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| | | Friends call him Royal. Interviewing is what she does in her working day occupation but quickly her spouse and her will begin their personal company. Some time in the past he chose to live in Kansas. What she loves doing is bottle tops collecting and she is trying to make it a profession.<br><br>My website: [http://Doldamgil.Co.kr/xe/?document_srl=331984 Doldamgil.Co.kr] |
| [[File:Magnetic mirror effect in a gas chamber.jpg|thumbnail|This is an image of an electron beam being reflected by the magnetic mirror effect.<ref>"A Demonstration of the Magnetic Mirror Effect" American Journal of Physics, Volume 30, Issue 12, pp. 867-869 (1962).</ref> ]]
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| [[File:Basic Magnetic Mirror.jpg|thumbnail|This shows a basic magnetic mirror machine including a charged particle's motion]]
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| A '''magnetic mirror''' happens any time a charged particle is reflected from a denser [[magnetic field]] region. This '''[[mirror]] effect''' will only occur when a particle has the appropriate velocity and angle of approach.
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| A charged particle with some velocity will experience a [[Lorentz force]] which will cause it to corkscrew along a magnetic field line. This motion has a radius of gyration (a [[gyroradius]]) along the magnetic field line. As it moves, it can enter a region of denser magnetic field lines. The combination of the radial component of the fields and the azimuthal motion of the particle results in a force pointed away from the dense field. It is this force that can reflect the particle.<ref>Fitzpatrick, Richard. "Magnetic Mirrors." Home Page for Richard Fitzpatrick. The University of Texas at Austin, 31 Mar. 2011. Web. 19 July 2011. .</ref>
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| == History ==
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| [[File:The Tandem Mirror Experiment.jpg|thumbnail|The Tandem Mirror Experiment (TMX) in 1979]]
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| [[File:A picture of the 2XII Magnetic Bottle.jpg|thumbnail|This is a picture of the 1978, 2X magnetic bottle experiment. Fred Coensgen is pictured.]]
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| [[File:The Mirror Fusion Test Facility During Construction.jpg|thumbnail|This is a picture of the MFTF during construction]]
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| In the late 1960s, magnetic mirror confinement was considered a viable technique for producing [[fusion energy]]. Efforts were initially funded under the [[United States Atomic Energy Commission]]s' [[Project Sherwood]]. A machine design was first published in 1967.<ref>G. G. Kelley, Plasma Phys. 2, 503 (1967)</ref> The concept was advocated by [[Richard F. Post]], Kenneth Fowler, Fred Coensgen and many others at the [[Lawrence Livermore National Laboratory]].<ref>"Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969.</ref> As a result of advocacy, the cold war, and the [[1970s energy crisis]] a massive magnetic mirror program was funded by the US federal government.
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| This program resulted in a series of large magnetic mirror devices including: 2X,<ref>Principals of plasma physics, Nicholas Krall, 1973, Page 273</ref> Baseball I, Baseball II, the [[Tandem Mirror Experiment]], the Tandem mirror experiment upgrade, the [[Mirror Fusion Test Facility]] and the MFTF-B.<ref>"Summary of results from the tandem mirror experiment, TMX group, February 26, 1981</ref><ref>"TMX Major Project proposal" Fred Coensgen, January 12, 1977</ref> These machines were built and tested at Livermore from the late 60's to the mid 80's.<ref name="autogenerated1987">Booth, William. "Fusion's $372-Million Mothball." Science [New York City] 9 Oct. 1987, Volume 238 ed.: 152-55. Print.</ref> A number of institutions collaborated on these machines, conducting experiments. These included the [[Institute for Advanced Study]] and the [[University of Wisconsin–Madison]].<ref>"ion losses from end-stoppered mirror trap" D P Chernnin, nuclear fusion 18 (1978)</ref><ref>"Experiments in a tandem mirror sustained and heated solely by rf" R Breun, Physical Review Letters, December 21, 1981</ref> The last machine, the [[Mirror Fusion Test Facility]] was 372 million dollars, at that time, the most expensive project in Livermore history. It opened on February 21, 1986 and was promptly shut down. The reason given was to balance the United States federal budget.<ref name="autogenerated1987"/> This program was supported from within the Carter and early Reagan administrations by [[Edwin E. Kintner]], a US Navy captain, under [[Alvin Trivelpiece]]. Kintner resigned in 1982 complaining that the federal government had not provided the resources needed for the research.<ref>KOPPEL, NIKO. "Edwin E. Kintner, Nuclear Power Pioneer, Dies at 90." The New York Times, Science Section. The New York Times, 20 May 2010. Web. 17 Apr. 2011. <http://www.nytimes.com/2010/05/21/science/21kintner.html?_r=1></ref>
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| The concept had a number of technical challenges including maintaining the non-Maxwellian velocity distribution. This meant that instead of many high energy ions hitting one another, the ion energy spread out into a bell curve. The ions then thermalized, leaving most of the material too cold to fuse. Collisions also scattered the charged particles so much that they could not be contained. Lastly, velocity space instabilities contributed to the escape of the [[Plasma (physics)|plasma]].
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| Magnetic mirrors play an important role in other types of [[magnetic fusion energy]] devices such as [[tokamak]]s, where the [[Toroidal and poloidal|toroidal]] magnetic field is stronger on the inboard side than on the outboard side. The resulting effects are known as '''neoclassical'''. Magnetic mirrors also occur in nature. Electrons and ions in the [[magnetosphere]], for example, will bounce back and forth between the stronger fields at the poles, leading to the [[Van Allen radiation belt]]s.
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| == Mathematical derivation ==
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| The mirror effect can be shown mathematically. You start by assuming that the particle's magnetic moment and total energy do not change. This is called [[Adiabatic invariant#The first adiabatic invariant, μ|adiabatic invariance of the magnetic moment]].<ref>F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, New York, 1984), Vol. 1, pp. 30–34. ISBN 978-0-306-41332-2</ref> This is lost when a particle occupies a null point or zone of no magnetic field.<ref>TG Northrop, "The Adiabatic Motion of Charged Particles" (Interscience, New York, 1963)</ref> The magnetic moment can be expressed as:
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| :<math>\mu=\frac{m v_{\perp}^2}{2 B}</math>
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| It is assumed that μ will remain constant while the particle moves into the denser magnetic field. Mathematically, for this to happen the velocity perpendicular to the magnetic field <math>v_{\perp}</math> must also rise. Meanwhile the total energy of the particle <math>\mathcal{E}</math> can be expressed as:
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| :<math>\mathcal{E} = q E + \mu B + \frac{1}{2} m v_{\parallel}^2 + \frac{1}{2} m v_{\perp}^2</math>
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| In regions with no electric field, if the total energy remains constant then the velocity parallel to the magnetic field must drop. If it can go negative then there is a motion repelling the particle from the dense fields.
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| === Mirror ratios ===
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| Magnetic mirrors themselves have a '''mirror ratio''' this is expressed mathematically as:<ref>"Particle Loss Rates from Electrostatic Wells of Arbitrary Mirror Ratios." Physics of Fluids 28.1 (1985): 352-57. Web. 15.</ref>
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| :<math> r_\text{mirror} = \frac{B_\text{max}}{B_\text{min}} </math> | |
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| At the same time, particles within the mirror have a [[Pitch angle (particle motion)|pitch angle]]. This is the angle between the particles' velocity vector and the magnetic field vector.<ref>Dolan, T. J. "Magnetic Electrostatic Plasma Confinement." Plasma Physics and Controlled Fusion 36 (1994): 1539-593. Print.</ref> Surprisingly, the particles with the small pitch angle can escape the mirror.<ref>G Gibson, Willard C Jordan, Eugene Lauer, Physical Review Letters, 5: 141 (1960)</ref> These particles are said to be in the '''loss cone'''. The reflected particles meet the following criteria:<ref>Principals of Plasma Physics, N Krall, 1973, Page 267</ref>
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| :<math>\frac{v_\perp}{v_\parallel} > \frac{1}{\sqrt{r_\text{mirror}}}</math>
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| Where <math>v_\perp</math> is the particle velocity perpendicular to the magnetic field and <math>v_\parallel</math> is the particle velocity parallel to the magnetic field.
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| This result was surprising because it was expected that heavier and faster particles, or those with less electric charge, would be harder to reflect. It was also expected that smaller magnetic field would reflect less particles. However, the [[gyroradius]] in those circumstances is also larger, so that the radial component of the magnetic field seen by the particle is also larger. It is true that the minimum volume and magnetic energy is larger for the case of fast particles and weak fields, but the mirror ratio required remains the same.
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| ==Adiabatic Invariance==
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| The properties of magnetic mirrors can be derived using the [[adiabatic invariance]] of magnetic flux under changes in magnetic field strength. As the field gets stronger, the velocity increases proportionally to the square root of B, and the kinetic energy is proportional to B. This can be thought of as an effective potential binding the particle.
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| == Magnetic bottles ==
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| [[File:Fields in magnetic bottles.jpg|thumbnail|This image shows how a charge particle will corkscrew along the magnetic fields inside a magnetic bottle, which is two magnetic mirrors placed close together. The particle can be reflected from the dense field region and will be trapped.]]
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| A '''magnetic bottle''' is two magnetic mirrors placed closed together. For example, two parallel coils separated by a small distance, carrying the same current in the same direction will produce a magnetic bottle between them. Unlike the full mirror machine which typically had many large rings of current surrounding the middle of the magnetic field, the bottle typically has just two rings of current. Particles near either end of the bottle experience a magnetic force towards the center of the region; particles with appropriate speeds spiral repeatedly from one end of the region to the other and back. Magnetic bottles can be used to temporarily trap charged particles. It is easier to trap [[electron]]s than ions, because electrons are so much lighter<ref>"A biased probe analysis of potential well formation in an electron only, low beta Polywell magnetic field" Physics of Plasma, May 9, 2013, Vol 20, 052504</ref> This technique is used to confine very hot plasmas with temperatures of the order of 10<sup>6</sup> K.
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| In a similar way, the Earth's non-uniform magnetic field traps charged particles coming from the sun in doughnut shaped regions around the earth called the "[[Van Allen radiation belt]]s", which were discovered in 1958 using data obtained by instruments aboard the [[Explorer 1]] satellite.
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| == Biconic cusps == | |
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| [[File:Biconic Cusp.jpg|thumbnail|A Biconic Cusp]]
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| If one of the poles in the '''magnetic bottle''' is reversed, it becomes a [[biconic cusp]], which can also hold charged particles.<ref>The motion of a charged particle near a zero field point (in english). New York: New York University: Courant Institute of Mathematical Sciences,. 1961.</ref><ref>Grad, H. Theory of Cusped Geometries, I. General Survey, NYO-7969, Inst. Math. Sci., N.Y.U., December 1, 1957</ref><ref>Berowitz, H Grad and H Rubin, in proceedings of the second United Nations International conference on peaceful uses of atomic energy, Geneva, 1958, Vol 31, Page 177</ref> [[Biconic cusp]]s were first studied by [[Harold Grad]] at the [[Courant Institute]], studies reveal the presence of different types of particles inside a Biconic cusp.
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| == See also ==
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| * [[tokamak]]
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| * [[Biconic cusp]]
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| * [[List of plasma (physics) articles]]
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| * [[Pitch angle (particle motion)]]
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| * [[Project Sherwood]]
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| * [[Polywell]]
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| * [[Harold Grad]]
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| * [[Mirror Fusion Test Facility]]
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| ==References==
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| {{Reflist}}
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| == External links ==
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| * [http://farside.ph.utexas.edu/teaching/plasma/lectures/node21.html Lecture Notes from Richard Fitzpatrick]
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| {{DEFAULTSORT:Magnetic Mirror}}
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| [[Category:Fusion power]]
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Friends call him Royal. Interviewing is what she does in her working day occupation but quickly her spouse and her will begin their personal company. Some time in the past he chose to live in Kansas. What she loves doing is bottle tops collecting and she is trying to make it a profession.
My website: Doldamgil.Co.kr