[3] We apply our 3D MHD model with a constant flux of H [*Ratkiewicz et al.*, 2008]. In our calculations at the inner boundary we use the solar wind pressures observed by V2 before the termination shock crossing [*Richardson et al.*, 2008a]. At the outer boundary we use the local interstellar medium (LISM) velocity *V*_{is} = 26.4 kms^{−1}, flowing from He direction (*λ*, *β*) = (254.7°, 5.2°) [*Lallement et al.*, 2005] and temperature *T*_{is} ∼ 6400 K. Other LISM physical quantities we treat as parameters of the problem. They are: the angle between the helium velocity and magnetic field vectors (called the inclination angle *α*) which varies from 0° to 90°, the strength of the magnetic field equal to 2.8, 3.5, 3.8 or 4.1 *μ*G, and the plasma number density which falls in the range of 0.04–0.11 cm^{−3} [*Izmodenov et al.*, 2003]. If we use the measurements of the atomic H density at the termination shock (= 0.100 ± 0.008 cm^{−3}) [*Izmodenov et al.*, 2003], the H number density in the LISM is *n*_{H} = 0.1–0.2 cm^{−3}.

[5] Figure 1 illustrates the geometry showing in the solar ecliptic coordinates the position of helium (He) inflow from a direction (*λ*, *β*) = (254.7°, 5.2°), the position of hydrogen (H) flowing from a direction (*λ*, *β*) = (252.5°, 8.8°), and defined by above H and He flow vectors the hydrogen deflection plane, called the nominal HDP. There are also shown the V1 and V2 positions, when they crossed the TS, and the angle *α* which corresponds to the angle between and . Note that for each *α* there is a set of magnetic field directions marked by crosses every 10°, that create a cone around He inflow vector. A position on the cone is measured from the HDP by the *β* angle. We made simulations for many combinations of SW and LISM physical parameters to see which of them are candidates to achieve our goal. The selection has been made using a method illustrated in Figure 2, which consists of nine panels. In these panels the TS crossing distance is indicated by horizontal solid line for V1 (at 94 AU) and dashed line for V2 (at 83.7 AU) [*Stone et al.*, 2008]. Curves indicate the heliocentric distance to the TS in the V1 (solid) or V2 (dashed) directions as a function of angle *β*. The vertical segments indicate *β* angles for which the TS is closer to the Sun in the V2 than in the V1 direction by about 10 ± 1 AU. To get both Voyagers at the proper positions we have to have vertical segments between the two horizontal lines, with solid curve at solid, and dashed curve at dashed horizontal line, respectively. For each set of data we were looking for a range of *α* and *β* angles, that would allow us to find the best fit. In Figure 2 we present results obtained for three sets of physical data. In the 1st row we use for the SW at 1 AU velocity *V*_{SW} = 400 kms^{−1}, number density *n*_{SW} = 6.36 cm^{−3} [*Richardson et al.*, 2008a], and temperature *T*_{SW} = 51109 K, for the LISM *V*_{is} = 26.4 kms^{−1}, *T*_{is} = 6400 K, *n*_{is} = 0.11 cm^{−3}, *n*_{H} = 0.11 cm^{−3}, *B*_{is} = 3.8 *μ*G. To illustrate the influence of changes in conditions of the SW we increased the SW speed at 1 AU up to 508 kms^{−1}, and decreased the number density to 5.0 cm^{−3} (the 2nd row). In the 3rd row we demonstrate results with the same parameters as in the 2nd row but the strength of the LIMF increased up to *B*_{is} = 4.1 *μ*G. The best fit was achieved for conditions presented in the 1st row for *α* = 30°, and *β* = 20°. For comparison see results for *α* = 25°, and for *α* = 35°. As shown in the 2nd row, the 10 AU difference is obtained for 30°, but both Voyagers are too far from the Sun. Their positions are improving for 40° and 45°, but the distance between them drops below 10 AU. In the 3rd row a step in *α* in subsequent panels is 1°. 10 AU distance is achieved, but not at desired Voyagers' positions. For *α* = 42° the distance between Voyagers decreases. To show asymmetry of the heliospheric configuration caused by the LIMF we use the *V*_{1}−*V*_{2} plane, which is determined by three points: the position of the Sun and both positions at which Voyagers crossed the TS. The *V*_{1}−*V*_{2} plane crosses the heliosphere showing a deformation of the TS for any particular direction of the LIMF. In Figure 3 the shape of the TS reflects the steady-state asymmetry ensuring the V2 crossing the TS at a distance to the Sun closer by 10 AU than V1 obtained for *α* = 30°, and *β* = 20°. In Figure 4 the plasma parameters such as a number density, temperature, and velocity along V1 and V2 directions are shown. Jumps of the physical parameters at the TS correspond well to positions of V1 and V2. The compression ratio in V2 direction is close to jumps of velocity and number density observed by V2 (see Figure 4 caption). Our temperature is higher according to the model (heating due to pickup ions is overestimated), however the thermal pressure is still two orders of magnitude smaller than dynamic pressure, and does not change our final results.