The strongest, naturally-occurring, fields are found on a new kind of neutron star called a magnetar. These fields can exceed 1000 trillion Gauss. For man-made fields that have been sustained in a lab, the number is about 400,000 Gauss. Fields over 1 million Gauss have been created momentarily by explosive compression for literally a split-second.
Galactic magnetic field 0.00001 Gauss Solar Wind 0.00005 Gauss Interstellar molecular cloud 0.001 Gauss Earth's field at ground level 1 Gauss Solar surface field 5 Gauss Massive star typical field (pre supernova) 100 Gauss Toy refrigerator magnet 100 Gauss Sun spot field 1000 Gauss Jupiter magnetic field 1000 Gauss Magnetic Stars such as BD+54 2846 12,000 Gauss White Dwarf star surfaces 1,000,000 Gauss Neutron star surface field 1,000,000,000,000 Gauss Magnetar field 1,000,000,000,000,000 Gauss
For more information on magnetars visit Science@NASA or the NASA Universe sites for news reports about the recent August 27, 1998 soft gamma repeater SGR 1806-20 which lit up the earth's ionosphere and was probably produced by a 'starquake' on a magnetar. Also, the May 21, 1998 issue of Nature gives more information on this new class of stars.
Note, if you compress a magnetic field 'adiabatically' you amplify its strength. For example, a solar magnetic field is on average a few gauss for a star about 1 million kilometers in radius. If you compress this to the size of a neutron star which is 20 kilometers in radius, the magnetic field energy density ( B^2/8 pi) is amplified by the ratio of the volumes which is 1.25 x 10^14. The field strength increases by the square root of 8 x pi times this number or 56 million Gauss for a 1 Gauss initial field. Neutron star fields can be higher than this because the process of core collapse is not exactly adiabatic (ie conserving the magnetic field energy). For highly-conducting bodies, the conserved quantity is the product of the field strength times the radius squared so that for a real star collapsing to a neutron star, the field will increase by (2,000,000/20)^2 = 10 billion times so that a 100 Gauss surface field for a progenitor star that supernovas to become a neutron star, is amplified to a 1 trillion Gauss neutron star surface field
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