On 8/13/18 11:48 AM, Richard D. Saam wrote:
The Eugene Parker Solar Probe has just launched
to investigate close up solar magnetic and electric fields.
In his book:
"Conversations on Electric and Magnetic Fields in the Cosmos"
Dr Parker notes:
a SI charge non 'mass, length and time' definition as coulomb
is a limitation for dimensional analysis of such EM problems.
One wonders if his 'mass, length and time' analysis
of such EM problems in cgs units system
provided him with scientific reasoning in regards to solar EM fields
deemed crazy by his peers at the time 50 years ago
but which are currently accepted as true
and the basis for his named solar probe.

Richard D Saam

[[Mod. note -- Actually, there's very little dimensional analysis in
Parker's 1958 paper. That paper can be read online (open-access!) at
http://adsabs.harvard.edu/full/1958ApJ...128..664P
-- jt]]

Thanks for Parker's paper.
His paper actually has a (mass(M), Length(L) Time(T)
dimensional point of view:

Dimensional
energy m*v^2 and k*T M^1*L^2*T^-2
gravitational force G*M*M/r^2
M^1*L^1*T^-2 = (M^-1*L^3*T^-2)(M^2*L^0*T^0)(M^0*L^-2*T^0)
thermal conductivity M^1*L^0*T^-3
appear throughout his paper
but consider the last equation (bottom of page 674)
that describes the torque
caused by spiraling waves from the sun's magnetic field (B)
with the physically descriptive equation:

Torque(M^1*L^2*T^-2) = force(M^1*L^1*T^-2)*distance(M^0*L^1*T^0)
=(9/15)*b^4(M^0*L^1*T^0)^4*omega((M^0*L^0*T^-1)*(1/v)(M^0*L^-1*T^1)
*B^2(M^1/2*L^-1/2*T^-1)^2*(1+b/r(M^0*L^0*T^0)

This conceptually reduces to

Torque ~ space volume containing magnetic field * magnetic field squared

or

Torque (in units of energy) = volume * energy/volume

The magnetic field B definition as

M^1/2*L^-1/2*T^-1

makes everything dimensionally flow.

Parker probably assumed the B and H field were equal (vacuum)
having the same M^1/2*L^-1/2*T^-1 units
where B = mu*H and permeability(mu) = 1

Of course, this all can be done in SI
with the Coulomb addition
but my mind hurts to think
how to make physical sense of it,
the finer points to which Parker addressed in his book.

One note:
Parker's secretary left out the '/sec'
after the angular velocity 2.7 x 10^-4
at the top of page 674.

Such a simple (and certainly not crazy)
scientific pen and paper reasoning thing
done by Parker
in part resulting in the Solar Probe in his name.

RDS