Calculation Method for Increment of Emitter Work Function Based on Hollow Cathode Dark Current

Abstract

A method for calculating the increment of the emitter work function based on the hollow cathode dark current proposed in this application keeps the temperature of the hollow cathode in the initial state constant and makes the temperature of the tungsten tip remain unchanged; an extraction electric field is applied to the emitter in the initial state, and an image of the square of the magnitude of the electric field strength versus the natural logarithm of the extraction current at the corresponding electric field strength is plotted, and the obtained image is linearly fitted to obtain the intercept of the emitter initial state image; the intercept of the emitter current state image in the current state of the emitter is obtained by the same method; furthermore, the intercept increment between the current state and the initial state of the emitter is obtained, and the emitter work function increment is obtained according to the intercept increment; the influence of the cathode structure factor on the measurement of the work function increment is excluded by calculating the intercept increment; the dark current discharge state of the cathode is used as the standard state to calculate the emitter work function, excluding the influence of gas discharge on the work function measurement; this method can be used to evaluate the increment of the emitter work function of the electric propulsion system in orbit.

Description

Technical Field

[0001] The present invention belongs to the technical field of calculating the work function increment of an emitter, and particularly relates to a method for calculating the work function increment of an emitter based on the hollow cathode dark current. Background Art

[0002] The space electric thruster adopts a propulsion mode of gas ionization and ion electrostatic acceleration, which has the advantages of high jet velocity and high specific impulse compared with the traditional chemical propulsion, and can greatly save the fuel of the thruster. The hollow cathode is the core component of the electric propulsion product and has a great impact on the reliability of the thruster. The hollow cathode continuously provides seed electrons for the thruster to maintain discharge through the thermionic emission effect occurring 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 all electrons required for the cathode discharge process. Therefore, the cathode state often determines whether the electric propulsion can maintain normal discharge and whether it can meet the requirements of the satellite for thrust and potential. The emitter is an important component of the hollow cathode, and the emitter determines the state of the hollow cathode. To ensure the stable operation of the hollow cathode, it is necessary to judge the state of the emitter. The traditional method of simply judging the state of the emitter based on the cathode discharge voltage is unreliable. There are problems of multi-parameter interference in the increase of the hollow cathode discharge voltage. Often, the increase of the cathode discharge voltage is not only related to the state of the emitter, but the erosion of the tungsten top hole of the cathode is also one of the important reasons for the increase of 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 property parameter that reflects the strength of the ability of the material surface to bind electrons. The increase of the emitter work function will cause insufficient electron emission of the cathode and unstable cathode operation, resulting in the thruster deviating from the design operating point and showing abnormal phenomena. The thermionic emission of the emitter material and the work function conform to the Richardson-Dushman equation. In theory, the work function of the emitter state at this time can be directly calculated by measuring the thermionic emission current. However, it is found in the experiment that the critical temperature of the thermionic emission electron generation temperature of the emitter during the plasma discharge process is lower than the theoretical value, which leads to a lower calculated work function value. The reason for the critical temperature of the thermionic emission electron generation temperature being lower than the theoretical value is unknown. Therefore, the work function value cannot be calculated during the hollow cathode plasma discharge process. Considering the complex structure inside the hollow cathode, the thermionic electrons emitted from the emitter surface will be absorbed by the emitter itself or the tungsten top again. There is a thermionic emission current correction coefficient in the Richardson-Dushman equation, and different cathode structures will result in differences in the thermionic emission current correction coefficient. Therefore, the emitter work function cannot be directly calculated by the Richardson-Dushman equation, and thus the state of the hollow cathode cannot be effectively evaluated. Summary of the Invention

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

[0005] A method for calculating the work function increment of an emitter based on the hollow cathode dark current includes:

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

[0007] Step 2: Apply an extraction electric field to the emitter in the initial state, change the electric field strength of the extraction electric field, and measure the corresponding extraction current at different electric field strengths; plot the correspondence between the square root of the electric field strength magnitude and the natural logarithm value of the corresponding extraction current, and perform linear fitting on the obtained correspondence to obtain the fitting curve of the emitter in the initial state;

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

[0009] Step 4: Heat the hollow cathode in the current state until the temperature of the hollow cathode is constant at T y , and keep the temperature of the tungsten tip unchanged after the temperature of the hollow cathode is constant; obtain the intercept of the fitting curve of the emitter in the current state of the emitter according to Step 2 and Step 3; the initial state and the current state are respectively two different lifetime states after abnormal discharge of the hollow cathode;

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

[0011] Beneficial effects

[0012] A method for calculating the work function increment of an emitter based on the hollow cathode dark current proposed in this application keeps the temperature of the hollow cathode in the initial state constant and keeps the temperature of the tungsten tip unchanged; an extraction electric field is applied to the emitter in the initial state, and an image of the square root of the magnitude of the electric field strength and the natural logarithm of the extraction current corresponding to the corresponding electric field strength is plotted, and the obtained image is linearly fitted to obtain the intercept of the emitter in the initial state image; the intercept of the emitter in the current state of the emitter is obtained by the same method; furthermore, the intercept increment between the current state and the initial state of the emitter is obtained, and the work function increment of the emitter is obtained according to the intercept increment; the influence of the cathode structure factor on the measurement of the work function increment is excluded by calculating the intercept increment; from the perspective of the accuracy of calculating the emitter work function, the cathode being in the dark current discharge state is used as the standard state to calculate the emitter work function, and the influence of gas discharge on the work function measurement is excluded; this method can be used to evaluate the work function increment of the on-orbit emitter of the electric propulsion system. Description of the Drawings

[0013] Figure 1 It is a flowchart of the method for calculating the work function increment of the emitter based on the hollow cathode dark current in the specific embodiment of this application. Specific Embodiment

[0014] The following will be combined with Figure 1 to illustrate this embodiment. This application is mainly applicable to the calculation of the work function of the hollow cathode emitter. There are multiple parameter interferences in the abnormal discharge of the hollow cathode. First, it is necessary to comprehensively judge whether the abnormal discharge of the hollow cathode is related to the work function of the emitter through parameters such as the 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 in the work function of the emitter, this method can be used to calculate the work function increment.

[0015] A method for calculating the work function increment of an emitter based on the hollow cathode dark current includes:

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

[0017] Heat the hollow cathode within the allowable range of the hollow cathode ignition condition. During this process, the hollow cathode is not supplied with gas, wait for the temperature of the hollow cathode to be constant, measure the temperature of the tungsten tip, and keep the same tungsten tip temperature during the subsequent measurement of the thermal emission current of the emitter.

[0018] Step 2: Apply an extraction electric field to the emitter in the initial state, change the electric field strength of the extraction electric field, and measure the corresponding extraction current at different electric field strengths; plot the corresponding relationship between the square root of the magnitude of the electric field strength and the natural logarithm of the corresponding extraction current, and linearly fit the obtained corresponding relationship to obtain the fitting curve of the emitter in the initial state;

[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 influence of thermally emitted electrons on the electric field can be ignored. Therefore, the electric field inside the hollow cathode is approximately considered 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. According to the experimental data, plot the corresponding relationship, and make a linear fit to the corresponding relationship to obtain the fitting curve of the initial state of the emitter.

[0020] Step 3: Obtain the intercept of the fitting curve of the initial state of the emitter according to the obtained fitting curve of the initial state 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 , and keep the temperature of the tungsten tip unchanged after the temperature of the hollow cathode is constant; obtain the intercept of the fitting curve of the current state of the emitter according to Step 2 and Step 3; the initial state and the current state are two different lifetime states after abnormal discharge of the hollow cathode;

[0022] Heat the hollow cathode in the current state to make the temperature of the hollow cathode constant at T y , measure the temperature of the tungsten tip, and keep the temperature of the tungsten tip unchanged to 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 intercept of the emitter state curve is also different;

[0023] Step 5: Obtain the intercept increment of the emitter from the initial state to the current state according to 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 of the emitter from the initial state to the current state according to the intercept increment.

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

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

[0026]

[0027] where I e is the extraction current, D is the correction coefficient of thermionic emission current, A is the thermionic emission constant, which is 1204000 A·m -2 ·K -2 ; S is the effective emission area of the emitter, T is the temperature of the emitter, with the unit of 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 strength, ε0 is the vacuum permittivity, and e is the natural constant; since it is difficult to measure the temperature of the emitter, in actual operation, the constant tungsten top temperature is used to replace the emitter temperature.;

[0028] According to the thermionic emission principle of the hot cathode, the thermionic emission of the emitter material and the work function conform to the Richardson-Dushman equation, that is J e is the thermionic emission current density, with the unit of A·m -2 ; In theory, the work function of the emitter at this state can be directly calculated by measuring the thermionic emission current. However, the spatial scale of the hollow cathode structure is relatively large, and it is impossible to effectively collect the electrons emitted by the material relying on the free movement of thermoelectrons. Therefore, an external electric field is needed to extract the thermionic electrons of the emitter. The Richardson-Dushman equation is the thermionic emission of the material under zero electric field. When there is an electric field on the cathode surface, it will reduce the work function of the material, and this effect is called the Schottky effect.

[0029] Under the action of the extraction electric field, the density formula of the extracted current of the emitter is:

[0030]

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

[0032] Considering the problem that the unknown effect during the hollow cathode plasma discharge causes the temperature required for the actual electron emission of the cathode to be lower than the theoretical value, the plasma discharge of the hollow cathode should be avoided when calculating the work function through the thermionic emission current of the emitter. Therefore, when the hollow cathode is not supplied with gas, the emitter is heated so that there are only thermionic electrons and no other charged particles - dark current in the hollow cathode cavity. At this time, it can be approximately considered that this effect on the thermionic electrons is eliminated.

[0033] Regarding the problem that it is difficult to determine the correction coefficient of the thermionic emission current, according to the conclusion obtained from the expression of the natural logarithm of the extracted current, when W f1 is constant, lnI e is linearly correlated with , and the intercept of this function is a constant related to W f1 . The structure of the same cathode basically does not change much during use. Therefore, it can be considered that the D (correction coefficient of thermionic emission current) of the same cathode is the same. When the temperature remains unchanged, the change in the work function of the emitter will only change the intercept of the fitting 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, and W f2 is the work function of the emitter in the current state.

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

[0037] Specifically, the emitter work function increment can be calculated through the intercept increment, avoiding inaccurate determination of the emitter state caused by errors in calculating the work function of the emitter state through the thermionic emission current.

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

[0039] Further, the electric field strength of the extraction electric field applied to the emitter > 50 V / m.

Claims

1. A method for calculating the increment of emitter work function based on hollow cathode dark current, characterized in that: including Step 1: Heat the hollow cathode in its initial state until the temperature of the hollow cathode is constant at T y , and keep the temperature of the tungsten tip unchanged after the temperature of the hollow cathode becomes constant; Step 2: Apply an extraction electric field to the emitter in the initial state, change the electric field strength of the extraction electric field, and measure the corresponding extraction current at different electric field strengths; Plot the correspondence between the square root of the electric field strength magnitude and the natural logarithm value of the corresponding extraction current, perform a linear fit on the obtained correspondence, and obtain the initial state fitting curve of the emitter; Step 3: Obtain 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, keep the temperature of the tungsten tip unchanged; obtain the intercept of the emitter current state fitting curve of the emitter in the current state according to Step 2 and Step 3; the initial state and the current state are two different life states after abnormal discharge of the hollow cathode; Step 5: Obtain the intercept increment of the emitter from the initial state to the current state according to the intercept of the initial state fitting curve of the emitter and the intercept of the current state fitting curve of the emitter, and obtain the work function increment of the emitter from the initial state to the current state according to the intercept increment; 2. The method for calculating the work function increment of an emitter based on the hollow cathode dark current according to claim 1, wherein: The expression of the extraction current corresponding to the emitter in the initial state under the extraction electric field strength is: Among them, I e is the extraction current, D is the correction coefficient of thermionic emission current, A is the thermionic 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, ε0 is the vacuum permittivity, and e is the natural constant.

3. The method for calculating the work function increment of an emitter based on the hollow cathode dark current according to claim 2, characterized in that: The expression for the natural logarithm of the extraction current corresponding to the emitter in the initial state under the electric field strength is: where D is the correction coefficient of thermionic emission current, A is the thermionic 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 temperature of the emitter, ε0 is the vacuum permittivity, and W f1 is the work function of the emitter in the initial state.

4. The method for calculating the work function increment of an emitter based on the hollow cathode dark current according to claim 1, wherein: 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 work function of the emitter in the current state, D is the correction coefficient of the thermionic emission current, A is the thermionic emission constant, S is the effective emission area of the emitter, T is the temperature of the emitter, k B is the Boltzmann constant.

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

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

7. A method for calculating the work function increment of an emitter based on the hollow cathode dark current according to claim 1, characterized in that: Hollow cathode constant temperature T y ≥ 1100 degrees Celsius.

8. A method for calculating the work function increment of an emitter based on the hollow cathode dark current according to claim 1, characterized in that: The electric field strength of the induced electric field > 50 V·m -1 .

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