We actually don't know the field that well. Although we can predict what is probably happening out there, the Pioneer and Voyager probes are the first manmade things to ever travel so far from the Sun. Recently, at least one of the Voyager probes probably crossed the heliopause (the boundary between the Sun's influence via the solar wind and interstellar space, much like the magnetopause which separates the Earth from the solar wind), and although the other hasn't travelled as far, it is at a significant angle to the equatorial plane and may have reached the heliopause as well. Contact was lost with both Pioneer probes before they got this far. I say they probably have reached the heliopause because we really don't know. None of these craft were designed to measure that sort of thing, and even if they had been, the only thing able to be recieved from that distance was telemetry data.
There have been essentially no measurements of fields or particles that far out in the Solar System. In fact, there has actually been very little measurement even close to Earth. This is why the Pioneer anomaly is an anomaly. We can tell that there is something going on, but we just don't know enough to say what it is. We can make some pretty good guesses, and make ballpark calculations to say that it definitely can't be certain things, but that's pretty much it.
