CN111605727B - A Method for Observational Verification of Interplanetary Slow Shock Waves - Google Patents

Abstract

The invention relates to the technical field of space technology and plasma, in particular to a method for observing and authenticating an interplanetary slow shock wave. The method comprises the following steps: firstly, determining constraint conditions; secondly, judging whether the physical quantity at two sides of the discontinuities meet constraint conditions or not; thirdly, judging whether the discontinuities meet the basic characteristics of slow shock waves; fourth, determine if it is a slow shock wave by the time difference observed by two or more satellites; by the method, misjudgment of TD (tangential discontinuity) as slow shock waves can be avoided; eliminating the uncertainty that exists in authenticating the type of discontinuity; the accuracy of the authentication of the slow shock wave is improved.

Description

A Method for Observational Verification of Interplanetary Slow Shock Waves

technical field

The invention relates to the fields of space technology and plasma technology, in particular to a method for observing and verifying interplanetary slow shock waves.

Background technique

A large number of observational facts show that the magnetic field is an important energy source in the process of celestial body activities. In order to solve how the magnetic energy is rapidly converted into the kinetic energy and thermal energy of the plasma during flares, magnetospheric substorms and other cosmic eruptions, astronomers are looking for a possible mechanism for the rapid annihilation of the magnetic field.

In 1946, Giovanelli first proposed the concept of magnetic field reconnection, which believed that discharges would occur near the neutral point or neutral line where the magnetic field strength is zero, and may have an important impact on the occurrence of solar flares. In 1958, according to the observation data of solar flare activities, Sweet and Parker proposed the first steady-state magnetic field reconnection model, that is, the Sweet-Parker reconnection model. The Sweet-Parker model believes that there is a macro-scale diffusion region in the middle region of the antiparallel magnetic field lines. The plasma carries the magnetic field from the upper and lower sides of the diffusion region into the diffusion region continuously. In this region, the magnetic energy is converted into plasma kinetic energy through Joule dissipation. and thermal energy. The plasma flows out of the diffusion region along both sides of the current sheet. However, according to the Sweet-Parker model, the rate of energy conversion is too slow, which is quite different from the actual observation results, and cannot well explain many eruptive processes in celestial bodies and space physics. In order to solve the problem of reconnection rate, based on the Sweet-Parker model, in 1964, Petschek proposed a new magnetic field reconnection model. In the Petscheck model, the reconnection diffusion region only exists in a small area near the neutral line, and there are two teams of slow standing shock waves on both sides of the diffusion region. In the Petschek model, two groups of slow shock pairs play a crucial role in the process of energy release and current sheet formation, and most of the plasma can be accelerated by slow shock waves without flowing through the diffusion region. Therefore, the conversion of magnetic energy is mainly completed by slow shock waves. So far, the solar wind is the only natural laboratory where satellites can directly detect the return of the magnetic field, so it is of great significance to correctly identify slow shock waves in interplanetary space.

According to the magnetic fluid (MHD) theory, there are usually various magnetic field discontinuities in the solar wind, referred to as discontinuities. Since the first discontinuity in the interplanetary magnetic field was observed in the 1960s, people have gradually realized that the discontinuity is a basic feature of the solar wind, and its average occurrence rate is 1-2 events. Among the discontinuities, most of them are tangential discontinuities, and only a few interplanetary discontinuities are certified as slow shocks. Although few slow-excitation events have been reported, the study of slow-shock waves is of great significance, because slow-shock waves play an important role in the process of magnetic field reconnection, and a correct understanding of the process of magnetic field reconnection is the key to solving solar physics, space The key to a series of problems in physics, magnetosphere physics and even plasma physics. At present, there is no relevant effective method to effectively verify the interstellar slow shock wave.

Contents of the invention

The purpose of the present invention is to solve the current problem of lack of an effective authentication method for interstellar slow shock waves, and to provide a method for observing and authenticating interplanetary slow shock waves.

The determination of the boundary and configuration of magnetic cloud has always been an important topic in the research of magnetic cloud, and almost all studies of magnetic cloud are inseparable from the determination of the boundary and configuration of magnetic cloud.

The coronal mass ejection (CME for short) phenomenon will interact with other different currents during the propagation of interplanetary space to produce various magnetic discontinuities, and the boundary of interplanetary magnetic flux ropes is usually a magnetic discontinuity. Due to the large uncertainty among different discontinuities, the identification of different types of discontinuities is the most basic problem in related research on discontinuities. In the past studies on discontinuities, the tangential discontinuity (TD) was often misjudged as the rotational discontinuity (RD), and even the shock wave was misjudged as the RD.

The technical solution adopted by the present invention to solve the technical problem is: a method for observing and verifying the interplanetary slow shock wave, the steps include:

First, determine the constraints;

Second, determine whether the physical quantities on both sides of the discontinuity meet the constraints;

Third, judge whether the discontinuity meets the basic characteristics of slow shock wave;

Fourth, judge whether it is a slow shock wave by the time difference observed by two or more satellites;

The time difference Δt observed by each satellite = ΔR·n/V _DD ;

ΔR is the displacement between the two satellites,

V _DD is the propagation velocity of the discontinuity in the stationary coordinate system,

V _DD and the normal direction n of the discontinuity can be calculated from local observations of the discontinuity, and their results depend on the type of discontinuity.

Preferably: the constraint condition is the compatibility condition of the discontinuous surface, that is, the R-H relationship:

[B _n ] = 0,

[ρV _n ]=0,

[V _t B _n −V _n B _t ]=0,

[V _n B _q −V _q B _n ]=0,

The subscripts n and t represent the normal direction and tangential direction respectively, and q represents the direction perpendicular to n-t;

Brackets indicate the difference of physical quantities on both sides of the discontinuity;

P is the thermal pressure, which can be expressed as:

P _|| and P _⊥ are the thermal pressure parallel and perpendicular to the magnetic field, respectively; ξ is the anisotropy parameter, and its definition is:

Preferably, when determining whether the physical quantities on both sides of the discontinuity meet the constraint conditions, the magnetic field discontinuity based on interplanetary space is not a completely ideal magnetic fluid discontinuity, and the physical quantities on both sides of the discontinuity are not required to strictly satisfy the R-H relationship.

Preferably, when determining whether the physical quantities on both sides of the discontinuity meet the constraint conditions, the R-H relationship is fitted using the least squares method for the observed value, and the difference between the observed value and the theoretical value is considered to satisfy the R-H relationship within the allowable range of error.

Preferably, the basic characteristics of the slow shock wave include:

(1) The intermediate Mach numbers of the upstream and downstream are all less than 1;

(2) The upstream slow Mach number is greater than 1, while the downstream slow Mach number is less than 1;

(3) From upstream to downstream, the magnetic field strength decreases, and the proton density and temperature increase.

The beneficial effect of the present invention is: through this method, can avoid misjudgment TD (tangential discontinuity) as slow shock wave; Eliminate the uncertainty that exists when authenticating discontinuity surface type; Improve the accuracy rate of authentication slow shock wave .

Description of drawings

What Fig. 1 provided is the shock wave coordinate system of the present invention.

Fig. 2 shows the variation curves with time of the magnetic field and plasma parameters of the discontinuity event observed by the Wind spacecraft in Embodiment 1 of the present invention on September 18, 1997.

What Fig. 3 provides is the comparison diagram of the magnetic field of the discontinuous event on September 18, 1997 observed by the spaceship Wind and ACE of Embodiment 1 of the present invention, wherein the dotted line is observed by ACE and its time series is shifted back by 34.2 minute.

What Fig. 4 provided is the variation curve with time of the magnetic field and plasma parameter of the discontinuity event on October 8, 2001 observed by the Wind spacecraft of Embodiment 2 of the present invention and the best fit of the upstream and downstream parameters obtained according to the R-H relationship value.

Fig. 5 shows the change curve of the observed magnetic field in the shock wave coordinate system of the discontinuous event on October 8, 2001 in Embodiment 2 of the present invention.

What Fig. 6 provided is the comparison chart of the magnetic field of the discontinuity event on October 8, 2001 observed by the spacecraft Wind and ACE in Embodiment 2 of the present invention, wherein the dotted line is observed by Geotail and its time series is moved backward 14.6 minutes.

FIG. 7 shows a schematic diagram of the normal direction of the discontinuous surface and the satellite position in Embodiment 2 of the present invention.

Detailed ways

The implementation will now be further refined. It should be understood that the following description is not intended to limit the embodiments to one preferred embodiment. On the contrary, it is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the described embodiments as defined by the appended claims.

In the following detailed description, while the embodiments are described in sufficient detail to enable those skilled in the art to practice the embodiments, it is to be understood that these examples are not limiting such that other examples may be used and may be used without Corresponding modifications are made without departing from the spirit and scope of the described embodiments.

A method for observing and verifying interplanetary slow shock waves, including:

First, determine the constraints;

Second, determine whether the physical quantities on both sides of the magnetic field discontinuity meet the constraints;

Third, judge whether the magnetic field discontinuity meets the basic characteristics of slow shock waves;

Whether it is a slow shock wave is judged by the time difference observed by two or more satellites.

The above constraints are based on the MHD theory. The physical quantities on both sides of the discontinuity must satisfy the basic physical laws of mass conservation, momentum conservation, energy conservation, and Maxwell’s equations. That is, the magnetic field and plasma parameters are subject to these conditions. constraint. The constraint condition is the compatibility condition of the discontinuous surface, that is, the R-H relationship:

[B _n ] = 0,

[ρV _n ]=0,

[V _t B _n −V _n B _t ]=0,

[V _n B _q −V _q B _n ]=0,

The subscripts n and t represent the normal direction and tangential direction respectively, and q represents the direction perpendicular to n-t;

Brackets indicate the difference of physical quantities on both sides of the discontinuity;

P is the thermal pressure, which can be expressed as:

P _|| and P _⊥ are the thermal pressure parallel and perpendicular to the magnetic field, respectively; ξ is the anisotropy parameter, and its definition is:

Through the above constraints, four kinds of discontinuities that satisfy the principle of entropy increase can be obtained: Contact Discontinuity (RD), Rotational Discontinuity (RD), Tangential Discontinuity (TD) and Shock ).

When judging whether a discontinuity is a slow shock wave, first of all, it is necessary to check whether the physical quantities on both sides of the discontinuity satisfy the above-mentioned R-H relationship. It is not a completely ideal magnetic fluid discontinuity, and the physical quantities on both sides of the discontinuity are not required to strictly satisfy the R-H relationship. In addition, the detection instruments on the satellite have systematic errors and measurement errors in the measurement process, and it is impossible for the measured values to completely satisfy the R-H relationship.

When judging whether the physical quantities on both sides of the discontinuity meet the constraint conditions, the usual practice is to use the least squares method to fit the R-H relationship to the observed values.

All magnetic fluid discontinuities are required to satisfy the R-H relationship, so satisfying the R-H relationship is only a basic condition, and it cannot determine the type of discontinuity.

To judge that a discontinuity is a slow shock, the discontinuity must not only satisfy the R-H relationship but also have the observation characteristics of a slow shock, which is also the standard commonly used by everyone to judge a slow shock. The basic characteristics of slow shock waves include:

(1) The intermediate Mach numbers of the upstream and downstream are all less than 1;

(2) The upstream slow Mach number is greater than 1, while the downstream slow Mach number is less than 1;

(3) From upstream to downstream, the magnetic field strength decreases, and the proton density and temperature increase.

As shown in Figure 1, Figure 1 is the shock wave coordinate system; in the figure, n _s is the normal direction of the shock wave, the upper and lower magnetic fields are in the plane n _s -t, and the st plane is the wave front of the shock wave; For TD, the s direction is the normal direction, and the n _s -t plane is the discontinuous plane.

For the MHD shock wave, the principle of coplanarity requires that the downstream magnetic fields B ₁ , B ₂ on the discontinuity plane and the normal direction n _s of the shock wave are in the same plane. In this way, the shock wave coordinate system can be defined as shown in Figure 1, the s direction is perpendicular to the surface where the upstream and downstream magnetic fields and normals are located, and the direction of the other coordinate axis t is: t=n _s ×s. In this way, the ts plane is the wave front of the shock wave, and the upstream and downstream magnetic fields are all in the n _s -t plane. For TD, since there is no normal magnetic field component, the magnetic field is in the TD plane. Therefore, the shock wave coordinate system can also be used to describe TD: the tn _s plane is the TD plane, and the normal direction of TD (n _TD ) points to s.

According to the R-H relationship, TD only requires two basic conditions:

(1) The velocity and magnetic field of the upstream and downstream are perpendicular to the TD plane,

(2) Total pressure balance between upstream and downstream.

For a slow shock wave, the upstream and downstream magnetic fields are both in the tn _s plane in the shock wave coordinate system. If the upstream and downstream flow velocities are also in this plane, then the slow shock wave satisfies the first condition of TD. In addition, for a slow shock wave, the upstream magnetic pressure is greater than the downstream one, and the thermal pressure across the shock wave surface increases, so the total pressure on both sides of the shock wave may reach equilibrium or close to equilibrium, which satisfies the second condition of TD. Therefore, there is great uncertainty in judging whether a discontinuity is a slow shock or TD based on the RH relationship only based on the observation data of one satellite, and a TD may be misjudged as a slow shock.

Therefore, the present application has added limiting conditions. This uncertainty is overcome by using two or more satellite observation methods.

Because each discontinuity can be regarded as an infinitely large plane in the interplanetary space, and the earth can be regarded as a point relative to the discontinuity in the solar wind, so the same discontinuity will always be observed by multiple scientific research satellites near the earth . Suppose the same discontinuity (slow shock or tangential discontinuity) is observed by two different satellites at different locations and at different times.

Time difference Δt=ΔR·n/V _DD observed by two satellites;

ΔR is the displacement between the two satellites,

V _DD is the propagation velocity of the discontinuity in the stationary coordinate system,

V _DD and the normal direction n of the discontinuity can be calculated from local observations of the discontinuity, and their results depend on the type of discontinuity.

As mentioned above, for the same discontinuity viewed as TD or slow shock wave, n will differ by 90 degrees (see Figure 1), that is to say, the positions of discontinuities that can be regarded as infinite planes differ by 90 degrees. In this way, the time difference t estimated by the TD model and the slow shock model through the two satellites may also vary greatly. How big the specific time difference t will be is also related to the position of the satellite, and specific events need to be analyzed in detail. The time difference between the two satellites actually observing the discontinuity can be easily obtained, if the time difference is basically the same as one of the time differences estimated by two different models, and the difference is larger than the other, which is beyond the allowable range of observation errors. Then, the type of this discontinuity may be determined more accurately. In this way, the slow shock wave can be authenticated intermittently and effectively in combination with the R-H relationship, and the TD will not be misjudged as a slow shock wave. Of course, it is also possible that two satellites observe the same discontinuity at a very short distance, but the type of discontinuity cannot be accurately identified. This requires more (more than three) satellite observation data, and the same method is used to rule out the discontinuity. Possibility of misjudging TD as slow shock.

Example 1: September 18, 1997 Intermittent Event.

Slow shock characteristics of the discontinuity: It is very important to determine the parameters of the shock wave by fitting to study the interplanetary shock wave, and the most important thing is to establish a relatively accurate shock wave coordinate system. For example, the coplanar principle and the MVA method are commonly used methods to determine the shock wave coordinate system. Here, a new shock wave fitting program recently proposed by Lin et al. [2006] is used to analyze the shock wave characteristics of this discontinuity. They use a complete set of R-H relationships (or modified R-H relationships) to combine The least squares method gives a solution that fits the R-H relationship within the error range of the observed data. Lin et al. divided their methods into method A and method B, where method A uses the usual R-H relationship, and method B uses the modified R-H relationship. For a detailed introduction of the fitting method, please refer to the relevant literature [Lin et al., 2006].

The Wind spacecraft observed this discontinuity near 0255:15UT on September 18, 1997. At that time, the spacecraft was located at (83.51,-13.58,-1.45) RE in the GSE coordinate system, and RE is the radius of the earth. Figure 2 shows the time-dependent curves of the magnetic field and plasma parameters for this event. Among them, the magnetic field is the data recorded by the MFI (Magnetic Field Investigation) magnetometer on the spacecraft with a time resolution of 3 seconds; the speed and density of protons are the data detected by the 3DP (3-DimensionPlasma) on the spacecraft. Also 3 seconds. In addition, Table 1 gives the magnetic field, density and velocity downstream and downstream of this discontinuity, the directions of the three coordinate axes of the shock wave coordinate system obtained by fitting, and the estimated shock wave propagation velocity. According to the conservation relation, the propagation speed of the shock wave in the interplanetary space can be calculated by the following formula:

The observations and shock fitting results in Fig. 2 and Table 1 show that this discontinuity event fully complies with the requirement of a slow shock:

(1) From upstream to downstream, the magnetic field strength decreases and the proton density increases;

(2) All observations can well satisfy the R-H relationship;

(3) In the shock wave coordinate system, the upstream normal velocity is greater than the local slow magnetoacoustic velocity, and the downstream normal velocity is smaller than the local slow magnetoacoustic velocity.

Therefore, according to the commonly used criteria for judging slow shock waves, it can be verified that this event is a slow shock wave.

TD characteristics of the discontinuity: Based on the magnetic fluid theory, if the discontinuity is regarded as TD, the magnetic field condition has been satisfied, only that there is no flow through the discontinuity in the coordinate system of the discontinuity and the total pressure on both sides is balanced. If this discontinuity is regarded as TD, the normal direction nTD(-0.43, 0.88, 0.17) should point to the s-axis direction of the shock wave coordinate system (see Figure 1). Table 2 gives estimates of the thermal, magnetic, and total pressures on both sides of this discontinuity. It can be seen from Table 2 that the total pressure on both sides of the discontinuity is very close, and the pressure difference between upstream and downstream only accounts for 3% of the upstream pressure. If the systematic error of the observation instrument and the standard deviation of the observed value are considered, it can be considered that the total pressure on both sides of the discontinuity is balanced, which satisfies the second basic condition of TD. In addition, the result of multiplying the upstream and downstream speed difference (W=V2-V1) by the normal vector nTD of the discontinuity is 0.66km/s. This indicates that almost no flow passes through the discontinuity, ie the first condition of TD is satisfied. This discontinuity therefore also meets all the requirements of TD.

Observations from multiple satellites: This discontinuity was also observed by the ACE satellite at 0221:01UT, when ACE was located at (193.31,-24.78,20.78)RE. Figure 3 shows the magnetic field curves near this discontinuity observed by Wind and ACE satellites, in which the solid line is observed by Wind, and the dotted line is observed by ACE, and the time series of ACE is delayed by 34.2 minutes . It can be seen from Figure 3 that the change profiles of the two sets of magnetic field curves are relatively consistent, but there are slight differences in some detailed structures. Since the two satellites do not observe the same position of the discontinuity, some differences in details are normal. Therefore, it can be determined that the two satellites observed the same discontinuity.

Next, the slow shock model and the TD model are used to estimate the time difference (Δt) between the two satellite observations. Assuming that this discontinuity is a slow shock wave, Δt _s = ΔR·n _s /v _sh Δt _s = ΔR·n _s /v _sh , the calculated time difference is 15.3 minutes, which is 34.2 minutes different from the actual time difference observed by the two satellites very big. If the TD model is used, Δt _TD =ΔR·n _TD /V _TD . Where V _TD is the propagation velocity of TD in the stationary coordinate system, which can be obtained by multiplying the upstream velocity (V _TD =n _TD ·V ₁ =160.22km/s) or the downstream velocity (V ₂ ) by the normal unit vector point of TD. Since there is almost no flow across the TD surface, there is little difference in the results whether the upstream velocity or the downstream velocity is used to estimate the TD propagation velocity. The estimated time difference between the two satellite observations is 35.6 minutes, which is very close to the actual observed time difference of 34.2 minutes. Considering the systematic errors of observations, it can be judged that this discontinuity is TD rather than slow shock in the large-scale structure.

Assuming that the discontinuity can be approximated as an infinitely large thin surface and the propagation velocity does not change with time and space, four satellites of the Cluster are used to determine the normal direction of the discontinuity. Four satellites can give three independent equations similar to Δt=ΔR·n/V _DD , plus the normal direction of the discontinuous surface as a unit vector, a set of closed equations can be obtained:

where Vn is the propagation velocity of the discontinuity, ΔR _1i is the position vector between Cluster 1 and Cluster i satellites, and Δt _i represent the time difference between their observations of the discontinuity. Four equations and four unknowns can solve the propagation speed and normal direction of the discontinuous surface. This method does not require the observed magnetic field and velocity, and the calculated results are relatively accurate.

The discontinuity on September 18, 1997 was also observed by Geotail satellite near 0312UT, (24.85,-11.57,-1.52) RE. In this way there are three satellites that can be used to calculate the normal direction of the discontinuity. Normally, magnetic field values observed by satellites are much more accurate than velocity values. So here use the equation: n·B ₁ =n·B ₂ instead of the equation i = one of 2to 4, a set of closed equations can be obtained:

Among them, ΔR _WG (Δt _WG ) represents the displacement (time difference) between Wind and Geotail satellite, ΔR _WA (Δt _WA ) represents the displacement (time difference) between Wind and ACE satellite, B1 and B2 are observed by Wind satellite The magnetic field upstream and downstream of the discontinuity. The normal direction n of the discontinuity surface and the propagation velocity Vn of the discontinuity surface can be solved by using the above four equations. The calculated n=(-0.42, 0.89, 0.15) is almost consistent with the above n _TD (-0.43, 0.88, 0.17) obtained from the magnetic field, and the calculated velocity V _n = 164.99km/s of the discontinuity is also consistent with the calculated V _TD (160.22km/s) is very close. This proves again that the discontinuity, as a large-scale planar structure, should be a TD rather than a slow shock. However, TD, as the interface of two different fluids, will interact near the boundary during the propagation process, and may form a local, local slow shock structure, and this local slow shock wave is almost impossible to be observed by the two satellites. Therefore, what Wind observes is also likely to be a local slow shock wave. As mentioned above, when analyzing the shock wave on this discontinuity, if the upstream and downstream time intervals are selected to be slightly longer, the observed value cannot satisfy the RH relationship well. This may be evidence of small-scale local shocks. In addition, during the 3D simulation of TD, some substructures will appear in the middle, which may also correspond to this local shock wave.

Example 2: The Oct. 8, 2000 discontinuity event.

The middle shock feature of the discontinuity: this discontinuity was observed by the Wind satellite at around 0117:30UT, RW=(37.20, -59.72, 4.91) RE. The second column of Fig. 4 shows the changing curves of the magnetic field and plasma for this event. In addition, Table 3 presents the observations upstream and downstream of this discontinuity and the shock parameters directly derived from these observations. These parameters include the normal direction ns of the shock wave, the directions of the other two axes t and s of the shock wave coordinate system,

Upstream and downstream plasma β values, upstream and downstream normal Alphen Mach numbers (M _AN =V _n /V _An ), upstream and downstream fast magnetic acoustic Mach numbers (M _F =V _n /V _f ) and slow magnetic acoustic waves Mach number (M _SL =V _n /V _sl ), magnetic field strength ratio between upstream and downstream (m=B ₂ /B ₁ ), density ratio between upstream and downstream (y=N ₁ /N ₂ ), tangent component ratio between upstream and downstream (u=B _t2 /B _t1 ) and the included angle between the shock normal and the upstream magnetic field θ _BN =cos ^-1 (B ₁ ·n _s /B ₁ ). In the above expression, V _An is the Alphen velocity using the normal magnetic field component (V _An =B _n /(μ ₀ ρ) ^1/2 ), V _n is the normal component of the flow velocity in the shock wave coordinate system, V _f and V _sl are the fast and slow magnetoacoustic wave velocities, respectively. We used the method of Lin et al. [2006] to fit the discontinuity, and the results obtained by method A and method B were basically the same. Table 3 also shows the fitting results obtained by method A and the corresponding parameter values, and Figure 5.4 also shows the fitting results of the upstream and downstream (horizontal dotted lines). Combining Figure 4 and Table 3, it can be seen that the observed values are very consistent with the fitting results.

According to the magnetic fluid theory, an intermediate shock wave has the following characteristics:

(1) The normal Alfen Mach number of the upstream is greater than 1 while that of the downstream is less than 1;

(2) The tangential components of the upstream and downstream magnetic fields are opposite;

(3) Density increases from upstream to downstream;

(4) Among all the 4 types of intermediate shocks, the 2→4 type has a larger density modulation than the other 3 types.

Figure 5 shows the change curve of the magnetic field in the shock wave coordinate system. It can be seen from Fig. 5 that the direction of the tangential component B _t is reversed after passing through the shock wave surface, the normal component B _n remains unchanged, and the B _s component is approximately zero. Combined with the fitting parameters given in Table 3, this discontinuity can well meet the requirements of the intermediate shock wave. In addition, the fast Mach numbers upstream and downstream of the shock wave are less than 1, and the slow Mach numbers are greater than 1. Therefore, based on these characteristics, it can usually be verified that this discontinuity is a type 2→3 intermediate shock.

TD characteristics of the discontinuity: Table 4 gives the thermal pressure, magnetic pressure and total pressure on both sides of the discontinuity. It can be seen from Table 4 that the total pressure on both sides of the discontinuity is basically the same. In addition, if this discontinuity is regarded as TD, the product of the upstream and downstream velocity difference times the unit vector n _TD (-0.689, -0.694, -0.210) of the normal of TD is also very small (~1.58km/s). That is, this discontinuous surface meets the two basic requirements of TD, that is, it may also be considered that this discontinuous surface is TD.

Observation results of multiple satellites: this discontinuity was also observed by the Geotail satellite at around 0102:50UT, when the satellite's position was R _G =(29.91,-7.11,4.13) _RE . Figure 6 shows the comparison diagram of the magnetic field observed by Wind and Geotail satellites, in which the solid line is observed by Wind, and the dotted line is observed by Geotail with its time series delayed by 14.6 minutes. It can be seen from Figure 6 that the contours of the two sets of curves are relatively consistent, and it can be clearly confirmed that they are the same discontinuous surface observed by different satellites.

Next, we take this discontinuity as the intermediate shock wave and TD to calculate the time difference between the two satellite observations. If this discontinuity is regarded as the intermediate shock wave, according to the normal direction of the shock wave (n _s ) and the displacement between the two satellites (ΔR=R _G –R _W ), Fig. 7a shows the A schematic diagram of the orientation. It can be seen from Fig. 7a that the result of multiplying the displacement between the two satellites by the shock normal vector n _s (-0.58, 0.36, 0.73) is positive. This means that the Wind satellite should observe the shock wave first, but the fact is that Geotail observed the shock wave first. If this discontinuity is regarded as TD, Fig. 7b shows the schematic diagram of the normal direction of TD (n _TD ) and the displacement of two satellites. It can be seen from the figure that n _TD ·ΔR<0, and the estimated time difference (Δt _TD =ΔR·n _TD /v _TD ) is minus 13.9 minutes, which is compared with the fact that Wind observed this discontinuity 14.6 minutes later than Geotail match. So this discontinuity may be a TD rather than an intermediate shock.

In addition, when analyzing the shock wave of this discontinuity event, the selected time interval between the upstream and downstream of the shock wave is also relatively short. If the selected time interval is slightly longer, the observed value cannot satisfy the R-H relationship well. So this discontinuity may also be a special structure: a local, local intermediate shock structure formed between a large TD structure. This intermediate shock wave is a local structure formed by the interaction of two different fluids near the interface.

In order to eliminate the uncertainty, multiple satellite observations can be used to calculate the observation time difference between any two satellites. Since the time difference calculated by the TD model and the slow (or intermediate) shock model is often very different, and then compared with the actually observed time difference, this uncertainty can be eliminated. For example, the discontinuity events on September 18, 1997 and October 8, 2000 satisfy all the conditions of slow shock and intermediate shock respectively; on the other hand, they both satisfy the conditions of TD. Through multiple satellite analyses, it can be confirmed that they are TDs rather than shocks on large scales. So we suggest that more care should be taken when confirming the slow (or intermediate) shock wave, and it is best to use multiple satellites for confirmation.

Although multiple satellites can be used to confirm that the above two discontinuities are TD on a large scale, TD, as the interface of two different flows, will interact near the boundary during the propagation process, and may also form a local, local The slow (or intermediate) shock wave structure of , and this possible local slow shock wave is almost impossible to be observed by the two satellites. This may be similar to the structure of the magnetopause. The magnetopause can be regarded as a TD in the large-scale structure, while the RD structure often exists in the small scale. Therefore, the two discontinuity events observed by Wind on September 18, 1997 and October 8, 2000 may also be local slow shock waves and intermediate shock waves respectively.

Table 1: Observation parameters on the discontinuity surface and downstream on September 18, 1997, each axis of the shock wave coordinate system obtained by fitting

direction and the estimated shock velocity.

Table 2: Pressures on both sides of the discontinuity on September 18, 1997.

Table 3: Observations on the upper and lower reaches of the discontinuity on October 8, 2001, and fitting parameters of the intermediate shock.

Table 4: Pressure on both sides of the discontinuity on October 8, 2001.

For ease of explanation, specific nomenclature was used in the above description to provide a thorough understanding of the described embodiments. It will be apparent, however, to one skilled in the art that these specific details are not required to practice the above-described embodiments. Thus, the foregoing descriptions of specific embodiments described herein are presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. It is obvious to those skilled in the art that certain modifications, combinations and variations can be made on the basis of the above teachings.

Claims (1)

1. A method for observing and verifying interplanetary slow shock waves, characterized in that: comprising: First, determine the constraints; Second, determine whether the physical quantities on both sides of the magnetic field discontinuity meet the constraints; Third, judge whether the magnetic field discontinuity meets the basic characteristics of slow shock waves; Fourth, judge whether it is a slow shock wave or not by observing the time difference observed by two or more satellites that observe the magnetic field discontinuity; The time difference Δt observed by each satellite = ΔR·n/V _DD ; ΔR is the displacement between the two satellites, V _DD is the propagation velocity of the discontinuity in the stationary coordinate system, V _DD and the normal direction n of the discontinuity can be calculated from local observations of the discontinuity, and their results depend on the type of discontinuity; The constraint condition is the compatibility condition of the discontinuous surface, that is, the R-H relationship: [B _n ] = 0, [ρV _n ]=0, [V _t B _n −V _n B _t ]=0, [V _n B _q −V _q B _n ]=0, The subscripts n and t represent the normal direction and the tangential direction, respectively, and q represents the direction perpendicular to the n-t plane; Brackets indicate the difference of physical quantities on both sides of the discontinuity; P is the thermal pressure, which can be expressed as: P _|| and P _⊥ are the thermal pressure parallel and perpendicular to the magnetic field, respectively; ξ is the anisotropy parameter, and its definition is: When judging whether the physical quantities on both sides of the discontinuity meet the constraint conditions, the magnetic field discontinuity based on interplanetary space is not a completely ideal magnetic fluid discontinuity, and the physical quantities on both sides of the discontinuity are not required to strictly satisfy the R-H relationship; When judging whether the physical quantities on both sides of the discontinuity meet the constraint conditions, the R-H relationship is fitted with the least square method for the observed value, and the difference between the observed value and the theoretical value is considered to meet the R-H relationship within the allowable range of error; The basic characteristics of slow shock waves include: (1) The intermediate Mach numbers of the upstream and downstream are all less than 1; (2) The upstream slow Mach number is greater than 1, while the downstream slow Mach number is less than 1; (3) From upstream to downstream, the magnetic field strength decreases, and the proton density and temperature increase; Assuming that the discontinuity can be approximated as an infinitely large thin surface and the propagation velocity does not change with time and space, use the four satellites of the Cluster to determine the normal direction of the discontinuity; the four satellites can give three independent similar Δt=ΔR The equation of n/V _DD , plus the normal direction of the discontinuous surface as a unit vector, can get a set of closed equations: where Vn is the propagation velocity of the discontinuity, ΔR _1i is the position vector between Cluster 1 and Cluster i satellites, and Δt _i represent the time difference between their observations of the discontinuity.