CN104612923A - Method for predicting supply current peak value of Hall thruster in start-up transient process - Google Patents

Abstract

The invention provides a method for predicting the supply current peak value of a Hall thruster in the start-up transient process and relates to the field of plasma propulsion of aerospace. According to the method, under the premise that the Hall thruster is not ignited, values of pressure in a channel under different mass flows are measured through an ionization gauge or a pressure measurement device. The supply current peak value is deduced in combination with the relation between the pressure values and various parameters in an ignition circuit of the Hall thruster, the supply current peak value generated in the ignition start-up transient process is determined, and prediction of the supply current peak value generated in the start-up transient process of the Hall thruster is achieved. The method is suitable for predicting the supply current peak value of the Hall thruster.

Description

A kind of hall thruster starts the Forecasting Methodology of the source current peak value in transient process

Technical field

The present invention relates to aerospace Plasma propulsion field.

Background technique

Hall thruster progressively becomes the important motivity device of the aerospace craft such as satellite and prober with features such as high efficiency, high specific impulse and low thrusts.The development of aerospace industry proposed requirements at the higher level to the performance of hall thruster in recent years.Ignition trigger process, as the first step of hall thruster successful operation, affects the Security of whole push system.And the current pulse in ignition trigger process not only can affect the life-span of power supply, also can light a fire with hall thruster successfully closely related.Therefore, in hall thruster ignition trigger transient process, the measurement of current pulse is the study hotspot of hall thruster always.

Hall thruster is in ignition trigger transient process, and the power circuit of hall thruster there will be a current pulse, and what time delicate current pulse duration is about, and the current peak of this current pulse is normal current decades of times.For security consideration, the overcurrent protection value of a setting power circuit usually, once the electric current in start-up course exceedes the overcurrent protection value of setting, power circuit will auto-breaking.Therefore, in ignition trigger process, the current peak in power circuit probably can exceed overcurrent protection value, thus causes hall thruster can not successful ignition.Therefore; carry out prediction to the size of the source current peak value that hall thruster starts in transient process to be very important; and this field is also not activated the correlation predictive method of source current peak value in process at present; it is uncertain that this will cause source current overcurrent protection value to exist, and then affect the reliable operation of hall thruster.

Summary of the invention

The present invention is starting the unpredictable problem of the source current peak value in transient process to solve current hall thruster, proposes the Forecasting Methodology that a kind of hall thruster starts the source current peak value in transient process.

Hall thruster starts a Forecasting Methodology for the source current peak value in transient process, source current peak I in the method _pobtained by following formula:

Source current peak value is $I_p=[{\left(\frac{2}{\mathrm{\π}}\right)}^{\frac{2}{b+2}}\·{\left(\frac{1}{{\mathrm{\μ}}_0\·a\·C\·S\·N^{b+2}\·{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\·{[e\·{\∫}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}};$ Described source current peak I _pthe concrete steps obtained are as follows:

Step one, according to the firing circuit of hall thruster and Kirchhoff's current law (KCL), the source current peak I of ignition point hall thruster _prepresentation be:

$I_p=I_{d0}+C\frac{{\mathrm{du}}_c}{\mathrm{dt}}$ Formula one;

Wherein, C is capacitor electrode capacitance; Du _cfor the voltage drop at electric capacity two ends caused by discharge current pulse; I _d0represent discharge current during hall thruster stable operation; Dt is the capacitor instantaneous duration of charge;

Step 2, due to capacitor instantaneous duration of charge dt very little, the voltage drop △ u within the dt time _cequal the voltage drop du at the electric capacity two ends caused by discharge current pulse in transient change process _c; Cumulative time △ t needed for capacitor charging equals the instantaneous duration of charge dt of capacitor;

Therefore, formula one is write as: $I_p=I_{d0}+C\frac{\mathrm{\Δ}{u}_c}{\mathrm{\Δt}}$ Formula two;

Step 3, due to I _d0< < I _p, therefore I _d0ignore, therefore formula two is write as:

$I_p=C\frac{\mathrm{\&Delta;}{u}_c}{\mathrm{\&Delta;t}}$ Formula three;

Cumulative time needed for capacitor charging again wherein π=3.14, L is inductance value; Voltage drop within the dt time q _ifor the xenon atom ionization quantity of electric charge; Therefore, formula three is write as:

$I_p=C\frac{{\mathrm{\&Delta;u}}_c}{\mathrm{\&Delta;t}}=\frac{\frac{Q_I}{C}}{\frac{\mathrm{\&pi;}}{2}\sqrt{\mathrm{LC}}}$ Formula four;

Step 4, owing to starting xenon atom ionization quantity of electric charge Q in transient process _i=eN _xe, wherein e is xenon electronic charge number; N _xefor the total atom number of xenon atom, therefore, formula four is also expressed as:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2\mathrm{LC}={\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ Formula five;

Step 5, again according to the relation L=μ between inductance and source current peak value ₀aSN ^b+2len ^-b-1i _p ^b, substituted into formula five as, therefore formula five is write:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2({\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}\&CenterDot;{I_p}^b)\&CenterDot;C{\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ Formula six;

Wherein _,μ ₀for permeability of vacuum; A and b is fitting coefficient; S is the cross-section area of inductance magnetic circuit; N is the inductance coil number of turn; Len is the inductance length of magnetic path;

Step 6, total atom number due to xenon atom wherein, p (l) is the pressure in the passage of hall thruster before igniting; R is ideal gas constant; T is xenon gas atoms temperature in hall thruster passage before igniting; N _afor the Avogadro constant of perfect gas; S _cfor hall thruster cross-sectional area; l ₁represent the axial coordinate of the initial position of the passage of hall thruster, usual l ₁=0; l ₂represent the axial coordinate of the channel outlet position of hall thruster; Dl represents integration variable;

Line translation of its substitution formula six being gone forward side by side obtains source current peak value representation:

$\begin{array}{c}{I}_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{(e\&CenterDot;N_{\mathrm{xe}})}^{\frac{2}{b+2}}\\ =[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}}\end{array}$ Formula seven;

Step 7, from formula seven, source current peak I _psize relevant with channel inner pressure p (l) of hall thruster before igniting; Therefore, corresponding source current peak I is namely obtained according to the size of channel inner pressure p (l) of hall thruster before igniting _p, that is: $I_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}};$

Step 8, the source current peak I obtained according to step 7 _pbe the predicted value of source current peak value.

Beneficial effect: under the prerequisite that this method misfires at hall thruster, utilizes ionization gauge or manometer to measure force value in different quality flow lower channel.In conjunction with the relation between the parameters in the firing circuit of force value and hall thruster, thus derivation obtains source current peak value, thus determine the size of source current peak value in ignition trigger transient process, achieve hall thruster in the prediction starting the source current peak value in transient process.Thus be convenient to staff according to predicting that the source current peak value that obtains is with practical power overcurrent value compared with, adjusts the source current overcurrent value of hall thruster, prevent hall thruster can not successful ignition.This method is that the probabilistic problem of aerospace field solution source current overcurrent value setting value provides solution; simultaneously for guaranteeing that hall thruster reliable ignition in orbit provides theoretical foundation; to in whole aerospace field, important evidence is provided to the setting of source current overcurrent value, solve aerospace field problem demanding prompt solution.The present invention is applicable to the prediction of the current peak of hall thruster.

Accompanying drawing explanation

Fig. 1 is the circuit connecting relation figure of the firing circuit of hall thruster;

Fig. 2 is the annexation figure of manometer;

Fig. 3 be mass flow rate and hall thruster passage in pressure between graph of a relation.

Embodiment

Embodiment one, reference Fig. 1 illustrate present embodiment, and a kind of hall thruster described in present embodiment starts the Forecasting Methodology of the source current peak value in transient process, source current peak I in the method _pobtained by following formula:

Source current peak value is $I_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}};$ Described source current peak I _pthe concrete steps obtained are as follows:

Step one, according to the firing circuit of hall thruster and Kirchhoff's current law (KCL), the source current peak I of ignition point hall thruster _prepresentation be:

$I_p=I_{d0}+C\frac{{\mathrm{du}}_c}{\mathrm{dt}}$ Formula one;

Wherein, C is capacitor electrode capacitance; Du _cfor the voltage drop at electric capacity two ends caused by discharge current pulse; I _d0represent discharge current during hall thruster stable operation; Dt is the capacitor instantaneous duration of charge;

Step 2, due to capacitor instantaneous duration of charge dt very little, the voltage drop △ u within the dt time _cequal the voltage drop du at the electric capacity two ends caused by discharge current pulse in transient change process _c; Cumulative time △ t needed for capacitor charging equals the instantaneous duration of charge dt of capacitor;

Therefore, formula one is write as: $I_p=I_{d0}+C\frac{\mathrm{\&Delta;}{u}_c}{\mathrm{\&Delta;t}}$ Formula two;

Step 3, due to I _d0< < I _p, therefore I _d0ignore, therefore formula two is write as:

$I_p=C\frac{\mathrm{\&Delta;}{u}_c}{\mathrm{\&Delta;t}}$ Formula three;

Cumulative time needed for capacitor charging again wherein π=3.14, L is inductance value; Voltage drop within the dt time q _ifor the xenon atom ionization quantity of electric charge; Therefore, formula three is write as:

$I_p=C\frac{{\mathrm{\&Delta;u}}_c}{\mathrm{\&Delta;t}}=\frac{\frac{Q_I}{C}}{\frac{\mathrm{\&pi;}}{2}\sqrt{\mathrm{LC}}}$ Formula four;

Step 4, owing to starting xenon atom ionization quantity of electric charge Q in transient process _i=eN _xe, wherein e is xenon electronic charge number; N _xefor the total atom number of xenon atom, therefore, formula four is also expressed as:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2\mathrm{LC}={\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ Formula five;

Step 5, again according to the relation L=μ between inductance and source current peak value ₀aSN ^b+2len ^-b-1i _p ^b, substituted into formula five as, therefore formula five is write:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2({\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}\&CenterDot;{I_p}^b)\&CenterDot;C{\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ Formula six;

Wherein, μ ₀for permeability of vacuum; A and b is fitting coefficient; S is the cross-section area of inductance magnetic circuit; N is the inductance coil number of turn; Len is the inductance length of magnetic path;

Step 6, total atom number due to xenon atom wherein, p (l) is the pressure in the passage of hall thruster before igniting; R is ideal gas constant; T is xenon gas atoms temperature in hall thruster passage before igniting; N _afor the Avogadro constant of perfect gas; S _cfor hall thruster cross-sectional area; l ₁represent the axial coordinate of the initial position of the passage of hall thruster, usual l ₁=0; l ₂represent the axial coordinate of the channel outlet position of hall thruster; Dl represents integration variable;

Line translation of its substitution formula six being gone forward side by side obtains source current peak value representation:

$\begin{array}{c}{I}_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{(e\&CenterDot;N_{\mathrm{xe}})}^{\frac{2}{b+2}}\\ =[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}}\end{array}$ Formula seven;

Step 7, from formula seven, source current peak I _psize relevant with channel inner pressure p (l) of hall thruster before igniting; Therefore, corresponding source current peak I is namely obtained according to the size of channel inner pressure p (l) of hall thruster before igniting _p, that is: $I_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}};$

Step 8, the source current peak I obtained according to step 7 _pbe the predicted value of source current peak value.

In present embodiment, as shown in Figure 1, the power circuit of hall thruster comprises the discharge power supply U between anode and cathode to the firing circuit of hall thruster ₁with the excitation power supply U providing field current for field coil ₂.RLC resonance circuitry comprises resistance R1, inductance L and electric capacity C, and inductance L is in parallel with resistance R1, discharge power supply U ₁positive pole connect one end of inductance L, the other end of inductance L connects one end of electric capacity C and the anode of hall thruster simultaneously; Discharge power supply U ₁negative pole connect the other end of electric capacity C; The other end of electric capacity C also connects the negative electrode of hall thruster.

The result of study that ignition trigger generally acknowledged in the world is at present instantaneous shows, ignition point discharge current pulse is that in the passage by hall thruster, the ionization of atom moment avalanche type is formed.Instantaneous high current to cause in the eliminator be made up of resistance, electric capacity and inductance three electric capacity both end voltage to decline, and electric capacity both end voltage is fallen, power supply can by inductance with resistance to capacitor charging, cause engine power end electric current formation pulse.

Working medium refers to xenon herein.According to actual needs, after injecting the working medium of different quality flow, in order to ensure that hall thruster can smooth ignition, first according to the mass flow value injected, source current peak value is predicted, then adjust source current overcurrent value and be greater than the source current peak value calculating and obtain, thus smooth ignition when ensureing hall thruster igniting.

Embodiment two, present embodiment start further illustrating of the Forecasting Methodology of the source current peak value in transient process to a kind of hall thruster described in embodiment one, in present embodiment, and I in step 3 _d0< < I _preason be: in hall thruster ignition trigger transient process, when source current reaches peak value, the discharge current in hall thruster firing circuit is basicly stable, therefore, I _d0< < I _p, I during calculating _d0ignore.

Embodiment three, present embodiment start further illustrating, in present embodiment, described in step 3 of the Forecasting Methodology of the source current peak value in transient process to a kind of hall thruster described in embodiment one obtaining method as follows: according to the firing circuit of hall thruster, dt is the capacitor instantaneous duration of charge, and needed for capacitor charging, cumulative time △ t equals instantaneous time dt; The harmonic period of RLC resonance circuitry again because capacitor charging time is 1/4th of harmonic period, therefore

Embodiment four, present embodiment start further illustrating of the Forecasting Methodology of the source current peak value in transient process to a kind of hall thruster described in embodiment one, in present embodiment, and the μ of L=described in step 5 ₀aSN ^b+2len ^-b-1i _p ^bacquisition process as follows:

Firing circuit according to hall thruster:

φ=BS formula May Day;

B=μ H formula five or two;

Hlen=NI _pformula five or three;

Wherein, φ is the magnetic flux by inductance coil; B is induction field intensity; S is the cross-section area of inductance magnetic circuit; μ is permeability; H is magnetic intensity, and N is the inductance coil number of turn, and len is the inductance length of magnetic path, I _pfor source current peak value; Definition according to inductance:

$L=\frac{N\&CenterDot;\mathrm{\&phi;}}{I_p}$ Formula the May 4th;

Formula May Day, formula five or two and formula five or three are substituted into formula formula the May 4th, obtain after abbreviation:

$L=\frac{\mathrm{\&mu;}\&CenterDot;N^2\&CenterDot;S}{\mathrm{len}}$ Formula five or five;

Again because the pass between permeability μ and magnetic intensity H is:

μ=a μ ₀h ^bformula five or six;

Wherein, a and b is fitting coefficient;

Integrated type five or five and formula five or six obtain: $\mathrm{\&mu;}={\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;{\left(\frac{N\&CenterDot;I_p}{\mathrm{len}}\right)}^b$ Formula five or seven;

Formula five or seven is substituted into formula five or five, obtains the variation relation formula of hall thruster inductance L in ignition trigger instantaneous process:

L＝μ ₀·a·S·N ^b+2·len ^-b-1·I _p ^b。

Embodiment five, reference Fig. 2 illustrate present embodiment, present embodiment starts further illustrating of the Forecasting Methodology of the source current peak value in transient process to a kind of hall thruster described in embodiment one, in present embodiment, channel inner pressure p (l) of described hall thruster is recorded by manometer under vacuum conditions; Described manometer comprises ionization gauge 1, compound vacuum gauge 2, stepper motor 3, support 4 and glass tube 5;

Ionization gauge 1 is fixed on stepper motor 3 by support 4, and glass tube 5 is for the passage of the working medium entrance and hall thruster that are communicated with ionization gauge; The pressure that stepper motor 3 moves around in Measurement channel in the passage of hall thruster for driving ionization gauge 1.

In present embodiment, another data terminal of compound vacuum gauge is also connected with Pirani gauge 6, and compound vacuum gauge just normally works under only having the condition connecting ionization gauge and Pirani gauge at the same time.

In Fig. 2, when injecting working medium (xenon) of different quality flow in the passage of hall thruster, stepper motor 3 drives ionization gauge 1 to move around in the passage of hall thruster, thus measures the pressure in the passage of hall thruster.In Fig. 2,6 is Pirani gauge, 7 be the passage, 8 of hall thruster is hall thruster anode, 9 be hall thruster negative electrode, 10 for hall thruster.

Embodiment six, present embodiment start further illustrating of the Forecasting Methodology of the source current peak value in transient process to a kind of hall thruster described in embodiment one, and in present embodiment, hall thruster model is HEP100.

Embodiment seven, present embodiment are an embodiment.

This experiment is carried out under vacuum experiment condition.

First, prepare a diameter 1.5m, the vacuum tank of wide 4m, adopt triplex system--two extraction pumps, degree of vacuum in it is evacuated to 10^ (-3) Pa by a diffusion pump and three mechanical pumps, and this vacuum system can be the vacuum environment that hall thruster provides ground simulation.

Secondly, the hall thruster adopted in experiment: model is HEP-100, outer ceramic sleeve diameter, 100mm; Interior ceramic sleeve diameter is 70mm, and channel width is 15mm, and passage length is 50mm.Hall thruster anode and gas distributor, be positioned at discharge channel entrance.Hollow cathode, as electron source and ion neutralizer, is positioned at distance hall thruster outlet 5mm-7mm place.

Again, the Forecasting Methodology of the source current peak value that a kind of hall thruster according to the application starts in transient process is predicted source current peak value:

Its process is as follows: get N=50; S=1 × 10 ^-5m ²; Len=0.14m; A=5.67; B=-0.61; C=10 μ F; μ ₀=4 π × 10 ^-7h/m; E=1.6 × 10 ^-9c; N _a=6.02 × 10 ²³; π=3.14; T=300K; R=8.3J/ (molK);

S _C＝4.0×10 ^-3m ²；l ₁＝0；l ₂＝50mm。

The xenon of 30sccm, 40sccm and 50sccm is injected respectively in hall thruster; The force value in the passage of the hall thruster of xenon is injected by ionization gauge; Then the force value recorded by ionization gauge substitutes into source current peak I _pformula in; Obtain source current peak value, thus set the source current overcurrent value of hall thruster, now, setting source current overcurrent value is 1.2I _{p (max)}, ensure that the moment of hall thruster ignition trigger, can not cause because source current peak value exceedes source current overcurrent value cannot successful ignition.

When studying the relation between the ignition trigger instantaneous power current peak of hall thruster and working medium mass flow rate, when utilizing ionization gauge to record 30sccm, 40sccm and 50sccm hall thruster passage in pressure, as shown in Figure 3, the above-mentioned force value recorded being substituted in source current peak value formula, obtaining following result respectively through calculating:

P (l) is prepass internal pressure variation rule curve of lighting a fire when mass flow rate is 30sccm, and utilize source current peak value formula to obtain hall thruster ignition trigger transient process, power end current peak is 150A.

P (l) is prepass internal pressure variation rule curve of lighting a fire when mass flow rate is 40sccm, and utilize source current peak value formula to obtain hall thruster ignition trigger transient process, power end current peak is 210A.

P (l) is prepass internal pressure variation rule curve of lighting a fire when mass flow rate is 50sccm, and utilize source current peak value formula to obtain hall thruster ignition trigger transient process, power end current peak is 320A.

Claims (5)

1. hall thruster starts a Forecasting Methodology for the source current peak value in transient process, it is characterized in that, source current peak I in the method _pobtained by following formula:

Source current peak value is $I_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}{]}^{\frac{2}{b+2}};$ Described source current peak I _pthe concrete steps obtained are as follows:

Step one, according to the firing circuit of hall thruster and Kirchhoff's current law (KCL), the source current peak I of ignition point hall thruster _prepresentation be:

$I_p=I_{d0}+C\frac{{\mathrm{du}}_c}{\mathrm{dt}}$ (formula one);

Wherein, C is capacitor electrode capacitance; Du _cfor the voltage drop at electric capacity two ends caused by discharge current pulse; I _d0represent discharge current during hall thruster stable operation; Dt is the capacitor instantaneous duration of charge;

Step 2, due to capacitor instantaneous duration of charge dt very little, the voltage drop △ u within the dt time _cequal the voltage drop du at the electric capacity two ends caused by discharge current pulse in transient change process _c; Cumulative time △ t needed for capacitor charging equals the instantaneous duration of charge dt of capacitor;

Therefore, (formula one) is write as: $I_p=I_{d0}+C\frac{{\mathrm{\&Delta;u}}_c}{\mathrm{\&Delta;t}}$ (formula two);

Step 3, due to I _d0< < I _p, therefore I _d0ignore, therefore (formula two) is write as:

$I_p=C\frac{{\mathrm{\&Delta;u}}_c}{\mathrm{\&Delta;t}}$ (formula three);

Cumulative time needed for capacitor charging again wherein π=3.14, L is inductance value; Voltage drop within the dt time q _ifor the xenon atom ionization quantity of electric charge; Therefore, (formula three) is write as:

$I_p=C\frac{{\mathrm{\&Delta;u}}_c}{\mathrm{\&Delta;t}}=\frac{\frac{Q_I}{C}}{\frac{\mathrm{\&pi;}}{2}\sqrt{\mathrm{LC}}}$ (formula four);

Step 4, owing to starting xenon atom ionization quantity of electric charge Q in transient process _i=eN _xe, wherein e is xenon electronic charge number; N _xefor the total atom number of xenon atom, therefore, (formula four) is also expressed as:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2\mathrm{LC}={\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ (formula five);

Step 5, again according to the relation L=μ between inductance and source current peak value ₀aSN ^b+2len ^-b-1i _p ^b, substituted into (formula five), therefore (formula five) is write as:

${I_p}^2{\left(\frac{\mathrm{\&pi;}}{2}\right)}^2({\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}\&CenterDot;{I_p}^b)\&CenterDot;C={\left(\frac{e\&CenterDot;N_{\mathrm{xe}}}{C}\right)}^2$ (formula six);

Wherein, μ ₀for permeability of vacuum; A and b is fitting coefficient; S is the cross-section area of inductance magnetic circuit; N is the inductance coil number of turn; Len is the inductance length of magnetic path;

Step 6, total atom number due to xenon atom wherein, p (l) is the pressure in the passage of hall thruster before igniting; R is ideal gas constant; T is xenon gas atoms temperature in hall thruster passage before igniting; N _afor the Avogadro constant of perfect gas; S _cfor hall thruster cross-sectional area; l ₁represent the axial coordinate of the initial position of the passage of hall thruster, usual l ₁=0; l ₂represent the axial coordinate of the channel outlet position of hall thruster; Dl represents integration variable;

Substituted into (formula six) line translation of going forward side by side and obtained source current peak value representation:

$\begin{array}{c}{I}_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{(e\&CenterDot;N_{\mathrm{xe}})}^{\frac{2}{b+2}}\\ =[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}\&CenterDot;{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;{[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}]}^{\frac{2}{b+2}}\end{array}$ (formula seven);

Step 7, from (formula seven), source current peak I _psize relevant with channel inner pressure p (l) of hall thruster before igniting; Therefore, corresponding source current peak I is namely obtained according to the size of channel inner pressure p (l) of hall thruster before igniting _p, that is: $I_p=[{\left(\frac{2}{\mathrm{\&pi;}}\right)}^{\frac{2}{b+2}}\&CenterDot;{\left(\frac{1}{{\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;C\&CenterDot;S\&CenterDot;N^{b+2}{\mathrm{len}}^{-b-1}}\right)}^{\frac{1}{b+2}}]\&CenterDot;[e\&CenterDot;{\&Integral;}_{l_1}^{l_2}\frac{p\left(l\right)}{\mathrm{RT}}{N}_A{S}_C\mathrm{dl}{]}^{\frac{2}{b+2}};$

Step 8, the source current peak I obtained according to step 7 _pbe the predicted value of source current peak value.

2. a kind of hall thruster according to claim 1 starts the Forecasting Methodology of the source current peak value in transient process, it is characterized in that, I in step 3 _d0< < I _preason be: in hall thruster ignition trigger transient process, when source current reaches peak value, the discharge current in hall thruster firing circuit is basicly stable, therefore, I _d0< < I _p, I during calculating _d0ignore.

3. a kind of hall thruster according to claim 1 starts the Forecasting Methodology of the source current peak value in transient process, it is characterized in that, described in step 3 obtaining method as follows: according to the firing circuit of hall thruster, dt is the capacitor instantaneous duration of charge, and needed for capacitor charging, cumulative time △ t equals instantaneous time dt; The harmonic period of RLC resonance circuitry again because capacitor charging time is 1/4th of harmonic period, therefore

4. a kind of hall thruster according to claim 1 starts the Forecasting Methodology of the source current peak value in transient process, it is characterized in that, the μ of L=described in step 5 ₀aSN ^b+2len ^-b-1i _p ^bacquisition process as follows:

Firing circuit according to hall thruster:

φ=BS (formula May Day);

B=μ H (formula five or two);

Hlen=NI _p(formula five or three);

Wherein, φ is the magnetic flux by inductance coil; B is induction field intensity; S is the cross-section area of inductance magnetic circuit; μ is permeability; H is magnetic intensity, and N is the inductance coil number of turn, and len is the inductance length of magnetic path, I _pfor source current peak value; Definition according to inductance:

$L=\frac{N\&CenterDot;\mathrm{\&phi;}}{I_p}$ (formula the May 4th);

(formula May Day), (formula five or two) and (formula five or three) are substituted into formula (formula the May 4th), obtain after abbreviation:

$L=\frac{\mathrm{\&mu;}\&CenterDot;N^2\&CenterDot;S}{\mathrm{len}}$ (formula five or five);

Again because the pass between permeability μ and magnetic intensity H is:

μ=a μ ₀h ^b(formula five or six);

Wherein, a and b is fitting coefficient;

Comprehensively (formula five or five) and (formula five or six) obtains: $\mathrm{\&mu;}={\mathrm{\&mu;}}_0\&CenterDot;a\&CenterDot;{\left(\frac{N\&CenterDot;I_p}{\mathrm{len}}\right)}^b$ (formula five or seven);

(formula five or seven) is substituted into (formula five or five), obtains the variation relation formula of hall thruster inductance L in ignition trigger instantaneous process:

L＝μ ₀·a·S·N ^b+2·len ^-b-1·I _p ^b。

5. a kind of hall thruster according to claim 1 starts the Forecasting Methodology of the source current peak value in transient process, it is characterized in that, channel inner pressure p (l) of described hall thruster is recorded by manometer under vacuum conditions; Described manometer comprises ionization gauge (1), compound vacuum gauge (2), stepper motor (3), support (4) and glass tube (5);

Ionization gauge (1) is fixed on stepper motor (3) by support (4), and glass tube (5) is for the passage of the working medium entrance and hall thruster that are communicated with ionization gauge; The pressure that stepper motor (3) moves around in Measurement channel in the passage of hall thruster for driving ionization gauge (1).