Design method for double-ring nested Hall thrusters, Hall thrusters

Abstract

This invention provides a design method and a Hall thruster for a double-ring nested Hall thruster, comprising: obtaining the target performance parameters of the thruster; based on the target performance parameters, initially setting the outer channel dimensions, corresponding operating parameters, and peak value of the magnetic flux density at the channel centerline; calculating the inner channel dimensions and corresponding operating parameters using an efficient calculation model of Hall channel 1D plasma transport based on the mathematical relationship between the peak value of the magnetic flux density at the channel centerline and the magnetic circuit space dimensions; determining whether the total performance parameters of the designed inner and outer channels meet the target performance parameters; if they do, determining the channel design scheme; if not, adjusting the corresponding operating parameters in the external design module, iteratively optimizing until the optimal inner and outer channel dimensions and corresponding operating parameters that meet the target performance parameters are obtained. The calculation error of this invention for thrust is 16.6%–20.8%, and the calculation time for a single operating condition is approximately 150 seconds.

Description

Technical Field

[0001] This invention relates to the field of space propulsion devices, and more specifically, to a design method for a double-ring nested Hall thruster and a Hall thruster. Background Technology

[0002] Nested Hall thruster propulsion is a propulsion technology based on coaxial multi-ring channel discharge, superimposing the thrust of each channel to improve space utilization. It features a compact structure, high thrust density, and a wide performance adjustment range, and is commonly used in large-scale GEO satellites, orbital transfer vehicles, space combat platforms, and nuclear-powered transport spacecraft. Patent document CN112483341A discloses a Hall thruster heat-conducting bracket and a Hall thruster containing this bracket. However, due to the multi-ring nested nature of the thruster channel structure, the magnetic field and plasma flow between the channels generate strong coupling effects. In structural design, this manifests as the need to consider both the realization of propulsion performance parameters for each channel and the constraints of the magnetic circuit space between channels when determining the channel size. Therefore, this design method differs significantly from the channel design method of single-ring Hall thrusters, and represents an important research direction for the performance optimization and engineering development of nested Hall thrusters.

[0003] To date, the channel size design of the X2 double-ring nested Hall thruster developed by the University of Michigan is based on the H6 thruster, while the magnetic field design concept is based on the P5 thruster (RAYMOND L. The combination of two concentric discharge channels into a nested Hall-effect thruster. PhD thesis. 2013). The X3 triple-ring nested Hall thruster developed by the University of Michigan draws inspiration from the H6, NASA-300M, NASA-400M, NASA-457Mv1, and X2 thrusters in terms of channel design, while the magnetic field configuration design is obtained through simulation using the third-party software Magnet 7 (ROLANDF. The X3 100-kW class nested-channel Hall thruster: motivation, implementation and initial performance. PhD thesis. 2014). The channel size of the N30 magnetically shielded nested Hall thruster also draws inspiration from the H6, H6MS, X2, and X3 thrusters, while the magnetic field design mainly references the magnetic shielding strategy of the H6MS (SARAH). C, et al. Development of a 30-kW class magnetically shielded nested Hallthruster. IEPC-2019-266). In summary, the channel designs of X2, X3, and N30 all draw on traditional single-ring Hall thrusters and do not propose a unique design method for the channel size of nested Hall thrusters. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a design method for a double-ring nested Hall thruster and a Hall thruster.

[0005] A design method for a double-ring nested Hall thruster according to the present invention includes: a design method for a double-ring nested Hall thruster, comprising:

[0006] Performance acquisition steps: Obtain the target performance parameters of the thruster, including power, thrust, and specific impulse;

[0007] External design steps: Based on the target performance parameters, initially set the external channel dimensions, corresponding operating parameters, and peak value of the magnetic induction intensity at the center of the channel;

[0008] Internal design steps: Based on the mathematical relationship between the peak value of the magnetic induction intensity at the centerline of the channel and the size of the magnetic circuit space, the internal channel size and corresponding operating parameters are calculated using an efficient calculation model of Hall channel 1D plasma transport.

[0009] Confirmation steps: Check whether the overall performance parameters of the designed internal and external channels meet the target performance parameters. If they do, determine the channel design scheme. If they do not, adjust the corresponding working parameters in the external design steps and iterate repeatedly until the optimal internal and external channel dimensions and corresponding working parameters that meet the target performance parameters are obtained.

[0010] Furthermore, in the internal design step, the peak value of the magnetic induction intensity B at the centerline of the channel... max The mathematical relationship with the magnetic circuit space dimension H is as follows:

[0011] H = 4.05 × 10 -14 ×(d out / 400) 1.5 ×exp[B max / (8.06-(d out / 150))]+15.3

[0012] Where, d out The diameter of the outer channel wall.

[0013] Furthermore, the calculation methods in the internal design step include:

[0014] First, the motion states of electrons and ions are solved using a non-time-domain particle motion solution method; second, the electron transport trajectory is simplified, reducing the 3D cyclotron motion path of electrons to a 1D axial migration path; third, the approximation setting of the initial distribution of spatial potential reduces the convergence time of spatial potential calculation.

[0015] Furthermore, a computational node is set between the anode point and the virtual cathode point on the center line of the channel. After the cathode electron flow enters the computational domain, it splits into two electron flows that enter the thruster channel respectively. One electron flows migrate towards the anode, while the other electron flows escape from the computational domain towards the virtual cathode. The electrons migrating towards the anode trigger ionization collisions with atoms, producing ionized electrons and ions. The electrons reaching the anode will escape into the circuit, while the ions will migrate towards the virtual cathode under the influence of the spatial potential. The electrons migrating towards the virtual cathode will undergo quasi-neutralization with the ions and then leave the computational domain in a quasi-neutral state.

[0016] Furthermore, the probability P of an electron colliding with an atom in a neutral gas within a very short time Δt is... en for:

[0017]

[0018] ΔL is the distance the electron travels within one time step, Δz is the displacement of the electron on the channel axis, and f en V is the frequency of electron-atom collisions. e The speed of electron movement;

[0019] ΔL=Δz·[-5.09+1642.45·(βB)-20151.91·(βB) 2 ]

[0020] Where β is the correction coefficient and B is the magnetic flux density at the center of the channel;

[0021] The spatial potential within the computational domain is solved using the Poisson equation:

[0022]

[0023] Where Δφ is the space potential, ρ charges Let ε0 be the net residual charge density in space and ε0 be the vacuum permittivity. In the one-dimensional model, the solution is obtained using the three-point difference method, and the difference equation is as follows:

[0024]

[0025] φ j Let n be the nodal potential, Δz be the spatial step size corresponding to the one-dimensional computational domain, and n be the nodal potential. i and n e Let be the ion number density and electron number density of the node, respectively. The boundary conditions are: when z is located on the anode surface, z = 0, φ = 500V; when z is located on the virtual cathode surface, the charge bubble boundary condition ρ is taken. ∞ =0;

[0026]

[0027] Where, φ potential (i) represents the spatial potential function along the computational domain, U represents the discharge voltage, N represents the number of nodes in the computational domain, i represents the node number (i = 1 to N), and c represents the ratio of the channel depth to the total length of the computational domain.

[0028] Furthermore, the magnetic material in the magnetic circuit is pure iron DT4C, a commonly used magnetic material in Hall thrusters, and the upper limit of magnetic saturation of the magnetic material is set at 1.2T.

[0029] Furthermore, 1000 computational nodes are set between the anode point and the virtual cathode point on the channel centerline, and the spatial step size can be set to be encrypted: the spatial step size of the ionization region is 0.05 mm, and the other regions gradually transition to 0.2 mm.

[0030] Furthermore, in the cathode electron flow I chAfter entering the computational domain, it splits into two electron streams that enter the thruster channels respectively. One electron stream I e,in Migrating towards the anode, another electron I ch -I e,in Escape the computational domain to the virtual cathode;

[0031] Secondly, electrons migrating towards the anode will trigger ionization collisions with atoms, producing ionized electrons and ions, and the electrons reaching the anode will... e,out When the escape space enters the circuit, the ions will migrate towards the virtual cathode under the influence of the space potential. i,out Electrons migrating toward the virtual cathode undergo quasi-neutralization with ions, and then leave the computational domain in a quasi-neutral state.

[0032] Furthermore, the convergence criterion for calculating the convergence time includes two steps: the first step is the quasi-neutrality determination of the plume boundary, i.e., the ion current I of the escaping plume. i,out Electron flow I with escape plume ch -I e,in The first step is the equality determination; the second step is the determination of the conservation of current-carrying charge in the circuit, and the electron flow I entering the computational domain from the cathode. ch Electron flow I entering the circuit from the computational domain e,out The equality determination;

[0033] Parameter 'a' represents the proportion of electron flow into the channel, initially set to 0.1. The iterative update algorithm for parameter 'a' is as follows:

[0034] a (2) =a (1) ×(I ch / I e,out ) 0.75

[0035] The index of 0.75 is an empirical value determined through multiple calculations and practices.

[0036] According to the present invention, a Hall thruster is obtained by adopting the design method for a double-ring nested Hall thruster.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This paper proposes a method for designing the channel dimensions of a double-ring nested Hall thruster, based on the peak magnetic induction intensity B at the channel centerline. max By analyzing the mathematical relationship between the magnetic circuit space and the channel size, the channel size is optimized and iteratively designed to ultimately obtain the optimal channel size that meets the target performance parameters. Attached Figure Description

[0039] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0040] Figure 1 A schematic diagram of the mesh distribution and boundary settings for a 1D plasma transport model;

[0041] Figure 2 A schematic diagram illustrating the convergence criteria for a 1D plasma transport model;

[0042] Figure 3 This is a flowchart of the process of the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0044] like Figure 3 As shown, the present invention provides a design method for a double-ring nested Hall thruster, comprising:

[0045] Performance acquisition steps: Obtain the target performance parameters of the thruster, including power, thrust and specific impulse.

[0046] External design steps: Based on the target performance parameters, initially set the external channel dimensions, corresponding operating parameters (gas flow rate, discharge current), and peak magnetic induction intensity B at the channel centerline. max (At this point, the channel size is generally insufficient to accommodate B) max (Required magnetic circuit space).

[0047] Internal design steps: Based on the mathematical relationship between the peak value of the magnetic induction intensity at the centerline of the channel and the size of the magnetic circuit space, the internal channel size and corresponding operating parameters are calculated using an efficient calculation model of Hall channel 1D plasma transport.

[0048] Peak magnetic field strength B at the center of the channel max The mathematical relationship with the magnetic circuit space dimension H is as follows:

[0049] H = 4.05 × 10 -14 ×(d out / 400) 1.5 ×exp[B max / (8.06-(d out / 150))]+15.3

[0050] Where, d out The diameter of the outer channel wall.

[0051] Confirmation steps: Check whether the overall performance parameters of the designed internal and external channels meet the target performance parameters. If they do, determine the channel design scheme. If they do not, adjust the corresponding working parameters in the external design steps and iterate repeatedly until the optimal internal and external channel dimensions and corresponding working parameters that meet the target performance parameters are obtained.

[0052] The efficient computational model for Hall channel 1D plasma transport includes the following sub-modules: first, mesh generation and boundary setting module; second, inter-particle collision module; third, particle-wall collision module; fourth, spatial potential module; and fifth, convergence determination module.

[0053] The mesh generation and boundary setting module sets up 1000 computational nodes between the anode point and the virtual cathode point along the channel centerline. The spatial step size can be set for refinement: 0.05mm in the ionization region, gradually transitioning to 0.2mm in other regions. The computational domain operates as follows: Figure 1 As shown, in the cathode electron flow (I ch After entering the computational domain, it splits into two electron streams that enter the thruster channels respectively. One stream of electrons (I) e,in One electron migrates towards the anode, while another electron (I) migrates towards the anode. ch -I e,in The electrons escape the computational domain towards the virtual cathode. Furthermore, electrons migrating towards the anode will trigger ionization collisions with atoms, producing ionized electrons and ions, reaching the anode electrons (Ia). e,out The escape space enters the circuit, and the ions migrate towards the virtual cathode under the influence of the space potential (I). i,out Electrons migrating toward the virtual cathode undergo quasi-neutralization with ions, and then leave the computational domain in a quasi-neutral state.

[0054] The interparticle collision module is as follows: The probability of an electron colliding with an atom in a neutral gas within a very short time Δt is:

[0055]

[0056] In equation (2), ΔL represents the distance traveled by the electron within one time step [m], not the displacement Δz of the electron on the channel axis. en V is the frequency of electron-atom collisions. e This represents the velocity of the electron. The values ​​of ΔL / Δz are described by B and E (electric field):

[0057] ΔL=Δz·[-5.09+1642.45·(βB)-20151.91·(βB) 2 (3)

[0058] Where β is the correction coefficient, which is 2.04 in the verification experiment, and B is the magnetic induction intensity at the center of the channel.

[0059] The space potential module is for calculating the space potential within the computational domain, which can be solved using the Poisson equation.

[0060]

[0061] Where Δφ is the space potential, ρ charges Net residual charge density in space [C / m 3 ], where ε0 is the vacuum permittivity, taken as 8.85 × 10⁻⁶. -12 F / m. In the one-dimensional model, it can be solved using the three-point difference method, and the difference equation is as follows:

[0062]

[0063] Where, φ j Let n be the nodal potential, Δz be the spatial step size corresponding to the one-dimensional computational domain, and n be the nodal potential. i and n e The ion number density of the nodes [m] are respectively -3 and electron number density [m -3 The boundary conditions are: at z = 0 (anode surface), φ = 500V; when z is located at the virtual cathode surface, the charge bubble boundary condition (ρ) is applied. ∞ =0). Equation (5) gives the initial function of the potential distribution along the one-dimensional axis of the computational domain, which is very close to the actual spatial potential distribution of the Hall thruster channel.

[0064]

[0065] Where, φ potential (i) represents the spatial potential function along the computational domain, U represents the discharge voltage, N represents the number of nodes in the computational domain (1000 in this paper), i represents the node number (from 1 to N), and c represents the ratio of the channel depth to the total length of the computational domain.

[0066] The convergence determination module consists of two parts: the first part is the quasi-neutrality determination of the plume boundary, i.e., the ion current I of the escaping plume. i,out With the electron flow of the escape plume (I) ch -I e,in The first step is to determine the equality of the electrons; the second step is to determine the conservation of current-carrying charge in the circuit, and the electron flow I entering the computational domain from the cathode. ch Electron flow I entering the circuit from the computational domain e,out The equality determination. For example, Figure 2 As shown, parameter a is the proportion of electron flow into the channel, with an initial value of 0.1. This value is close to the published experimental measurement data. The iterative update algorithm for parameter a is as follows:

[0067] a (2) =a (1) ×(I ch / I e,out ) 0.75 (7)

[0068] Here, (I ch / I e,out ) 0.75 The index "0.75" is an empirical value determined through multiple calculations and practices.

[0069] The design method of this invention has a thrust calculation error of 16.6% to 20.8%, and the Hall channel 1D plasma transport model in the method takes about 150 seconds to calculate under a single working condition.

[0070] This invention establishes an efficient computational model for 1D plasma transport in a Hall channel, and combines the mathematical relationship between the peak value of the magnetic induction intensity at the channel centerline and the magnetic circuit space to perform coupled iterative design of the channel size, ultimately obtaining the optimal channel size that meets the target performance parameters. All empirical coefficient corrections, thruster non-magnetic material replacements, gas type replacements, and equivalent formula transformations made within this spirit and principle should be included within the scope of protection of this invention.

[0071] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A design method for a double-ring nested Hall thruster, characterized in that, include: Performance acquisition steps: Obtain the target performance parameters of the thruster, including power, thrust, and specific impulse; External design steps: Based on the target performance parameters, initially set the external channel dimensions, corresponding operating parameters, and peak value of the magnetic induction intensity at the center of the channel; Internal design steps: Based on the mathematical relationship between the peak value of the magnetic induction intensity at the centerline of the channel and the size of the magnetic circuit space, the internal channel size and corresponding operating parameters are calculated using an efficient calculation model of Hall channel 1D plasma transport. Confirmation steps: Check whether the overall performance parameters of the designed internal and external channels meet the target performance parameters. If they do, determine the channel design scheme. If they do not, adjust the corresponding working parameters in the external design steps and iterate repeatedly until the optimal internal and external channel dimensions and corresponding working parameters that meet the target performance parameters are obtained. The calculation methods in the internal design steps include: First, the motion states of electrons and ions are solved using a non-time-domain particle motion solution method; second, the electron transport trajectory is simplified, reducing the 3D cyclotron motion path of electrons to a 1D axial migration path; third, the approximation setting of the initial distribution of spatial potential reduces the convergence time of spatial potential calculation. A computational node is set between the anode point and the virtual cathode point on the channel centerline. After the cathode electron flow enters the computational domain, it splits into two electron flows that enter the thruster channel respectively. One electron flows migrate towards the anode, while the other electron flows escape from the computational domain towards the virtual cathode. The electrons migrating towards the anode trigger ionization collisions with atoms, producing ionized electrons and ions. The electrons reaching the anode will escape into the circuit, while the ions will migrate towards the virtual cathode under the influence of the space potential. The electrons migrating towards the virtual cathode will undergo quasi-neutralization with the ions and then leave the computational domain in a quasi-neutral state. An electron in a neutral gas, in a very short time Collision probability between internal atoms P en for: The distance an electron travels within one time step. f en The frequency of electron-atom collisions. V e The speed of electron movement; in, For correction factor, B The magnetic field strength is at the center of the channel. The spatial potential within the computational domain is solved using the Poisson equation: in, Space potential, The net residual charge density in space. Let be the vacuum permittivity. In the one-dimensional model, it is solved using the three-point difference method. The difference equation is as follows: For nodal potential, z This represents the spatial step size corresponding to the one-dimensional computational domain. and Let z be the ion number density and electron number density of the node, respectively. The boundary condition is: z is located on the anode surface. z =0, ;when z Located on the virtual cathode surface, take charge bubble boundary conditions ; in, Let be the spatial potential function along the computational domain. U This is the discharge voltage. N The number of nodes in the computation domain. i Number the nodes. i=1~N , c This is the ratio of the channel's internal depth to the total length of the computational domain. The convergence criterion for calculating the convergence time includes two steps: the first step is the quasi-neutrality determination of the plume boundary, i.e., the ion flow escaping the plume. I i,out Electron flow with escape plume I ch - I e,in The first step is the equality determination; the second step is the determination of the conservation of current-carrying charge in the circuit, and the electron flow entering the computational domain from the cathode. I ch Electron flow entering the circuit from the computational domain I e,out The equality determination; parameter a The proportion of electron flow into the channel is set to an initial value of 0.1, parameter... a The iterative update algorithm is as follows: The index of 0.75 is an empirical value determined through multiple calculations and practices.

2. The design method for a double-ring nested Hall thruster according to claim 1, characterized in that, In the internal design steps, the peak value of the magnetic induction intensity at the centerline of the channel... B max With magnetic circuit space size H The mathematical relationship is as follows: in, d out The diameter of the outer channel wall.

3. The design method for a double-ring nested Hall thruster according to claim 1, characterized in that, The magnetic material in the magnetic circuit is pure iron DT4C, a common magnetic material used in Hall thrusters, and the upper limit of magnetic saturation of the magnetic material is set at 1.2 T.

4. The design method for a double-ring nested Hall thruster according to claim 1, characterized in that, A total of 1000 computational nodes are set between the anode point and the virtual cathode point on the channel centerline. The spatial step size can be set to be encrypted: the spatial step size of the ionization region is 0.05 mm, and the spatial step size of other regions gradually transitions to 0.2 mm.

5. The design method for a double-ring nested Hall thruster according to claim 1, characterized in that, In cathode electron flow I ch After entering the computational domain, it splits into two electron streams that enter the thruster channels separately. One electron stream... I e,in Migrating towards the anode, another stream of electrons I ch - I e,in Escape the computational domain to the virtual cathode; Secondly, electrons migrating towards the anode will trigger ionization collisions with atoms, producing ionized electrons and ions, and electrons reaching the anode... I e,out When the escape space enters the circuit, the ions will migrate towards the virtual cathode under the influence of the space potential. I i,out Electrons migrating toward the virtual cathode undergo quasi-neutralization with ions, and then leave the computational domain in a quasi-neutral state.

6. A Hall thruster, characterized in that, The design method for a double-ring nested Hall thruster as described in any one of claims 1-5 is adopted.

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