2.2.1. Estimate of the Shock Using Oblique Shock Model
[9] 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) R_{E} 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. [2006], Lepping et al. [2005], Wu et al. [2006], Wu and Lepping [2007]. 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 (B_{x}, B_{y}, B_{z}), the x, y, z components of the proton speed (V_{x}, V_{y}, V_{z}), the proton density (N_{p}), the proton and electron temperatures (T_{p}), respectively. It can be seen from Figure 2 that the proton number density N_{p}, the proton and electron temperatures T_{p} and T_{e}, 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.
[10] The selected up and downstream intervals for fitting are indicated by the vertical lines in Figure 2. The selection of the intervals representative of the up and downstream 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.
[11] 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 downstream variables, respectively. Note that the density N is an effective plasma number density calculated from N = N_{p} + 4N_{a}, where N_{p} is the proton number density and N_{a} 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 AlfvénMach number (M_{AN} = V_{n}/V_{A}), the fastmode Mach number (M_{F} = V_{n}/V_{f}) in the upstream/downstream region, and the shock normal angle, θ_{BN1} = cos^{−1}(B_{1} • n/B_{1}), between the shock normal and the upstream magnetic field vector. Here, V_{A} = B_{n}/(μ_{0}ρ)^{1/2} is the Alfvén speed based on the magnetic field component normal to the shock front, V_{n} is the normal component of the bulk velocity to the shock front and measured in the shock frame of reference, and V_{f} is the speed of the fastmagnetosonic wave in the direction of the shock normal.
Table 1. Observed and Model Solution of the 1 August 2002 Discontinuity EventParameter  Observed Values^{a}  Fast Shock Model Solution  Switchon Shock Model Solution 


B_{1} (nT)  (5.79, −4.88, −3.36)  (6.69, −4.77, −3.36)  (6.84, −4.36, −3.76) 
B_{2}  (5.98, −0.66, −11.76)  (6.17, −1.01, −12.22)  (5.45, −1.30, −11.75) 
N_{1}, N_{2} (cm^{−3})  3.30, 7.18  3.11, 7.13  3.25, 6.99 
V_{1} (km/s)  (−385.3, 4.8, −47.4)  (−385.1, 5.6, −48.8)  (−385.1, 5.6, −48.8) 
V_{2} (km/s)  (−471.5, 96.3, −94.8)  (−464.6, 91.7, −88.2)  (−467.9, 78.1, −82.5) 
β_{1}, β_{2}  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) 
M_{AN1}, M_{NA2}  1.559, 1.062  1.608, 1.063  1.465, 1.000 
M_{F1}, M_{F2}  1.549, 0.592  1.600, 0.577  1.465, 0.594 
θ_{BN1}  6.40°  5.55°  0.00° 
[12] 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 fastmode Mach number is greater than unity in the preshock state and less than unity in the postshock state, (2) the normal AlfvénMach number (M_{AN}) is greater than unity in the preshock state and almost equal to unity in the postshock state, and (3) the shock normal angle (θ_{BN1}) 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 (B_{t}) is nearly vanished. However, across the shock the tangential component of the magnetic field is “switchedon” significantly. In addition, it can also be seen that the normal component (B_{n}) is nearly constant across the shock, while the other component (B_{s}) is nearly zero.
2.2.2. Estimate of the Shock Using the Switchon Model
[13] In order to have a more comprehensive understanding of whether the shock is switchon or not, we modify the MSF procedure based on a switchon model, and we apply it to analyze the data independently. For a switchon 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, θ_{BN1.} The other two coordinates are then obtained by
Here, t represents the tangential direction of the shock.
[14] For a switchon shock, u (≡B_{t1}/B_{t2}) ∞ and θ_{BN1} = 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. [2006]. 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 B_{1}·n and B_{2}·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, σ_{bn}, using the standard errors of the up and downstream magnetic field. It is calculated as
[15] Employing the modified fitting procedure, we obtain a best fit solution which satisfies the RH relations for a switchon shock. Table 1 lists the best fit shock parameters. In addition, Figure 3b shows the magnetic field profiles in the optimized switchon 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 switchon shocks are close to one another. Therefore, we suggest that the spacecraft may have observed a switchon shock.