A method for estimating the propagation velocity of the dipolarization front in the magnetotail using single satellite observations

Abstract

The application discloses a method for estimating the propagation speed of a magnetic tail dipolarization front by using single-satellite observation, and belongs to the field of earth space environment detection. When a dipolarization front (DF) propagation event is observed by a satellite located at the center of a plasma sheet, if particle detection load data shows that there is a clear flux truncation feature behind the front, and the magnetic field intensity of a strong magnetic field region behind the front is relatively stable, the method can be used to estimate the DF propagation speed. The basic idea is to obtain a group of information about particle flux truncation time and corresponding characteristic velocity by satellite observation, and then perform least square fitting on the data according to the cyclotron reflection model of particles on the dipolarization front, so as to obtain the unknown parameter DF propagation speed in the model. Different from the current multi-satellite measurement method, the application provides a method for estimating the DF propagation speed by using single-satellite data, which can help us understand the material and energy transport process in the earth magnetic tail, and has high applicability.

Description

Technical Field

[0001] This invention relates to the fields of magnetospheric physics and space exploration, and in particular to a technical method for estimating the propagation velocity of a magnetotail dipole front. Background Technology

[0002] High-speed magnetotail flows are generally considered to be products of magnetic reconnection. These plasma flows can reach speeds of hundreds or even thousands of kilometers per second, propagating both ground- and tail-oriented, transporting matter and energy into the near-Earth magnetosphere and interplanetary space. The magnetic field and plasma characteristics of these high-speed flows differ significantly from those of the background plasma sheet. A boundary at the inertial scale of ions forms at the leading edge of the high-speed flow; this is the dipole-front (DF), also known as the reconnection front. The dipole-front can also be understood as a local magnetic structure that moves with the high-speed flow in either the ground or tail direction, typically propagating over tens of kilometers per second. E The above is accompanied by a significant increase in the intensity of the north and south components of the magnetic field, a decrease in plasma density, and an increase in temperature. The ion and electron energy spectra and pressure will also change accordingly. The strong magnetic field region immediately following the front is generally called the dipole flux bundle (DFB).

[0003] Besides its role in the transport of matter and magnetic flux in the magnetotail, the dipole-frontal (DF) also plays a crucial role in the following aspects: influencing the interruption of the equatorial terminator current and the generation of the field-direction current, thereby affecting the magnetosphere-ionosphere coupling; driving energy conversion related to the magnetotail; accelerating particles; and exciting various types of plasma waves. The propagation speed of the dipole-front is an important property, closely related to matter transport and particle acceleration, making its measurement and estimation meaningful.

[0004] Currently, the most accurate method for estimating the propagation velocity of a dipole front is the timing method. Assuming the front has a quasi-planar structure, it can be estimated using a tetrahedral constellation of four satellites (e.g., the Cluster satellite and MMS satellite programs). Let the positions of the satellites in the GSM spatial coordinate system be r1, r2, r3, and r4. If the time scale is very small during the propagation of the dipole front through the constellation, the satellite positions can be considered constant. Let the times for the four satellites to cross the dipole front be t1, t2, t3, and t4, and the magnitude of the propagation velocity of the dipole front be V, with the unit vector of the direction of motion being n. Then, according to geometric relationships:

[0005] (r i -r4)·n=V(t i -t4)

[0006] The propagation speed and direction of the dipole front can be obtained from the above equation. Although the timing method is relatively accurate, it has high requirements for the number of satellites and constellation configuration, making it difficult to capture the propagation events of the magnetotail dipole front and hindering routine monitoring of the magnetotail environment. This invention proposes a method for estimating the propagation speed of the dipole front using observation data from a single satellite, based on a cyclotron reflection model of particles facing the front. This method does not require a specific satellite constellation and has high applicability. Summary of the Invention

[0007] 1. The technical problem to be solved

[0008] The purpose of this invention is to overcome the shortcomings and deficiencies of existing methods and to provide a method for estimating the propagation speed of a dipole front using observation data from a single satellite.

[0009] 2. Technical Solution

[0010] The objective of this invention is achieved as follows: When a satellite located in the magnetotail plasma sheet observes a dipole front propagation event, magnetic field and particle-related observation data can be obtained using the satellite payload. The time t0 when the satellite passes through the front is determined based on the magnetic field changes; an energy spectrum is plotted based on the three-dimensional ion velocity distribution data to obtain typical flux cutoff characteristics that vary with energy; based on these characteristics, the characteristic ion velocity, flux cutoff time, corresponding characteristic throw angle, and average magnetic field [v] in different energy channels i are determined. i , t i α i B i Based on the cyclotron reflection model of particles on a dipole front, a theoretical value t for the flux cutoff time is established. i ′ The expression contains the frontal propagation speed v as a parameter. DF Based on data groups [ v i, t i ,α i B i The expression is fitted using least squares to obtain the frontal propagation speed v. DF Estimated value.

[0011] 3. Beneficial effects

[0012] Compared with existing methods, the present invention has the following advantages and positive effects:

[0013] ① It does not require multiple satellites to form a specific constellation configuration. Only one satellite is needed for single-point observation to estimate the propagation speed of the magnetotail dipole front. The observation cost is low and it is easy to organize and implement.

[0014] ② Considering the limitations of orbital period and observation location, the limited number of satellites can be fully utilized to achieve monitoring for a longer period of time, avoiding missed reports and detections of related dipole front propagation events. Attached Figure Description

[0015] Figure 1 A schematic diagram of the cyclotron reflection of particles by a dipole front;

[0016] Figure 2 A schematic diagram showing the relationship between particles of different energies and the flux cutoff position behind the front;

[0017] Figure 3 The specific implementation process of the estimation method;

[0018] Figure 4 Schematic diagram of cutoff time for different channel fluxes;

[0019] Figure 5 A schematic diagram of the geometric relationship between velocity components at the flux cutoff moment;

[0020] In the picture:

[0021] 1-Dipole front position marking

[0022] 2-Magnetic field lines

[0023] 3-Magnetic tail tail lobe region

[0024] 4-Central region of the magnetotail plasma sheet

[0025] 5-Particle cyclotron reflection trajectory projection

[0026] 6-B x Vertical magnetic field plane at =0

[0027] 7-Strong Magnetic Field DFB Region Detailed Implementation

[0028] The following is a detailed explanation with reference to the accompanying drawings:

[0029] 1. Main Mechanism

[0030] This invention primarily estimates the propagation velocity of a dipole-polarized front based on a cyclotron reflection model of particles on the front. In the GSM coordinate system, we simplify the description of an ideal front propagation event, assuming the magnetic field has no y-component, neglecting the motion of ions in the z-direction, and assuming a uniform strong magnetic field region behind the front that propagates along the x-direction. Then, ions initially distributed in the plasma sheet in front of the front will, due to the propagation of the DF (dipolar polarization) wave, pass through the front and enter the strong B (dipolar polarization) region. z The region, subsequently subjected to the Lorentz force in the plane perpendicular to the magnetic field (v perp1 -V perp2 The energy carried by the front is reflected back to the front through gyratory motion.y The electric field accelerates the energy, increasing it. Assume the propagation speed of the dipole front in this process is v. DF Without change, through the Lorentz transformation, in the frontal reference frame, ions incident along the frontal normal will undergo a half-cycle cyclotronic motion behind the front, and their position in B... x The projection of the motion trajectory of the perpendicular magnetic field plane at point = 0 is as follows: Figure 1 As shown.

[0031] In a vertical plane, ions with different energies have different radii of rotation, meaning they can reach different depths behind the front, such as... Figure 2 As shown. i have different energies (let the characteristic velocity be v). i For ions of the same type (with the same charge and mass), their vertical velocities in the frontal reference frame are v0 and v1 respectively. ⊥i ′, then combining the magnitude of the magnetic field, we can obtain its corresponding cyclotron radius as r. i This can be understood as the furthest distance an ion can reach after reaching the front. Once this distance is exceeded, the particle flux in that energy band will decrease significantly, which is reflected in the energy spectrum as flux cutoff. (The last sentence appears to be incomplete and possibly refers to a technical term or indicator.) i =(t i -t0)v DF We can achieve the flux cutoff position r i With flux cutoff time t i The conversion between them.

[0032] Based on the aforementioned cyclotron reflection model of ions on a front, we have established the relationship between the motion of ions with different energies and the flux cutoff time, which includes the parameter v. DF Using observational data from satellite payloads, we can obtain the particle flux cutoff times t at different energy levels. i and key speed information v ⊥i By fitting the above relationship, the unknown parameter v can be obtained. DF Size.

[0033] 2. Implementation Steps

[0034] The implementation process of this method is as follows: Figure 3 As shown, the details are as follows:

[0035] Step 1: Based on the observation data from the satellite payload, determine whether the satellite's position and magnetic field changes meet the estimation conditions. The satellite should be located near the center of the magnetotail plasma sheet, with the criterion being β>1, where β is the ratio of local plasma thermal pressure to magnetic pressure. When the satellite passes through the dipole front, it will observe a sharp increase in the north-south component of the magnetic field, with the criterion being a magnetic field increment δB>10nT within 30 seconds. The time corresponding to the point of maximum magnetic field acceleration during this period is defined as time t0. Subsequently, the satellite enters the strong magnetic field region DFB, where the magnetic field must be free from strong disturbances greater than 5nT.

[0036] Step 2: Determine whether the required accuracy of the three-dimensional ion velocity distribution data has been obtained, and whether typical flux cutoff characteristics with energy variation are observed after the front. Based on the three-dimensional ion velocity distribution data obtained from satellite observations, we can integrate to obtain ion distribution data for different throw angles, azimuth angles, and energy channels, with an angular resolution of at least 22.5°. The flux cutoff phenomenon is specifically manifested as a significant decrease in ion flux in the ion energy spectrum after the front, and the higher the energy channel, the later the flux cutoff time.

[0037] Step 3: Determine the characteristic velocities, flux cutoff times, corresponding characteristic throw angles, and average magnetic fields of ions in different energy channels i. i , t i α i B i Ion characteristic velocity v i By (2E) i / m) 1 / 2 The calculation yields E i Let m be the characteristic energy of channel i, and m be the ion mass of the corresponding probe component; the flux cutoff time t is... i Let i be the moment corresponding to the point where the slope of the decrease in flux i behind the front is the largest as it changes over time. Figure 4 As shown; throwing angle α i The angle between the direction of ion motion and the direction of the magnetic field can be determined by t. i Once the throwing angle distribution of energy channel i observed at time i is determined, then the characteristic velocity v i The gyroscopic velocity v in the direction perpendicular to the magnetic field lines in the frontal reference frame ⊥i Existence Relationship:

[0038]

[0039] like Figure 5 As shown; Average magnetic field B i From t0 to t i The average value of the magnetic field at any given time.

[0040] Step 4: Based on v DF The constant assumption and Lorentz transformation, using δx=(t-t0)vDF Data observed by the satellite at different times is mapped to data observed at different distances relative to the front position, where t represents the observation time and δx represents the distance between the observation point and the front position. Then, based on the cyclotron reflection model of particles on a dipole-polarized front—that is, in the front reference frame, ions undergo approximately half a period of cyclotronic motion after entering the front—the theoretical value t for the flux cutoff time is established. i The expression for ':

[0041]

[0042] Where m is the mass of the corresponding component ion and e is the unit charge.

[0043] Step 5: Based on the expression in Step 4, fit the data set [v] using the least squares method. i , t i α i B i [To obtain the frontal propagation speed v] DF Estimated value. Let:

[0044] L=∑ i [t i -t′ i (v i α i B i ,v DF )] 2 ,

[0045] L is the sum of the variances between the observed and theoretical flux cutoff values ​​for all channels i at the corresponding times. According to the least squares method, when L reaches its minimum value L... min When, the corresponding v DF This is the estimated propagation speed of the dipole front:

[0046] V DF =L -1 (L min )

[0047] 3. Method Validation

[0048] This method was used to estimate the propagation speed of the DF event observed by the Cluster satellite on August 5, 2001. The Cluster-1 satellite is located in the magnetotail X. GSM ~-17R E Near the center of the plasma sheet, and at 14:03:39 UT crossed the DF and entered the DFB region, behind the front B z The magnetic field strength remained relatively stable at around 20 nT. Based on CODIF observation data from the Cluster satellite, we found that its O +A significant flux cutoff was observed in the energy spectrum, so we adopted this method to analyze the O2 of six channels within the energy range of ~9keV to ~38keV. + Flux truncation analysis estimated the propagation speed of the DF to be approximately 151 km / h. Timing analysis using four satellites in the Cluster yielded a propagation speed of approximately 173 km / h in the x-direction, with a relative error within 15%. This error is primarily influenced by instrument accuracy; improving instrument resolution could further reduce the error. Therefore, this method can be considered as an alternative when the timing method is not feasible in practical observations.

Claims

1. A method for estimating the propagation velocity of a magnetotail dipole-polarized front using single-satellite observations, characterized in that, Includes the following steps: Step 1: Based on the observation data from the satellite payload, determine whether the changes in the satellite's position and magnetic field meet the estimation conditions. If so, determine the time t0 when the satellite passes through the front and proceed to Step 2. Step 2: Determine whether three-dimensional velocity distribution data of ions has been obtained, and whether typical flux cutoff characteristics with energy change have been observed after the front. If yes, proceed to step 3. Step 3: Determine the characteristic velocities v of ions in different energy channels i i Flux cutoff time t i , the size of the characteristic throwing angle α when truncation is achieved i With average magnetic field B i Determine the data group [v] i , t i α i B i ]; Step 4: Based on the cyclotron reflection model of particles on a dipole front, in the front reference frame, the particles undergo a half-period cyclotron motion after entering the front. Therefore, the theoretical value t for the flux cutoff time can be established. i The expression for ': Among them, the frontal propagation speed v DF Let m be the mass of the corresponding component ion and e be the unit charge. Step 5: Based on the expression in Step 4, use the least squares method to analyze the data set [v] i , t i α i B i By fitting the data, the frontal propagation speed v can be obtained. DF Estimated value.

2. The method according to claim 1, characterized in that, The satellite observation data in step 1 includes magnetic field vectors, overall ion velocity vectors, and ion density and temperature-related data.

3. The method according to claim 1 or 2, characterized in that, In step 1, the satellite should be located near the center of the magnetotail plasma sheet, with the criterion being β > 1, where β is the ratio of local plasma thermal pressure to magnetic pressure. When the satellite passes through the dipole front, it will observe a sharp increase in the north-south component of the magnetic field, with the criterion being that the magnetic field increment δB > 10nT within 30s. During this period, the moment corresponding to the maximum magnetic field increase is defined as the time t0 when the satellite passes through the front. Subsequently, the satellite enters a strong magnetic field region, where there must be no strong disturbances in the magnetic field greater than 5nT.

4. The method according to claim 1, characterized in that, In step 2, based on the three-dimensional velocity distribution data of ions obtained from the satellite, the ion distribution data of different throwing angles, different azimuth angles, and different energy channels can be integrated, and the angular resolution should be above 22.5°.

5. The method according to claim 1 or 4, characterized in that, In step 2, the flux cutoff phenomenon is specifically manifested as a significant decrease in the flux of ions in different energy channels in the ion energy spectrum after the front, and the higher the energy of the ion, the later the decrease in flux occurs.

6. The method according to claim 1, characterized in that, In step 3, the characteristic velocity v of the ions i By (2E) i / m) 1 / 2 The calculation yields E i Let m be the characteristic energy of channel i, and m be the ion mass of the corresponding probe component; the flux cutoff time t is... i The moment corresponding to the maximum slope of the decrease in flux i after the front over time; the throwing angle α i The angle between the direction of ion motion and the direction of the magnetic field can be determined by t. i The throwing angle distribution of energy channel i, observed at each moment, is determined; the average magnetic field B i From t0 to t i The average value of the magnetic field at any given time.

7. The method according to claim 1, characterized in that, In step 4, by assuming v DF When the value remains constant, use δx=(t-t0)v DF The data observed by the satellite at different times is mapped to the data observed at different distances relative to the frontal position, where t represents the observation time of the satellite and δx represents the distance between the observation point and the frontal position.

8. The method according to claim 1 or 7, wherein the theoretical expression for the flux cutoff time is based on v DF It is obtained from the constant assumption and the Lorentz transformation.

9. The method according to claim 1, characterized in that, In step 5, set L is the flux cutoff time t for all channels i. i The theoretical value of flux cutoff time t′ i The sum of variances, according to the least squares method, when L reaches its minimum value L min v corresponding to time DF This is the estimated propagation speed of the dipole front: v DF =L -1 (L min )。

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