energy electron accelerator; simultaneously shuts down the accelerator's beam output to completely de-heat the output window, achieving hardware-level safety protection.

[0113] The method provided in this embodiment, in its first aspect, involves real-time acquisition of the accelerator's current operating current intensity, the first energy loss of the electron beam on the grid ribs, and the second energy loss through the window foil. It also integrates the window's three-dimensional spatial geometric configuration parameters, including the grid rib width, gap width, and half-length of the grid ribs. By jointly solving the energy distribution loss equation, the weighted total loss power for a single cycle is calculated. This breaks the limitation of traditional temperature control relying solely on static design parameters or amortized current for rough estimation. It organically integrates the complex physical barrier effect with the real-time dynamic beam bombardment energy degradation, thereby enabling real-time capture of the overall thermal load input closest to the actual physical environment as the accelerator sweeping conditions change. This provides a high-dynamic-fidelity initial heat source data matrix for the subsequent accurate derivation of the full-domain multi-level temperature field.

[0114] Secondly, the calculated single-cycle weighted total power loss is first substituted into a one-dimensional ordinary differential heat conduction degradation model as a constant internal heat source to quickly analyze the highest linear reference temperature of the grid ribs based on the cooling water boundary temperature, stripped of the Gaussian aggregation effect. Based on this, features reflecting the spatial Gaussian distribution aggregation degree of the electron beam are extracted, and an algebraic polynomial engineering correction factor for the beam concentration is constructed. Nonlinear temperature rise superposition compensation is then applied to this reference temperature, thus mapping the actual highest temperature of the grid ribs under actual non-uniform heat source distribution. Mathematically, this method ingeniously avoids the enormous computational overhead and convergence lag caused by directly solving nonlinear partial differential equations containing transcendental Gaussian error functions in the field microprocessor. It cleverly degenerates the complex non-uniform heat conduction solution into microsecond-level elementary operations of "linear base + algebraic correction," perfectly balancing the accuracy of capturing the central peak hotspot of the Gaussian beam spot. It also eliminates the underlying technical barrier that prevents traditional numerical simulations from being used for real-time closed-loop control in industrial settings due to long calculation cycles and severe iteration lags.

[0115] Thirdly, a one-dimensional steady-state heat transfer differential equation in the transverse gap axis direction was independently established. Using zero relative temperature difference at the contact surfaces of the two grid ribs as the first boundary condition and zero temperature gradient along the geometric centerline as the second boundary condition, a quadratic spatial integration was performed to analytically derive the maximum transverse temperature difference at the central axis of the window foil's suspended area. Finally, this maximum transverse temperature difference was linearly superimposed with the aforementioned actual highest temperature of the longitudinal grid ribs across dimensions to lock the absolute highest temperature across the entire electronic output window. In terms of physical heat transfer modeling, a complete understanding of the longitudinal long axis temperature field of the grid ribs and the transverse span temperature field of the window foil was achieved. Spatial decoupling eliminates local omissions and thermal blind spots caused by the interweaving of temperature fields and crosstalk between multiple components. It also deeply matches the true thermodynamic physical nature of the window foil in the suspended bombardment area, where the internal heat source generates heat relative to the water-cooled contact surfaces on both sides, resulting in a secondary spatial temperature rise. The final output absolute maximum temperature can reflect the extreme temperature rise state of the most dangerous point in the weak configuration system of the lead-out window without reservation. This provides an undistorted physical judgment boundary for the final control system to perform active defense actions such as precise reduction of current intensity, expansion of scan width, or millisecond-level interlocking cutoff voltage.

[0116] Corresponding to the aforementioned embodiment of a thermal safety control method for an electron output window of a low-energy electron accelerator, this application also provides an embodiment of a thermal safety control device for an electron output window of a low-energy electron accelerator.

[0117] Figure 3 This is a schematic diagram of the thermal safety control device for the electron output window of a low-energy electron accelerator provided in Embodiment 2 of this application. Please refer to... Figure 3 The apparatus provided in this embodiment includes an acquisition module 210, a determination module 220, a calculation module 230, a compensation module 240, and an adjustment module 250.

[0118] The acquisition module 210 is used to acquire the window structure parameters and operation and debugging parameters of the low-energy electron accelerator.

[0119] The determining module 220 is used to determine the single-cycle weighted total loss power of the electronic output window based on the window structure parameters and the operation and debugging parameters.

[0120] The calculation module 230 is used to substitute the single-cycle weighted total loss power as a known heat source term into the ideal heat conduction degradation model to calculate the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution.

[0121] The compensation module 240 is used to determine an engineering correction factor based on the operating and debugging parameters and the window structure parameters, and to perform nonlinear compensation on the reference maximum temperature based on the engineering correction factor to obtain the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution; the engineering correction factor reflects the electron beam concentration.

[0122] The calculation module 230 is also used to calculate the maximum lateral temperature difference of the window foil in the lateral gap direction based on the single-cycle weighted total loss power, and to superimpose the maximum lateral temperature difference with the actual highest temperature to obtain the absolute highest temperature of the electronic output window.

[0123] The adjustment module 250 is used to dynamically adjust the operating parameters of the low-energy electron accelerator according to the absolute maximum temperature.

[0124] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0125] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0126] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0127] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for thermal safety control of the electron output window of a low-energy electron accelerator, characterized in that, The method includes: Obtain the window structure parameters and operation and debugging parameters of the low-energy electron accelerator; Based on the window structure parameters and the operation and debugging parameters, determine the single-cycle weighted total loss power of the electronic output window; The single-cycle weighted total loss power is substituted into the ideal heat conduction degradation model as a known heat source term to calculate the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution. Based on the operating and debugging parameters and the window structure parameters, an engineering correction factor is determined. Based on the engineering correction factor, nonlinear compensation is performed on the reference maximum temperature to obtain the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution. The engineering correction factor reflects the electron beam concentration. The maximum lateral temperature difference of the window foil in the lateral gap direction is calculated based on the single-cycle weighted total loss power. The maximum lateral temperature difference is then superimposed with the actual highest temperature to obtain the absolute highest temperature of the electronic output window. The operating parameters of the low-energy electron accelerator are dynamically adjusted based on the absolute maximum temperature.

2. The method according to claim 1, characterized in that, Based on the window structure parameters and the operation and debugging parameters, the single-cycle weighted total power loss of the electronic output window is determined, including: Extract the grid rib width and grid gap width from the window structure parameters and use them as the area weighting coefficient of the spatial period. Based on the electron beam current distribution density in the operation and debugging parameters, and combined with the first energy loss term of the electron beam on the grid ribs and the second energy loss term when the electron beam passes through the window foil, the loss power density distribution of the grid ribs and the window foil in a single cycle is determined accordingly. Using the area weighting coefficient, the power loss density distributions of the grid ribs and the window foil are weighted and superimposed according to their spatial proportions within a single grid space period; By combining the total beam current of a single cycle with spatial dimension integral substitution, a quantitative mapping relationship is established between the operation and debugging parameters and the heat source term of the one-dimensional steady-state heat conduction equation, and the weighted total loss power of a single cycle is obtained by solving the equation.

3. The method according to claim 1, characterized in that, Substituting the single-cycle weighted total power loss as a known heat source term into the ideal heat conduction degradation model, the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution is calculated, including: The single-cycle weighted total power loss is equivalent to a constant internal heat source uniformly distributed along the entire length of the grid ribs, and substituted into the one-dimensional steady-state heat transfer equation. The reference temperature of the cooling water channel in the operation and debugging parameters is introduced as the temperature boundary condition of the one-dimensional steady-state heat transfer equation at the contact surface on both sides of the grid rib length direction. The one-dimensional steady-state heat transfer equation containing the constant internal heat source and the temperature boundary conditions is solved by quadratic integration to obtain a quadratic temperature distribution function expressed in elementary algebra. The maximum value of the quadratic temperature distribution function is extracted at the origin of the center of symmetry along the length of the grid rib, and the maximum value is determined as the reference maximum temperature of the grid rib under an ideal uniform heat source distribution.

4. The method according to claim 1, characterized in that, The engineering correction factor is determined based on the running and debugging parameters and the window structure parameters, including: Extract the standard deviation of the normal distribution from the running and debugging parameters, and the grid half-length from the window structure parameters; Calculate the ratio of the standard deviation of the normal distribution to the half length of the grid to obtain a dimensionless independent variable used to characterize the spatial concentration of the electron beam current density; The dimensionless independent variable is substituted into the preset quadratic polynomial fitting curve equation for algebraic calculation, and an engineering correction factor that dynamically matches the spatial concentration is output.

5. The method according to claim 1, characterized in that, Based on the engineering correction factor, nonlinear compensation is performed on the reference maximum temperature to obtain the actual maximum temperature of the grid ribs under actual non-uniform heat source distribution, including: Calculate the difference between the highest reference temperature and the reference temperature of the cooling water channel in the operation and debugging parameters to obtain the reference temperature rise of the grid ribs under an ideal uniform heat source distribution; Multiply the reference temperature rise by the engineering correction factor to obtain the actual temperature rise under the actual non-uniform heat source distribution; The actual temperature rise is added to the reference temperature of the cooling water channel to output the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution.

6. The method according to claim 1, characterized in that, The maximum lateral temperature difference of the window foil in the lateral gap direction is calculated based on the single-cycle weighted total power loss, including: Based on the single-cycle weighted total loss power and the normal distribution standard deviation in the operation and debugging parameters, determine the peak heat source intensity of the actual non-uniform heat source at the position of the longitudinal normal distribution central axis. When the grid gap width in the window structure parameters meets the preset distance threshold, the heat source distribution in the transverse gap direction is simplified to a uniform distribution, and the peak heat source intensity is substituted as a constant internal heat source term into the transverse one-dimensional steady-state heat transfer equation. The contact surfaces of the two edges of the transverse gap in the width direction are used as the first boundary condition for a relative temperature difference of zero, and the transverse geometric symmetry center line is used as the second boundary condition for a temperature gradient of zero. The horizontal one-dimensional steady-state heat transfer equation is solved analytically by quadratic integration to obtain the maximum temperature difference between the window foil and the contact surfaces of the grid ribs on both sides at the horizontal geometric symmetry center line. The maximum temperature difference is determined as the horizontal maximum temperature difference.

7. The method according to claim 6, characterized in that, The method further includes: When the standard deviation of the normal distribution in the running and debugging parameters is within the range of one-half to one-tenth of the grid half length in the window structure parameters, the function value of the Gaussian error function term introduced by the longitudinal normal distribution integral is directly set to a constant 1.

8. The method according to claim 1, characterized in that, Dynamically adjusting the operating parameters of the low-energy electron accelerator based on the absolute maximum temperature includes: The absolute maximum temperature is compared with a preset safety control threshold in real time; the safety control threshold includes at least an early warning temperature control threshold and an interlocking shutdown threshold. When the absolute maximum temperature reaches or exceeds the warning temperature control threshold but is less than the interlock shutdown threshold, a real-time derating control command is generated, and at least one adjustment action is executed according to the real-time derating control command; the adjustment action includes reducing the total beam current, increasing the beam transverse scanning width, and increasing the water flow rate in the cooling channel. When the absolute maximum temperature reaches or exceeds the interlocking shutdown threshold, the low-energy electron accelerator is controlled to instantly cut off the operating voltage and shut down the beam output.

9. The method according to claim 1, characterized in that, The window structure parameters include the grid rib width, grid gap width, grid half length, total length of the electron output window, and window foil thickness; the operation and debugging parameters include the operating voltage of the low-energy electron accelerator, total beam current, reference temperature of the cooling water channel, electron beam current distribution density, and the standard deviation of the normal distribution fitted by the electron beam current distribution density.

10. A thermal safety control device for the electron output window of a low-energy electron accelerator, characterized in that, The device includes an acquisition module, a determination module, a calculation module, a compensation module, and an adjustment module; The acquisition module is used to acquire the window structure parameters and operation and debugging parameters of the low-energy electron accelerator. The determining module is used to determine the single-cycle weighted total loss power of the electronic output window based on the window structure parameters and the operation and debugging parameters. The calculation module is used to substitute the single-cycle weighted total loss power as a known heat source term into the ideal heat conduction degradation model to calculate the reference maximum temperature of the grid ribs under an ideal uniform heat source distribution. The compensation module is used to determine an engineering correction factor based on the operating and debugging parameters and the window structure parameters, and to perform nonlinear compensation on the reference maximum temperature based on the engineering correction factor to obtain the actual maximum temperature of the grid ribs under the actual non-uniform heat source distribution; the engineering correction factor reflects the electron beam concentration. The calculation module is also used to calculate the maximum lateral temperature difference of the window foil in the lateral gap direction based on the single-cycle weighted total loss power, and to superimpose the maximum lateral temperature difference with the actual maximum temperature to obtain the absolute maximum temperature of the electronic output window. The adjustment module is used to dynamically adjust the operating parameters of the low-energy electron accelerator based on the absolute maximum temperature.

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