Astrophysicists refer to magnetic fields in plasmas as "frozen in" and "carried along with the plasma." However, we know from many sources that Maxwell's Wonderful Equations define a specific relationship between electric current and magnetic fields. Magnetic fields are a byproduct of electric currents. Granted, the feeling is mutual insofar as changing magnetic fields can induce an electric current. Hence electricity and magnetism are bound up in "electromagnetism." But how does this all apply to plasmas?
I'd refer folks back to Don Scott's paper on "Real Properties of Electromagnetic Fields and Plasma in the Cosmos."
Specifically, the section "VI. FROZEN-IN MAGNETIC FIELDS."
Don Scott wrote: Astrophysicists often assume that plasmas are perfect conductors, and as such, any magnetic field in any plasma must be “frozen” inside it ... It was based on the observation that, since plasmas were thought to be perfect conductors, they cannot sustain electric fields.
Alfvén’s original motivation for proposing “frozen-in” fields stemmed from another one of Maxwell’s equations, i.e.,
∇×E = −dB/dt
This implies that if the electric field in a region of plasma is identically zero valued (as it would have to be if the medium had zero resistance—perfect conductivity), then any magnetic field within that region must be time invariant (must be frozen). Thus, if all plasmas are ideal conductors (and thus cannot support electric fields), then any magnetic fields inside such plasmas must be frozen in, i.e., cannot move or change in any way with time.
But what of Maxwell's equations. Just because magnetic fields are considered "frozen in" to plasma, doesn't mean that no current exists. As I was thinking about it, the titular question of this thread came up. If magnetic fields were "frozen in" to plasma, wouldn't that imply that electric currents were also "frozen in" to the plasma?
If you think about it, it kind of makes sense in a twisted way (granted we know it's not true, 'cause plasma doesn't work that way)... IE, if the plasma were a superconductor (it's not, as can be easily demonstrated), then it could conduct a current essentially indefinitely without resistance. If a current flowed indefinitely, the magnetic field would be sustained indefinitely.
So, it seems to me like the statement that magnetic fields can be "frozen-in" to plasma is equivalent to saying that since plasma is considered a super conductor, any electric current causing or caused by the magnetic field would also have to be "frozen in" to the plasma (whatever that means).
So, the next time an astronomer mentions a "frozen in" magnetic field carried along with the plasma, I think I'll flip the script and ask him if that means it also has a "frozen in" electric current carried along with it... *Wink*
Wonder what kind of a horrified, shocked reaction that will engender!
Anyway, on to disproving the "frozen in" condition completely... It's quite simple really, if you consider the above analogy. For plasma's magnetic fields to be "frozen in," it requires plasma to be a superconductor. A superconductor is a conductor where resistance is zero-valued and a current will flow indefinitely with no losses.
Wikipedia wrote:Superconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance ...
Hyperphysics wrote:If a current is generated in a superconducting lead ring, it will persist because of the zero resistivity. Currents have been maintained in lead rings for several years to test the zero resistance condition. An induced current in an ordinary metal ring would decay rapidly from the dissipation of ordinary resistance, but superconducting rings had exhibited a decay constant of over a billion years!
http://hyperphysics.phy-astr.gsu.edu/hb ... is.html#c2
Is plasma a superconductor? Nope! (At the very least, not the low-density plasma of space, the sun's corona, etc. etc. It's doubtful that other plasma regimes are superconductive either.)
First a quick definition of terms.
Resistance R (measured in ohms) is considered to be the ratio of voltage V (measured in volts) to current I (measured in ampères). This can be simply expressed by the equation R = (V / I).
So, how can we know whether plasma's resistance is zero? Thankfully, there's a chart of plasma discharge regimes that comes in especially handy, as it compares voltage to current.
As can be clearly seen in the plot of voltage versus current, the plot never touches the X-axis (or would that be the I-axis?)...
Pick any point on the voltage - current graph and draw a ray from the origin through that point. The ray will always have a positive non-zero slope, except AT the origin where there is zero current. Since V is never zero-valued, the entire expression (V / I) is never zero-valued (except at the origin where there is zero current). Thus R is never zero-valued. Resistance is non-zero for all current flowing through a low-density plasma (one assumes high density plasmas will also suffer resistive losses / joule heating).
Ergo, since plasma resistivity is non-zero, plasma is not a superconductor.
Even if it was a superconductor, and steady magnetic fields were frozen inside, it seems to me that steady electric currents would also have to be frozen inside... Ya' can't get away from them that easily!
Returning to Don Scott's paper for a moment, his remarks thus seem cogent:
Don Scott wrote:Thus, although plasmas are excellent conductors, they are not perfect conductors. Weak longitudinal electric fields can and do exist inside plasmas. Therefore, magnetic fields are not frozen inside them ... Now, we know that there are slight voltage differences between different points in plasmas. Many astrophysicists are still unaware of this property of plasmas, and so, we often still read unqualified assertions ...
Don Scott wrote:VII. CONCLUSION
Maxwell showed that magnetic fields are the inseparable handmaidens of electric currents and vice versa. This is as true in the cosmos as it is here on Earth. Those investigators who, for whatever reason, have not been exposed to the now well-known properties of real plasmas and electromagnetic field theory must refrain from inventing “new” mechanisms in efforts to support current-free cosmic models. “New science” should not be invoked until all of what is now known about electromagnetic fields and electric currents in space plasma has been considered. Pronouncements that are in contradiction to Maxwell’s equations ought to be openly challenged by responsible scientists and engineers.
Astrophysicists can put that in their pipe and smoke it!