Method for measuring charge density of rarefied medium and related device

Abstract

The application discloses a kind of rare thin medium charge density measurement method and related equipment, the method includes: the centroid of potential probe array is obtained, the potential probe array is obtained by arranging by predetermined number of potential probe;According to the preset algorithm, the potential of the centroid and the second time derivative of the potential, the first gradient and the second gradient are calculated, and the charge density of the centroid is calculated based on the potential, the second time derivative, the first gradient and the second gradient.The application proposes the principle of multi-point measurement of space potential, can realize the breakthrough of space charge measurement zero, by utilizing the potential of different space points measured by multiple probes, the potential space distribution is obtained, so that the net charge density is measured, and high-precision measurement of electric field is realized;In addition, the application is not only suitable for steady-state situation, but also can measure the charge density under the condition of transient electromagnetic field with high precision.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic field measurement technology, and in particular to a method, terminal, and computer-readable storage medium for measuring the charge density of a rarefied medium. Background Technology

[0002] Currently, the techniques for observing particles, electric fields, and magnetic fields are largely mature. However, there is still no instrument to directly measure the charge density in rarefied media. The Faraday barrel method is used to measure the charge density of terrestrial fluids (e.g., the atmosphere). However, the Faraday barrel method is not suitable for measuring low charge densities in rarefied media and cannot be applied to measuring the charge density in rarefied space plasmas or terrestrial plasmas. Space plasmas are extremely rarefied, with charge densities as low as 1 cm². 3 It contains only a few charged particles, and the net charge density is several orders of magnitude lower, which makes it very difficult to directly detect the net charge density in space.

[0003] Charge distribution is a crucial aspect of understanding the dynamics, evolution, and effects of electromagnetic fields, and the measurement of charge density in rarefied media has wide-ranging applications. Developing a space charge detector and conducting actual observations of space charge are urgent needs for the development of space science and the safety of aerospace activities. The technology for measuring charge density in rarefied media can also be applied to measuring charge density in atmospheric, oceanic, and terrestrial plasmas. Therefore, existing technologies have limitations in measuring charge density in rarefied space plasmas and terrestrial plasmas.

[0004] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0005] The main objective of this invention is to provide a method and related equipment for measuring the charge density of a rarefied medium, aiming to solve the problem that the existing technology cannot be applied to the measurement of charge density in rarefied space plasma and terrestrial plasma.

[0006] To achieve the above objectives, the present invention provides a method for measuring the charge density of a rarefied dielectric, the method comprising the following steps:

[0007] Obtain the centroid of the potential probe array, which is obtained by arranging a predetermined number of potential probes;

[0008] The electric potential of the centroid and its second time partial derivative, first gradient, and second gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential, the second time partial derivative, the first gradient, and the second gradient.

[0009] Optionally, in the method for measuring the charge density of a rarefied medium, the predetermined number is ten, seven, or eight.

[0010] Optionally, in the method for measuring the charge density of a rarefied dielectric, when the predetermined number is ten, the method specifically includes:

[0011] The ten potential probes are arranged to form a ten-potential probe array, and the centroid of the ten-potential probe array is obtained.

[0012] The electric potential of the centroid and its quadratic gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential and the quadratic gradient. The calculation method is as follows:

[0013]

[0014] Where ρ is the charge density at the center of mass, c is the speed of light in vacuum, and ε0 is the vacuum dielectric constant. Let φ be the second time partial derivative of the potential at the center of mass. c The electric potential at the center of mass, This represents the second gradient of the electric potential at the center of mass.

[0015] Optionally, in the method for measuring the charge density of a rarefied dielectric, when the predetermined number is seven, the method specifically includes:

[0016] The six potential probes are arranged symmetrically along the x, y, and z axes of the Cartesian coordinate system, and the remaining potential probes are placed at the center of the Cartesian coordinate system to obtain a seven-probe potential measurement array.

[0017] At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the third and second gradients of the potential probe at the center in the z-axis direction are calculated according to the third formula.

[0018] Based on the first quadratic gradient, the second quadratic gradient, and the third quadratic gradient, the charge density at the center is calculated using the fourth formula.

[0019] Optionally, in the method for measuring the charge density of a rarefied dielectric, the first formula is:

[0020]

[0021] The second formula is:

[0022]

[0023] The third formula is:

[0024]

[0025] The fourth formula is:

[0026]

[0027] in, Let φ0 be the second time partial derivative of the potential along the x-axis, and φ0 be the potential at the origin. x1 The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is L, which is the potential along the positive x-axis. x This represents the distance from the probe to the center origin on the x-axis. Let φ be the second time partial derivative of the potential along the y-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is L, which is the potential along the positive y-axis. y This represents the distance from the probe to the center origin on the y-axis. Let φ be the second time partial derivative of the potential along the z-axis. z1 The potential of the probe is φ, which is the potential of the negative z-axis. z2 The potential of the probe is L, which is the potential along the positive z-axis. z Let ρ be the distance from the probe to the origin on the z-axis, ρ be the charge density at the center of mass, c be the speed of light in vacuum, and ε0 be the dielectric constant in vacuum. Let φ be the second time partial derivative of the potential at the center of mass. c Let φ be the electric potential at the center of mass, and φ0 be the electric potential at the center of mass.

[0028] Optionally, in the method for measuring the charge density of a rarefied dielectric, when the predetermined number is eight, the method specifically includes:

[0029] The six potential probes are arranged symmetrically along the x, y and z axes of the Cartesian coordinate system, and the remaining two potential probes are arranged symmetrically at a predetermined distance on the z axis to obtain an eight-probe potential measurement array.

[0030] At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the fourth and second gradients of the potential probe at the center in the z-axis direction are calculated according to the fifth formula.

[0031] Based on the first quadratic gradient, the second quadratic gradient, and the fourth quadratic gradient, the charge density at the center is calculated using the sixth formula.

[0032] Optionally, in the method for measuring the charge density of a rarefied dielectric, the fifth formula is:

[0033]

[0034] The sixth formula is:

[0035]

[0036] in, Let φ be the second time partial derivative of the potential along the z-axis. z1 The potential of the first potential probe along the negative z-axis, φ z2 The potential of the second potential probe is φ, which is the negative z-axis. z3 The potential of the third potential probe is φ, which is the positive z-axis. z4 The potential of the fourth potential probe is the z-axis positive half-axis. z Let ρ be the distance between two adjacent potential probes on the same side of the z-axis, ρ be the charge density at the center of mass, c be the speed of light in vacuum, and ε0 be the dielectric constant in vacuum. Let φ be the second time partial derivative of the potential at the center of mass. c Let φ be the electric potential at the center of mass, and φ0 be the electric potential at the center of mass.

[0037] Optionally, the method for measuring the charge density of a rarefied dielectric, wherein the potential probes are symmetrically arranged along the x, y, and z axes of a Cartesian coordinate system, and two potential probes are symmetrically arranged at a predetermined distance along the z-axis to obtain an eight-probe potential measurement array, further includes:

[0038] At the center, the first gradient of the potential probe at the center in the x-axis direction is calculated according to the seventh formula, the second gradient of the potential probe at the center in the y-axis direction is calculated according to the eighth formula, and the third gradient of the potential probe at the center in the z-axis direction is calculated according to the ninth formula.

[0039] Based on the first gradient, the second gradient, and the third gradient, the electric field at the center is calculated using the tenth formula.

[0040] The seventh formula is as follows:

[0041]

[0042] The eighth formula is:

[0043]

[0044] The ninth formula is:

[0045]

[0046] The tenth formula is:

[0047]

[0048] in, Let φ be the first gradient of the potential probe along the x-axis. x1 The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is L, which is the potential along the positive x-axis. x This represents the distance from the probe to the center origin on the x-axis. φ represents the second gradient of the potential probe along the y-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is L, which is the potential along the positive y-axis. y This represents the distance from the probe to the center origin on the y-axis. Let φ be the third gradient of the potential probe along the z-axis. z1 The potential of the first potential probe along the negative z-axis, φ z2 The potential of the second potential probe is φ, which is the negative z-axis. z3 The potential of the third potential probe is φ, which is the positive z-axis. z4 The potential of the fourth potential probe is the z-axis positive half-axis. z L is the distance between two adjacent potential probes on the same side of the z-axis. z Let E be the distance from the probe to the center origin on the z-axis, and E be the electric field at the center. The unit direction vector of the x-axis. The unit direction vector of the y-axis. It is the unit direction vector of the z-axis.

[0049] Furthermore, to achieve the above objectives, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a rarefied dielectric charge density measurement program stored in the memory and executable on the processor, wherein when the rarefied dielectric charge density measurement program is executed by the processor, it implements the steps of the rarefied dielectric charge density measurement method as described above.

[0050] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a measurement program for rarefied dielectric charge density, and when the rarefied dielectric charge density measurement program is executed by a processor, it implements the steps of the rarefied dielectric charge density measurement method as described above.

[0051] In this invention, the centroid of a potential probe array is obtained, the array being formed by arranging a predetermined number of potential probes. The potential of the centroid, its second-order time partial derivative, first-order gradient, and second-order gradient are calculated according to a preset algorithm. Based on the potential, the second-order time partial derivative, the first-order gradient, and the second-order gradient, the charge density of the centroid is calculated. This invention proposes a multi-point measurement principle for spatial potential, achieving a breakthrough in measuring spatial charge density. By using multiple probes to measure the potential at different spatial points, the spatial distribution of the potential is obtained, thereby measuring the net charge density and achieving high-precision measurement of the electric field. The originality and outstanding advantages of this invention are that it is applicable not only to steady-state conditions but also to the high-precision measurement of charge density under transient electromagnetic field conditions. Attached Figure Description

[0052] Figure 1 This is a flowchart of a preferred embodiment of the method for measuring the charge density of a rarefied medium in this invention;

[0053] Figure 2 This is a schematic diagram of the spatial distribution of ten potential probes in an embodiment of the method for measuring the charge density of a rarefied medium in this invention;

[0054] Figure 3 This is a schematic diagram of the spatial distribution of seven potential probes in an embodiment of the method for measuring the charge density of a rarefied medium in this invention.

[0055] Figure 4 This is a schematic diagram of the spatial distribution of eight potential probes in an embodiment of the method for measuring the charge density of a rarefied medium in this invention.

[0056] Figure 5 This is a schematic diagram of the operating environment of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0058] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0059] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0060] The preferred embodiment of the present invention describes a method for measuring the charge density of a rarefied dielectric, such as... Figure 1 As shown, the method for measuring the charge density of the rarefied dielectric includes the following steps:

[0061] Step S10: Obtain the centroid of the potential probe array, which is obtained by arranging a predetermined number of potential probes.

[0062] Specifically, by detecting the electric potential of the electric field at multiple points in space and using the established algorithm [Shenetal., 2021a], the electric field strength and charge density can be estimated, and the charge density can be calculated using multi-point potential measurement data. For example... Figure 2 As shown, ten potential probes are used to measure the potential. The spatial position vectors of the ten potential probes are r1, r2, r3, r4, r5, r6, r7, r8, r9, and r 10 That is, the spatial position vector of the α-th potential probe is r. α (α = 1, 2, ..., N); without loss of generality, let the centroid C of the probe array be the origin, that is, let The potential measured by the α-th probe is φ. (α) =φ(t,r α ), (α=1,2,···,N), where t is the measurement time, and is a time series measurement.

[0063] Step S20: Calculate the electric potential of the centroid and the second time partial derivative, first gradient and second gradient of the electric potential according to the preset algorithm, and calculate the charge density of the centroid based on the electric potential, the second time partial derivative, the first gradient and the second gradient.

[0064] Specifically, in this embodiment of the invention, based on the potential probe scheme in step S10 above, the potential φ at the centroid C can be obtained according to the algorithm [Shenetal., 2021a]. c and the first gradient of the potential at the centroid C and the second gradient of the potential at the centroid C Therefore, based on the first gradient, the electrostatic field at the centroid C can be obtained as follows: The charge density at the centroid C is obtained from the d'Alembert equation, which describes the spatiotemporal variation of electric potential and its relationship with the source. Where ρ is the charge density at the center of mass, c is the speed of light in vacuum, and ε0 is the vacuum dielectric constant. Let C be the second time partial derivative of the potential at the centroid; and the expression for the potential at the centroid C in the equation is: The second time partial derivative of the potential at the centroid C It can be determined by a multi-point potential measurement time series; using the least squares method, the potential φ at the centroid C can be obtained. c The first gradient of the electric potential at the center of mass C The second gradient of the potential at the center of mass C Satisfy the following three tensor equations:

[0065]

[0066]

[0067]

[0068] in, The position vector of the α-th potential probe is r. α (α = 1, 2, ..., N) Coordinate components along the i-th coordinate axis; then define a second-order tensor R. ij (As shown in Equation 4), the third-order tensor R ikm (As shown in Equation 5), the fourth-order tensor R ijkm (As in Formula 6), the definition is as follows:

[0069]

[0070]

[0071]

[0072] Based on this new principle, instruments for measuring the charge density of rarefied media (such as space and ground plasma) can be developed. Simulation calculations and tests on the electric potential field generated in a uniformly charged sphere show that the relative errors of the measured electric field and charge density are generally less than 5%; relative to the probe spacing, the relative error of the electric field reaches second order, and the relative error of the charge density reaches first order. The relative error of the charge density is inversely proportional to the number of probes in the constellation; the more probes, the higher the measurement accuracy.

[0073] Furthermore, in the above In the context of the Laplace operator where charge density depends on potential (Here, x, y, and z are three coordinates in a Cartesian coordinate system.) Since there are no overlapping terms and three independent parameters are omitted, seven appropriately arranged probes are sufficient to detect the Laplace operator of the electric potential. To further reduce the number of probes required for charge density measurement, this invention proposes a seven-probe detection scheme. Six potential probes are symmetrically arranged along the x, y, and z axes of a Cartesian coordinate system, with another potential probe positioned at the center of the Cartesian coordinate system, forming a seven-probe potential measurement array. Figure 3 As shown in the figure, x1 is the potential probe set on the negative x-axis, x2 is the potential probe set on the positive x-axis, y1 is the potential probe set on the negative y-axis, y2 is the potential probe set on the positive y-axis, z1 is the potential probe set on the negative z-axis, z2 is the potential probe set on the positive z-axis, and φ0 is the potential at the central origin. x1 The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is the positive x-axis. Let φ be the second time partial derivative of the potential along the y-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is the potential along the positive y-axis. Let φ be the second time partial derivative of the potential along the z-axis. z1 The potential of the probe is φ, which is the potential of the negative z-axis. z2 The potential of the potential probe is the positive z-axis; set x2 = -x1 = L x y1=-y2=L y z2 = -z1 = L z L x L y L z The distances from the probe to the origin on the x, y, and z axes are respectively. By using differential calculations, the first and second gradients of the potential at the center can be obtained with second-order accuracy, thereby obtaining the charge density at the center.

[0074] Specifically, at the center, the electric potential has a first gradient in the x-axis direction. and quadratic gradient for:

[0075]

[0076] Similarly, at the center, the electric potential has a first gradient in the y-axis direction. and quadratic gradient for:

[0077]

[0078] At the center, the electric potential has a first gradient along the z-axis. and quadratic gradient for:

[0079]

[0080] The calculation accuracy of the first and second gradients of the above potential is 2nd order.

[0081] The charge density at the center is:

[0082]

[0083] Furthermore, the aforementioned seven-probe charge density measurement scheme can be applied to the measurement of electric field and charge density in atmospheric and ground plasmas. However, in actual space measurements, the central probe is located within the satellite body and cannot accurately measure the potential. Therefore, the seven-probe charge density measurement scheme is improved by placing two more potential probes symmetrically on the z-axis extension rod to replace the central probe. The resulting eight-probe charge density measurement scheme involves symmetrically arranging six potential probes along the x, y, and z axes of a Cartesian coordinate system, and symmetrically arranging the remaining two potential probes at a predetermined distance along the z-axis, thus obtaining an eight-probe potential measurement array. Figure 4 As shown, φ0 is the electric potential at the central origin, φ x1 The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is L, which is the potential along the positive x-axis. x φ is the distance from the probe to the center origin on the x-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is L, which is the potential along the positive y-axis. y φ is the distance from the probe to the center origin on the y-axis. z1 The potential of the first potential probe along the negative z-axis, φ z2 The potential of the second potential probe is φ, which is the negative z-axis. z3 The potential of the third potential probe is φ, which is the positive z-axis. z4 The potential of the fourth potential probe is L, which is the positive z-axis. z Let x2 or z3 be the distance from the probe to the center origin; let x2 = -x1 = L x y1=-y2=L y z3 = -z2 = L z z4 = -z1 = L z +l z , l zIt is the distance between two adjacent probes on the same side of the z-axis (upper side, such as z3 and z4, and lower side, such as z1 and z2); then at the center, the first gradient, second gradient, and potential along the z-axis are:

[0084]

[0085] The accuracy of the second gradient of the electric potential along the z-axis reaches order 2; the accuracy of the electric potential at the center and its first gradient along the z-axis reaches order 4. For example, in a seven-probe charge density measurement scheme, the first and second gradients along the x and y axes of the eight-probe charge density measurement scheme satisfy the calculations of the first and second gradients along the x and y axes at the center in the seven-probe charge density measurement scheme; wherein, the accuracy of the first and second gradients of the electric potential along the x and y axes reaches order 2. Therefore, the electric field E and charge density ρ at the center can be obtained; the electric field E at the center is:

[0086]

[0087] in, and It is the unit direction vector of the x, y, and z coordinate axes; by d'Alembert's equation, the charge density ρ at the center is:

[0088]

[0089] Wherein, the second time partial derivative of the potential φ0 at the centroid C is... The measurement accuracy of charge density reaches second order, and the measurement accuracy of electric field strength reaches fourth order, determined by a multi-point potential measurement time series. Simulation tests of an eight-probe measurement scheme for the electric field generated by a uniformly charged sphere show that the absolute error of charge density and the second-order accuracy of the potential gradient are both second order. For one-dimensional structures, such as a calm atmosphere and an ideal magnetopause boundary layer, three-point potential detection is sufficient to determine the first and second gradients of the potential, thereby deriving the electric field strength and charge density. The multi-point measurement principle of space potential proposed in this invention can achieve a breakthrough in space charge measurement, filling a long-standing gap in international space electromagnetic detection. The originality and outstanding advantage of this invention are that this technology is not only applicable to steady-state conditions but also capable of measuring charge density with high precision under transient electromagnetic field conditions.

[0090] Furthermore, such as Figure 5 As shown, based on the above-described method for measuring the charge density of a rarefied medium, the present invention also provides a terminal, which includes a processor 10, a memory 20, and a display 30. Figure 5 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0091] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc. Further, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a rarefied dielectric charge density measurement program 40, which can be executed by the processor 10 to implement the rarefied dielectric charge density measurement method of this application.

[0092] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as performing the method for measuring the charge density of the rarefied medium.

[0093] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.

[0094] In one embodiment, when the processor 10 executes the measurement program 40 for the charge density of the rarefied dielectric in the memory 20, the following steps are performed:

[0095] Obtain the centroid of the potential probe array, which is obtained by arranging a predetermined number of potential probes;

[0096] The electric potential of the centroid and its second time partial derivative, first gradient, and second gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential, the second time partial derivative, the first gradient, and the second gradient.

[0097] The predetermined quantity is ten, seven, or eight.

[0098] When the predetermined number is ten, the method for measuring the charge density of the rarefied dielectric specifically includes:

[0099] The ten potential probes are arranged to form a ten-potential probe array, and the centroid of the ten-potential probe array is obtained.

[0100] The electric potential of the centroid and its quadratic gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential and the quadratic gradient. The calculation method is as follows:

[0101]

[0102] Where ρ is the charge density at the center of mass, c is the speed of light in vacuum, and ε0 is the vacuum dielectric constant. Let φ be the second time partial derivative of the potential at the center of mass. c The electric potential at the center of mass, This represents the second gradient of the electric potential at the center of mass.

[0103] When the predetermined number is seven, the method for measuring the charge density of the rarefied dielectric specifically includes:

[0104] The six potential probes are arranged symmetrically along the x, y, and z axes of the Cartesian coordinate system, and the remaining potential probes are placed at the center of the Cartesian coordinate system to obtain a seven-probe potential measurement array.

[0105] At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the third and second gradients of the potential probe at the center in the z-axis direction are calculated according to the third formula.

[0106] Based on the first quadratic gradient, the second quadratic gradient, and the third quadratic gradient, the charge density at the center is calculated using the fourth formula.

[0107] The first formula is:

[0108]

[0109] The second formula is:

[0110]

[0111] The third formula is:

[0112]

[0113] The fourth formula is:

[0114]

[0115] in, Let φ0 be the second time partial derivative of the potential along the x-axis, and φ0 be the potential at the origin. x1 The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is L, which is the potential along the positive x-axis. x This represents the distance from the probe to the center origin on the x-axis. Let φ be the second time partial derivative of the potential along the y-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is L, which is the potential along the positive y-axis. y This represents the distance from the probe to the center origin on the y-axis. Let φ be the second time partial derivative of the potential along the z-axis. z1 The potential of the probe is φ, which is the potential of the negative z-axis. z2 The potential of the probe is L, which is the potential along the positive z-axis. z Let ρ be the distance from the probe to the origin on the z-axis, ρ be the charge density at the center of mass, c be the speed of light in vacuum, and ε0 be the dielectric constant in vacuum. Let φ be the second time partial derivative of the potential at the center of mass. c Let φ be the electric potential at the center of mass, and φ0 be the electric potential at the center of mass.

[0116] When the predetermined number is eight, the method for measuring the charge density of the rarefied dielectric specifically includes:

[0117] The six potential probes are arranged symmetrically along the x, y and z axes of the Cartesian coordinate system, and the remaining two potential probes are arranged symmetrically at a predetermined distance on the z axis to obtain an eight-probe potential measurement array.

[0118] At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the fourth and second gradients of the potential probe at the center in the z-axis direction are calculated according to the fifth formula.

[0119] Based on the first quadratic gradient, the second quadratic gradient, and the fourth quadratic gradient, the charge density at the center is calculated using the sixth formula.

[0120] The fifth formula is as follows:

[0121]

[0122] The sixth formula is:

[0123]

[0124] in, Let φ be the second time partial derivative of the potential along the z-axis. z1 The potential of the first potential probe along the negative z-axis, φ z2 The potential of the second potential probe is φ, which is the negative z-axis. z3 The potential of the third potential probe is φ, which is the positive z-axis. z4 The potential of the fourth potential probe is the z-axis positive half-axis. z Let ρ be the distance between two adjacent potential probes on the same side of the z-axis, ρ be the charge density at the center of mass, c be the speed of light in vacuum, and ε0 be the dielectric constant in vacuum. Let φ be the second time partial derivative of the potential at the center of mass. c Let φ be the electric potential at the center of mass, and φ0 be the electric potential at the center of mass.

[0125] The process involves symmetrically arranging the potential probes along the x, y, and z axes of a Cartesian coordinate system, with two potential probes symmetrically arranged at a predetermined distance along the z-axis to obtain an eight-probe potential measurement array. The process further includes:

[0126] At the center, the first gradient of the potential probe at the center in the x-axis direction is calculated according to the seventh formula, the second gradient of the potential probe at the center in the y-axis direction is calculated according to the eighth formula, and the third gradient of the potential probe at the center in the z-axis direction is calculated according to the ninth formula.

[0127] Based on the first gradient, the second gradient, and the third gradient, the electric field at the center is calculated using the tenth formula.

[0128] The seventh formula is as follows:

[0129]

[0130] The eighth formula is:

[0131]

[0132] The ninth formula is:

[0133]

[0134] The tenth formula is:

[0135]

[0136] in, Let φ be the first gradient of the potential probe along the x-axis. x1The potential of the probe is φ, which is the potential along the negative x-axis. x2 The potential of the probe is L, which is the potential along the positive x-axis. x This represents the distance from the probe to the center origin on the x-axis. φ represents the second gradient of the potential probe along the y-axis. y1 The potential of the probe is φ, which is the potential along the negative y-axis. y2 The potential of the probe is L, which is the potential along the positive y-axis. y This represents the distance from the probe to the center origin on the y-axis. Let φ be the third gradient of the potential probe along the z-axis. z1 The potential of the first potential probe along the negative z-axis, φ z2 The potential of the second potential probe is φ, which is the negative z-axis. z3 The potential of the third potential probe is φ, which is the positive z-axis. z4 The potential of the fourth potential probe is the z-axis positive half-axis. z L is the distance between two adjacent potential probes on the same side of the z-axis. z Let E be the distance from the probe to the center origin on the z-axis, and E be the electric field at the center. The unit direction vector of the x-axis. The unit direction vector of the y-axis. It is the unit direction vector of the z-axis.

[0137] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a measurement program for rarefied dielectric charge density, and the measurement program for rarefied dielectric charge density, when executed by a processor, implements the steps of the method for measuring rarefied dielectric charge density as described above.

[0138] In summary, this invention provides a method for measuring the charge density of a rarefied medium. The method includes: obtaining the centroid of a potential probe array, wherein the potential probe array is obtained by arranging a predetermined number of potential probes; calculating the potential of the centroid and the second time partial derivative, first gradient, and second gradient of the potential according to a preset algorithm; and calculating the charge density of the centroid based on the potential, the second time partial derivative, the first gradient, and the second gradient. This invention proposes a multi-point measurement principle for spatial potential, which can achieve a breakthrough in measuring spatial charge density. By using multiple probes to measure the potential at different spatial points, the spatial distribution of the potential is obtained, thereby measuring the net charge density and achieving high-precision measurement of the electric field.

[0139] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0140] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0141] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for measuring the charge density of a rarefied dielectric, characterized in that, The method for measuring the charge density of the rarefied dielectric includes: Obtain the centroid of the potential probe array, which is obtained by arranging a predetermined number of potential probes, wherein the predetermined number is ten, seven or eight; The electric potential of the centroid and its second time partial derivative, first gradient, and second gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential, the second time partial derivative, the first gradient, and the second gradient. When the predetermined number is ten, the method for measuring the charge density of the rarefied dielectric specifically includes: The ten potential probes are arranged to form a ten-potential probe array, and the centroid of the ten-potential probe array is obtained. The electric potential of the centroid and its quadratic gradient are calculated according to a preset algorithm, and the charge density of the centroid is calculated based on the electric potential and the quadratic gradient. The calculation method is as follows: ； in, Let be the charge density at the center of mass, and c be the speed of light in vacuum. The dielectric constant in vacuum is . Let be the second time partial derivative of the potential at the center of mass. The electric potential at the center of mass, This represents the second gradient of the electric potential at the center of mass; When the predetermined number is seven, the method for measuring the charge density of the rarefied dielectric specifically includes: The six potential probes are arranged symmetrically along the x, y, and z axes of the Cartesian coordinate system, and the remaining potential probes are placed at the center of the Cartesian coordinate system to obtain a seven-probe potential measurement array. At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the third and second gradients of the potential probe at the center in the z-axis direction are calculated according to the third formula. Based on the first quadratic gradient, the second quadratic gradient, and the third quadratic gradient, the charge density at the center is calculated using a fourth formula. The first formula is: ； The second formula is: ； The third formula is: ； The fourth formula is: ； in, Let be the first and second gradients of the electric potential along the x-axis. The electric potential at the central origin, The potential of the probe is the negative x-axis. The potential of the probe is the positive x-axis. This represents the distance from the probe to the center origin on the x-axis. Let be the second and fourth gradients of the electric potential along the y-axis. The potential of the probe is the potential along the negative y-axis. The potential of the probe is the potential along the positive y-axis. This represents the distance from the probe to the center origin on the y-axis. Let be the third and second gradient of the potential along the z-axis. The potential of the probe is the potential along the negative z-axis. The potential of the probe is the potential along the positive z-axis. This represents the distance from the probe to the center origin on the z-axis. Let be the charge density at the center of mass, and c be the speed of light in vacuum. The dielectric constant in vacuum is . Let be the second time partial derivative of the potential at the center of mass. The electric potential at the center of mass, The electric potential at the central origin; When the predetermined number is eight, the method for measuring the charge density of the rarefied dielectric specifically includes: The six potential probes are arranged symmetrically along the x, y and z axes of the Cartesian coordinate system, and the remaining two potential probes are arranged symmetrically at a predetermined distance on the z axis to obtain an eight-probe potential measurement array. At the center, the first and second gradients of the potential probe at the center in the x-axis direction are calculated according to the first formula, the second and second gradients of the potential probe at the center in the y-axis direction are calculated according to the second formula, and the fourth and second gradients of the potential probe at the center in the z-axis direction are calculated according to the fifth formula. Based on the first quadratic gradient, the second quadratic gradient, and the fourth quadratic gradient, the charge density at the center is calculated using the sixth formula. The fifth formula is: ； The sixth formula is: ； in, Let be the fourth and second gradient of the potential along the z-axis. Let z1 be the potential of the first potential probe along the negative z-axis. The potential of the second potential probe z2 is the negative z-axis. The potential of the third potential probe z3 is the positive z-axis. The potential of the fourth potential probe z4 is the positive z-axis. This is the distance between two adjacent potential probes on the same side of the z-axis. The distance from the second potential probe z2 (negative z-axis) or the third potential probe z3 (positive z-axis) to the central origin. Let be the charge density at the center of mass, and c be the speed of light in vacuum. The dielectric constant in vacuum is . Let be the second time partial derivative of the potential at the center of mass. The electric potential at the center of mass, The potential at the central origin is denoted as .

2. The method for measuring the charge density of a rarefied dielectric according to claim 1, characterized in that, The process involves symmetrically arranging the potential probes along the x, y, and z axes of a Cartesian coordinate system, with two potential probes symmetrically arranged at a predetermined distance along the z-axis to obtain an eight-probe potential measurement array. The process further includes: At the center, the first gradient of the potential probe at the center in the x-axis direction is calculated according to the seventh formula, the second gradient of the potential probe at the center in the y-axis direction is calculated according to the eighth formula, and the third gradient of the potential probe at the center in the z-axis direction is calculated according to the ninth formula. Based on the first gradient, the second gradient, and the third gradient, the electric field at the center is calculated using the tenth formula. The seventh formula is as follows: ； The eighth formula is: ； The ninth formula is: ； The tenth formula is: ； in, This represents the first gradient of the potential probe along the x-axis. The potential of the probe is the negative x-axis. The potential of the probe is the positive x-axis. This represents the distance from the probe to the center origin on the x-axis. This represents the second gradient of the potential probe along the y-axis. The potential of the probe is the potential along the negative y-axis. The potential of the probe is the potential along the positive y-axis. This represents the distance from the probe to the center origin on the y-axis. Let be the third gradient of the potential probe along the z-axis. Let z1 be the potential of the first potential probe along the negative z-axis. The potential of the second potential probe z2 is the negative z-axis. The potential of the third potential probe z3 is the positive z-axis. The potential of the fourth potential probe z4 is the positive z-axis. This is the distance between two adjacent potential probes on the same side of the z-axis. The distance from the second potential probe z2 (negative z-axis) or the third potential probe z3 (positive z-axis) to the central origin. The electric field at the center is The unit direction vector of the x-axis. The unit direction vector of the y-axis. It is the unit direction vector of the z-axis.

3. A terminal, characterized in that, The terminal includes a memory, a processor, and a measurement program for rarefied dielectric charge density stored in the memory and executable on the processor. When executed by the processor, the measurement program for rarefied dielectric charge density implements the steps of the method for measuring rarefied dielectric charge density as described in any one of claims 1-2.

4. A computer-readable storage medium having a computer program stored thereon, the computer-readable storage medium storing a measurement program for rarefied dielectric charge density, the measurement program for rarefied dielectric charge density being executed by a processor to implement the steps of the method for measuring rarefied dielectric charge density as claimed in any one of claims 1-2.

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