Here we describe one of the most fascinating features of the magnetic field lines in the solar wind (the "interplanetary magnetic field" or IMF) which is their average spiral geometry in the Ecliptic plane. This particular geometry is due to these three facts: (1) the solar wind blows out almost radially from the Sun, (2) the Sun's magnetic field lines are attached to the solar wind parcels as they flow out, i.e., the field is "frozen into" the solar wind, and (3) the sources of the interplanetary field-lines are attached to a rotating Sun. These circumstances give rise to the spiral field as shown in Figure 1. In this figure we see that the pattern of the solar wind parcels given by the numbers 1 through 8 are a spiral, even though the parcels themselves are all flowing out directly (along radial lines) from the Sun. Also we see that the spiral field line connects these parcels, because of the field-wind attachment. This is analogous to what we see when a water sprinkler shoots out a spray of water radially outward (in the frame of reference of the lawn being watered), as the sprinkler rotates. The pattern of these parcels of water is seen as having a spiral pattern. The spiral pattern is consistent with the path of the water itself (not just the pattern) in the frame of reference of the rotating sprinkler.

Now we show how we can estimate the pitch of the spiral field line, i.e., the direction of the magnetic field in the solar wind with respect to the radial direction. We will consider the solar wind to be flowing purely radially in an inertial (fixed) frame of reference. In reality there are side-ways components, and up/down components of the solar wind flow velocity, but these are usually much smaller than the radial speed and are on average (over about a month) very close to zero. In a spherical coordinate reference frame, fixed with and therefore rotating with the Sun's equator velocity, where j is the longitude (measured with respect to the Earth-Sun line, i.e., where j = 0° ), q is latitude (q = 0° in the Ecliptic plane), and R is the radial distance from the Sun, we see that ideally:

where w_S = 2.7 x 10^-6 radians/s is the angular velocity of the Sun's rotation; this corresponds to the Sun's equator rotating once every 27 days from the point of view of the spacecraft measurements. It is important to realize that V_j is due to the transformation to the rotating system.

From Figure 2 we see that tan j = |w_SR/V_R|,

where q = 0, since the figure refers to the Ecliptic plane. We will consider the case where V_R is 400 km/s, an average speed of the solar wind at R = 1 AU (1.5 x 10⁸ km). Hence,

j= tan^-1{|w_SR/V_R|} = tan^-1{(2.7 x 10^-6 s^-1 x 1.5 x 10⁸n km)/400 km/s} = 45° .

Hence, the magnetic field, which is aligned with the apparent flow direction (if, in the rotating coordinate system) either parallel or anti-parallel, near the Sun, will be at an angle of 45º with respect to the Earth-Sun line at 1 AU. We call this Case A. It is obvious that the angle j , at a given radial distance from the Sun, will vary only according to the radial solar wind speed, V_R, since w _S R is then constant. For example, for V_R = 800 km/s we see that

j = tan^-1{(2.7 x 10^-6 s^-1 x 1.5 x 10⁸ km)/800 km/s} = 27° ,

and the field-line will then be much closer to the Earth-Sun line. For V_R = 250 km/s we see that

j = tan^-1{(2.7 x 10^-6 s^-1 x 1.5 x 10⁸ km)/250 km/s} = 60° ,

and the field-line will then be much farther from the Earth-Sun line. We call this Case B. Figure 3 shows examples of two (A and B) of these three cases. It is instructive to point out that (again for R = 1 AU)

w_SR = 405 km/s.