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More counter rotation evidence to support Dr. Scott's Birkeland current model.

Discussion in 'Physical & Life Sciences' started by Michael, Oct 18, 2019.

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  1. sjastro

    sjastro Newbie

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    Wrong.
    Alfven’s ideal MHD equations are the fluid mechanics analogues of Maxwell’s equation and are based on plasma being infinitely conductive.
    Not bad for a “wrong” model that led its originator to a Nobel Prize.

    Wrong refer to Alfven’s ideal MHD equations.

    Word salad

    Wrong refer to Alfven’s ideal MHD equations.

    Nonsense the same electrical current would not heat up a vacuum which simulates the particle number density of the corona.

    Word salad.

    Wrong EU/PC models do not work in the lab while magnetic reconnection has been produced in the lab.
     
    Last edited: Jan 21, 2020
  2. sjastro

    sjastro Newbie

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    You might find this interesting.
    Why do we deal only with large scale magnetic fields in astrophysics, and not electric fields?
     
  3. Michael

    Michael Contributor Supporter

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    It's more than a little amusing that you're trying to *misuse* the beliefs and statements of Hannes Alfven to make your case about mythical "infinitely conductive* plasma, when in fact Alfven personally *rejected* the use of MHD theory in *numerous* instances where the mainstream continues to rely upon those models, in favor of (drum roll) *circuit theory*. For instance, like Birkeland, Alfven used *circuit* theory to describe coronal loops, magnetosphere activity, events associated with "magnetic reconnection", etc. In fact AFAIK, Alfven virtually *never* used MHD theory to describe high energy events in cosmological plasma. All his cosmological models are based on circuit theory, not MHD theory.

    In fact Alfven *admonished* those who erroneously promoted the notions of "frozen" magnetic fields in light and hot plasma environments and flat out rejected "magnetic reconnection" models as "pseudoscience". He used his double layer model to explain such events, and stated quite bluntly that his double layer paper made the whole reconnection model irrelevant and obsolete in all current carrying environments.

    In low or *non* current carrying dense cold plasma, there may be a few limited instances where the "high conductivity" aspect of plasma allows one to *ignore* the electric field aspects of plasma and get reasonably useful results, but certainly not in high current environments where the electric field does all the actual work.

    It's rather telling that you're trying to misrepresent Alfven's own beliefss, when in fact he personally *rejected* the use of MHD theory alone to describe magnetosphere and solar atmospheric activity in favor of circuit theory.

    Any ordinary plasma ball demonstrates that electric fields and electric current causes plasma to generate *filaments* of higher density plasma, which are surrounded by evacuated regions around the filament that act to insulate the current carrying threads from the surrounding plasma, thus allowing those plasma threads to act like "wires" to carry current over vast distances. The "high (but not infinite) conductivity" aspect of plasma enable currents to *easily* flow through plasma.

    However, every single z-machine experiment demonstrates that plasma *resists* the flow of current, and that resistance generates very high temperature plasma in very highly conductive plasma. You've simply "made up" a completely mythical properly of plasma that doesn't even actually exist in nature. There is no such thing as an "infinitely conductive" plasma. No such thing exists except in your head.
     
    Last edited: Jan 22, 2020
  4. Michael

    Michael Contributor Supporter

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    You might also be interested in at least six instances where it's better to use a particle/circuit approach to modeling the behaviors of plasma from Alfven's book Cosmic Plasma, page 7:

    One can easily "oversimplify" plasma to the point of absurdity, as in the case of magnetic reconnection models. Alfven flat out rejected that entire concept and he relied almost exclusively on circuit theory to describe high energy events in cosmological plasma.
     
  5. Michael

    Michael Contributor Supporter

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    Pure projection (again). You absolutely did "make up" the mythical concept of infinitely conductive plasma. They are as "real" as a mythical unicorn. Neither one exists.

    There is no such thing as "infinitely conductive" plasma, or infinitely conductive unicorns. They do not exist.

    No, actually it just makes your erroneous claim about infinitely conductive plasma look just that much more ridiculous. It also highlights the primary misunderstanding of plasma that has led to utter confusion on the part of the mainstream. Alfven warned them repeatedly and often about misusing the concepts of 'frozen' magnetic fields and of not paying attention to the limits of the conductive properties of plasma. The mainstream has consistently misrepresented his statements and his models, just as you are still doing today.

    There's not much to discuss so long as you continue to misrepresent *your own misstatements* and your own misunderstandings as "fact". If you can't even come to grips with the fact that there is no such thing as a mythical form of infinitely conductive plasma, there's simply no hope whatsoever that you will ever admit to your own mistakes with respect to Scott's models.

    If and when you finally admit that there is not such thing as your mythical infinitely conductive plasma, I'll be happy to move on to your misunderstanding of Scott's model, but there's no point in trying if you're unwilling to admit even your most *obvious* mistakes.
     
  6. sjastro

    sjastro Newbie

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    As I suspected the mathematical detail and the irony behind this post went right over your head as I used your link on Beltrami vector fields as further evidence to show why Scott’s model is wrong.
    Once again you have been caught out lying for even suggesting you understand what a Beltrami vector field is given you are completely unaware it contradicts Scott’s model.

    Even if this inconvenient truth was ignored your “supposed understanding” of Beltrami vector fields doesn’t make right the algebraic error in point (4), the consequences of the error in points (5),(6) and (7) nor the contradiction in observation in point (2) in the rebuttal.

    All you have confirmed is your dishonesty, you are hopelessly out of your depth, and certainly have not demonstrated any maths skills.



    Given you are doubling down on your lies in deliberately misinterpreting me indicates this extends to a pathological level.
    It is quite evident you no have no guilt or shame in lying and the transparency of your lies indicates your have no issues in being caught out either.
    To turn this thread around as an attack on your integrity is truly bizarre.
     
    Last edited: Jan 22, 2020
  7. Michael

    Michael Contributor Supporter

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    No, actually you tried to apply the concept to *solids* and "wires" without respect to the moving and and flowing and spiraling nature of current carrying plasma which only leads to more misunderstandings on your part.

    From your post which I previously cited right after I corrected your math error with respect to Beltrami vector fields:

    We aren't talking about *wires* and solids, we're discussing *moving* plasma particles which are themselves a type of "current" which moves in a corkscrew pattern and direction that is effectively parallel (in one axis) to the magnetic fields which also move with the plasma:

    Birkeland current - Wikipedia

    [​IMG]

    This statement is right up there with your "infinitely conductive plasma" mythology in terms of how wrong you actually are, and in typical sjastro fashion, it's also a 'personal attack'. Sheesh. You're a one trick pony.

    This from the guy that erroneously believes that plasma is infinitely conductive in *spite* of the fact that every single z-machine experiment falsifies that erroneous belief.

    Here's what you said:

    It's a false statement. There's no such thing as infinitely conductive plasma or infinitely conductive unicorns, and Alfven never claimed there was such a thing as "infinitely conductive plasma". You simply made that up on your own. Period.

    LOL! You quite literally turn every single discussion between us into a personal attack by calling me a liar in virtually every post, and/or by projecting your own ignorance of physics or math onto me. It's boring and irrational behavior. It's impossible to have a rational discussion with you because you simply refuse to admit that you're wrong even when it's blatantly obvious that you're ridiculously wrong. There is no such thing as infinitely conductive plasma! That is utter nonsense. Deal with it.
     
    Last edited: Jan 23, 2020
  8. sjastro

    sjastro Newbie

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    If you have "corrected my math error" with respect to Beltrami vector fields which somehow validates Scott's model then why have you ignored the following issues.
    (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.
    (2) Show how a Beltrami vector field addresses and corrects the issues in my rebuttal of Scott’s model.

    Instead you concoct a nonsensical piece of word salad which includes a Birkeland current diagram which clearly shows the magnetic field and current are aligned but not parallel which not only violates the Beltrami vector field condition but it cannot be a force free field either which forms the basis of Scott's model.
    It confirms yet again you are completely out of your depth and making bald faced lies about correcting my "math error" when you don't have the vaguest idea what a Beltrami vector field is or how it saves Scott's model.

    I’ve counted six references involving infinite conductive plasma mentioned in your posts which blind Freddie can plainly see is designed to be trollish and yet here is another example that exposes your dishonesty when a plasma cosmology website of all things makes the same “utter nonsense” comments about infinite conductive plasmas.

    It then goes on to define the conditions where where infinitely conductive plasmas can be applicable.
    Magnetohydrodynamics | Plasma-Universe.com
    The plasma universe site is simply describing the ideas developed by Alfven.
    You have put your foot in your mouth so many times but this one is right at the top of the list.

    On the subject of you being supposedly victimized the equation is simple; stop lying such as claiming I made up the idea on infinite conductive plasmas and you won’t be called out for lying.
    Since you are always the victim would you care to explain why you are the one who always ends up being suspended or banned.
     
    Last edited: Jan 23, 2020
  9. Michael

    Michael Contributor Supporter

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    I haven't ignored them, I explained it to you. First you tossed out a little "math salad" at me and erroneously tried to claim that:

    I then had to point out to you that Beltrami vector fields falsify your bogus claim.

    I just did that for you and you simply ignored my explanation entirely. dE/dt is necessarily zero since Scott specifically simplified the model to scenarios where the electric field isn't changing over time.

    In a *moving plasma* (as opposed to solid wires), the magnetic field winds around in the general direction of the flow of the current and it's roughly parallel along the z axis. They're out of phase with each other in the other two axis of course, but they are parallel along the axis of the flow of current.

    I even provided visual aids and showed you the diagram of a Birkeland current.

    Oh Vey. I just did. I even corrected your erroneous math salad.

    You really have a bad habit of tossing out your own erroneous statements as "fact". The diagram I provided to you shows that the current and the magnetic field move more or less parallel, and in the same direction along the Z axis. It's 'force free' only in the sense that the electric field isn't changing over time, instead it's constant, so everything 'goes with the flow". All of these concepts are somewhat *oversimplified* of course, but that's true for virtually all models related to plasma, particularly the "frozen" concept in MHD theory.

    Blah, blah, personal attack blah. I don't think you even knew that Beltrami vector fields existed until I personally pointed them out to you! It's obvious that you're projecting again.

    Ya, because you *refuse* to simply cop to and admit your *obvious* (and numerous) errors! If you simply admitted that it's a false claim we'd be done with that issue by now. Since you refuse to admit that "infinitely conductive plasma" is a myth, I have to keep returning to your bogus error.

    I don't care how many times you try to oversimplify the resistivity of plasma, it's never going to be "infinitely conductive". It's not a superconductor.

    There are some few instances where plasma can be "treated" that way for purposes of "simplification", but it's not actually infinitely conductive. How can you even continue to support that nonsense?

    Alfven *railed* against the notion of 'frozen in" fields, particularly when the concept was applied to light current carrying plasma scenarios, and/or "magnetic reconnection" models. He called that kind of stuff "pseudoscience" in fact.

    Pure projection (again) I'm afraid:

    Notice the qualifiers in that sentence? Notice the terms "simplest", "so little resistivity" and "treated as". There is no such thing as 'infinitely conductive plasma", nor infinitely conductive unicorns.

    Sure, it's possible to *simplify* concepts and use them in instances/scenarios where they're "more or less" valid, but it's irrational to try to oversimplify the process entirely and ignore the facts. Plasma, while being an "excellent" conductor, is still not "infinitely conductive", ever! It's certainly not infinitely conductive in z-machine experiments or inside coronal loops or "magnetic rope" scenarios involving massive currents. Even a "little' resistivity" turns into a lot of heat in such instances.

    Oh for goodness sake. You falsely asserted that plasma is "infinitely conductive" when even the links that you cite refute your own claim (little resistivity) and yet you have the sheer audacity to accuse me of "lying" even after I had to fix your Beltrami vector field error no less. Wow!

    You did make up the idea of "infinitely conductive plasma" out of whole cloth. Even the link that you *just cited* included the logical qualifiers (simplest, so little resistivity, treated as) that you simply left out entirely!

    If you won't admit to your own *obvious* errors, we'll get nowhere in this conversation.
     
    Last edited: Jan 24, 2020
  10. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    Are you sure you mean current heating? One of the problems with early plasma nuclear fusion research (lab work!) was that current heating is only useful for the initial heating of the plasma because plasma resistance drops rapidly with increasing temperature.

    If current heating of plasma works differently in the solar corona, in what respects is it different?
     
  11. Michael

    Michael Contributor Supporter

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    Sure resistance drops off rapidly with increasing temperatures as the plasma becomes more ionized, but there's also a limit in terms of when plasma "pinches" occur and particles start slamming into each other due to the excessively high volume of current flowing through the plasma. As massive current flowing through the plasma increases, at some point, plasma pinches, and runaway particle collision processes takes over and we end up million degree temperatures, and even the potential for exploding double layers and complete circuit failure.

    In the case of coronal loops it is the so called "small" resistance to current that *sustains* those tens of millions of degree temperatures over hours and days on end, and results in exploding double layers and "solar flares".

    The (small) resistance to current is what *sustains* those high coronal temperatures, not just the initial heating.
     
  12. sjastro

    sjastro Newbie

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    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.
    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.

    Well here is your opportunity to put your money where your mouth is by proving how my *obvious errors* shows that Scott never made a gross algebraic error as I mentioned in my previous response.

    Now if everything goes to plan since you can’t do this, it will end up like your idiotic attempts to extricate yourself through trolling after being caught out lying that infinite conductive plasma is my idea.
    When this occurs then the conversation can be ended as your decision to troll, lie, flame etc including a substantial serving of word salad was motivated by being exposed you have no comprehension of Scott’s model let alone its flaws and your support of the model is based on an abnormal emotional attachment.
     
    Last edited: Jan 24, 2020
  13. Michael

    Michael Contributor Supporter

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    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:

    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.

    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.

    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.
     
    Last edited: Jan 25, 2020
  14. sjastro

    sjastro Newbie

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    FB,

    Instead of cringing or face palming when encountering word salad nonsense like this I turn it into an exercise into finding as many flaws as possible.
    I doubt the list is exhaustive so here are some of them.

    (1) Since the solar corona is extremely thin a term that comes back to bite Michael is that it can be treated as an infinitely conductive plasma.
    Since there is practically nothing in the solar corona to resist the current there are very few collisions to warm the corona to millions of degrees.

    (2) The density of the corona is around 10⁻¹⁵ g/cm³.
    At this extremely low density photons emitted from the surface very rarely interact with the plasma and pass straight through the corona resulting in it being transparent. Alternatively if the corona is being heated through resistance, the photons emitted through collisions would no longer make the corona transparent.

    (3) The sun would become an extremely powerful emitter for X-ray and γ photons and we wouldn’t be having this discussion as the Earth’s atmosphere would have been stripped long ago. This is not a problem with the mainstream model as X-ray and γ photons from the core lose most of their energy by the time they reach the surface.

    (4) Since one would expect photons to be emitted in all directions including back towards the surface, the upper photosphere would be heated and it would impossible to explain the heat convection cells observed on the Sun’s surface.

    (5) Analysis of ion/electron velocities of the solar wind in the lower corona reveals a Maxwellian distribution.
    Any double layer would accelerate or retard the solar wind ions and electrons (or vice versa) and the distribution would no longer be Maxwellian.

    (6) Why aren’t we fried by Birkeland currents in our own ionosphere which is considerably denser than the corona and would provide more “resistance”.

    (7) There is absolutely no evidence of any giant external currents in the first place which carry their own magnetic field.
    The strength of the interplanetary magnetic field at any given point is fully accounted for by the magnetic field carried by the solar wind plus the motion of interplanetary plasma through this field which induces currents which in turn produces localized magnetic fields.
     
    Last edited: Jan 25, 2020
  15. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    Thanks - it was the diffuse nature of the coronal plasma (as in your 1 & 2) that made the 'current heating' model intuitively implausible to me - even allowing for a suitable current source; if it's self-limiting in the lab, with plasma densities many orders of magnitude higher than the corona, it really doesn't make sense that it could happen in the corona. The rest of your analysis seems to confirm it.
     
  16. Michael

    Michael Contributor Supporter

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    https://thesurfaceofthesun.com/Alfven/Currents In The Solar Atmosphere And A Theory Of Solar Flares.pdf

    All of sjastro's arguments are as flawed as his points 1 & 2 actually, or they actually destroy his own argument (coronal loops are prolific emitters of x-rays and even gamma rays). Alfven explained why sjastro is wrong, and Alfven included the math.

    Birkeland currents tend to "pinch" the plasma into dense current carrying filaments (like a plasma ball), so the "average" density of the corona is absolutely irrelevant. It's the density of the filaments that matter. According to Alfven's estimates, the operating voltage of the sun is around 1 billion volts. Birkeland put it at around 600 million volts.

    Points 3 and 7 are directly refuted by SDO x-ray images of the sun which clearly demonstrate that the sun is a prolific emitter of x-rays, and massive "magnetic ropes" (aka Birkeland currents) have been shown to connect the sun to various planets and they even show up in the atmosphere of Venus:

    Magnetic Rope Observed For The First Time Between Saturn And The Sun - Physics-Astronomy.com
    NASA - NASA Spacecraft Make New Discoveries About Northern Lights
    Baffling Magnetic Structures Spotted in Venus' Atmosphere | Space

    The evidence of magnetic ropes, aka Birkeland currents in the interplanetary medium and the solar corona is *overwhelming*. Those so called "baffling" magnetic structures on Venus are predictable structures in a current carrying plasma environment. NASA has yet another goofy name for Birkeland currents in the Earth's upper atmosphere. NASA calls them "Steve".

    Meet 'Steve,' the Aurora-Like Mystery Scientists Are Beginning to Unravel | Space

    In fact the mainstream uses lots of goofy terms like "space slinky", flux ropes, magnetic ropes, magnetic portals, STEVE and anything *except* their proper scientific name, "Birkeland currents". In fairness however, Alfven used the term "magnetic rope" as well, but he explained them:

     
    Last edited: Jan 25, 2020
  17. Michael

    Michael Contributor Supporter

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    By the way, the *least* applicable scenario in terms of your false 'infinite conductivity' claim is in *thin/hot* plasma. The thin/hot parts of the corona aren't even carrying the bulk of the current. It's those x-ray emitting 'magnetic ropes" that carry the bulk of the current though the solar atmosphere, and SDO (Yohkoh,SOHO,TRACE,STEREO,GOES) images all demonstrate that coronal loops are *prolific* emitters of x-rays.
     
    Last edited: Jan 25, 2020
  18. Michael

    Michael Contributor Supporter

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    https://www.researchgate.net/public...and_Anomalous_Resistivity_in_the_Solar_Corona

    It's really odd (and incorrect) to think *only* in terms of magnetic field energy being turned into heat. The only way to have 'magnetic field energy' in plasma in the first place is to also have currents. It's not necessarily an either/or scenario in all cases.

    Even if Alfven's flare model, magnetic field energy that is stored in the current carrying loops is converted into kinetic energy as the loop experiences a catastrophic failure, and the circuit is disrupted. A massive change in the magnetic field around the loop also induces particle movement in the plasma.

    I'm sure there is *some* amount of magnetic field energy being converted into particle kinetic energy, but there is also kinetic energy found in the electrons flowing off of the cathode surface, and kinetic energy found in the cosmic rays coming into the solar atmosphere.

    I think it's overly-simplistic to assume it has to be one or the other, but rather I'm sure it's a combination of both resistivity and induced motion in many instances, particularly in flare type events.
     
  19. sjastro

    sjastro Newbie

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    Ohmic heating of the corona as shown is straightforward to debunk, one can also use MHD which though far more complicated gives an insight in how Alfvenic waves alone can be used to explain how energy in a magnetic field is converted to heat.

    The mechanism involves the passage of an Alfvenic wave of frequency ω through a plasma of frequency Ω.
    Since plasma is composed of ions and electrons held together by electrostatic forces, these forces act as restoring forces.
    If an external force is applied which increases the mean distance between ions and electrons and then removed the plasma will go into oscillation like a simple harmonic oscillator with a frequency Ω.
    As electrons are considerably less massive than ions, the electrons are modelled to oscillate relative to the stationary ions.
    The plasma frequency Ω is defined by the formula;
    Ω² = e²nₑ/mₑεₒ
    e is the electron charge, nₑ is the electron number density, mₑ is the electron mass, εₒ is the permittivity of free space.

    The magnetic tension of a field also acts as restoring force and when subject to a perturbation such as by the magnetic field of an external current can also undergo oscillation with a frequency ω and generate Alfvenic waves with a velocity;
    vₐ = B/√μₒρ
    B is the magnetic field strength, μₒ is the permeability of the vacuum, ρ is the plasma mass density.

    When an Alfvenic wave of frequency ω passes through plasma with frequency Ω, the velocity equation is of the form;
    v = +/- cω/√(ω²-Ω²)
    This is known as a dispersion equation.
    If ω < Ω the velocity takes on an imaginary value.
    Where ω < Ω without going into the gory details which is beyond the scope of this post, the Alfvenic waves are found to be damped and lose their energy to the plasma which is heated.

    For the solar corona the plasma frequencies are very small due to the low density and Alfvenic waves which must be smaller than this frequency will carry very little energy (since energy is a function of the frequency of the wave).
    As a result even if all the energy was transferred to the solar corona through damping, heating of the corona would be very small in magnitude.

    The general subject of heating of the solar corona is very complicated involving a number of mechanisms used in conjunction with Alfvenic waves.
    In this case the Alfvenic waves are in the region ω > Ω where energy loss by damping does not occur.
    Instead these high frequency Alfvenic waves carry large amounts of energy and lose it when the magnetic field undergoes resonance due to Alfvenic waves of a given frequency.
    MHD Alfvenic waves are far more complicated than originally envisaged by Alfven and are kinetic Alfvenic waves which have a perpendicular or transverse wavelength when comparable to the gyroradius of ions in plasma results in resonant absorption of the wave which heats up the plasma.
     
    Last edited: Jan 27, 2020
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  20. Michael

    Michael Contributor Supporter

    +1,160
    Christian
    Since I provided a paper on the topic, you should find it straightforward to "debunk"? :scratch:

    The fact that coronal heating might be explained some other way in no way "debunks" the methods listed in the paper that I cited. By the way, that specific paper itself only demonstrates a *method* by which resistivity can be calculated in plasma, it doesn't actually explain all the heating of the corona that way, rather it suggests that:

    In other words, the "assumptions" used in the paper wouldn't necessarily explain coronal heating this way, but they discuss assumptions that would and could make a big difference in terms of the results.
     
    Last edited: Jan 27, 2020
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