Emitter work function increment calculation method based on hollow cathode dark current

Abstract

According to the hollow cathode dark current-based emitter work function increment calculation method provided by the invention, the temperature of a hollow cathode in an initial state is kept constant, and the temperature of a tungsten top is kept unchanged; applying an extraction electric field to the emitter in the initial state, drawing an image of the square of the intensity of the electric field and the natural logarithm value of the extraction current under the corresponding intensity of the electric field, and performing linear fitting on the obtained image to obtain the image intercept of the initial state of the emitter; obtaining the current state image intercept of the emitter in the current state through the same method; obtaining the intercept increment of the current state and the initial state of the emitter, and obtaining the work function increment of the emitter according to the intercept increment; the influence of a cathode structure factor on work function increment measurement is eliminated through a method of calculating intercept increment; an emitter work function is calculated by taking a cathode in a dark current discharge state as a standard state, and the influence of gas discharge on work function measurement is eliminated; the method can be used for evaluating the on-orbit emitter work function increment of the electric propulsion system.

Description

Technical Field

[0001] The invention belongs to the technical field of emitter work function increment calculation, and in particular relates to an emitter work function increment calculation method based on hollow cathode dark current. Background Art

[0002] Space electric thrusters use gas ionization and ion electrostatic acceleration to propel space propulsion. Compared with traditional chemical propulsion, they have the advantages of high jet speed and high specific impulse, which can greatly save thruster fuel. The hollow cathode is the core component of electric propulsion products and has a huge impact on the reliability of thrusters. The hollow cathode continuously provides seed electrons for the thruster to maintain discharge through the thermal electron emission effect that occurs at high temperatures, and at the same time provides an equal amount of neutralizing electrons for the ejected positive ion beam. It is the source of electrons required for all cathode discharge processes. Therefore, the cathode state often determines whether the electric propulsion can maintain normal discharge and whether it can meet the satellite's thrust and potential requirements. The emitter is an important component of the hollow cathode. The emitter determines the state of the hollow cathode. In order to ensure the stable operation of the hollow cathode, the state of the emitter needs to be judged. The traditional method of judging the state of the emitter based solely on the cathode discharge voltage is unreliable. The increase in the discharge voltage of the hollow cathode has the problem of multi-parameter interference. Often, the increase in the cathode discharge voltage is not only related to the state of the emitter, but the erosion of the cathode tungsten top hole is also one of the important reasons for the cathode discharge voltage.

[0003] To evaluate the state of the hollow cathode, a very important parameter is the work function of the emitter. The work function is a physical parameter that indicates the ability of the material surface to bind electrons. The increase in the work function of the emitter will cause insufficient electron emission from the cathode and instability in the cathode operation, which will cause the thruster to deviate from the design operating point and cause abnormal phenomena. The relationship between the thermal electron emission and the work function of the emitter material conforms to the Richardson-Dushman equation. In theory, the work function of the emitter at this time can be directly calculated by measuring the thermal emission current. However, it was found in the experiment that the critical temperature of the emitter generating thermal emission electrons during the plasma discharge process is lower than the theoretical value, which leads to a low calculated work function value. The reason why the critical temperature of the thermal emission electron temperature is lower than the theoretical value is unknown, so the work function value cannot be calculated during the hollow cathode plasma discharge process. Considering the complex structure inside the hollow cathode, the thermal electrons emitted from the emitter surface will be absorbed again by the emitter itself or the tungsten top. There is a thermal emission current correction coefficient in the Richardson-Dushman equation. Different cathode structures will lead to differences in the thermal emission current correction coefficient. Therefore, the emitter work function cannot be directly calculated by the Richardson-Dushman equation, and the hollow cathode state cannot be effectively evaluated. Summary of the invention

[0004] In order to solve the problem in the prior art that the emitter work function cannot be calculated, resulting in the inability to effectively evaluate the emitter state, the present application proposes a method for calculating the emitter work function increment based on the hollow cathode dark current, calculates the emitter work function increment, and evaluates the emitter performance through the emitter work function increment.

[0005] A method for calculating the emitter work function increment based on hollow cathode dark current, comprising:

[0006] Step 1: Heat the hollow cathode in the initial state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top remains constant;

[0007] Step 2: applying an extraction electric field to the emitter in the initial state, changing the electric field strength of the extraction electric field, and measuring the corresponding extraction current under different electric field strengths; plotting the corresponding relationship between the square root of the electric field strength and the corresponding natural logarithm of the extraction current, performing linear fitting on the obtained corresponding relationship, and obtaining a fitting curve of the initial state of the emitter;

[0008] Step 3: Obtaining the intercept of the initial state fitting curve of the emitter according to the obtained initial state fitting curve of the emitter;

[0009] Step 4: Heat the hollow cathode in the current state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top is kept constant; according to step 2 and step 3, the intercept of the current state fitting curve of the emitter of the current state emitter is obtained; the initial state and the current state are two different life states after the abnormal discharge of the hollow cathode;

[0010] Step 5: Obtain the intercept increment from the initial state to the current state of the emitter based on the intercept of the fitting curve of the initial state of the emitter and the intercept of the fitting curve of the current state of the emitter, and obtain the work function increment from the initial state to the current state of the emitter based on the intercept increment.

[0011] Beneficial Effects

[0012] The present application proposes a method for calculating the increment of the work function of an emitter based on the dark current of a hollow cathode, which keeps the temperature of the hollow cathode in the initial state constant and keeps the temperature of the tungsten top constant; applies an extraction electric field to the emitter in the initial state, plots the square root of the electric field intensity and the natural logarithm of the extraction current under the corresponding electric field intensity, performs linear fitting on the obtained image, and obtains the intercept of the image of the initial state of the emitter; obtains the intercept of the image of the current state of the emitter in the current state of the emitter by the same method; then obtains the intercept increment of the current state and the initial state of the emitter, and obtains the work function increment of the emitter based on the intercept increment; eliminates the influence of cathode structure factors on the measurement of the work function increment by calculating the intercept increment; from the perspective of the accuracy of the calculation of the emitter work function, uses the cathode in the dark current discharge state as the standard state to calculate the emitter work function, and eliminates the influence of gas discharge on the work function measurement; this method can be used to evaluate the work function increment of the on-orbit emitter of the electric propulsion system. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of a method for calculating the emitter work function increment based on hollow cathode dark current according to a specific implementation of the present application. DETAILED DESCRIPTION

[0014] The following will be combined Figure 1 , explaining this implementation mode, this application is mainly applicable to the calculation of the work function of hollow cathode emitters. There are multiple parameter interferences in the abnormal discharge of hollow cathodes. First, it is necessary to comprehensively judge whether the abnormal discharge of hollow cathodes is related to the work function of the emitter through parameters such as hollow cathode temperature, voltage oscillation, current oscillation, cathode gas pressure, and discharge voltage. If it is determined that the cathode abnormality is caused by the increase of the emitter work function, this method can be used to calculate the work function increment.

[0015] A method for calculating the emitter work function increment based on hollow cathode dark current, comprising:

[0016] Step 1: Heat the hollow cathode in the initial state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top remains constant;

[0017] Heat the hollow cathode within the range allowed by the hollow cathode ignition conditions. During this process, the hollow cathode is not supplied with gas. Wait for the hollow cathode temperature to become constant, measure the tungsten top temperature, and maintain the same tungsten top temperature during the subsequent measurement of the emitter thermal emission current.

[0018] Step 2: applying an extraction electric field to the emitter in the initial state, changing the electric field strength of the extraction electric field, and measuring the corresponding extraction current under different electric field strengths; plotting the corresponding relationship between the square root of the electric field strength and the corresponding natural logarithm of the extraction current, performing linear fitting on the obtained corresponding relationship, and obtaining a fitting curve of the initial state of the emitter;

[0019] Turn on the hollow cathode ignition power supply and apply an extraction electric field to the emitter. Since there is no plasma environment around the emitter, the effect of thermal emission electrons on the electric field can be ignored. Therefore, the electric field inside the hollow cathode is approximately considered to be a uniform electric field. By changing different ignition voltages, the electric field strength of the extraction electric field is changed, and the corresponding extraction current is measured. The experimental data is plotted. The corresponding relationship and A linear fit is made based on the corresponding relationship to obtain the fitting curve of the initial state of the emitter.

[0020] Step 3: Obtaining the intercept of the initial state fitting curve of the emitter according to the obtained initial state fitting curve of the emitter;

[0021] Step 4: Heat the hollow cathode in the current state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top is kept constant; according to step 2 and step 3, the intercept of the current state fitting curve of the emitter of the current state emitter is obtained; the initial state and the current state are two different life states after the abnormal discharge of the hollow cathode;

[0022] Heat the hollow cathode in the current state to keep the temperature of the hollow cathode constant at T y , measure the tungsten top temperature, keep the tungsten top temperature constant, and ensure that the hollow cathode in the initial state and the hollow cathode in the current state are constant at the same temperature; the emitter state is different, and the emitter state curve intercept is also different;

[0023] Step 5: Obtain the intercept increment from the initial state to the current state of the emitter based on the intercept of the fitting curve of the initial state of the emitter and the intercept of the fitting curve of the current state of the emitter, and obtain the work function increment from the initial state to the current state of the emitter based on the intercept increment.

[0024] Specifically, the intercept increment is calculated according to the curve intercepts of the emitter in different states; and the work function increment of the current state of the emitter compared with the initial state is calculated according to the intercept increment.

[0025] Furthermore, the expression of the corresponding extraction current under different electric field strengths is:

[0026]

[0027] Among them, I e is the extraction current, D is the thermal emission current correction factor, and A is the thermal emission constant, which is 1204000A·m -2 ·K -2 ; is the effective emission area of ​​the emitter, T is the emitter temperature, unit is K; W f1 is the work function of the emitter in the initial state, k Bis the Boltzmann constant, which is 1.38·J·K -1 ; E is the electric field intensity, ε0 ​​is the vacuum dielectric constant, and e is the natural constant; Since the emitter temperature is difficult to measure, in actual operation, the constant tungsten top temperature is used instead of the emitter temperature. ;

[0028] According to the principle of thermal electron emission of hot cathodes, the relationship between thermal electron emission and work function of the emitter material conforms to the Richardson-Dushman equation, that is, J e is the thermal emission current density, in A·m -2 Theoretically, the work function of the emitter at this time can be calculated directly by measuring the thermal emission current. However, the hollow cathode structure has a large spatial scale, and the electrons emitted by the material cannot be effectively collected by relying on the free movement of thermal electrons. Therefore, an external electric field is required to induce the thermal emission electrons of the emitter. The Richardson-Dushman equation is the thermal electron emission of the material under zero electric field. When there is an electric field on the cathode surface, the work function of the material will be reduced. This effect is called the Schottky effect.

[0029] When the emitter is subjected to the extraction electric field, the density formula of the extraction current is:

[0030]

[0031] Furthermore, the formula for the natural logarithm of the extracted current is:

[0032] Taking into account the problem that the temperature required for actual electron emission from the cathode is lower than the theoretical value due to unknown effects during hollow cathode plasma discharge, hollow cathode plasma discharge should be avoided when calculating the work function through the thermal emission current of the emitter. Therefore, the emitter is heated when the hollow cathode is not supplied with gas, so that only thermally emitted electrons exist in the hollow cathode cavity without other charged particles - dark current. At this time, it can be approximately considered that the influence of this effect on thermally emitted electrons is eliminated.

[0033] As for the problem that the thermal emission current correction coefficient is difficult to determine, according to the conclusion drawn from the natural logarithm expression of the extraction current, when W f1 When a certain time, lnI e and There is a linear relationship between them, and the intercept of this function is W f1 The structure of the same cathode will not change much during use, so it can be considered that the D (thermal emission current correction factor) of the same cathode is the same. When the temperature remains unchanged, the work function of the emitter will only change The intercept of the fitted image.

[0034] Furthermore, the expression of the intercept increment between the current state and the initial state of the emitter is:

[0035] Where Δb is the intercept difference, W f2 It is the work function of the emitter in the current state.

[0036] Furthermore, the calculation formula for the emitter work function increment is obtained according to the intercept increment: ΔW = k B TΔb,k B is the Boltzmann constant, which is 1.38·J·K -1 .

[0037] Specifically, the emitter work function increment can be calculated by intercept increment, so as to avoid inaccurate emitter state judgment caused by errors in calculating the work function of the emitter state through thermal emission current.

[0038] Furthermore, the hollow cathode constant temperature T y ≥1100 degrees Celsius.

[0039] Furthermore, the extraction electric field strength applied to the emitter is greater than 50 V / m.

Claims

1. A method for calculating the emitter work function increment based on hollow cathode dark current, Features: include Step 1: Heat the hollow cathode in the initial state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top remains constant; Step 2: applying an extraction electric field to the emitter in the initial state, changing the electric field strength of the extraction electric field, and measuring the corresponding extraction current under different electric field strengths; The corresponding relationship between the square root of the electric field intensity and the corresponding natural logarithm of the extraction current is plotted, and a linear fit is performed on the obtained corresponding relationship to obtain a fitting curve of the initial state of the emitter; Step 3: Obtaining the intercept of the initial state fitting curve of the emitter according to the obtained initial state fitting curve of the emitter; Step 4: Heat the hollow cathode in the current state until the temperature of the hollow cathode is constant at T y , after the temperature of the hollow cathode is constant, the temperature of the tungsten top is kept constant; according to step 2 and step 3, the intercept of the current state fitting curve of the emitter of the current state emitter is obtained; the initial state and the current state are two different life states after the abnormal discharge of the hollow cathode; Step 5: Obtain the intercept increment from the initial state to the current state of the emitter based on the intercept of the fitting curve of the initial state of the emitter and the intercept of the fitting curve of the current state of the emitter, and obtain the work function increment from the initial state to the current state of the emitter based on the intercept increment.

2. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 1, Features: The expression of the corresponding extraction current of the emitter in the initial state under the extraction electric field strength is: Among them, I e is the extraction current, D is the thermal emission current correction coefficient, A is the thermal emission constant, S is the effective emission area of ​​the emitter, T is the emitter temperature, W f1 is the work function of the emitter in the initial state, k B is the Boltzmann constant, E is the extraction electric field strength, ε 0 is the dielectric constant of vacuum, and e is a natural constant.

3. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 2, Features: The expression of the natural logarithm of the lead-out current corresponding to the electric field strength of the emitter in the initial state is: Where D is the thermal emission current correction coefficient, A is the thermal emission constant, S is the effective emission area of ​​the emitter, k B is the Boltzmann constant, E is the extraction electric field strength, T is the emitter temperature, ε 0 is the vacuum dielectric constant, W f1 is the work function of the emitter in the initial state.

4. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 1, Features: The expression of the intercept increment between the current state and the initial state of the emitter is: Where Δb is the intercept increment, W f1 is the work function of the emitter in the initial state, W f2 is the current state emitter work function, D is the thermal emission current correction coefficient, A is the thermal emission constant, S is the effective emission area of ​​the emitter, T is the emitter temperature, k B is the Boltzmann constant.

5. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 4, Features: The calculation formula for the work function increment of the emitter from the initial state to the current state is obtained according to the intercept increment: ΔW = k B TΔb, ΔW is the work function increment of the emitter from the initial state to the current state, T is the emitter temperature, k B is the Boltzmann constant.

6. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 5, Features: Boltzmann constant k B Take 1.38 J·K -1 .

7. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 1, Features: Hollow cathode constant temperature T y ≥1100 degrees Celsius.

8. The method for calculating the emitter work function increment based on hollow cathode dark current according to claim 1, Features: The extraction electric field strength is > 50 V·m -1 .

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