Method for ionospheric vehicle stealth based on regulating electron distribution of tail region

Abstract

The application discloses a method for realizing ionosphere aircraft stealth based on regulating and controlling electron distribution of tail area, first, evolution time scales under different non-extended parameters are calculated; and according to the superhot electron energy and particle flux per unit time required by different non-extended parameters, a radio frequency discharge plasma generator is controlled to generate plasma corresponding to the non-extended parameters; then, in the grid electric field, electrons enter the acceleration field area, and ions are directly discharged to the tail area of the aircraft without acceleration; the regulation and control duration under different non-extended parameters is determined by the evolution time scale corresponding to the non-extended parameter. The application changes the electron distribution of the ionosphere aircraft tail area by randomly injecting high-energy electrons into the tail area of the aircraft, regulates and controls the evolution law and characteristic scale of the non-linear local cavity in the tail area which cannot be eliminated, makes the anti-stealth method of monitoring the motion of the density cavity to detect the ionosphere stealth aircraft invalid, and thus realizes the stealth of the ionosphere stealth aircraft.

Description

Technical Field

[0001] This invention belongs to the technical field of stealth methods for ionospheric stealth aircraft, specifically relating to a method for achieving ionospheric stealth based on controlling the electron distribution in the tail region. Background Technology

[0002] Li [1] The nonlinear governing equations describing the unsteady interaction between ionospheric plasma and moving objects in the static limit were theoretically derived, and it was found that the interaction between high-frequency electromagnetic waves and plasma can induce electromagnetic solitons; Ma and Li [2] Numerical calculations were performed on the unsteady interaction equations in the static limit, and the results show that density cavities and potential solitons are caused by modulation instabilities; Hu and Li [3] A new set of unsteady nonlinear control equations under the nonstatic limit is derived. Numerical calculations reveal that supersonic collapse dominates as modulation instability develops. Evolutionary images of density cavities and electromagnetic solitons in the tail region of the spacecraft are also presented. (Hu and Luo) [4] The evolution of density cavities and electromagnetic solitons in the tail region of the spacecraft was analyzed; Liao et al. [5] The modulation instability of plasma in the tail region of a spacecraft under the nonstatic limit was theoretically studied; Wang et al. [6] The detailed characteristics of plasma modulation instability in the tail region of a spacecraft under unsteady and nonstatic limits were analyzed.

[0003] The above research indicates that the density cavities generated by modulation instabilities in the interaction between plasma and aircraft cannot be eliminated. This provides a practical anti-stealth method for detecting ionospheric stealth aircraft by monitoring the motion of these density cavities. In other words, when conventional radar-stealth aircraft move in the plasma of the ionosphere, modulation instabilities generate density cavities with definite evolution patterns in their tail region plasma, rendering the stealth strategy of ionospheric stealth aircraft ineffective. Numerous domestic and international publications report the use of this method for anti-stealth detection of ionospheric aircraft, but currently, no literature documents a method that can overcome this anti-stealth detection challenge.

[0004] References

[0005] [1] Li XQ, Astrophys. Space Sci. (1989), 153:311.

[0006] [2] Hu TP and Li XQ, Chinese Astronomy and Astrophysics (2003), 27:252.

[0007] [3] Ma SJ and Li XQ, J. Plasma Physics (2002), 67:205.

[0008] [4] Hu TP and Luo Q, Chinese Physics (2007), 16:0179-07.

[0009] [5] Liao JJ, Deng Q and Qu W, Phys. Scr. (2012), 85:065902.

[0010] [6] Wang B; Yang XS; Chen H; Liu SQ, Physica Scripta (2021), 96(10): 105602. Summary of the Invention

[0011] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for achieving ionospheric stealth of aircraft based on the regulation of electron distribution in the tail region. By injecting accelerated electrons, the modulation instability law of the tail region is significantly altered, thereby changing the electron distribution in the tail region of the ionospheric aircraft to regulate the evolution law and characteristic scale of the nonlinear structure in the tail region that cannot be eliminated. This solves the problem that traditional radar stealth aircraft, when moving in the plasma of the ionosphere, suffer from the failure of ionospheric stealth strategies due to the generation of density cavities in the tail region plasma by modulation instability that have a definite evolution law and cannot be erased.

[0012] To achieve the above objectives, the present invention adopts the following technical solution.

[0013] A method for achieving ionospheric stealth of aircraft based on controlling the electron distribution in the tail region includes the following steps:

[0014] Step S1: Based on the theory of modulation instability of non-extensive electrons in the tail region of ionospheric spacecraft, calculate the maximum growth rate of modulation instability under different non-extensive parameters, and then obtain the evolution timescale corresponding to different non-extensive parameters from the reciprocal of the maximum growth rate.

[0015] Step S2: Obtain the required superthermal electron energy and particle flux per unit time for different non-extensive parameter conditions based on the non-extensive statistical equation.

[0016] Step S3: Establish a database of evolution timescales, electron energies and particle fluxes corresponding to different non-extensive parameters, and store it in the data control center of the aircraft stealth control system.

[0017] Step S4: Randomly generate non-extensive parameters through the aircraft stealth control system, and then control the gas flux and power of the radio frequency discharge plasma generator according to the particle flux corresponding to the non-extensive parameters to generate plasma corresponding to the non-extensive parameters.

[0018] Step S5: Inject the plasma generated by the radio frequency discharge plasma generator into a pair of gate electric fields containing a magnetic field, so that electrons and ions are separated. Electrons enter the acceleration field region, and the separated ions are discharged directly to the tail region of the spacecraft without acceleration.

[0019] Step S6: Generate the corresponding voltage for controlling the electron acceleration field based on the electron energy corresponding to the non-extensive parameter. After the electrons are accelerated in the acceleration field region, they are injected into the tail region of the aircraft.

[0020] Step S7: Determine the operating time of the entire system under the corresponding non-extensive parameters based on the evolution timescale corresponding to the non-extensive parameters. Repeat steps S4 to S7 to make the tail region of the aircraft exhibit a series of irregular modulation instability features under different non-extensive parameters that have fully developed. This will render the method of anti-stealth by detecting the evolution law of density cavities in the tail region of the stealth aircraft ineffective, thereby achieving the stealth of the ionospheric aircraft.

[0021] Specifically, the theory for regulating the modulation instability of the ionospheric tail region by non-extended electrons in step S1 includes:

[0022] Under the same conditions, the growth rate of transverse instability is always much greater than that of longitudinal instability; the growth rate of modulation instability increases with the non-extensive parameter. q It increases with the increase of the non-extensive parameter. q The decrease in the rate of increase of high-energy electrons leads to a continuous decrease in the rate of increase of modulation instability, but the characteristic scale of the nonlinear local field and density cavity will increase; non-extensive parameters q The impact on modulation instability is far greater than the initial pump wave field intensity. And electron / ion temperature, and the influence of non-extensive parameters on transverse modulation instability is much greater than that on longitudinal parameters. Therefore, electron non-extensive parameters can effectively control the final characteristics of the nonlinear local structure of plasma in the tail region of the spacecraft.

[0023] Furthermore, the process of calculating the maximum growth rate of modulation instability under different non-extensive parameters in step S1 is as follows:

[0024] Due to the characteristic speed of the moving aircraft The thermal velocity is much greater than that of ions. Therefore, the interaction between the ion flow and the spacecraft is much greater than the impact of collisions; in a coordinate system fixed on the spacecraft ( x ,y , z In this study, based on the collisionless Boltzmann equations for ion distribution, and under low-frequency and quasi-neutral approximation conditions, the influence of slowly varying potentials on ions in the plasma at the tail region of the spacecraft is obtained by investigating the interaction between plasma and the spacecraft surface.

[0025] ;

[0026] In the above formula, to simplify the calculation, the aircraft is assumed to be spherical. and These are the particle densities under undisturbed and disturbed states, respectively. This represents the ion charge, corresponding to the plasma in the tail region of an ionospheric spacecraft. Equal to electron charge ; A slowly changing electric potential; It is the ion temperature; Let be the interaction function between the spacecraft surface and the surrounding plasma. , The thermal velocity of ions, R 0 For the radius of the aircraft, Represents an exponential function; x , y , z For spatial coordinates, z The axis is positioned on the aircraft's axis, pointing towards the tail region of the aircraft;

[0027] Based on the study of the interaction between plasma and the spacecraft surface, and considering the mass-driven dynamics of non-extensive electrons, we obtain the acoustic motion equations that include both the interaction and the mass-driven dynamics of non-extensive electrons:

[0028] ;

[0029] In the above formula, The sign for partial derivatives; For time; For non-extensive parameters of electrons; For specific heat ratio, The value of is determined by the transport process according to the kinetic theory; For electron thermal velocity; For electronic quality; For gradient operators;

[0030] Introduce the following dimensionless variables:

[0031] ;

[0032] In the above formula, The plasma frequency; The speed of sound for ions; The mass-to-charge ratio, ; For spatial length; Electric field strength; For electron temperature; The speed of the aircraft;

[0033] For convenience, the superscript "'" of the dimensionless variables above is omitted, resulting in the following set of dimensionless nonlinear coupling equations:

[0034] ;

[0035] ;

[0036] ;

[0037] In the above formula, It is an imaginary number; These are cylindrical coordinate components, representing the vertical distance from the aircraft's axis.

[0038] The above nonlinear coupling equations describe the density perturbation and slowly varying envelope of the high-frequency field in the spacecraft wake plasma, when the parameters... q When =1, the nonlinear coupling formula conforms to the Maxwell distribution;

[0039] By studying the stability of the nonlinear coupling equations in the Liapunov sense for nonlinear monochromatic waves, the initial solution of the nonlinear coupling equations in the plane wave form is obtained:

[0040] ;

[0041] ;

[0042] ;

[0043] In the above formula, The initial pump wave electric field; The initial pump wave electric field amplitude vector; The wave vector of the initial pump wave field; It is a spatial coordinate vector; The eigenfrequency of the initial pump wave field; It is a unit vector. , Let be the initial pump wave electric field amplitude constant, and , Represents a conjugate vector; The initial perturbation density;

[0044] Since Q is primarily related to the velocity of the aircraft, assuming the aircraft is moving at a constant speed, Q only determines the initial state, and its disturbance... To study the stability of the initial solution, it is assumed that the spacecraft has a small perturbation in the initial pump wave field. If small perturbations are amplified, the solution in the Liapunov sense becomes unstable. By linearizing the perturbation using the nonlinear coupling equations, we obtain:

[0045] ;

[0046] ;

[0047] In the above formula: The vector of the perturbation electric field; The perturbation density; The vector is the conjugate of the perturbation electric field;

[0048] Further consider the following forms of disturbance:

[0049] ;

[0050] ;

[0051] In the above formula, The amplitude of the disturbance density; Let be the amplitude vector of the first transverse perturbation field. , This is the first transverse disturbance field; Let be the amplitude vector of the second transverse perturbation field. , This is the second transverse perturbation field; It is a vector whose amplitude is conjugate to the first transverse perturbation field. , It is the conjugate of the amplitude of the first transverse perturbation field; It is a vector whose amplitude is conjugate to the second transverse perturbation field. , It is the conjugate of the amplitude of the second transverse perturbation field; , , , The vector is the resultant vector of the initial pump wave vector and the disturbance wave vector; , , For perturbation wave vector; , This is the vector difference between the disturbance wave vector and the initial pump wave vector; , It is the superposition of the disturbance wave frequency and the initial pump wave frequency. , The difference between the frequency of the disturbance wave and the frequency of the initial pump wave; and , , The value is irrelevant. It is a real unit vector;

[0052] Will disturbance and Substituting into formula (6), we get:

[0053] ;

[0054] ;

[0055] Further, the eigenfrequency of the initial pump wave field Substituting into formulas (10) and (11) and simplifying, we get:

[0056] ;

[0057] ;

[0058] In the above formula, The initial pump wave field;

[0059] The initial perturbation density is obtained from the simplified formula. The elimination of the relevant terms indicates that modulation instability is indirectly related to the initial perturbation density distribution, which means that modulation instability has a more general significance.

[0060] Similarly, disturbance and Substituting into formula (7), we get:

[0061] ;

[0062] In the above formula, The dot product of the perturbation wave vector and itself;

[0063] Combining formulas (12) and (14), the dispersion relation expression is obtained as follows:

[0064] ;

[0065] In the above formula, The dot product of the wave vector of the initial pump wave field and itself;

[0066] Assumption It is a real unit vector, and is defined as follows: yes and The angle between them yes and The angle between them yes and The angle between them, where ; yes and The angle between them, where ; yes and The angle between them, where Then formula (15) can be rewritten as:

[0067] ;

[0068] In the above formula, ; This represents the dot product of the perturbation wave vector and the wave vector of the initial pump wave field;

[0069] Equation (16) describes the development of modulation instabilities of longitudinal and transverse perturbations in the contrail plasma of a spacecraft, taking into account The amplitude is determined by The amplitude modulation will only be considered in the subsequent analysis. In this case, formula (16) involves 6 complex roots with 5 angles, making it difficult to obtain a direct result. Therefore, we need to further analyze the characteristics of the horizontal and vertical patterns theoretically.

[0070] Lateral disturbance In the case of, assuming Approximate assumptions are made along the aircraft's central axis in the direction of its wake. and Then the dispersion relation expression for the transverse perturbation is further obtained as:

[0071] ;

[0072] when When the solution to the dispersion relation expression for the transverse perturbation has imaginary roots, indicating the existence of modulation instability, the corresponding transverse perturbation instability growth rate... for:

[0073] ;

[0074] In the above formula, To modulate the instability growth rate, superscript t Indicates the lateral perturbation mode;

[0075] Longitudinal disturbance In the case of approximate assumptions and Then, the dispersion relation expression for the longitudinal perturbation is further obtained as:

[0076] ;

[0077] when When the solution to the dispersion relation expression for the longitudinal perturbation has imaginary roots, i.e., modulation instability exists, the corresponding growth rate of the longitudinal perturbation instability is:

[0078] ;

[0079] In the above formula, To modulate the instability growth rate, superscript l Indicates the longitudinal perturbation mode;

[0080] Due to the plasma in the spacecraft's contrail According to formulas (18) and (20), the horizontal disturbance growth rate of instability is much greater than the vertical disturbance growth rate. In summary, the maximum growth rate of modulation instability in step S1 is calculated by formula (18).

[0081] The competition among all unstable modes during the development of modulation instability ultimately reveals the unstable mode with the highest growth rate in the space wake plasma; the calculation results of formula (16) above show that the growth rate of modulation instability varies with the non-extensive parameter. q The characteristic scale of the local field and density cavity increases with the increase of the length; the influence of the non-extensive parameter on the growth rate of modulation instability of the transverse mode and the characteristic scale of modulation instability of the transverse mode is significantly greater than that on the longitudinal mode. These analytical results indicate that selectively injecting high-energy electrons into the tail region of the spacecraft can change the electron distribution, which will change the characteristics of the nonlinear local density cavity caused by modulation instability, making it difficult for stealth spacecraft to detect accurately.

[0082] Furthermore, in step S1, the evolution timescales corresponding to different non-extensive parameters are obtained from the reciprocal of the maximum growth rate. The calculation process is as follows:

[0083] Based on the plasma parameters measured in the tail region of the spacecraft, a certain non-extensive parameter is selected. q Value, substitute into the equation

[0084] In the middle, different wavenumbers were calculated. k Corresponding growth rate Then, further comparative analysis was conducted to obtain different wavenumbers. k The largest growth rate The value, then by Get the qThe timescale T required for the unstable mode corresponding to the value to evolve and develop.

[0085] Specifically, step S2 involves obtaining the required superthermal electron energy and particle flux per unit time based on non-extensive statistics to achieve different non-extensive parameters. The process is as follows:

[0086] Based on the measured plasma parameters in the tail region of the spacecraft, substituting them into the non-extensive statistical equations and... In the McElligott statistical equation, the expression for the non-extensive statistical equation is as follows:

[0087] ;

[0088] In the above formula, Let be the three-dimensional equilibrium distribution function of the aircraft; It is the ionic momentum; The normalization constant is ; As a parameter, when hour, ;when When, the equilibrium distribution function It is divergent, when At that time, the particle's momentum has an upper limit. ,when When it approaches 1, Approaching infinity, formula (21) reverts to the classic Boltzmann distribution function; The thermal velocity of the particle;

[0089] The average electron energy and number of particles to be injected are calculated based on the difference between the results of the two statistical equations. Then, the time scale T required for the evolution of the unstable mode is combined to obtain the required superthermal electron energy and particle flux per unit time.

[0090] Specifically, in step S3, a database of evolution timescales, electron energies, and particle fluxes corresponding to different non-extensional parameters is established, as follows:

[0091] By selecting a series of non-extensive parameters q The value is then calculated by repeating steps S1 and S2 to obtain a series of data, namely each non-extensive parameter. q The corresponding evolution timescale T, electron energy, and particle flux are stored in a database for easy access in subsequent steps.

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] The method of this invention significantly alters the modulation instability law of the tail region by injecting accelerating electrons. This solves the problem that traditional radar-stealing aircraft, when moving in the plasma of the ionosphere, suffer from the failure of their stealth strategy due to the generation of density cavities in the tail region plasma caused by modulation instability, which have a definite evolution law and cannot be erased. This renders anti-stealth weapons that track the density cavities in the tail region of ionospheric stealth aircraft, such as cruise missiles that are stealthy against radar detection, ineffective. Thus, ionospheric stealth aircraft can still achieve stealth when facing such anti-stealth weapons. Attached Figure Description

[0094] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of this disclosure and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0095] Figure 1 This is a flowchart of the method of the present invention;

[0096] Figure 2 This is a schematic diagram illustrating how the invention alters the electron distribution in a plasma environment by injecting high-energy electrons into the tail region of a spacecraft.

[0097] Figure 3 The longitudinal modulation instability as a function of wavenumber in this embodiment of the invention k A diagram illustrating the growth rate;

[0098] Figure 4 The transverse modulation instability as a function of wavenumber in this embodiment of the invention k A diagram illustrating the growth rate;

[0099] Figure 5 The maximum growth rate of the longitudinal disturbance and its corresponding wavenumber in the embodiments of the present invention. k With non-extended parameters A graph showing the changes;

[0100] Figure 6 The maximum growth rate of the transverse disturbance and its corresponding wavenumber in the embodiments of the present invention. k With non-extended parameters A graph showing the changes. Detailed Implementation

[0101] To facilitate understanding and implementation of the present invention by those skilled in the art, the various steps of the method proposed in this invention are described in detail below. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various modifications or alterations to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0102] Example 1

[0103] like Figure 1 As shown, this invention discloses a method for achieving ionospheric stealth of spacecraft based on controlling the electron distribution in the tail region, comprising the following steps:

[0104] Step S1: Based on the theory of modulation instability of non-extensive electrons in the tail region of ionospheric spacecraft, calculate the maximum growth rate of modulation instability under different non-extensive parameters, and then obtain the evolution timescale corresponding to different non-extensive parameters from the reciprocal of the maximum growth rate.

[0105] Step S2: Obtain the required superthermal electron energy and particle flux per unit time for different non-extensive parameter conditions based on the non-extensive statistical equation.

[0106] Step S3: Establish a database of evolution timescales, electron energies and particle fluxes corresponding to different non-extensive parameters, and store it in the data control center of the aircraft stealth control system.

[0107] Step S4: Randomly generate non-extensive parameters through the aircraft stealth control system, and then control the gas flux and power of the radio frequency discharge plasma generator according to the particle flux corresponding to the non-extensive parameters to generate plasma corresponding to the non-extensive parameters.

[0108] Step S5: Inject the plasma generated by the radio frequency discharge plasma generator into a pair of gate electric fields containing a magnetic field, so that electrons and ions are separated. Electrons enter the acceleration field region, and the separated ions are discharged directly to the tail region of the spacecraft without acceleration.

[0109] Step S6: Generate the corresponding voltage for controlling the electron acceleration field based on the electron energy corresponding to the non-extensive parameter. After the electrons are accelerated in the acceleration field region, they are injected into the tail region of the aircraft.

[0110] Step S7: Determine the operating time of the entire system under the corresponding non-extensive parameters based on the evolution timescale corresponding to the non-extensive parameters. Repeat steps S4 to S7 to make the tail region of the aircraft exhibit a series of irregular modulation instability features under different non-extensive parameters that have fully developed. This will render the method of anti-stealth by detecting the evolution law of density cavities in the tail region of the stealth aircraft ineffective, thereby achieving the stealth of the ionospheric aircraft.

[0111] Specifically, the theory for regulating the modulation instability of the ionospheric tail region by non-extended electrons in step S1 includes:

[0112] Under the same conditions, the growth rate of transverse instability is always much greater than that of longitudinal instability; the growth rate of modulation instability increases with the non-extensive parameter. q It increases with the increase of the non-extensive parameter. q The decrease in the rate of increase of high-energy electrons leads to a continuous decrease in the rate of increase of modulation instability, but the characteristic scale of the nonlinear local field and density cavity will increase; non-extensive parameters q The impact on modulation instability is far greater than the initial pump wave field intensity. And electron / ion temperature, and the influence of non-extensive parameters on transverse modulation instability is much greater than that on longitudinal parameters. Therefore, electron non-extensive parameters can effectively control the final characteristics of the nonlinear local structure of plasma in the tail region of the spacecraft.

[0113] Furthermore, the process of calculating the maximum growth rate of modulation instability under different non-extensive parameters in step S1 is as follows:

[0114] Considering the non-extensive distribution of electrons, through hydrodynamic analysis, the continuity equation and momentum equation for non-extensive electrons can be expressed as follows:

[0115] ;

[0116] ;

[0117] in: ; ; ;

[0118] In the above formula, The sign for partial derivatives; Electron density; For time; For gradient operators; For electron velocity; Let be the charge of one electron; For electronic quality; Electric field strength; The speed of light; It represents the magnetic flux density; For non-extensive parameters of electrons; For specific heat ratio, The value is determined by the transport process according to the kinetic theory; For electron temperature; Ion density; This refers to the ion velocity.

[0119] In ordinary plasma, due to the significant difference in oscillation frequencies between electrons and ions, two timescales can be clearly distinguished: the fast timescale and the fast timescale. and slow time scale Based on the dual-timescale approximation theory, all physical quantities It can be divided into fast timescale components and slow timescale components:

[0120] ;

[0121] In the above formula, For fast time-scaled components; For slow time-scale components;

[0122] Assume that the average of the fast timescale with respect to the slow timescale is equal to zero. Furthermore, the quasi-neutrality condition is valid on a slow time scale, i.e., there exists , ,in, This is the slowly varying component of electron density; This represents the slowly varying component of ion density; This is a slowly varying density component; and These are the particle densities under undisturbed and disturbed states, respectively.

[0123] exist and Under approximate conditions, where For turbulence parameters, For fast-changing electric field components, For frequency, Let be the plasma frequency. Substituting the fast and slow time-scale components of all physical quantities into the continuity and momentum equations for non-extensive electrons, we obtain the slow motion continuity and momentum equations for electrons, as well as the transport equations for the rapid oscillations of the electric field, as follows:

[0124] ;

[0125] ;

[0126] ;

[0127] In the above formula, It is a slow-changing speed; A slowly changing electric potential; The initial pump wave field intensity; It is an imaginary number; For plasma frequency, ; For electron thermal velocity;

[0128] For small perturbations By combining the continuity equation and momentum equation for the slow motion of electrons, as well as the transport equation for the rapid oscillation of the electric field, we obtain the equation for the acoustic motion driven by coupled non-thermal effects and mass dynamics:

[0129] ;

[0130] Due to the characteristic speed of the moving aircraft The thermal velocity is much greater than that of ions. Therefore, the interaction between the ion flow and the spacecraft is much greater than the impact of collisions; in a coordinate system fixed on the spacecraft ( x , y , z In this study, based on the collisionless Boltzmann equations for ion distribution, and under low-frequency and quasi-neutral approximation conditions, the influence of slowly varying potentials on ions in the plasma at the tail region of the spacecraft is obtained by investigating the interaction between plasma and the spacecraft surface.

[0131] ;

[0132] In the above formula, to simplify the calculation, the aircraft is assumed to be spherical. and These are the particle densities under undisturbed and disturbed states, respectively. This refers to the ionic charge, which corresponds to the plasma in the tail region of an ionospheric spacecraft and is equal to the electron charge. ; A slowly changing electric potential; It is the ion temperature; Let be the interaction function between the spacecraft surface and the surrounding plasma. , The thermal velocity of ions, R 0 For the radius of the aircraft, Represents an exponential function; x , y , z For spatial coordinates, z The axis is positioned on the aircraft's axis, pointing towards the tail region of the aircraft;

[0133] Based on the study of the interaction between plasma and the spacecraft surface, and considering the mass-driven dynamics of non-extensive electrons, we obtain the acoustic motion equations that include both the interaction and the mass-driven dynamics of non-extensive electrons:

[0134] ;

[0135] In the above formula, The sign for partial derivatives; For time; For non-extensive parameters of electrons; For specific heat ratio, The value of is determined by the transport process according to the kinetic theory; For electron thermal velocity; For electronic quality; For gradient operators;

[0136] Introduce the following dimensionless variables:

[0137] ;

[0138] In the above formula, The plasma frequency; The speed of sound for ions; The mass-to-charge ratio, ; For spatial length; Electric field strength; For electron temperature; The speed of the aircraft;

[0139] For convenience, the superscript "'" of the dimensionless variables above is omitted, resulting in the following set of dimensionless nonlinear coupling equations:

[0140] ;

[0141] ;

[0142] ;

[0143] In the above formula, It is an imaginary number; These are cylindrical coordinate components, representing the vertical distance from the aircraft's axis.

[0144] The above nonlinear coupling equations describe the density perturbation and slowly varying envelope of the high-frequency field in the spacecraft wake plasma, when the parameters... q When =1, the nonlinear coupling formula conforms to the Maxwell distribution;

[0145] By studying the stability of the nonlinear coupling equations in the Liapunov sense for nonlinear monochromatic waves, the initial solution of the nonlinear coupling equations in the plane wave form is obtained:

[0146] ;

[0147] ;

[0148] ;

[0149] In the above formula, The initial pump wave electric field; The initial pump wave electric field amplitude vector; The wave vector of the initial pump wave field; It is a spatial coordinate vector; The eigenfrequency of the initial pump wave field; It is a unit vector. , Let be the initial pump wave electric field amplitude constant, and , Represents a conjugate vector; The initial perturbation density;

[0150] Since Q is primarily related to the velocity of the aircraft, assuming the aircraft is moving at a constant speed, Q only determines the initial state, and its disturbance... To study the stability of the initial solution, it is assumed that the spacecraft has a small perturbation in the initial pump wave field. If small perturbations are amplified, the solution in the Liapunov sense becomes unstable. By linearizing the perturbation using the nonlinear coupling equations, we obtain:

[0151] ;

[0152] ;

[0153] In the above formula: The vector of the perturbation electric field; The perturbation density; The vector is the conjugate of the perturbation electric field;

[0154] Further consider the following forms of disturbance:

[0155] ;

[0156] ;

[0157] In the above formula, The amplitude of the disturbance density; Let be the amplitude vector of the first transverse perturbation field. , This is the first transverse disturbance field; Let be the amplitude vector of the second transverse perturbation field. , This is the second transverse perturbation field; It is a vector whose amplitude is conjugate to the first transverse perturbation field. , It is the conjugate of the amplitude of the first transverse perturbation field; It is a vector whose amplitude is conjugate to the second transverse perturbation field. , It is the conjugate of the amplitude of the second transverse perturbation field; , , , The vector is the resultant vector of the initial pump wave vector and the disturbance wave vector; , , For perturbation wave vector; , This is the vector difference between the disturbance wave vector and the initial pump wave vector; , It is the superposition of the disturbance wave frequency and the initial pump wave frequency. , The difference between the frequency of the disturbance wave and the frequency of the initial pump wave; and , , The value is irrelevant. It is a real unit vector;

[0158] Will disturbance and Substituting into formula (6), we get:

[0159] ;

[0160] ;

[0161] Further, the eigenfrequency of the initial pump wave field Substituting into formulas (10) and (11) and simplifying, we get:

[0162] ;

[0163] ;

[0164] In the above formula, The initial pump wave field;

[0165] The initial perturbation density is obtained from the simplified formula. The elimination of the relevant terms indicates that modulation instability is indirectly related to the initial perturbation density distribution, which means that modulation instability has a more general significance.

[0166] Similarly, disturbance and Substituting into formula (7), we get:

[0167] ;

[0168] In the above formula, The dot product of the perturbation wave vector and itself;

[0169] Combining formulas (12) and (14), the dispersion relation expression is obtained as follows:

[0170] ;

[0171] In the above formula, The dot product of the wave vector of the initial pump wave field and itself;

[0172] Assumption It is a real unit vector, and is defined as follows: yes and The angle between them yes and The angle between them yes and The angle between them, where ; yes and The angle between them, where ; yes and The angle between them, where Then formula (15) can be rewritten as:

[0173] ;

[0174] In the above formula, ; This represents the dot product of the perturbation wave vector and the wave vector of the initial pump wave field;

[0175] Equation (16) describes the development of modulation instabilities of longitudinal and transverse perturbations in the contrail plasma of a spacecraft, taking into account The amplitude is determined by The amplitude modulation will only be considered in the subsequent analysis. In this case, formula (16) involves 6 complex roots with 5 angles, making it difficult to obtain a direct result. Therefore, we need to further analyze the characteristics of the horizontal and vertical patterns theoretically.

[0176] Lateral disturbance In the case of, assuming Approximate assumptions are made along the aircraft's central axis in the direction of its wake. and Then the dispersion relation expression for the transverse perturbation is further obtained as:

[0177] ;

[0178] when When the solution to the dispersion relation expression for the transverse perturbation has imaginary roots, indicating the existence of modulation instability, the corresponding transverse perturbation instability growth rate... for:

[0179] ;

[0180] In the above formula, To modulate the instability growth rate, superscript t Indicates the lateral perturbation mode;

[0181] Longitudinal disturbance In the case of approximate assumptions and Then, the dispersion relation expression for the longitudinal perturbation is further obtained as:

[0182] ;

[0183] when When the solution to the dispersion relation expression for the longitudinal perturbation has imaginary roots, i.e., modulation instability exists, the corresponding growth rate of the longitudinal perturbation instability is:

[0184] ;

[0185] In the above formula, To modulate the instability growth rate, superscript l Indicates the longitudinal perturbation mode;

[0186] Due to the plasma in the spacecraft's contrail According to formulas (18) and (20), the horizontal disturbance growth rate of instability is much greater than the vertical disturbance growth rate. In summary, the maximum growth rate of modulation instability in step S1 is calculated by formula (18).

[0187] Furthermore, in step S1, the evolution timescales corresponding to different non-extensive parameters are obtained from the reciprocal of the maximum growth rate. The calculation process is as follows:

[0188] Based on the plasma parameters measured in the tail region of the spacecraft, a certain non-extensive parameter is selected. q Value, substitute into the equation

[0189] In the middle, different wavenumbers were calculated. k Corresponding growth rate Then, further comparative analysis was conducted to obtain different wavenumbers. k The largest growth rate The value, then by Get the q The timescale T required for the unstable mode corresponding to the value to evolve and develop.

[0190] Specifically, step S2 involves obtaining the required superthermal electron energy and particle flux per unit time based on non-extensive statistics to achieve different non-extensive parameters. The process is as follows:

[0191] Based on the measured plasma parameters in the tail region of the spacecraft, substituting them into the non-extensive statistical equations and... In the McElligott statistical equation, the expression for the non-extensive statistical equation is as follows:

[0192] ;

[0193] In the above formula, Let be the three-dimensional equilibrium distribution function of the aircraft; It is the ionic momentum; The normalization constant is ; As a parameter, when hour, ;when When, the equilibrium distribution function It is divergent, when At that time, the particle's momentum has an upper limit. ,when When it approaches 1, Approaching infinity, formula (21) reverts to the classic Boltzmann distribution function; The thermal velocity of the particle;

[0194] The average electron energy and number of particles to be injected are calculated based on the difference between the results of the two statistical equations. Then, the time scale T required for the evolution of the unstable mode is combined to obtain the required superthermal electron energy and particle flux per unit time.

[0195] Specifically, in step S3, a database of evolution timescales, electron energies, and particle fluxes corresponding to different non-extensional parameters is established, as follows:

[0196] By selecting a series of non-extensive parameters q The value is then calculated by repeating steps S1 and S2 to obtain a series of data, namely each non-extensive parameter. q The corresponding evolution timescale T, electron energy, and particle flux are stored in a database for easy access in subsequent steps.

[0197] The following verification of the proposed theory on the modulation instability of the tail region of ionospheric spacecraft by non-extended electrons demonstrates the scientific validity of the method.

[0198] Since the dispersion relation formula (16) for modulation instability involves 6 complex roots at 5 angles, the following analysis will be performed using numerical calculation methods:

[0199] First, set the parameters of the spacecraft and its wake plasma: .

[0200] In order to obtain and The effect on modulation instability, Under the given conditions, in this example, we approximate... , , and ;

[0201] like Figure 3 As shown in (a), Different angles Growth rate and wave number A relationship curve graph, where each curve corresponds to a different relationship from bottom to top. , , , The growth rate at that time; by Figure 3 As can be seen in (a), the growth rate of longitudinal modulation instability increases with angle. It increases with the increase of, and The maximum value is found at the point where the longitudinal modulation instability relation (20) is obtained.

[0202] like Figure 3 As shown in (b), Different initial pump field strengths The graph below shows the relationship between the growth rate and the wave number k, where each curve corresponds to a different value from bottom to top. The growth rates are 2.87, 3.5, and 5.0.

[0203] like Figure 3 Figure (c) shows when and Time growth rate and non-extensive parameters A relationship curve graph, where each curve corresponds to a different relationship from bottom to top. The growth rates are 0.65, 1.0, and 2.6.

[0204] like Figure 3 The diagram in (d) shows when , The graph shows the effect of the ratio of ion temperature to electron temperature on the instability growth rate, where each curve corresponds to a different value from bottom to top. The growth rates are for 3000K, 2000K, and 1000K.

[0205] Similarly, for and The effect on modulation instability can also be approximated by taking , , and ;

[0206] like Figure 4 Figure (a) shows when Different angles growth rate and wave number at the location A relationship curve graph, where each curve corresponds to a different relationship from top to bottom. , , and The growth rate at that time, from Figure 4 As can be seen in (a), the growth rate of transverse modulation instability increases with angle. The increase decreases, There is a maximum growth rate, which corresponds to the transverse modulation instability relation (18).

[0207] like Figure 4 Figure (b) shows when Different intensities Growth rate and wave number A relationship curve graph, where each curve corresponds to a different relationship from bottom to top. The growth rates are 2.87, 3.5, and 5.0.

[0208] like Figure 4 Figure (c) shows when and Time-indefinite parameters The graph shows the impact of the growth rate, where each curve corresponds to the following from bottom to top: The growth rates are 0.65, 1.0, and 2.6.

[0209] like Figure 4 The diagram in (d) shows when , The graph shows the effect of the ratio of ion temperature to electron temperature on the instability growth rate, where each curve corresponds to a different value from bottom to top. The growth rates are for 3000K, 2000K, and 1000K.

[0210] Figure 5 (a) and Figure 5 (b) represents when The maximum growth rate of longitudinal disturbance and its corresponding wavenumber k With non-extended parameters A graph showing the changes.

[0211] Figure 6 (a) and Figure 6 (b) represents when The maximum growth rate of the transverse disturbance and its corresponding wavenumber k With non-extended parameters A graph showing the changes.

[0212] contrast Figure 3 (a) and Figure 4 In (a), it can be observed that, under the same conditions, the growth rate of lateral instability is always much greater than the growth rate of longitudinal instability; in contrast... Figure 3 (b) and Figure 4 In (b), it can be observed that the rate of increase of instability increases with intensity. The maximum growth rate of modulation instability increases with the increase of intensity, and is approximately equal to the increase of intensity. The growth rate of modulation instability is directly proportional to the non-extensive parameter. It increases with the increase of; and Figure 3 (c) and Figure 4 As shown in (c), this corresponds precisely to the non-extensive statistical equation in Maxwell's distribution at that time; comparison Figure 3 (d) and Figure 4 As can be seen in (d), the growth rate of the instability growth rate increases slightly as the ratio of ion temperature to electron temperature increases.

[0213] like Figure 5 (a) and Figure 6 Figure (a) shows the longitudinal and lateral perturbations in the non-extensive parameter. The maximum growth rate below; such as Figure 5 (b) and Figure 6 Figure (b) shows the maximum wavenumbers for longitudinal and lateral disturbances under the non-spreading parameters, respectively; (Comparison) Figure 5 (a) and Figure 6 As shown in (a), the maximum growth rate of modulation instability and its corresponding wavenumber vary with the non-extensive parameter. The characteristic scale of the nonlinear local field and density increases with the increase of the value of the density, and can be derived from the fact that the characteristic scale of the nonlinear local field and density can be derived from the fact that the characteristic scale of the density increases with the increase of the value of the density. Obtain; Compare Figure 5 (b) and Figure 6 As shown in (b), with the non-extensive parameter The decrease in energy, i.e. the increase in high-energy electrons, reduces the growth rate of modulation instability, but the characteristic scale and density of the nonlinear local field will increase; and the influence of nonthermal effects on transverse modulation instability is much greater than that on longitudinal modulation instability. In addition, transverse modulation instability will determine the final characteristics of the wake plasma.

[0214] Based on the above analysis, it can be seen that the growth rates of both horizontal and vertical modulation instability increase with the non-extensive parameter. q The influence of non-extensive parameters on transverse modulation instability increases with the increase of the longitudinal mode. As modulation instability evolves in the wake plasma, transverse modulation instability determines the characteristic scale of the local field and density cavity, and the characteristic scale increases with the increase of the longitudinal mode. q The increase in the value decreases the value of the non-extensional parameter. A smaller non-extensional parameter corresponds to a larger free energy in the system. The accumulation of free energy suppresses the development of modulation instability, leading to an expansion of the characteristic scale of the nonlinear local structure. Compared with the adjustment of other parameters, the non-extensional parameter... q The most effective and feasible control method is the one proposed in this invention. These results are consistent with the theory of non-extended electron modulation instability in the tail region of ionospheric spacecraft proposed in this invention. This shows that the electron distribution can be changed by selectively injecting high-energy electrons into the tail region. This will change the characteristics of the nonlinear local density cavity caused by modulation instability, making it difficult for stealth spacecraft to detect accurately. This proves the feasibility and scientific nature of the method proposed in this invention.

[0215] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for achieving ionospheric stealth of aircraft based on controlling the electron distribution in the tail region, characterized in that, Includes the following steps: Step S1: Based on the theory of modulation instability of non-extensive electrons in the tail region of ionospheric spacecraft, calculate the maximum growth rate of modulation instability under different non-extensive parameters, and then obtain the evolution timescale corresponding to different non-extensive parameters from the reciprocal of the maximum growth rate. The theory of non-extended electron modulation instability in the tail region of ionospheric spacecraft includes: Under the same conditions, the growth rate of transverse instability is always much greater than that of longitudinal instability; the growth rate of modulation instability increases with the non-extensive parameter. q It increases with the increase of the non-extensive parameter. q The decrease in the rate of increase of high-energy electrons leads to a continuous decrease in the rate of increase of modulation instability, but the characteristic scale of the nonlinear local field and density cavity will increase; non-extensive parameters q The impact on modulation instability is far greater than the initial pump wave field intensity. And electron / ion temperature, and the influence of non-extensive parameters on transverse modulation instability is much greater than that on longitudinal parameters. Therefore, electron non-extensive parameters can effectively control the final characteristics of the nonlinear local structure of plasma in the tail region of the spacecraft. The process of calculating the maximum growth rate of modulation instability under different non-extensibility parameters is as follows: Due to the characteristic speed of the moving aircraft The thermal velocity is much greater than that of ions. Therefore, the interaction between the ion flow and the spacecraft is much greater than the impact of collisions; in a coordinate system fixed on the spacecraft ( x , y , z In this study, based on the collisionless Boltzmann equations for ion distribution, and under low-frequency and quasi-neutral approximation conditions, the influence of slowly varying potentials on ions in the plasma at the tail region of the spacecraft is obtained by investigating the interaction between plasma and the spacecraft surface. ； In the above formula, to simplify the calculation, the aircraft is assumed to be spherical. and These are the particle densities under undisturbed and disturbed states, respectively. This refers to the ionic charge, which corresponds to the plasma in the tail region of an ionospheric spacecraft and is equal to the electron charge. ; A slowly changing electric potential; It is the ion temperature; Let be the interaction function between the spacecraft surface and the surrounding plasma. , The thermal velocity of ions, R 0 For the radius of the aircraft, Represents an exponential function; x , y , z For spatial coordinates, z The axis is positioned on the aircraft's axis, facing the tail region of the aircraft; Based on the study of the interaction between plasma and the spacecraft surface, and considering the mass-driven dynamics of non-extensive electrons, we obtain the acoustic motion equations that include both the interaction and the mass-driven dynamics of non-extensive electrons: ； In the above formula, The sign for partial derivatives; For time; For non-extensive parameters of electrons; For specific heat ratio, The value of is determined by the transport process according to the kinetic theory; For electron thermal velocity; For electronic quality; For gradient operators; Introduce the following dimensionless variables: ； In the above formula, The plasma frequency; The speed of sound for ions; The mass-to-charge ratio, ; For spatial length; Electric field strength; For electron temperature; The speed of the aircraft; For convenience, the superscript "'" of the dimensionless variables above is omitted, resulting in the following set of dimensionless nonlinear coupling equations: ； ； ； In the above formula, It is an imaginary number; These are cylindrical coordinate components, representing the vertical distance from the aircraft's axis. The above nonlinear coupling equations describe the density perturbation and slowly varying envelope of the high-frequency field in the spacecraft wake plasma, when the parameters q When =1, the nonlinear coupling formula conforms to the Maxwell distribution; By studying the stability of the nonlinear coupling equations in the Liapunov sense for nonlinear monochromatic waves, the initial solution of the nonlinear coupling equations in the plane wave form is obtained: ； ； ； In the above formula, The initial pump wave electric field; The initial pump wave electric field amplitude vector; The wave vector of the initial pump wave field; It is a spatial coordinate vector; The eigenfrequency of the initial pump wave field; It is a unit vector. , Let be the initial pump wave electric field amplitude constant, and , Represents a conjugate vector; The initial perturbation density; Since Q is primarily related to the velocity of the aircraft, assuming the aircraft is moving at a constant speed, Q only determines the initial state, and its disturbance... To study the stability of the initial solution, it is assumed that the spacecraft has a small perturbation in the initial pump wave field. If small perturbations are amplified, the solution in the Liapunov sense becomes unstable. By linearizing the perturbation using the nonlinear coupling equations, we obtain: ； ； In the above formula: The vector of the perturbation electric field; The perturbation density; The vector is the conjugate of the perturbation electric field; Further consider the following forms of disturbance: ； ； In the above formula, The amplitude of the disturbance density; Let be the amplitude vector of the first transverse perturbation field. , This is the first transverse disturbance field; Let be the amplitude vector of the second transverse perturbation field. , This is the second transverse perturbation field; It is a vector whose amplitude is conjugate to the first transverse perturbation field. , It is the conjugate of the amplitude of the first transverse perturbation field; It is a vector whose amplitude is conjugate to the second transverse perturbation field. , It is the conjugate of the amplitude of the second transverse perturbation field; , , , The vector is the resultant vector of the initial pump wave vector and the disturbance wave vector; , , For the perturbation wave vector; , This is the vector difference between the disturbance wave vector and the initial pump wave vector; , It is the superposition of the disturbance wave frequency and the initial pump wave frequency. , The difference between the frequency of the disturbance wave and the frequency of the initial pump wave; and , , The value is irrelevant. It is a real unit vector; Will disturbance and Substituting into formula (6), we get: ； ； Further, the eigenfrequency of the initial pump wave field Substituting into formulas (10) and (11) and simplifying, we get: ； ； In the above formula, The initial pump wave field; The initial perturbation density is obtained from the simplified formula. The elimination of the relevant terms indicates that modulation instability is indirectly related to the initial perturbation density distribution, which means that modulation instability has a more general significance. Similarly, disturbance and Substituting into formula (7), we get: ； In the above formula, The dot product of the perturbation wave vector and itself; Combining formulas (12) and (14), the dispersion relation expression is obtained as follows: ； In the above formula, The dot product of the wave vector of the initial pump wave field and itself; Assumption It is a real unit vector, and is defined as follows: yes and The angle between them yes and The angle between them yes and The angle between them, where ; yes and The angle between them, where ; yes and The angle between them, where Then formula (15) can be rewritten as: ； In the above formula, ; This represents the dot product of the perturbation wave vector and the wave vector of the initial pump wave field; Equation (16) describes the development of modulation instabilities of longitudinal and transverse perturbations in the contrail plasma of a spacecraft, taking into account The amplitude is determined by The amplitude is modulated, and only the amplitude is considered in the subsequent analysis. In this case, formula (16) involves 6 complex roots with 5 angles, making it difficult to obtain a direct result. Therefore, we need to further analyze the characteristics of the horizontal and vertical patterns theoretically. Lateral disturbance In the case of, assuming Approximate assumptions are made along the aircraft's central axis in the direction of its wake. and Then the dispersion relation expression for the transverse perturbation is further obtained as: ； when When the solution to the dispersion relation expression for the transverse perturbation has imaginary roots, indicating the existence of modulation instability, the corresponding transverse perturbation instability growth rate... for: ； In the above formula, To modulate the instability growth rate, superscript t Indicates the lateral perturbation mode; Longitudinal disturbance In the case of approximate assumptions and Then, the dispersion relation expression for the longitudinal perturbation is further obtained as: ； when When the solution to the dispersion relation expression for the longitudinal perturbation has imaginary roots, i.e., modulation instability exists, the corresponding growth rate of the longitudinal perturbation instability is: ； In the above formula, To modulate the instability growth rate, superscript l Indicates the longitudinal perturbation mode; Due to the plasma in the spacecraft's contrail According to formulas (18) and (20), the horizontal disturbance growth rate of instability is much greater than the vertical disturbance growth rate. In summary, the maximum growth rate of modulation instability in step S1 is calculated by formula (18). Step S2: Obtain the required superthermal electron energy and particle flux per unit time for different non-extensive parameter conditions based on the non-extensive statistical equation. Step S3: Establish a database of evolution timescales, electron energies and particle fluxes corresponding to different non-extensive parameters, and store it in the data control center of the aircraft stealth control system. Step S4: Randomly generate non-extensive parameters through the aircraft stealth control system, and then control the gas flux and power of the radio frequency discharge plasma generator according to the particle flux corresponding to the non-extensive parameters to generate plasma corresponding to the non-extensive parameters. Step S5: Inject the plasma generated by the radio frequency discharge plasma generator into a pair of gate electric fields containing a magnetic field, so that electrons and ions are separated. Electrons enter the acceleration field region, and the separated ions are discharged directly to the tail region of the spacecraft without acceleration. Step S6: Generate the corresponding voltage for controlling the electron acceleration field based on the electron energy corresponding to the non-extensive parameter. After the electrons are accelerated in the acceleration field region, they are injected into the tail region of the aircraft. Step S7: Determine the operating time of the entire system under the corresponding non-extensive parameters based on the evolution timescale corresponding to the non-extensive parameters. Repeat steps S4 to S7 to make the tail region of the aircraft exhibit a series of irregular modulation instability features under different non-extensive parameters that have fully developed. This will render the method of anti-stealth by detecting the evolution law of density cavities in the tail region of the stealth aircraft ineffective, thereby achieving the stealth of the ionospheric aircraft.

2. The method for achieving ionospheric stealth of a spacecraft based on controlling the electron distribution in the tail region according to claim 1, characterized in that, In step S1, the evolution timescales corresponding to different non-extensive parameters are obtained from the reciprocal of the maximum growth rate. The calculation process is as follows: Based on the plasma parameters measured in the tail region of the spacecraft, a non-extensive parameter is selected. q Value, substitute into the equation In the middle, different wavenumbers were calculated. k Corresponding growth rate Then, further comparative analysis was conducted to obtain different wavenumbers. k The largest growth rate The value, then by Get the q The timescale T required for the unstable mode corresponding to the value to evolve and develop.

3. The method for achieving ionospheric stealth of a spacecraft based on controlling the electron distribution in the tail region according to claim 2, characterized in that, The process described in step S2, which involves obtaining the required superthermal electron energy and particle flux per unit time for different non-extensive parameters based on non-extensive statistics, is as follows: Based on the measured plasma parameters in the tail region of the spacecraft, substituting them into the non-extensive statistical equations and... In the McElligott statistical equation, the expression for the non-extensive statistical equation is as follows: ； In the above formula, Let be the three-dimensional equilibrium distribution function of the aircraft; It is the ionic momentum; The normalization constant is ; As a parameter, when hour, ;when When, the equilibrium distribution function It is divergent, when At that time, the particle's momentum has an upper limit. ,when When it approaches 1, Approaching infinity, formula (21) reverts to the classic Boltzmann distribution function; The thermal velocity of the particle; The average electron energy and number of particles to be injected are calculated based on the difference between the results of the two statistical equations. Then, the time scale T required for the evolution of the unstable mode is combined to obtain the required superthermal electron energy and particle flux per unit time.

4. The method for achieving ionospheric stealth of a spacecraft based on controlling the electron distribution in the tail region according to claim 1, characterized in that, In step S3, an evolution timescale, electron energy, and particle flux database corresponding to different non-extensional parameters is established. The process is as follows: By selecting a series of non-extensive parameters q The value is then calculated by repeating steps S1 and S2 to obtain a series of data, namely each non-extensive parameter. q The corresponding evolution timescale T, electron energy, and particle flux are stored in a database for easy access in subsequent steps.

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