Amongst this mass of word salad is another bald faced lie; claiming to have addressed the rebuttals in Scott’s model when it is blindingly obvious you haven’t.
FYI, our conversations would be a lot more rational and a whole lot more enjoyable if your ceased *falsely* accusing me of "lies" simply because you personally disagree with me. That's irrational behavior. It's entirely possible to have a disagreement without anyone intentionally "lying". You've made several mistakes now in our discussion of Scott's paper/model, but I haven't accused you of lying.
Yes, I have definitely addressed your various so called "rebuttal's" of Scott's model. Let's recap, shall we?
I can only surmise by the *first two* very basic mistakes/misstatements that you have made about this topic that you are completely unfamiliar with Beltrami fields and flows which have been known about and associated with plasma physics for *many decades*, if not an entire *century* in the case of Birkeland currents.
First you erroneously and falsely asserted that it was impossible for the current and fields to be moving in parallel, basically suggesting that there was no such thing as a Beltrami field in general, or a Birkeland current. I showed you very specifically (with appropriate references) that your *erroneous assumption* is incorrect, and it's entirely possible in *three* dimensional processes for such things to occur. To your credit, you did in fact admit to that first mathematical error, but then you promptly made another error.
You also made a second misstatement of fact related to physics rather than math when you erroneously said:
Hence for infinitely conductive plasmas, the overall electric field is zero.
When I tried to point out to you that there is no such thing as "infinitely conductive plasma", you tried to justify your false claim by quoting Alfven, and then another link, neither of which ever said any such thing! In both instances, the authors *qualified* the use of such *oversimplifications* and in Alfven's case, he specifically cited numerous examples of where such oversimplifications do not apply and cannot be used.
Since no plasma is "infinitely conductive", the electric field cannot ever be "zero". It can be a very small number in some instances and locations in the plasma, however that certainly has nothing to do with fact that an electric field can exist and the beginning and end of "Birkeland current" and that electric field can be the "driving force" of the entire current flow process.
You *still* have not acknowledged that physics error related to *real* plasma. It's impossible for me to take you seriously when you steadfastly refuse to acknowledge that point. Until you do, this conversation is going nowhere.
Apparently your "new" error/argument is based on a presumption that Scott cannot *simplify* his model (as MHD is simplified), simply because you say so. Like your first "math salad" error, you expect me personally to refute your erroneous claim *personally*. From prior conversations, I've experienced first hand you taking my statements (and even my formulas) out of context and blatantly misrepresent my statements and my meaning. It's therefore not in anyone's interest for us to go down that same road. Instead I provided you with a *diagram* which refutes your claim, and shows that in *three* dimensions, it's entirely appropriate to associate Beltrami fields/flows with Birkeland currents.
(1) Show how a Beltrami vector field is applicable to Scott’s use of Maxwell’s 4th equation ∇× B = µ₀j + ε∂E/∂t in his 2015 paper which he uses to derive his equations.
https://www.researchgate.net/public...Fusion_and_Inertial_Fusion_Plasma_Experiments
Advanced Electromagnetism: Foundations: Theory And Applications
For *decades* now, Beltrami fields, and Beltrami flows have been shown to have application not only to hydrodynamic processes, but also to *magnetohydrodynamic processes* as well, including Birkeland currents.
Scott has simply "simplified" his Birkeland current model by "assuming" that dE/dt is zero. You've also made a (false) "big deal" about the fact that a Birkeland current cannot be "force free". That's like claiming that is "false" to assume that magnetic fields are "frozen" into plasma. Both statements are technically correct, because of the fact that plasma is not actually "infinitely conductive", so ideal MHD theory along with everything associated with "absolute conditions" (frozen, collisionless, incompressible, force free) are merely *approximations* that are "close" to correct in some few instances, but not *completely* correct in *all possible* instances. In the specific instance that Scott is describing (dE/dt = 0), it's "close enough* to being a "force free" condition as any other "approximation' related to plasma using "ideal MHD" theory.
I will give you the opportunity to correct this by showing how my “math salad(?)” results in making it algebraically valid not to substitute the Bz(0) term as Scott has done as described in point(4) of the rebuttal.
You don’t even have to address any other points in the rebuttal.
Why on *Earth* would I choose to personally "bark math" on command for you when you have already *misrepresented* the meaning of the math and formulas that I have presented to you in the past? You took a *single* variable in my last mathematical presentation an turned it into *two separate variables* simply because I used two letters to represent the *single* variable in my formula and you built a completely *strawman* argument.
Both of the two references I have provided (along with the diagram I provided you earlier) make it *abundantly* clear that current and fields can move "parallel" to each other along one axis, specifically the axis of the moving current, and demonstrate that Beltrami fields have been associated with plasma physics *for decades* if not a full century.
Just as I did *not* try to "debunk" your previous mathematical error personally, I'm not going to do so now either. IMO you already have an established track record of making strawmen out of my equations, and you've made at least *two other* errors in this debate already, three actually.
There's no "emotional" attachment on my part to *physics that actually enjoys laboratory support*, including Beltrami fields and Birkeland currents. They simply work in the lab, therefore I trust the validity of their use in various mathematical models.
As I said earlier, I can only presume that Beltrami fields and flows were "news" to you personally, and their associated use in plasma physics is also "news" to you personally, but they do exist and they are routinely used in plasma physics and applicable to plasma physics.