debye

At a separation of just ten Debye lengths, the ion's effective charge has been reduced by a factor 0.000045; at a separation of one hundred Debye lengths, the factor is 3.72e-44, for all practical purposes zero.

Charged plate conversion system require the plate spacing be lower than the Debye radius of the plasma.

Zubrin's paper has Debye length all over it; it's a crucial consideration.

When the Debye length is short compared to the field gradient (i.e.

Near is all that matters in a plasma, since charged particles leaving the device will get screened and decouple from it within a few Debye lengths.

As one straightforward example, their estimate of the (change in) Debye length ignores that their equations (2 and 3) are in terms of the square of the Debye length, so the purported change should be only sqrt as large.

Snipping wildly: Following up on de Broglie's ideas, physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation.

Hameroff's group also suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding actin gel might enhance the ordering of water, further screening noise.

The Debye length in low Earth orbit is measured in millimeters [1][2], so for any device significantly larger than that, the far field which you keep invoking is completely negligible.

But an ion still begins it's journey out at the bottom of a large potential well; one which is particularly steep because of the debye length, but still just as deep.

To account for that, include a Debye factor: the coupling between electric field E and ion with naked charge q goes from E * q to E * q * exp(-r/l_D) where r is distance from the plate and l_D is the Debye length [1].

We only need to concern ourselves with the simple case of zero frequency, in which case the external electric field E at distance r from a plate with surface field E_0 is E = E_0 * exp( -r / l_D ) with l_D denoting Debye length.

The result is called the Debye–Hückel equation and is identical to the one shown in the "with math" section.

So, the effect of the "stiffness" term is reducing the range of the electric interactions to λ, which is called the Debye length.

Google "Dulong-Petit Law" and "Debye Model" if you'd like to see why.

If you want to read more, this concept is called "Debye Screening" Anyway, this might be a more helpful approach than trying to imagine a spring - a "stiff" field equation is an equation for a field in a medium that polarizes to oppose it, and you can think of space as polarizing to oppose the existence of a Z Boson in a way that it doesn't polarize to oppose the existence of a photon.

Inspired by Debye's remark, Schrödinger decided to find a proper 3-dimensional wave equation for the electron.

His students include Heissenburg, Debye, Bethe, Pauli.