From:    Tim Thompson
To:      All                                    Msg #45, Sep-10-93 04:33PM
Subject: Re: Earth's magnetic field and Cowling's (sp?)

Organization: Jet Propulsion Laboratory
From: tjt@scn1.Jpl.Nasa.Gov (Tim Thompson)
Message-ID: <26r6d4$qae@elroy.jpl.nasa.gov>
Reply-To: tjt@scn1.Jpl.Nasa.Gov
Newsgroups: talk.origins

In article dkm@news.mic.ucla.edu, rush@eggneb.astro.ucla.edu () writes:
>I don't understand:  why is it such a big deal for Barnes to use
>Cowling's theory to day that a dynamo isn't generating the earth's
>magnetic field? Or, is that even what's he's saying.
>
>I read the FAQ but couldn't understand this.
>
>-Brian

   Well, I'm not sure what constitutes a "big deal", but, in a nutshell, Barnes
is wrong.
   Cowling's Theorem was published in the Monthly Notices of the Royal
Astronomical Society about 1934 (I don't recall the reference specifically
righ now, but I think it was in the FAQ?). It shows that no magnetic field
that is axially symmetric, nor one mathematically similar, could be maintained
via axially symmetric current flow. Cowling's intended application was
sunspots,
but he noted in his paper that his derivation was applicable in the general
case.
   A pure dipole field is axially symmetric, and therefore would not be
generated/supported by currents flowing in a planetary core, the dynamo
mechanism theorized for the presence of the Earth's magnetic field. This is
no problem for the Earth, because it's field is not a dipole, except in the
crudest sense; it has copious energy involved in higher order terms, and
therefore can be dynamo supported, as is the case for all known planetary or
stellar magnetic fields.
   To get around this problem, Barnes postulates, without any justification,
that only the dipole component of the Earth's magnetic field is generated by
currents flowing in the core, and that all higher order terms are the result
of magnetic features at the surface, or telluric currents generated as a
reaction to the solar magnetic field impinging on the Earth's magentic
field, solar wind, thubderstorms, and etc. Tossing out the higher order
components allows him to invoke Cowling's theorem and deny the existence,
or even the possibility, of dynamo maintenance for the Earth's magnetic field.
   Barnes's method is silly. The verious order terms of a harmonic expression
of the Earth's magnetic field are dominated by features of approximately the
same physical size as the field component. For instance, and surface feature
on the Earth that could influence the quadrapole moment of the Earth's field
would have to cover about 1/8 the surface of the Earth. Telluric currents
are scaled very much smaller than that, and even the largest concentrations
of magnetised rock are nowhere near that large. Add to this the fact that
there is a significant westward drift in even the lower order elements of the
field (quadrapole, octopole, etc.), and explain how magnetised rocks move
over the surface much faster than the continents they are attached to.
   I know I have jargonized this to some extent, but a detailed explanation
in plain language calls for a lot of words, as it depends on the meaning of
the language Barnes uses, or mis-uses. The definition of terms is really
important here.
   Hope this helps.


---
------------------------------------------------------------
Timothy J. Thompson, Earth and Space Sciences Division, JPL.
Assistant Administrator, Division Science Computing Network.
Secretary, Los Angeles Astronomical Society.
Member, BOD, Mount Wilson Observatory Association.

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