2.2.1. Estimate of the Shock Using Oblique Shock Model
 The shock was observed by Wind at ∼0519:28 UT on August 1, 2002, when Wind was located at (20.9, 86.5, 4.8) RE in the GSE coordinate system. The shock is found prior to a magnetic cloud, and it may be a product in the leading medium as the medium is pushed and compressed by the trailing magnetic cloud. A magnetic cloud is defined empirically in terms of its magnetic field and plasma having the following properties: (1) a high magnetic field strength compared to the ambience, (2) a smooth change in field direction as observed by a spacecraft passing through the cloud, and (3) a low proton temperature compared to the ambient proton temperature [Burlaga et al., 1981; Burlaga, 1991]. Figure 1 shows the magnetic field and proton temperature data of the magnetic cloud as well as the leading shock. It can be seen that the event satisfies the three criterions mentioned above. In addition, this event was identified as a magnetic cloud by R. P. Lepping et al. (http://lepmfi.gsfc.nasa.gov/mfi/mag_cloud_pub1.html), Jian et al. , Lepping et al. , Wu et al. , Wu and Lepping . Figure 2 shows 13 minutes of the magnetic field and plasma data of this shock observed by Wind. From top to bottom the panels show the magnitude of the total magnetic field (∣B∣), the x, y, z components of the magnetic field (Bx, By, Bz), the x, y, z components of the proton speed (Vx, Vy, Vz), the proton density (Np), the proton and electron temperatures (Tp), respectively. It can be seen from Figure 2 that the proton number density Np, the proton and electron temperatures Tp and Te, and the total magnetic field strength ∣B∣ increase across the discontinuity. As can also be seen, the protons are thermalized to a very high temperature across the shock in comparison to the unperturbed state. However, it is not the case for the electrons. In addition, across the shock the proton velocity ∣V∣ (not shown here) also increases by 112 km/s. All these jump signatures are consistent with the requirements for a fast shock.
Figure 1. Interplanetary magnetic field and proton temperature data measured by the Wind spacecraft during the 1–2 August 2002 Magnetic cloud passages. FB and RB are the estimated front and rear boundaries, respectively.
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Figure 2. The interplanetary magnetic field and plasma data measured by Wind in GSE coordinate system on 1 August 2002.
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 The selected up- and down-stream intervals for fitting are indicated by the vertical lines in Figure 2. The selection of the intervals representative of the up- and down-stream regions is difficult and important, and a certain amount of subjectivity seems unavoidable. We try to select the intervals which are close to the transition layer and in which the magnetic field and plasma are relatively stable in order to reduce the effect of waves as well as the disturbances associated with the other structures.
 Table 1 lists the observed mean values and standard deviations of the magnetic field vector B, the solar wind velocity vector V, and the number density N. Subscripts 1 and 2 refer to the up- and down-stream variables, respectively. Note that the density N is an effective plasma number density calculated from N = Np + 4Na, where Np is the proton number density and Na is the number density of alpha particles. From the optimized solution obtained by the MSF procedure, we have the corresponding shock parameters. They are listed in Table 1. These parameters are the shock normal vector n, the other two axes of the shock coordinate system t and s, the plasma beta (β), the normal Alfvén-Mach number (MAN = Vn/VA), the fast-mode Mach number (MF = Vn/Vf) in the upstream/downstream region, and the shock normal angle, θBN1 = cos−1(B1 • n/B1), between the shock normal and the upstream magnetic field vector. Here, VA = Bn/(μ0ρ)1/2 is the Alfvén speed based on the magnetic field component normal to the shock front, Vn is the normal component of the bulk velocity to the shock front and measured in the shock frame of reference, and Vf is the speed of the fast-magnetosonic wave in the direction of the shock normal.
Table 1. Observed and Model Solution of the 1 August 2002 Discontinuity Event
|Parameter||Observed Valuesa||Fast Shock Model Solution||Switch-on Shock Model Solution|
|B1 (nT)||(5.79, −4.88, −3.36)||(6.69, −4.77, −3.36)||(6.84, −4.36, −3.76)|
|B2||(5.98, −0.66, −11.76)||(6.17, −1.01, −12.22)||(5.45, −1.30, −11.75)|
|N1, N2 (cm−3)||3.30, 7.18||3.11, 7.13||3.25, 6.99|
|V1 (km/s)||(−385.3, 4.8, −47.4)||(−385.1, 5.6, −48.8)||(−385.1, 5.6, −48.8)|
|V2 (km/s)||(−471.5, 96.3, −94.8)||(−464.6, 91.7, −88.2)||(−467.9, 78.1, −82.5)|
|β1, β2||0.167, 0.652||0.161, 0.695||0.154, 0.624|
|n||(−0.701, 0.643, 0.308)||(−0.762, 0.578, 0.291)||(−0.765, 0.488, 0.421)|
|t||(0.019, 0.449, −0.893)||(−0.054, 0.390, −0.919)||(−0.232, 0.400, −0.887)|
|s||(−0.713, −0.620, −0.327)||(−0.644,−0.717,−0.266)||(−0.601, −0.776, −0.193)|
|MAN1, MNA2||1.559, 1.062||1.608, 1.063||1.465, 1.000|
|MF1, MF2||1.549, 0.592||1.600, 0.577||1.465, 0.594|
 As can be seen in Table 1, the best fit values are close to the observed means, namely, the data can be interpreted as an oblique fast shock (with small shock normal angle). The shock solution demonstrates the following properties: (1) the fast-mode Mach number is greater than unity in the preshock state and less than unity in the postshock state, (2) the normal Alfvén-Mach number (MAN) is greater than unity in the preshock state and almost equal to unity in the postshock state, and (3) the shock normal angle (θBN1) is very small. Figure 3a shows the magnetic field profiles in the shock coordinates. It can be seen that the tangential component of the upstream magnetic field (Bt) is nearly vanished. However, across the shock the tangential component of the magnetic field is “switched-on” significantly. In addition, it can also be seen that the normal component (Bn) is nearly constant across the shock, while the other component (Bs) is nearly zero.
Figure 3. The observed magnetic fields on 1 August 2002 in the shock coordinate system, (a) the fast shock model, and (b) the switch-on model.
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2.2.2. Estimate of the Shock Using the Switch-on Model
 In order to have a more comprehensive understanding of whether the shock is switch-on or not, we modify the MSF procedure based on a switch-on model, and we apply it to analyze the data independently. For a switch-on shock, the shock normal is parallel to the upstream magnetic field. Therefore, in the modified procedure, we calculate the shock normal by
with the Monte Carlo calculation. Therefore, we have a zero degree shock normal angle, θBN1. The other two coordinates are then obtained by
Here, t represents the tangential direction of the shock.
 For a switch-on shock, u (≡Bt1/Bt2) ∞ and θBN1 = 0°, there are some uncertain situations in the values of the calculated velocity and plasma betas in equations (8) to (11) of Lin et al. . The expressions of these parameters should be modified to
Since in the modified procedure the shock normal is not obtained by the magnetic coplanarity theorem, the normal magnetic fields B1·n and B2·n do not have to be equal to one another. For finding an optimized solution for the divergence free condition of the magnetic field, we add a term in the loss function for the normal magnetic field. The term is expressed as . Here, we calculate the error, σbn, using the standard errors of the up- and down-stream magnetic field. It is calculated as
 Employing the modified fitting procedure, we obtain a best fit solution which satisfies the R-H relations for a switch-on shock. Table 1 lists the best fit shock parameters. In addition, Figure 3b shows the magnetic field profiles in the optimized switch-on shock coordinates. As can be seen in Table 1 and Figure 3, the solution of this modified procedure is close to the data as well. We also find that the solutions of the two independent analyses based on oblique and switch-on shocks are close to one another. Therefore, we suggest that the spacecraft may have observed a switch-on shock.