Talk:Magnetic mirror

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I've never seen a clear explanation for this effect. I expected wikipedia would have one. -- Euyyn

Better now? Art Carlson 2005 June 30 09:38 (UTC)

There are 2 misleading statements in the given explanation. It is not just a function of particle direction vs magnetic angle. It should be made clear that total particle velocity plays a critical role in determining whether reflection will occur or not; faster particles have a better chance of escaping even when they ARE NOT moving parallel to their local field lines, and all particles moving parallel to their field lines WILL ESCAPE. <== Surely this is undeniable. It is the escape of fast particles which renders the solenoidal approach to magnetic mirror fusion so very difficult because, by preferentially allowing the hottest particles to escape, it destroys the very desirable Maxwellian velocity distribution which had been counted on to produce ions at velocities (and hence temperatures) far above the average of the already very high bulk temperature. Also, since the rate of fusion reactions goes up faster than temperature, it is very desirable to have at least a portion of the fusion plasma particles at a temperature higher than the minimum temperature required for overcoming the Coulomb repulsion between nuclei, and thus eligible for creating "hot fusion" reactions. (Particle velocity and particle Energy can both be expressed in Electron Volts, and since 1 eV = 11600 Kelvins, velocity and temperature are closely related.) For a more detailed explanation, see http://farside.ph.utexas.edu/teaching/plasma/lectures/node21.html about which I note that they are for some reason discussing attempts to maintain a magnetic mirror fusion device at a high, flat single temperature rather than the normal curved Maxwellian temperature distribution.

Also, Art, please respond to Shawn's comments. 24.136.234.65 10:48, 3 October 2005 (UTC) Essen (updated 19 Nov 2005 by Essen)

You are mistaken. The Web site you mention clearly derives a loss cone criterion that is independent of the total velocity, just as I did in this article. You also seem to have trouble keeping the concepts of velocity and temperature straight. --Art Carlson 19:46, 3 October 2005 (UTC)

Art, this article is very interesting and well written. I have tried to research this topic more broadly, but the explanations I have found use vector calculus extensively, which is not my strength. Your equation is compact, simple and elegant, easily within the grasp of an educated lay reader. I understand the general idea, but can you clarify some questions for me without resorting to vector calculus?

I like the given equation, but since no units are specified and no caveats are listed, I worry that it may possibly be a bit misleading. Can it really be true that a proton travelling at say, an overall velocity of 3,000,000 meters per second, is equally well reflected and has the same Critical Angle (splitting out the vectors for V-perpendicular and V-parallel) for reflection by two different magnetic mirrors, one of 1 nanotesla --> 10 nanotesla and the other a mirror of 1 gigatesla --> 10 gigatesla ??? At the very least this would seem to imply radically different "thicknesses" for the two mirrors, but does it also imply something about the requirements of other magnetic properties of the mirrors, such as their total magnetic flux? It also seems implicit in all these discussions that the magnetic field must extend far enough so that the particle under consideration does not stray outside the volume of the identified magnetic system.

Also, does the equation you gave apply equally well to all collections of charged particles, even plasmas: charged, uncharged and with charge unequally distributed? (I realize that the latter case could introduce some additional complications.) And if a particle is relativistic, wouldn't it be better to speak of momentum rather than velocity? How does plasma density affect the whole question of mirror requirements? What happens if a plasma carries a magnetic field of its own?

Please give a mirror design example for a proton with velocity, momentum, accelerations, energy, B-field strengths, etc.

This is a very interesting topic. I think that by illustrating the physical meaning and implications of magnetic mirrors, you could significantly enhance the value of an already very well-written article.

24.27.61.121 21:01, 16 October 2005 (UTC) ShawnM

November 19

Please add new comments at the bottom rather than editing older comments. It's confusing. I do deny that total particle velocity plays any role in determining whether reflection will occur or not in an ideal mirror. If you will state your question more clearly, I will be happy to respond. --Art Carlson 17:12, 20 November 2005 (UTC)

I believe that magnetic mirror calculations generally assume that the gyro radius is small compared to the size of the machine, which makes total velocity irrelevant. Paul Studier 09:20, 14 January 2007 (UTC)

Words are nice, but a picture would really help very much. Doublehp. Nov 3rd 2012. — Preceding unsigned comment added by 2A01:E35:8BA8:E140:213:CEFF:FED8:7684 (talk) 10:37, 3 November 2012 (UTC)

WikiHelper2134

On June 4 and June 10, 2013, WikiHelper2134 made a serious of edits. I haven't reviwed them all, but I assume they are constructive. The notation in the equations, however, needs a lot of fixing, and at least one equation (the one for total energy) is wrong. I'd fix it myself, but I'm short on time. Art Carlson (talk) 07:55, 11 June 2013 (UTC)

I fixed the total energy equation. Brianbleakley (talk) 19:36, 30 May 2014 (UTC)

 Magnetic Bottle diagram has the current in the wrong direction for the B field shown.  — Preceding unsigned comment added by 98.125.195.25 (talk) 20:02, 13 April 2019 (UTC) 

This article is attempting to cover a rather technical concept. It used to seem somewhat clear, like in 2006. Now I don't know what to think of it. With all the "assumptions" made about the derivations, it has either run off the road and into the weeds, or exposed some flaws in the very old versions, for failing to mention all the assumptions being made then. There have been literally hundreds of changes to the article over time, far too many to see where it went astray. Was it due to the many changes made by WikiHelper2134? Maybe; I don't know. I'm sure most everyone has good intentions, but that is no guarantee of being comprehensible to anyone. For myself, I do not trust my own explanations to be comprehensible to anyone I am not talking to directly. I rely on feedback to know if I am being understood. Therefore, I confine myself to these comments, in hopes that someone more experienced in technical communications will be inspired to do something helpful for general audiences. Earth's natural magnetic mirrors are mentioned, but I find that it is only in the Talk pages that any explanation is given, and only very indirectly, for how cosmic rays can penetrate through Earth's natural magnetic mirrors: there is insufficient magnetic flux to make the particles spiral or gyrate in the given volume and intensity of field. It would help to extend that explanation. If the same field intensity was expressed over a much larger volume of space, that would be more total flux, and incoming cosmic rays would be curved more and slowed more. This actually happens in the case of the Sun's magnetic field, which deflects a lot of the less-energetic cosmic rays, which thus never make it to Earth's region of the Sun's magnetic field. But the more energetic cosmic rays do make it to us, often with paths so curved it is not possible to see where they came from. This natural example seems to offer a way to show magnetic mirrors as more than incomprehensible abstract objects. But I fear it is still too complex to use as a starting point. For something close to the end of the article it may be fine. The very specialized use of magnetic mirrors in fusion research seems to shed no light on this kind of mirror. As in any specialized area, the researchers in that field obviously work under a set of assumptions that need not be stated among themselves, but most definitely need to be stated for everyone else. They may have trouble doing so because of being so accustomed to their form of shorthand, a problem which shows up whenever specialists try to communicate about their field with those outside it. So, what to do? I know this will not be "encyclopedic phrasing", but it may be a starting point for better wording... I think an explanation might be clearly phrased as something like "For any particle to be reflected by a magnetic mirror, that particle must cross enough magnetic flux lines to bend its path quite significantly. Like objects in space responding to gravity, for which an excessive speed will result in an open orbit (parabolic or hyperbolic), so a charged particle entering a magnetic mirror at too-high speed will not spiral or gyrate in the field. In extreme cases, the particle will pass through the field with barely any deflection. That is somewhat like a visiting interstellar comet or asteroid passing far from the Sun: crossing space-time that is only slightly curved, its path will barely curve. This is analogous to crossing only a small amount of magnetic flux. But if the visiting object passes close to the Sun, it encounters much more pronounced curvature of space-time and its path will curve strongly. This is analogous to crossing a lot of magnetic flux. If the incoming object is slow enough, or passes very close to the Sun, its direction of travel can be nearly reversed. It can be reflected." While that explanation uses an analogy that is essentially 2-dimensional as opposed to the magnetic mirror causing curves in 3 dimensions, the simpler case may be a good starting point for achieving greater clarity on the matter of magnetic mirrors. If nothing else, it seems beneficial to give also the simpler cases of charged particles crossing a uniform magnetic field. When travelling perpendicular to the field, the particle will curve in a way somewhat analogous to a fast-moving object responding to gravity: At a certain speed it will travel in a circle, just like an object orbiting Earth, the Sun, or any massive body. At higher speeds, the path will curve less. Once that basic understanding is achieved, with due attention to the formula for gyroradius of a charged particle in a magnetic field, the readers will have a foundation for the more complex motions. Crossing a uniform magnetic field at an angle, a charged particle path will curve or spiral in a way that takes account of the portion of its velocity that is perpendicular to the magnetic flux, while the portion of velocity parallel to the flux is ignored. Finally it might be shown that when the magnetic field becomes more and more intense in a certain direction, a charged particle heading in somewhat that direction, but not directly towards the most intense flux, will have a path curved in a way that can sometimes push it away from the region of intense flux. All this would be much easier to visualize in a video form, like a marble rolling around inside a funnel. (A conical funnel will be simplest and clearest, I think.) At a certain speed, maintained by a small circular motion of the funnel, the marble will execute a comfortable circular orbit. At a lower speed the marble will spiral down towards the neck of the funnel. If it is then given more speed, the marble will spiral back up the funnel, and may even depart over the rim. I hope some use can be made of my rambling comments. YodaWhat (talk) 08:48, 2 May 2020 (UTC)