CN108009386B - Optimization design method for aperture of hollow cathode holding electrode - Google Patents

Optimization design method for aperture of hollow cathode holding electrode Download PDF

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CN108009386B
CN108009386B CN201711488117.9A CN201711488117A CN108009386B CN 108009386 B CN108009386 B CN 108009386B CN 201711488117 A CN201711488117 A CN 201711488117A CN 108009386 B CN108009386 B CN 108009386B
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aperture
touch electrode
electrode
minimum
hollow cathode
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宁中喜
孟天航
于达仁
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Harbin Institute of Technology
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Abstract

An optimization design method for the aperture of a hollow cathode touch electrode relates to the field of aerospace electric propulsion hollow cathodes, and aims to solve the problems that the existing optimization for the aperture of the touch electrode lacks theoretical guidance, only samples of different sizes can be adopted to carry out experiments one by one, the workload is large, and the reliability is poor. The method is to measure the magnetic field intensity near the contact minimum hole; calculating the electron cyclotron Larmor diameter to obtain the minimum value of the aperture of the touch pole; and measuring a throttling and boosting curve of the aperture of the touch electrode and the air pressure, obtaining the minimum air pressure according to the criterion condition of ionization stability, wherein the aperture of the touch electrode corresponding to the minimum air pressure is the maximum value of the aperture of the touch electrode, selecting a numerical value between the minimum value and the maximum value of the aperture of the touch electrode, preparing a sample of the aperture of the touch electrode, and testing the discharge performance, wherein the aperture of the touch electrode when the discharge performance is optimal is the optimal aperture of the touch electrode. The method is suitable for optimally designing the aperture of the touch electrode.

Description

Optimization design method for aperture of hollow cathode holding electrode
Technical Field
The invention relates to the field of aerospace electric propulsion hollow cathodes.
Background
The Hall thruster is an aerospace propulsion device which realizes particle acceleration by means of low-temperature plasma discharge. As with low temperature plasma discharges in various other industries, the discharge characteristics of hall thrusters are very sensitive to the geometry of the component parts. Determining these dimensions requires a priori knowledge of the numerous and complex plasma effects, and design by physical criteria. Since a strong electric field establishment mechanism in the Hall thruster has certain subversion on the traditional theory, main research energy is put into a main body discharge channel and relatively little input is put into a peripheral auxiliary structure since half a century.
As a negative electrode of the plasma discharge, the hollow cathode is called "heart of hall thruster". However, due to subjective reasons in part of history and reasons such as too compact and narrow structure and difficulty in fine experiments, physical effects in the hollow cathode still have a lot of dead zones. As one of the most important dimensions of a hollow cathode, the pore size of the anode has not been designed by theoretical guidance at present. The international common practice is "trial and error", i.e. preparing samples of multiple sizes to be contrasted with each other, and substituting the final one with the best discharge performance into the next design link. This "black box" strategy is undoubtedly crude and unreliable compared to the tightly designed logic of up to 10 criteria for the main discharge channel.
Disclosure of Invention
The invention aims to solve the problems that the prior optimization of the aperture of the contact electrode lacks theoretical guidance, only samples with different sizes can be adopted for one-by-one experiment, the workload is large, and the reliability is poor, thereby providing an optimization design method of the aperture of the contact electrode of the hollow cathode.
The invention relates to an optimal design method for the aperture of a hollow cathode holding electrode, which comprises the following steps:
determining the installation position of a hollow cathode, and measuring the magnetic field intensity near a contact minimum hole;
step two, calculating the electron cyclotron Larmor diameter according to the magnetic field intensity obtained in the step one, and obtaining the minimum value of the aperture of the touch pole according to the electron cyclotron Larmor diameter;
step three, keeping the air supply flow of the hollow cathode unchanged, and measuring the air pressure of different contact and hold electrode apertures to obtain a throttling and boosting curve of the contact and hold electrode apertures and the air pressure;
step four, obtaining the minimum value of the gas density according to the criterion condition of the ionization stability, wherein the gas pressure corresponding to the minimum gas density is the minimum gas pressure;
step five, finding the aperture of the touch electrode corresponding to the minimum air pressure in the step four in the throttling and boosting curve in the step three, wherein the aperture of the touch electrode is the maximum value of the aperture of the touch electrode;
and sixthly, selecting a numerical value between the minimum value and the maximum value of the contact electrode aperture, preparing a contact electrode aperture sample, and testing the discharge performance, wherein the contact electrode aperture when the discharge performance is optimal is the optimal contact electrode aperture.
Preferably, the step four is specifically: calculating the Debye length of the ions according to the ion temperature and the ion number density;
Figure BDA0001535114060000021
wherein n isiIs the ion number density, e is the electron charge amount, K is the Boltzmann constant, TiIs the ion temperature, λD,iIs the ionic debye length;
then obtaining the minimum value of the gas density according to the criterion condition of the ionization stability;
the criterion conditions of ionization stability are as follows:
Figure BDA0001535114060000022
wherein the content of the first and second substances,<σeα>for ionizing collision cross-section, n0Is the gas density.
Preferably, the ionization collision cross-section is obtained by searching an atomic collision cross-section database according to the electron temperature<σeα>。
Preferably, in the sixth step, the aperture of the touch electrode with the lowest discharge voltage and the lowest oscillation amplitude of the electron current is the optimal aperture of the touch electrode.
According to the method, the optimized interval is obtained through calculation, the sample is prepared in the optimized interval, the optimal numerical aperture is found, the trial and error interval can be greatly reduced according to the theoretical guidance of the optimized interval, the workload is reduced, and the reliability of the obtained optimal touch electrode aperture can be ensured.
Drawings
FIG. 1 is a flow chart of an optimized design method for the aperture of a hollow cathode holding electrode according to the present invention;
FIG. 2 is a plasma electron temperature axial profile;
FIG. 3 shows electron cyclotron Larmor diameters corresponding to different apertures of a touch pole;
FIG. 4 is a graph of a contact potential versus an electron current oscillation waveform;
FIG. 5 is a graph of parallel magnetic field strength versus electron current relative oscillation amplitude;
FIG. 6 is a graph of parallel magnetic field strength versus anode discharge voltage.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
The hollow cathode is a constant current discharge device which is regulated by power supply feedback. When the local current is lost for some reason, the power supply voltage is inevitably increased, the local electric field is increased, and the discharge is unstable. The applicant carries out theoretical derivation on the physical mechanism of instability to obtain the criterion condition of ionization stability,
Figure BDA0001535114060000031
it can be seen that, when the neutral gas density n is0Lower, ionizing collision cross-section<σeα>Smaller, larger ionization mean free path, where the ion debye shielding is insufficient to shield the extended ionization regionSo that the electric field is continuously enhanced, the ionization is gradually enhanced, and the amplitude is gradually increased. When a part of the electron current flows through the touch electrode, the local electric field is enhanced, and the process is started. The larger the hijack flow, the larger the starting initial value, and the larger the final amplitude, the more unstable. On the contrary, when there is no stream hijacking, the initial starting value is very small and may even be stable. The turbulence then disappears and the discharge voltage decreases. It is conceivable that this wake-up phenomenon can be eliminated when the magnetic field strength is such that the diameter of the electron beam is smaller than the touch pole aperture.
The above equation also demonstrates that increasing the neutral gas density can effectively suppress ionization instability. The neutral gas density is increased so that the ionization length is returned to within the ion debye length. This is consistent with previous experimental observations. Typically the region of maximum oscillation energy is located downstream of the sustaining pole rather than at the exit of the orifice where the gas density is highest. When the supply gas flow exceeds a certain threshold, the oscillations are suddenly reduced and the discharge voltage is suddenly reduced, i.e. shifted from the so-called "plume mode" to the "spot mode".
To verify this theory, the inventors carried out experimental verification. First, it was confirmed that the minimum inflection point in the "magnetic field strength-discharge voltage" curve is indeed correlated with the bore diameter of the touch pole. After measuring the electron temperature near the touch minimum hole (as shown in fig. 2), the electron cyclotron larmor diameter corresponding to the minimum value is compared with the touch minimum hole diameter (as shown in fig. 3), and the two are well matched. The inventors then confirmed that when there is no magnetic field (touching the pole to hijack the current of electrons), the local oscillation is an ionizing oscillation. The contact potential oscillates in anti-phase with the local electron current in fig. 4, which is a typical sign of ionization oscillations. Finally, the inventors confirmed that before and after the hijacking current shock is eliminated, the oscillation is significantly reduced (as shown in fig. 5), and the discharge voltage is significantly reduced (as shown in fig. 6).
In summary, the inventors have found the adverse effect of the wake-up current excitation on the hollow cathode discharge. The main ideas for eliminating the shock of the hijack flow are two at present: one is to try to reduce the electron beam diameter, isolating it from other components; secondly, the air pressure of the sensitive point is improved in an effort to effectively shield the charge separation. The former requires the contact electrode to have a pore diameter as large as possible, and the latter requires the contact electrode to have a pore diameter as small as possible. The minimum value can be determined according to the cathode mounting position (magnetic field strength). From the supply air flow, the maximum value can be determined, thus determining the optimization interval.
An optimal design method for the aperture of a hollow cathode holding electrode comprises the following steps:
determining the installation position of a hollow cathode, and measuring the magnetic field intensity near a contact minimum hole;
step two, calculating the electron cyclotron Larmor diameter according to the magnetic field intensity obtained in the step one, and obtaining the minimum value of the aperture of the touch pole according to the electron cyclotron Larmor diameter;
the electron cyclotron Larmor diameter is the minimum value of the aperture of the touch pole, and when the aperture of the touch pole is larger than or equal to the electron cyclotron Larmor diameter, the hijacking current shock can be eliminated.
Step three, keeping the air supply flow of the hollow cathode unchanged, and measuring the air pressure of different contact and hold electrode apertures to obtain a throttling and boosting curve of the contact and hold electrode apertures and the air pressure;
step four, obtaining the minimum value of the gas density according to the criterion condition of the ionization stability, wherein the gas pressure corresponding to the minimum gas density is the minimum gas pressure;
the method specifically comprises the following steps: calculating the Debye length of the ions according to the ion temperature and the ion number density;
Figure BDA0001535114060000041
wherein n isiIs the ion number density, e is the electron charge amount, K is the Boltzmann constant, TiIs the ion temperature, λD,iIs the ionic debye length;
then obtaining the minimum value of the gas density according to the criterion condition of the ionization stability;
the criterion conditions of ionization stability are as follows:
Figure BDA0001535114060000042
wherein the content of the first and second substances,<σeα>for ionizing collision cross-section, n0Is the gas density.
Obtaining ionization collision cross section by searching atom collision cross section database according to electron temperature<σeα>。
Step five, finding the aperture of the touch electrode corresponding to the minimum air pressure in the step four in the throttling and boosting curve in the step three, wherein the aperture of the touch electrode is the maximum value of the aperture of the touch electrode;
and sixthly, selecting a numerical value between the minimum value and the maximum value of the aperture of the touch electrode, preparing a sample of the aperture of the touch electrode, and testing the discharge performance, wherein the aperture of the touch electrode with the lowest discharge voltage and the smallest oscillation amplitude of the electronic current is the optimal aperture of the touch electrode.

Claims (4)

1. An optimal design method for the aperture of a hollow cathode holding electrode is characterized by comprising the following steps:
determining the installation position of a hollow cathode, and measuring the magnetic field intensity near a contact minimum hole;
step two, calculating the electron cyclotron Larmor diameter according to the magnetic field intensity obtained in the step one, and obtaining the minimum value of the aperture of the touch pole according to the electron cyclotron Larmor diameter;
step three, keeping the air supply flow of the hollow cathode unchanged, and measuring the air pressure of different contact and hold electrode apertures to obtain a throttling and boosting curve of the contact and hold electrode apertures and the air pressure;
step four, the criterion condition of the ionization stability is as follows:
Figure FDA0002767040970000011
wherein the content of the first and second substances,<σea>for ionizing collision cross-section, n0Obtaining the minimum value of the gas density according to the criterion condition of ionization stability, wherein the gas pressure corresponding to the minimum gas density is the minimum gas pressure;
step five, finding the aperture of the touch electrode corresponding to the minimum air pressure in the step four in the throttling and boosting curve in the step three, wherein the aperture of the touch electrode is the maximum value of the aperture of the touch electrode;
and sixthly, selecting a numerical value between the minimum value and the maximum value of the contact electrode aperture, preparing a contact electrode aperture sample, and testing the discharge performance, wherein the contact electrode aperture when the discharge performance is optimal is the optimal contact electrode aperture.
2. The optimal design method for the pore diameter of the hollow cathode holding electrode according to claim 1, wherein the step four is specifically as follows: calculating the Debye length of the ions according to the ion temperature and the ion number density;
Figure FDA0002767040970000012
wherein n isiIs the ion number density, e is the electron charge amount, K is the Boltzmann constant, TiIs the ion temperature, λD,iIs the ionic debye length;
then, the minimum value of the gas density is obtained according to the criterion condition of the ionization stability.
3. The method for optimally designing the aperture of the hollow cathode holding electrode according to claim 2, wherein the ionization collision cross section is obtained by searching an atomic collision cross section database according to the electron temperature<σea>。
4. The method as claimed in claim 1, wherein in step six, the optimum diameter of the contact electrode is the diameter of the contact electrode with the lowest discharge voltage and the lowest oscillation amplitude of the electron current.
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