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Since plasma is a superconductor, doesnít that mean charges instantly neutralize and electric fields canít exist inside it?


Short Answer

No. Superconductors are materials that do not hinder the flow of electric current. They have precisely zero resistance (the measure of a material's opposition to the flow of electric current) and the current will continue to flow almost indefinitely with no additional energy input required. Electric currents that flow through plasma experience non-zero resistance and will eventually cease if additional energy is not added, therefore plasma is not a superconductor.

Owing largely to the fact that plasma is not a superconductor, regions with non-neutral charges do not "instantly neutralize." It is known from experimental plasma physics in the laboratory that electric fields do exist between discrete localized regions of differing charge inside an overall "quasi-neutral" plasma.

Long Answer:

For years it was assumed that plasmas were perfect conductors and now astronomers and astrophysicists have come to treat plasma as though it is a perfect conductor (superconductor) and any charge imbalance will be "instantly neutralized." Sadly, for such an 'elegant' theory, the only true superconductors that have been created in the lab have been achieved using cryogenic temperatures (approaching 'absolute zero'). The more we can reduce random (thermal, collisional) motion, the better the conductivity will be. However, plasmas contain high 'temperature' electrons and ions. Unfortunately, the thermal motions of charge carriers in a current will still cause them to occasionally crash into one another.

The electrical conductivity of any material, including plasma, is determined by two factors: the density of the population of available charge carriers (the ions) in the material, and the mobility of these carriers. In any plasma, the mobility of the ions is extremely high, meaning that the charge carriers (the +ions and -electrons) are extremely free to move. This gives plasma a high conductivity. The trick with plasma is that it tends to be very low-density, therefore conductivity is less than 'ideal' in plasma. Despite being a very good conductor, plasma is not a perfect conductor (it is not a zero-resistance superconductor).

This can be demonstrated simply by applying the mathematical definition of resistance to the diagram of plasma discharge modes. Resistance is defined by the equation R = V / I. Resistance R (measured in ohms) is the ratio of voltage V (measured in volts) to current I (measured in amperes).
Plasma Discharges
Plasma discharge regimes.
[Click to enlarge]
It is quite clear from the diagram above that if you draw a line from the origin of the graph in the lower left to any point on the diagram of plasma's discharge regimes, the slope of the line (V / I) will always be positive and non-zero. That is to say, the diagram never touches the X axis at any point. Voltage V never decreases to zero. Ergo resistance R never decreases to zero. Ergo plasma is not a superconductor.

We now know that there can be slight voltage differences between different points within plasmas. Non-trivial electric fields can and do exist inside plasmas.

Many astrophysicists are still unaware of this property of plasmas, and so, we often still find many incorrect assumptions and assertions in astrophysical papers and popular news stories. If astrophysicists would do away with the inapplicable notion that plasma is a superconductor and acknowledge that electric fields can exist within plasmas, perhaps they would then also realize that (as a corollary) magnetic fields cannot be "frozen in" to plasmas but must be dynamically generated by electric currents therein.

These more accurate understandings may open an entirely new vista for researches into the astrophysical machinations of the cosmos at large, of which up to 99.999% of the observable constituents are known to be in the plasma state.
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