Re: Inertial-dampening systems

From: Timo Nieminen (uqtniemi_at_mailbox.uq.edu.au)
Date: 02/12/05 

Date: Sat, 12 Feb 2005 10:30:31 +1000

On Sat, 11 Feb 2005 msadkins04@yahoo.com wrote:

> Timo Nieminen wrote:
> > On Fri, 10 Feb 2005 msadkins04@yahoo.com wrote:
> >
> > > Timo Nieminen wrote:
> > >
> > > > According to Hansen, it would be wise to check if the
> > > > current induced by the changing magnetic field is
> > > > dangerously high. Conductivity of tissue at
> > > > low frequencies is about 1 S/m, which tells you the
> > > > resistance. Then one just needs to know the capacitance,
> > > > and dB/dt. Is the peak current biologically dangerous?
> > >
> > > More interestingly, what do you mean by "low frequency" in
> > > the current application? A static magnetic field of some
> > > particular strength is increased in strength. What is
> > > the "frequency" of a change in field strength that occurs
> > > only once? Does its "frequency" depend upon the magnitude
> > > of the change? The time in which the change occurs?
> > > Remember, this change occurs in connection with some
> > > acceleration. The parameters are wide open.
> >
> > As you presumably know, writing the constitutive equations
> > with permittivity (which I'll write as e), permeability (m),
> > and conductivity (s) as constants is at best a crude
> > approximation, and the usual "solution" to this problem
> > is to consider them as functions of frequency (w):
> > D(w) = e(w) E(w), B(w) = m(w) H(w), J(w) = s(w) E(w)
>
> <snip>
>
> You may be optimistic. :) Now, I do not mean to dismiss what appears
> to be a carefully wrought piece of technical exposition, and perhaps it
> is simple-minded of me, but I asked a very simple question as to how
> "frequency" can be defined in such a case, and I do not see a clear
> response to this question in your reply. Does the concept of frequency
> apply in such a case, meaningfully?

As I wrote in the portion you cut, there is no single frequency; there is
a frequency spectrum. The Fourier transform of B(t) gives you the
spectrum. And, depending on the spectrum, there may well be a useful
characteristic frequency. Especially in the case
of dispersion being not-too-large in the dominant regions of the spectrum,
using the electromagnetic properties of tissue in this spectral region and
the power in that region might give a reasonable estimate.

Now, since I didn't write anything above that I didn't write in the
previous post, I don't except you to get the point yet. Since the above
explanation is inadequate for your purposes, perhaps you could take the
time to explain what you find unclear about B(t), B(w), and finding B(w)
from B(t) by Fourier transform?

> Now, as long as we are on the subject of possibly stupid questions, let
> me pose the following to you.
>
> A transformer primary coil is fed half-wave rectified current in the
> form of a train of DC pulses (each from zero to peak and back to zero).
> This produces a series of varying magnetic pulses.
[cut]
> The current induced in the new circuit can flow in only one direction.
> Which of the two horizontal wires "flips its polarity", and why? Does
> the magnetic field act non-locally? Does it know that the circuit
> configuration (but not the orientation of the original wire sections
> near the primary) has changed? Doesn't the magnetic pulse induce EMF
> in those original sections nearest the primary *before* propagating to
> parts of the circuit which are farther away? How do the field lines
> moving through near portions know what the configuration of the rest of
> the circuit is?

First, realise that circuit theory is one of the classic cases of the
quasi-static approximation. If you're talking circuit theory, you assume
that changes propagate everywhere in negligible time.

If propagation time is important, then don't use circuit theory. What is
wrong with circuit theory in this case? Basically, the assumption that the
current in a closed circuit is the same everywhere along the circuit.
Basically, your statement that "current induced in the new circuit can
flow in only one direction" is only correct within the regime of
applicability of circuit theory.

So, sure, there is a current induced in the near wire before the magnetic
pulse reaches the far wire. So, sure, the current is different in
different parts of the circuit. So, sure, the charge density becomes
non-zero in parts of the circuit.

If you were to put that circuit into an increasing electric field parallel
to the two main wires, then the current along both wires would flow in the
direction of the electric field (which is in opposite directions in the
usual circuit sense). A little thought about receiving antennas might
suggest that two straight wire antennas side-by-side will still work even
if joined at the tips. A little further thought about transmitting
antennas (eg centre-fed straight wire antennas) might suggest that not
only is there no fundamental prohibition of currents being different in
different parts of a circuit, there's also no problem with transient
currents in open circuits.

The main difference between the circuits/antennas above and your
frog/astronaut is that the conductivity of tissue is about 10^7 times
lower than that of the wires, and the approach to electrostatic
equilibrium will be much longer.

The key question is: How quickly do the magnetic fields change
signigicantly? On a time-scale of microseconds and faster, or slower? It's
not just a matter of how quickly the controlling computer can respond, the
size of the magnetic is important, too. Now, to get the effect you want,
you need to have, if the acceleration is in the z-direction, a field as
uniform as possible in the x and y directions, which suggest the use of a
source comparable in size to the protected area. This suggests that the
times over which the fields change will be longer than a microsecond, in
turn implying that the quasistatic approximation will be good enough for
an initial analysis.

Now, the quasistatic approximation, and the further approximation that
dB/dt is uniform throughout the frog/astronaut, gives a simple model that
can actually give an analytical solution.

Otherwise, FDTD is your friend. 

-- 
Timo

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