Magnetic Portals Connect Sun and Earth
science.nasa.gov
science.nasa.gov
Of course, I'm sure the people doing this are looking into that.
They might not be.
The magnetic interaction between Jupiter and the Sun is stronger than between earth and the sun, so one might go looking for flux transfer events between Jupiter and the sun with a period of 43.2 minutes (the time it takes for light from the sun to reach Jupiter).