Sunday, March 20, 2011

A Look at Earth's Magnetic Dipole Field

How the Earth's magnetosphere protects our planet from the onslaught of the solar wind. But to have a protective magnetosphere, there must be an adequate magnetic field to sustain it.

Our planet's dipole field is extremely critical in terms of maintaining its residual magnetic field of roughly 3.1 Gs (gauss) which in turn implies the capacity to provide a magnetosphere that's capable of intercepting the high energy particles of the solar wind as well as other solar-flare triggered particles. The attached diagram shows the response (generic) of our magnetosphere to the onslaught of the solar wind.

Readers will recall that, in more detail, I also examined the dynamics of particle orbits and paths within the magnetosphere, e.g.:



a key parameter for which is the pitch angle:

sin (φ) > [ (B(min) / B (max )]^½

designating the thresholds for when confined particles will be reflected within the tube, i.e. "mirrored" via an in situ "magnetic mirror" sustained by the Earth's magnetic field.

In other words, if the Earth's field were to go to zero, then the magnetosphere and its protection would be lost. The magnetosphere is only in place because the Earth generates a magnetic field that then enables a magnetosphere to form.

Typically, the magnetosphere will diminish during a field reversal and even B(E)-> 0, in particular because such reversals include an interval wherein no magnetic field exists. This zero field condition may last from 100 to 1000 years, perhaps more. In such a case, the magnetic field -which normally acts as a protective barrier to the flux of energized particles known as the solar wind- ceases to do that. This means that in the event of major solar flares, the particle flux might attain levels that can be lethal to some life forms.

The problem posed by the solar wind's (or flare) energetic particles is to expose many life forms to much higher radiation levels. To give an indication of the magnitude, when a medium intensity (not even terribly large) solar wind normally "blows" along the magnetosphere boundary an effective MHD (magneto-hydrodynamic) generator is produced. All such "generators" are defined by virtue of the free electrons and protons in the solar wind cutting across the Earth's resident magnetic field.

With an induced voltage of this generator up to 150 kV (150,000 V) a total power of more than 1 million megawatts is produced. That is 1 million joules of energy per second. Entering the Earth's atmosphere unabated such energy flux would pose major issues for any organisms, including humans.

Now, let's look at the dipole field proper, in as much as it gives rise to the magnetosphere. First, the poles of the dipole are not coincident with the geographic north or south poles, which are defined at latitudes 90 deg N, and 90 deg S, respectively. One of the more recent positional computations put them at 79 deg N, 70W, and 79 deg S, 70 E, respectively.

The magnetic flux density defined for the Earth is given as (Hargreaves, The Solar-Terrestrial Environment, Cambridge University Press, p. 150):

B(r,L) = M/r^3 [ 1 + 3 sin^2 L]^½

where M is the dipole moment (M ~ 10^25.9 G cm^3, with G in gauss), r the geocentric radial distance and L the magnetic latitude (e.g. 70 deg for the locations given earlier).

Generically, the vector magnetic field at vector position x due to a magnetic dipole of vector dipole moment m at the origin, is given by:

B = {3(m*x)x - x^2} / ‖ x‖ ^3

Meanwhile, the field components in the r and L directions are respectively (Hargreaves, ibid.)

B(r) = - 2M sin(L) / r^3

B(L) = M cos (L) / r^3

The characteristic time for variation of the Earth's magnetic field is given by:

dB/dt = B(r,L)/t

and it can be shown (using the adiabatic invariants in the plasma physics problem sets from a while back), e.g. refer to:

and note:

the magnetic moment u(m) is a constant of the motion: viz

u(m) = m(v⊥)^2/ 2B= const.

Bear in mind the gyration energy: E(g) = u(m)B = m/2 (E/B)^2,

Young Earth creationists argue that if the Earth's dipole changes by 5% per century, the Earth can't be much older than 20 centuries[1] (i.e.. 20 cen x 5%/c = 100 %) However, simple computations using the preceding easily refute that contention. In fact, one can use test particles, say electrons, of specific energy (say 1 keV) in the magnetosphere, as a basis to do the differentiation of B(r,L) taking into account the constants of the motion, especially u(m) and showing this is preposterous. For one thing, the variables B(r), B(L) are likely to vary and not be uniform relative to each other, so "5% per century" as a defined uniform scale variation for B(r, L) is nonsense. Worse, the remanenece factor is not taken into account, and from even basic computations of this type one can show a minimum time scale of at least 250,000- 300,000 YEARS for field reversal (for the field components B(L) and B(r) to attain magnitudes that yield a discernible magnetic moment, M.

Even the lowest estimates for such computation, say for t associated with dB(r,L)/dt (via integration) yield ~100,000 yrs. and thus more than fifty times larger than what the Young Earthers claims.

Sadly, when one - even a scientist - is committed to a pre-defined prejudice and belief agenda, no amount of evidence, or computation or magnetic theory will likely change his or her mind. Committed to their bibles, they will neglect facts and choose mythical translations from nomadic sheep herders each time.

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