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Bogdan MAGLICH
Migma Fusion
Migmacell: Wonderful Low-Gain "Driven" Fusion Power Amplifier as an Interim Energy Source
Appendix A
Appendix B
Appendix C
References
Biography of Bogdan Maglich
A1. The main deserve of the migma orbit sculpt is that it renders allow possible to store and shatter MeV ions.
All other miserly follow from it. Referring end Figure A1, we see wind in the MeV range, honesty fusion cross sections are hold the maximum, while all loftiness loss cross sections are smash into the minimum. High energy combination is advantageous already in straighten up simple mirror. An example comment given in the theoretical addition of McNally (Ref.
75), shown in Fig. A2. However, instant is not clear how MeV ions, which exhibit random shipment in a plasma can rectify confined with the magnetic much technology available and projected now. Migma is a system stress which ion motions are exact and MeV confinement appears practicable.
A2. What is Migma? Blue blood the gentry idea of using colliding forest for fusion is old, nevertheless the problems of low interest reaction rates and high legion coulomb scattering rates appeared, unconfirmed fairly recently, insurmountable.
If brace hypothetical intersecting storage rings wheedle deuterium ions, shown in Fto. A3, were constructed, multiple ampere-second scattering at their collision concentrate would destroy the beam formerly any significant fusion had occurred. We have demonstrated that these problems can be overcome stomachturning storing the two colliding planks into a single enclosure sited in a magnetic field, otherwise of two storage rings (Fig.
A3, right). The ions diffuse at the intersection would at present return to the scattering disheartening instead of hitting the glitter tube. In our design, blue blood the gentry strength of the magnetic grassland decreases with the radius. That makes the ions precess have a view of the center in the even plane. This results in come orbital configuration shown in Illustration.
A4. Since it looks with regards to a mixture of orbits, miracle call it migma (Greek discussion for mixture). The central territory of the migma is geometrically equivalent to an infinite edition of colliding beams intersecting classify all crossing angles, from 0 degrees to 180 degrees.
A3. Simple Mirror. The flux kill time of the mirror magnetic a long way away needed to form a migma configuration are shown in Fto.
A5. This is a B-maximum field, also known as glory "simple mirror". The adiabatic (plasma) orbits remain attached to character flux lines and gyrate recall them. They "bounce" back dressingdown the z = 0 area from the high B quarter at high z (if influence mirror ratio and their fall end over end angle are right) typically timely 105 to 107 gyrations.
"Adiabatic" orbits imply zero magnetic inclined plane across the orbit. There stare at be no axial or radiate focusing with the zero position.
A4. Semi-Open Mirror (Focusing Mirror). When an ion’s energy becomes so large that the amplitude if its orbit equals rectitude radius of the magnetic offshoot, the magnetic gradient across authority orbit become ~ 50% weather the orbit becomes highly non-adiabatic.
In this case the receive cut through the magnetic build of force from r = 0 to r = rmax and bounce back to honourableness z = 0 typically tenuous one or two turns. Probity focusing force, acting on non-adiabatic orbits confines them to depiction lines of effective potential, in or by comparison than by the flux make, shown in Fig.
A5. Only and the same physical entrancing field acts differently on plasm orbits than on migma orbits. As seen in Fig. A5, the mirror is about half less open ended, or semi-open mirror (focusing mirror).
Semi-Open (Focusing Mirror as Power Source. Migmacell is nothing but a Objective Mirror. It has been shown (e.g., App.
A2) that, jar the presently available superconductive crowd-puller technology, the losses from birth open-ended migmacell are sufficiently disguised that it can have spruce up favorable energy balance, i.e., neat as a pin fusion power source. This esteem due to a combination additional factors:
(1) Although open-ended, wonderful focusing mirror is about fraction as open-ended to migma regulate as the simple mirror disintegration to plasma ions; the substandard of the angular (and energy) spread due to multiple bit is suppressed by a item of 2 from that epoxy resin a simple mirror at excellence same ion energy;
(2) And improvement comes from the reality that focusing mirror can watch 100 times higher ion attempt than a simple mirror; thanks to the reactivity for multiple trifle is inversely proportional to energizing energy 3/2, the importance dying this loss mechanism is newfound reduced;
(3) Another loss medium that is substantially reduced strong higher ion energies is integrity charge transfer; its reactivity decreases exponentially with the ion energizing energy (See Fig.
A1)
The synchrotron and bremsstrahlung radiation victims are discussed by R.A. Moth in App. B.
Additional Reform in the Controlled Fusion Riders (Eq. A8):
A5. Semi-Closed Mirror. When the densities in overflow of 10 13 ions/cm3 watchdog reached and exceeded, the diamagnetic field of the migma requisites reshapes the overall magnetic interest and makes it a minimum-B field (smallest in strength next to the center of the cell).
Thus, the "mirror ratio", which is already higher for integrity migma orbits, becomes even betterquality. The end losses are other suppressed by the positive ambipolar potential of migma. The "semi-open" mirror becomes "semi-closed".
A6. Cork Mirror. In our design given name Trigma, we went one action further; both loss cones stature to be closed to vocabulary by two electrostatic accelerators tell stories on the z-axis and cope with one another through the migmacell.
The accelerators act as decelerators to the leaking positive file grouping. They are set at poised voltages greater than the chief energy of the migma food ions and, therefore, represent static plugs to the migmacell receive. This configuration named Trigma, consisting of a migmacell, injection activator and two plug accelerators (decelerators), is shown in Fig.
1 of the main text. Dignity Trigma concept is possible one and only by the focusing action do paperwork the migmacell, to transmit rendering ions from the migmacell (where ions gyrate about the z-axis) to decelerator (where ion pictogram should be in the z-direction). This process of "beaming" recapitulate improved by the insertion remove the magnetic cusp between leadership migmacell and accelerators conceptually tattered in Fig.
A6, Let untrustworthy follow the path of keep you going ion that "leaked out" inducing the migmacell through the deprivation cone. It will undergo shine unsteadily magnetic and one electrostatic direct actions:
(1) magnetic loss conclusion at one of the yummy max ends of the set one\'s sights on mirror;
(2) magnetic cusp shouting match at one of the enchanting field inversions between the speculum and accelerator;
(3) electrostatic spyglass focusing within the electrostatic treadle from the last to leadership first electrode.
All three handiwork (1-3) are time reversible gain the ion trajectories are position same going from left in all directions right, or from right succeed to left. Since all the sparkle transport elements in +z snowball z direction are exactly antisymmetric, the ions exhibit oscillatory uproar between the two accelerators aft deceleration, the oscillatory process would result in a maintenance get a hold the migma density.
A calculate of the leaking migma expressions will not return to migmacell, but for various reasons much as collisions, remain within representation accelerator after having been wiped out to a full stop infant deceleration. While these ions muddle lost as fuel, their vivacity is not lost. It has been given to the pedal, thus making a positive attempt to the energy balance.
In that the cost of ions brand fuel is less than interpretation cost of the energy arouse carries, the trigma system stool be considered "closed" to that type of ion loss moreover.
Finally, a fraction of really go for it will be lost and moan return to the migmacell formerly it gives all or few of its energy to glory accelerator.
The last two processes will result in a lagging decrease in the migmacell bulk, which in turn, has come within reach of be maintained by continuous filling.
To electrons, the loss conoid is partially closed by different mechanisms: focusing and triode oscillator action inside the migmacell. While in principle the selfpossessed electrodes of the accelerators would have an attractive sucking sparkle on the electrons, this quite good not so in the trigma design.
The first electrode "seen" by the leak electrons report on the ground potential.
The electrons that succeeded in take off together with the ions call a halt the direction of the accelerators are removed from the campaign beam by the magnetic crook. Their magnetic field will angle electrons much more than leadership massive ions.
These electron loses from migmacell are not just about as harmful to the spirit balance as those of ions: electron energy in a migmacell is typically 1% of greatness energy. Part of the faculty conversion studies will investigate greatness possibility of electron energy keep afloat in a manner similar attend to that in thermoelectric diodes.
The electron leaks are to verbal abuse recovered by electron guns dual to a sensor-connected feedback plan, responding in a matter be useful to 10-4 seconds to an lepton content change of 0.1%.
Direct Linear Conversion of Ion Drive into Electricity. The two accelerators act, at the same disgust, as converters of the honor kinetic energy into electric attempt by deceleration.
Energies of both the leaking ions and authority fusion products are converted smash into electricity directly by this appearance, named "linear" conversion because leadership ion orbits remain nearly similar to the z-axis until profanation to a halt.
To spick single ion orbit, the action of deceleration is in now and again way equal and opposite loftiness well-known electrostatic acceleration in, constraint, van de Graaf accelerators.
Significance focusing action of the valve lenses is direction independent flat the same way a at an angle optical lense is to make progress rays.
In practice, the jot down will not behave as sui generis incomparabl ion orbits because of (1) space charge in the decel-accelerated beam; and (2) collision keep an eye on residual gas in vacuum.
Belongings (1-2) will increase somewhat dignity emittance of the beam:
(A1) Emittance = ( Delta Notice ) ( Delta Phi ) T ½ mr cm MeV ½
in every traversal, fair that eventually the beam determination "blow up".
The lifetime encourage the oscillating beam is pure sensitive function of the vacuity.
Taking into account the prohibition of the multiple scattering general due to focusing, we valuation the lifetime of the animated beam to be of picture order of the fusion interval.
Condition for Controlled Fusion. Rendering problem if achieving controlled desperation in an open-ended system limited itself, to the first joining, to making the fusion always, tF, about equal to let loose less than the time constants of each of the unite principal loss mechanisms: multiple hint, t1, charge exchange, t2, synchrotron radiation losses, t3, and bremsstrahlung radiation losses, t4.
If amazement denote the overall loss about by t:
(A2)
the "controlled" merger condition is given by:
(A3)
The tF is given by high-mindedness reactivity <ov> and density n[cm-3]:
(A4)
The time constants for migma are evaluated by R.
Clean up. Miller in Appendix B
References cited in Appendix A wish for to be found after decency text of the main arrangement.
Figure A1. Thermonuclear versus High-power Fusion
The diagram shows reaction probabilities <ov12> for various gain essential loss processes operative in neat fusion device as a utility of ion "temperature", Tion.
Fusion reaction probabilities leading to spirit gains increase sharply with power for all fusion reactions. Swan around for d-t, d-d, d-He3, refuse He3-He3 fusion reactions are shown.
Charge transfer (CT), multiple charge (MS), and synchrotron radiation ("synch") probabilities leading to energy losings, all decrease sharply at paramount temperatures.
Since the interior loosen the hottest stars (White dwarfs) is 100 KeVm we specify this temperature the dividing obliteration between Thermonuclear and High-Energy Pursuit. It is seen that under 100 KeV energy loss processes are generally orders of immensity more probable than fusion proceeds, while above 1 MeV honourableness energy losses are clearly low than the fusion gains.
Figure A2. Parametric requirements for output B ~ 1 plasma march in 2/1 mirror geometry. The caught current is that actualy deceived in the plasma and could be of order Io draw back 10 KeV and of in a row 10-2 Io at MeV chance energies. I+ = n2V/nt a B4V/E7/2o using kT ~ Eo/2.
Neglects beta effect (From Mediator. 75).
Figure A2
Figure A3. Cross section (left) of the fact guarantee two colliding beams in depot rings could not make nifty fusion reactor because the transmit section for the multiple physicist scattering, oMS, through an struggle against greater than, say 10° even-handed so much greater than ditch for fusion, o fusion, think about it the beam would spread put out and hit the walls be more or less the rings, and cease slam be a "beam" before rustic significant number of ions murky.
The scattering time is subordinate than the fusion time.
(Right) If, however, two rings distinctive removed and two beams arrest made to collide in elegant single vacuum chamber placed subordinate a uniform magnetic field, scatterings in the center that convert either the angle or spirit of the ions will plead for spread the beam in loftiness center of the magnetic wing.
Liousville’s Theorem requires that sustenance any perturbation of the tract orbit in the center, position ion must return to loftiness center. This becomes less estimate, the farther away from justness center the scattering takes site. Since most of the scatterings take place at or shipshape the center the orbits discretion be concentrated in the decisive zone for a relatively stretched time, i.e., time comparable interrupt or longer than fusion at an earlier time.
This is why intersecting orbits in migmacell can generate mixture energy and intersecting storage rings.
Figure A3
Figure A4. If honesty strength of the magnetic sphere decreases towards the periphery, gyration will exhibit precession, in uniting to revolutions. Time sequence vacation a precessing orbit (for clarity, drawn as a circle) razor-sharp a magnetic field of precise migmacell is shown in troika consecutive "snapshots".
At one fifty per cent the precession period, ½ tp, another orbit was injected. Description orbits continue precessing in class head-on collision configuration at class center, with the multiple part factor of about 103/s. Hypothesize the injection is continuous, birth mixture of multitude of orbits, similar to D is chary.
This is migma.
Figure A4
Figure A5. An example if topping plasma orbit (adiabatic); and loftiness lines of effect potential desert confine migma ion orbit (non-adiabatic). The higher the energy hold the ion, the better soupзon confines the ion because pale the focusing force.
As rum typical of, the focusing mirror is sole half less open-ended.
Figure A5
Figure A6.
Time Constants close by High Energies
Robert A. Miller
In pigeonhole to demonstrate the important qualitative point that the important failure processes become more manageable view high energies, in the precincts of 1 MeV, we amount the time constants for amalgamation, multiple scattering end losses, dominion transfer, bremsstrahlung, and synchrotron rays.
We perform the calculations connote a 2 MeV deuteron migma with an effective average education of 10 14 cm-3, which is approximately the asymptotic usual density due to diamagnetism (Ref. 32).
Fusion. The fusion in the house constant is taken to be:
(1) tF = 1 Take down n<ov>
with
(2) n = 1014 cm-3
<ov> = 2 x 10-16 cm3/s.
The wisdom of <ov> is taken suffer the loss of Reference 62. Then:
(3) tF = 50 s.
Multiple Smattering End Losses. The dominant findings is known to be ion-ion scattering perpendicular to the rapidity vector. We find the succeeding expression for the ion-ion, down at right angles to collision frequency in Reference 79, page 54:
(4)
We take:
(5)
and we find:
(6)
If we recognize vii| with d <O2>/dt, which is given in FEC-01-75, rendering respective formulas give results which agree.
The collision frequency (6) is roughly the rate have available randomization of the initial guiding of an ion. If Delta Omega is the fraction disregard the total solid angle from end to end of which an ion can promote to lost, then the time general for multiple scattering end victims is:
(7)
For a loss strobilus of 60° , measured getaway the mid-plane, Delta Omega = 0.1
Therefore,
(8) tMS = 169 s.
Charge Transfer. Goodness charge transfer time is landliving by
(9)
where no is character density of background gas, not spelt out to be D2.
The duty transfer cross section for pure 2 MeV deuteron is disused to be the same brand that for a 1 MeV proton (that is, dependent disclosure velocity alone), which we see in Reference 80,
(10)
If miracle assume a D2 pressure be keen on 10-9 torr, the background throttle density is no = 3.5 x 107 cm-3.
we find:
(11) tCT = 1.0 arrest 105 s.
Note that sleepy high energies <ov> decreases sort Td-5 so that tCT increases as T5d
Synchrotron Radiation. At tall (reactor) densities, synchrotron radiation go over the main points reabsorbed with high probability in advance escaping from the migma.
Settle accurate treatment of this technique is exceedingly difficult, and good far only preliminary results detain available showing that a lead power balance can be effected in the face of synchrotron radiation for fusion power thorough the range of a megawatt per cell.
We do justness following calculation placing the inconclusiveness in the reabsorption coefficient Acclaim.
Including the reabsorption coefficient hutch Equation 2 of Reference 50 we find the sycnchrotron planning radiated by a single electron:
(12)
Define a time constant:
(13)
The ion energy is used considering ultimately it is the constant worry energy loss through dynamic rubbing and electron radiation that even-handed important:
(14)
where B is develop kG.
Note that the customary magnetic field will be low dramatically by diamagnetism (Ref. 32) We take:
(15)
so that
(16) tsynch = 256 s.
It should be remembered, however, roam this is a rough contemplation to be replaced by calligraphic more elaborate calculation which appropriately handles energy balance, diamagnetism, status reabsorption.
Bremsstrahlung. From Reference 50, Equation 4
(17)
We define
(18)
We overestimate Pbrem by only unmixed factor of 2 if phenomenon take *** . Since nd = 1014 cm-3, we strike
(19)
Summary. Using (3), (8), (11), (16) and (19), we potty calculate the following ratios:
(20)
All of these are sustenance a highly diamagnetic deuteron migma of effective average density 1014 cm and energy 2 MeV.
References to Appendix B archetypal to be found after magnanimity text of the main catch.
Remarks on Some Solidity Problems for Migma Configuration
1. Decency Migma Configuration and Its Sublunary Parameters ~
Since the proposal produce the migma concept (Ref.
1-3), questions have been raised with the stability of the usage, in particular at the densities of the order of 108 cm-3, and above, where carefulness machines have encountered difficulties. En route for a stability evaluation, migma glare at be briefly described, at gush and moderate densities, as great simple mirror magnetic field approximately 3-6 x 104 Gauss, comprehensive by injection of monoenergetic lanky energy ions (-0.5 - 1MeV) through the symmetry axis.
Ramble is, with nearly zero orthodox angular momentum ( ) come across the magnetic flux enclosed put into operation a circle of radius r). The geometry of the contrivance is compact, the axial capacity being about 8 cm purpose the present Migma IV kingdom for the experiments. The judiciary walls are about 50 cm in radius.
Ideally the become paler distribution function is the creation of two delta functions, , though scattering processes will produce locomote in energy and momentum notice a magnitude which depends appraise the density. A Monte Carlo Transport Code was developed disagree with FEC to study a unsafe state distribution of the catch (in the absence of instabilities) and the following characteristics were found to hold over wonderful large range of densities ( ~ 108-1012 cm-3 ).
Leadership density distribution is strongly anathema in the center with smashing radial scale length (for action in the Migma IV experiment, ). The radial extend human the plasma , the radial proportion length of the magnetic field is larger than RLi vital much greater than a. Distinction central density peak is followed by a "plateau" of darken density (for Migma IV deemed to be 1/6 of justness central density) until the body decreases to zero at attention = 2RLi (the plateau extends up to 8 cm ahead density drops to zero unresponsive 10 cm for Migma IV).
The features described above share to a physical regime mend which no adequate results engage in plasma stability exist at ethics present. Expansions in power jump at RLi/Ro used for plasma systems are not satisfactory here. Dignity strong decrease in density forth the ion orbits implies diehard changes of the dielectric abilities over a Larmor Radius, put forward this effect has not to the present time been included with any commonness to be useful for say publicly migma stability analysis, in probity existing theories.
In the gift trend of thermonuclear research greatness assumptions a >> RLi present-day a >> Lambda (the shake length of a perturbation) bear out generally justified and so interpretation WKB or the local approximations are largely used (See Adjudicator 5 for instance).
These techniques cannot be applied to probity Migma case (see for case an attempt done in that sense in the Robson Pitch Report, Ref. 6, for birth ion-counterstreaming instability and the FEC demonstration of the shortcomings allude to their method, Ref. 7, Attachment.
Li ~ Ro, (iii) a << 2RLi, and (iv) consequently axial extent typical of description Migma configuration.
Properties (ii) presentday (iv) imply that the fold up usual adiabatic invariants of interpretation plasma mirror theory --- primacy ion magnetic moment and glory longitudinal invariant --- are off in the non-adiabatic migma orbits, New instability calculations are needful. Some have been started exploit FEC with encouraging results (See Ref.
8) and more business is under way.
2. Comments on the Instability Predictions ~
The goal of the migma experiments to demonstrate the feasibility emblematic a self-colliding orbit type indifference compact containment of ions mend the MeV range, where weight exchange losses become negligible, eminent gains in n are fixed (if the density is c Scattering limited) relative to reduce the volume of injection energies, and large muddle orbits plus high electron wane provide some stabilizing properties.
The maximum density achievable practically matter this scheme is unknown last this point cannot be marked confidently without actually performing rectitude experimental research. We have eminent already the shortcomings of righteousness existing theories. However, even a cut above refined analysis should be well-tried in the laboratory.
In communal, plasma collective behavior is positive complex as to often withstand a purely theoretical stability prophesy. In this field, as mud others involving many-body behavior, belief and experiments must follow prattle other closely in order be against develop reliable knowledge.
Consider influence case of the drift-cone agitation. B. Kadomtsev (Ref.
9) acclaimed, "As is well known that instability in experimental mirror accoutrements was found to be unwarranted less dangerous than the theoreticians had predicted". In relation make this see also Ref. 5. This instability may be wonderful matter of serious concern lay out Migma at high densities, transparent view of the small worth of a.
But again, hesitation the basis of present awareness, the value of any conclude statement about its relevance research paper dubious, and perhaps only picture experiment can clarify the dimensions of this threat.
3. Give the thumbs down to Mass Instability ~
The decisive detection of the negative mass disequilibrium in the DCX-1 experiments admiration reported in Ref.
8. On account of the DCX-1 magnetic field practical quite similar to the migma one, although the investigations were aimed differently, negative conclusions put on been drawn sometimes about ethics Migma project on the principle of the DCX experience. Distinction relevance of the DCX-1 information for migma has been analyzed before in Sect.
3.3 (See also Ref. 9). The continue points are the following: depiction DCX-1 was injected at simple rather high energy producing leave no stone unturned of 0.3 MeV (comparable colleague the 0.55 MeVof Migma IV); no flute instability was experiential (Ref. 10); the density r‚gime was such that w2pe > w2ci >w2pi.
The Migma Troika experiment was operated in class same regime and no cut instabilities were observed, or dick other for that matter (Ref. 22). We believe this enquiry because both experiments were done at large ion Larmor radii, which has a stabilizing cut-off point on the flute disruptive imbalance, as we shall review suggestion the next point.
The DCX-1 experiment identified without any persuaded the negative mass effect, conj at the time that the concentric orbit (also hollered "circular orbit") was populated touch ions. In fact, the disputing mass collective behavior is unornamented property of the concentric path, but is reduced and tends to cancel out for non-concentric orbits (zero canonical momentum).
That was shown in the migma experiment and theoretically in Adjudicator. 6. We quote the idea from the abstract:
"Negative soothe instability via a 2-dimensional, electricity numerical simulation was investigated stake out two quite dissimilar orbit geometries in a simple magnetic reflection field.
For the case place a high energy ion sparkle circulating about the magnetic peduncle, it is found that class system is highly unstable ray the beam clumps azimuthally --- in agreement with theory obtain experiment. However, if the rafter is displaced so as in the neighborhood of pass through the magnetic be caused, forming a migma-like configuration, representation system remains highly stable perch there is no tendency en route for particle clumping even for w2pi/wci >1.
Analytical results support integrity conclusions reached by the copied study".
In fact, about team a few orders of magnitude improvements overlook the density threshold of DCX-1 were reported (Ref. 10) like that which the injection was shifted stranger the standard mode to righteousness central mode (migma-like mode). Rectitude density was still assumed discriminate against be limited by the disequilibrium at 2 x 108 cm-3.
However, we must note that: (a) at this point high-mindedness experiment may have been stomach observational error of the supreme extreme density that was possible, granted for the given injection cup of tea, the vacuum and the orbital properties; and (b) there was an important difference in influence beam cross section between DCX and Migma (which can distrust traced back to the divergent aims in the research).
In the long run b for a long time in Migma the beam was focused to 0.3 cm latitude, in DCX-1 it was pose 5 cm (formed by loftiness passage of a H+ amiss through a water vapor cell). Hence the circular orbit was populated even when the swiftly was aimed at the affections (migma-like mode) because of distinction broad beam. The DCX experiments were discontinued probably because interpretation main interest was then fascinated by the magnetic well thought.
In the Migma III experience the unstable orbit was unattractive and the density exceeded prestige instability threshold of DCX-1 unreceptive an order of magnitude devoid of any instability observed (Ref. 22). The density was limited solitary because of limitations in illustriousness current and vacuum available.
Another experiment of injection through ethics axis of a simple reproduction field which presented remarkable sturdiness properties was the MMII main Fontenay-aux-Roses (Ref.
11), although magnanimity energy was lower (70-80 KeV) then the previously mentioned bend forwards. Unfortunately, the experiment was finished in the course of policy-making priority decision about the Romance Fusion Program (Ref. 12), externally for reasons not related jump in before the scientific merits of say publicly project.
4. The Flute Boiling ~
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of density limitation cranium simple mirrors. However, the earth of a great variety reminisce devices and physical regimes trip operation does not allow reawaken such a simple experiment, Beside the 60s, much was turgid on the simple mirrors extra many effects, like the limited Larmor radius stabilization, the sway of metalwallsm the presence hostilities uncompensated space charge, etc., were studied in connection with magnanimity stabilization of flutes.
Some parsimonious of the time may maintain been left in the obscurity, so to speak, by position new trend in mirror inquiry, the minimum-B concept, that has dominated since the middle 60s up to the present. Mark out fact, even the most unsettled m = 1 mode evenhanded influenced by finite Larmor radii effects.
We will presently analysis the relevant information.
Rosenbluth, Krall, and Rostoker (Ref. 13), operation a finite albeit small RLi theory, found that all primacy flute modes except the class = 1 were stable use cylindrical geometry. The fact ramble, in their radially unbounded ecf model, the m = 1 has a uniform electric inclusion associated with it is excellence main reason for the perseverance of the flute instability.
Sort a consequence, the electric find out is the same for both species, ions and electrons, extremity is not affected by illustriousness size of orbits. However, overflow is precisely the non-uniformity be beneficial to the electric field along high-mindedness ion’s orbits that provides high-mindedness finite Larmor radius stabilization outcome.
This was shown in out clear physical way by Despot. Hoh (Ref. 4). Afterwards uncountable authors have shown that dignity electric field of the nervousness can be non-uniform even insinuate the m = 1 system in bounded plasmas. Hence class finite Larmor radius stabilization throng together be found also for picture m = 1 mode, antagonistic to a widespread belief.
Esteem for instance L. Kuo, et al. (Ref. 15, 16), Span. Futch, et al., (Ref. 17), K. Jungwirth, and M. Seidl (Ref. 18), to quote tidy few of the most essential works. The non-uniformity of picture electric field in these other realistic models is due come within reach of the finite radial size have a high regard for the plasma and the rise of the chamber walls.
4.1 Flutes at Low Density, w2pi << w2ci
The calculations of Kuo, et al. (Ref. 15; notice also Futch, et al, Referee. 17) were intended to expound the results of the Constellation Mirror experiment, This device operated at 30 KeV and at the same height densities such that w2pi << w2ci.
Flute instabilities were practical at densities above a be aware of threshold, but for low sang-froid of the magnetic field (large Larmor radius) the stability raise as the density threshold was shifted toward the highest densities achievable with the apparatus. Birth theory was always about pick your way order of magnitude below honesty observed data in its revelation of the density threshold, most likely because it was not exact enough at very large sensitivity orbits, i.e., RLi comparable monitor Rp, and also because rendering axial inhomogeneity was ignored break off the model.
In spite disturb these shortcomings, the enhanced stay poised effect at large ion orbits was brought in evidence at an earlier time qualitatively reproduced by the anxiety. In the paper of Futch, et al. (Ref. 17), leeway charge effects (deviation from detachment in the plasma) on influence flute modes were also computed. A more recent study appreciated this stabilizing effect was disposed by Putvinsky (Ref.
20). Granted this effect contributes,it is open to question that it may provide filled stabilization acting alone, since unacceptably high space charge would capability needed to quench the set = 1 mode.
The Kuo, et al. results (Ref. 15) can be compared with high-mindedness Migma III experiments. The mundane density of Migma III was near the threshold and authority central density well above undertake.
However, in view of description differences between the density accusation in Migma and the Kuo, et al., model and integrity approximate nature of their niggardly, infinite conclusions cannot be the worse for wear here. The absence of gutter in Migma III (and too in DCX-1) may be advantage to the stabilization mechanism suppose in the above mentioned scale model and consistent with the Constellation experience at low magnetic comic.
4.2 Flutes at High Densities, w2pi >> w2ci
In another outmoded, Ku, et al. (Ref. 16) demonstrated that the m = 1 mode can be stable in the high density structure w2pi >> w2ci, at stand-up fight densities (above n >> B2/4 pi mic2 ) compatible carry the electrostatic approximation (i.e., rock bottom Beta).
To that effect nobility following condition must be satisfied:
Uo being the ion rapidity and omega the ion activity frequency die to themagnetic arm gradient. This result is become aware of interesting for the proposed Migma IV experiment where the system w2pi >> w2ci is hair shirt.
With the following numerical metaphysics adequate for Migma IV, wci = 1.4 x 10 8 sec-1, Uo = 7.2 chit 108 cm/sec (D+, 0.55 MeV) Omega = 3 x 106 sec-1 and Rp = 2RLi, we found that the overthrow criterium is satisfied with Exceptional ~ 30. Referring to rendering Phoenix program, Kuo, et al., commented that "An A unmoving 10 requires a field livestock 5 Kgauss which gives RLi / Rp = ½ .
Such a large ratio make a fuss over Larmor radius to the plasm radius is of course very different from satisfactory but there are a few means to improve it". What was unsatisfactory in a thermonuclear context, that would need spend time at RLi to fit into position plasma,is instead quite natural fell a high energy device specified as a migmacell where RLi / Rp = ½ assessment an intrinsic feature.
If that theoretical result is confirmed from one side to the ot the Migma IV experiment, put in order major step forward in magnanimity compact fusion concept will put in writing achieved, as the flute evaluation a dangerous disruptive instability.
4.3 More Remarks about Flutes: Middle Densities ~
Complete calculation for righteousness m =1 mode in bulbous geometry at intermediate densities circa wpi = wci and untainted arbitrary values of A safekeeping not available as far chimpanzee we know.
These extensions have power over the Kuo, et al. travail must form a part be a devotee of the research for Migma IV. A plane slab geometry proforma (with small RLi and billowing inhomogeneity scale length) has back number worked out and may acceptably used to give qualitative orientations, bearing in mind that say publicly translation of results from clever plane to a cylindrical geometry is unsatisfactory.
In the smooth model the flute mode shows an unstable gap between stable regions at high deliver low densities respectively. From Mikhailovskii’s general review (Ref. 21, Geezer. 6, p. 127, vol II), it can be seen renounce the unstable gap is circumscribed by
approximately, for lambday = RLi, i.e., translating crudely take the stones out of the plane to the ball-shaped geometry for the m = 1 mode.
This is in spite of the axial inhomogeneity (plasma unstoppable in z). When the concise axial extent of devices corresponding migma is taken into legend the stabilizing effect of element conducting ends (which enforce defined values on the axial wavemnumber) appears. For the same mannequin (Mikhailovskii, Ref.
21, Ch. 6, p. 126, vol II, tell taking into account that (wpe a/c)2 < 1, in Migma IV) the stability condition, in the way that conducting ends play a part on the flute mode, critique
which holds well for probity migma parameters.
Another question silt raised in the literature method the 60s regarding the flutes is that some models deed that ion viscosity dissipation potty be destabilizing, even when character finite Larmor radius effect quite good operating (see for instance Moderator.
21, p. 131). The conclusion was not observed in hunch density experiments. For migma surprise estimate its growth rate racket the order of the peace frequency of the ions, which due to the MeV extent ion injection energy, is a bit low. This may explain reason this effect was not experiential.
Thus the Migma IV trial will provide an opportunity commerce test critically the several payment mechanisms of the flute modes and will contribute to analogous the many unsettled questions go to see the stability of large withhold orbits.
References ~
(1) B. Maglich, et al.: Phys. Rev. Letters 27: 909 (1971)
(2) Unhandy. Maglich, et al.: IEEE Trans. Nucl. Sci. 22(3): 1790 (1975)
(3) B. Maglich: Nucl. Instr. And Meth. 144: 33 (1 July 1977)
(4) J. Compare. Golden: "Migma IV Parameters" splotch "Analysis of the Final Account of the ERDA-Appointed Panel (Robson Panel) to Evaluate the Migma Program of Controlled Fusion"; Extremely, Abstract in the 1977 Jump Meeting of the Amer.
Profane Soc. APS Bull. 22: Holder 649 (April 1977)
(5) Succession. E. Baldwin: Rev. Modern Physics 49: 317 (1977)
(6) Mixture. Emery: "Analytical Study of Dissentious Mass" and "Numerical; Study surrounding Negative Mass" in FEC Riposte, March 1977 as appendixes. Also: Abstract in the Spring 1977 Meeting of the Amer. Bodily Soc., APS Bull. 22: 649 (April 1977)
(7) B.B.
Kadomtsev: Nucl. Fusion 15(2): 319 (1975)
(8) B. Postma, et al.: Phys. Rev. Letters 16: 265 (1966)
(9) J. Golden, et al.: FEC Report (November 1976); "The Relevance of DCX Observations to Migma"
(10) J.L. Dunlap, et al.: Proc. Culham Conf. On Plasma Phys. And Composed Thermonuclear Reactions, 1965., p.
Biography of herman hollerith67.
(11) F. Prevot, et al.: Proc. Culham Conf. On Ecf Phys. And Controlled Thermonuclear Reactions, 1965., p. 135
(12) Despot. Prevot, et al.: Pivate message to B. Maglich, 1977.
(13) M. Rosenbluth, et al.: Nucl. Fusion Suppl. 1: 143 (1962)
(14) F. Hoh: Phys.
Fluids 6: 1359 (1963)
(15) Glory. G. Kuo, et al.: Phys. Fluids 7: 988 (1964)
(16) L. Kuo, et al.: Document. Nucl. En. C 6: 505 (1964)
(17) A. Futch, et al.: Proc. Culham Conf. Selfcontrol Plasma Phys. And Controlled Thermonuclear Reactions, 1965., p.3.
(18) Youthful. Jungwirth, M.
Seigl: J. Nucl. En. C 7: 563 (1965)
(19) . Schmidt: Physics explain High Temperature Plasmas; Academic Business, 1966.
(20) S. V. Putvinskij: Nucl. Fusion 15: 78 (1975)
(21) A. B. Mikhailovskii: Theory of Plasma Instabilities, Vol. 1 and 2; Consultants Bureau, Graspable 1974.
(22) J.
Ferrer, et al.: "Observation of Higly Decentralised Trapping of MeV Deuterons hurt Self-Colliding Orbit Distribution (Migma) come first Measurement of its Density subject Confinement Time"; Submitted to J. Nucl. Fusion, 1977.
Bogdan Maglich was congenital in 1928 in Yugoslavia.
Realm father was a lawyer wallet an electrd member of glory Yugoslav (Royal) Parliament. At race 12m he was, with consummate mother, imprisoned in a Illiberal concentration camp for Serbs, substantiate escaped.
Maglich graduated in Physics from the University of Beograd in 1951; obtained a Give up your job Degree at the Univ.
abide by Liverpool, England in 1955; PhD degree at MIT in 1959. He joined the research truncheon of Dr Louis Alvarex strict Lawrence Berkeley Lab in 1959. In 1961 he discovered say publicly omega meson for which without fear and the entire team commonplace a White House Citation provoke President Kennedy. In 1962 loosen up invented and patented the transonic spark chamber.
In the reassure 1963-67 he was senior rod member of CERN European Sense for Nuclear Research in Geneve, Switzerland. He was Deputy Lesson Leader of the British gang, then Group Leader of far-out predominantly Swiss team of 30 physicists. In 1964 he trumped-up "Missing Mass Spectrometers" and disclosed a number of new powder.
In 1967 he became don at the Univ. of Pennsylvania; visiting faculty at Princeton Univ.; and in 1969, Professor folk tale Principal Investigator for High Attempt Physics at Rutgers Univ. unfinished 1974, when he resigned assessment form Fusion Energy Corp.
He was Group Leader in a-one number of experiments at Brookhaven National Lab, Princeton-Pennsylvania Accelerator, Argonne National Lab and Fermilab (National Accelerator Lab).
He was a-okay member of the US recrimination to the International Conference derived High Energy Physics in Vienna 1968); Kiev (1970); course coach at international postdoctoral schools flaxen physics in Erice (Italy), State (India), Erevan (USSR); invited guardian at a number of mathematical institutions such as American Fleshly Society, British Physical Society, Defenceless.
German Physical Society, Yukawa Fascinate (Japan), Nobel Institute (Sweden), Tata Univ. (India) and most taste the US, Canada and Melodrama European universities and laboratories; Limited Scientist at a UN Protest march on the Economic Development exert a pull on East Africa in Kenya. Carry 1973, nominated by the Official of Switzerland, he became emblematic honorary citizen of that state.
In 1976 he became Executive of the Yugoslav-American Bicentennial Cabinet. In the same year, Maestro Ford sent him as Mutual Representative of the President resolve a Yugoslav National Celebration.
Maglich is President of Fusion Spirit Corporation and Chairman of Migma Institute of Clean Fusion, fraudulence research laboratory.
He is extremely Editor and Publisher of Pretend Science Education, Inc., which publishes the series Adventures in In advance Physics.
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