Negatively Charged open-Ended Plasma to Strip and Confine Heavy Ions

Stix, Thomas H.

doi:10.1103/physrevlett.23.1093

Cited by 31 publications

(5 citation statements)

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“…We combine this current with f s * in (6) to obtain the total surface cur-rent f *, where we have used 4ira = V • £ and v D « E x Bc/i? 2 .…”

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confidence: 99%

Toroidal Fusion Plasma with Powerful Negative Bias

Stix

1970

Phys. Rev. Lett.

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Imposition of a powerful electrostatic bias allows a dense uniform-pressure plasma to be held in a static equilibrium in a toroidal closed-magnetic-line system. A small wall current of 3.5-MeV d-t alpha particles easily maintains the 6-MV/cm electric field necessary for controlled thermonuclear reaction conditions. As ions can be confined in an enormously deep energy well, the system lends itself also to production of highly stripped heavy nuclei.Since inception around 1952 the main thrust of controlled-nuclear-fusion research has been toward the confinement of neutral plasmas by strong static magnetic fields. In the present Letter it is pointed out that the imposition of a large electrostatic bias introduces a new degree of freedom into the design of plasma equilibria and allows several interesting objectives to be immediately attained. In particular, a dense, static, uniform-pressure plasma can be confined in a pure-toroidal closed-line magnetic field with toroidal electrostatic potential surfaces. In the proposed controlled thermonuclear reaction (CTR) device the ions are held in an energy well of enormous depth and the necessary bias is spontaneously maintained by a small wall current of 3.5-MeV d-t alpha particles. The stability of the electron-plasma heavy-ion plasma accelerator (HIPAC) system, analyzed and documented by Daugherty et al., 1 lends considerable encouragement that the proposed configuration may also be well behaved.We start the analysis of the toroidal equilibrium state by examining the equations for single-particle motion. In cylindrical coordinates (r, 0 ,z), symmetry in the azimuthal (9) direction provides that the angular momentum p e is a constant of the motion. With static fields the particle energy is also a constant and we make use of the approximate invariance of the magnetic moment ii. The particle energy H can then be writtenwhere q is the particle charge. The motion of the particle guiding center is restricted to the surface H-const; the guiding-center drift velocity along this surface is given to lowest order in Larmor radius byWe have chosen 6 = 0J3(r). The second term in-troduces 2 the effect of centrifugal force due to curved drift orbits. We now consider a region of space filled with density n(r) of particles of the same /i and J. The conservation law dn/dt+ V• (nv D ) =0 has an exact time-independent solution 3 [we make use of vx(g/r) = 0], n(n,J,r) = (B/r)[l + Cl~1(e*VXv D )]f(H),with Q = qB/mc. Inasmuch as the guiding center current differs from the perpendicular particle current only by the divergence-free magnetization current density VXM ? the guiding-center density in (3) is also the particle density to this order of approximation, Self-consistency of the low-/3 static equilibrium comes from the solution of the Poisson equation vV = -4?re £ £w/(M,«7,r)-^e(jU,J,r),in which the density terms are to be evaluated using the previous three equations.To avoid the undesirable buildup of electrostatic potentials large compared with kT/e in the interior of the proposed CTR plasma...

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“…We combine this current with f s * in (6) to obtain the total surface cur-rent f *, where we have used 4ira = V • £ and v D « E x Bc/i? 2 .…”

mentioning

confidence: 99%

Toroidal Fusion Plasma with Powerful Negative Bias

Stix

1970

Phys. Rev. Lett.

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“…If the density of the non-neutral plasma is growing, the maximum confined density is defined by the Brillouin flow condition and the resonance frequency becomes exactly half-gyrofrequency. We have shown that the resonance at half-gyrofrequency (10) is much stronger than for all the other external wave frequencies, so it could very well be a reason of the observed in the experiment higher x-ray energy and intensity compared to a conventional ECR.…”

Section: Discussionmentioning

confidence: 69%

“…When in the core of the plasma T e T i (ECR case), τ ei /τ ii is generally greater than unity and ions tend to leak faster, which means, in particular, that there is some noncompensated electron charge in plasma. This principle of ion confinement was also described by Stix [10] and Wiesemann [11].…”

Section: Confinement Criteria Summary and Calculationmentioning

confidence: 61%

Mechanism of resonant electron acceleration at half gyrofrequency in non-neutral plasmas

Ivanov¹,

Bacal²

2003

Plasma Phys. Control. Fusion

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The experiments studying the electron heating in a magnetic trap by an incident wave at half gyrofrequency showed that there is an essential increase in electron energy and the intensity of the produced x-rays compared to the acceleration at gyrofrequency. The estimates of the influence of various non-linearities do not allow for a satisfactory explanation of this phenomenon. Proposed in this paper is the interpretation of the experimental results in the framework of a non-neutral plasma model. We show the existence of a strong resonance of an incident wave at half gyrofrequency in non-neutral plasma created by an excess of electron density. The analysis of confinement of a cylindrical electron layer is carried out both in radial and in axial directions; we have taken into account several factors such as mirror geometry, pulse mode and relativistic influence. We made separate estimates for each mechanism independently. They show that the proposed mechanisms are quite adequate for the explanation of the increase in x-ray energy and intensity.

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“…1>2 Stix has also proposed a device to electrostatically confine ions by surrounding them with an envelope of electrons in a magnetic field of toroidal or PIG geometry. 3 ' 4 The experimental studies presented here are concerned with electrostatic confinement of ions in a Q-machine plasma column.…”

Section: Ary Though There Is a Small Displacement Of The Minimummentioning

confidence: 99%

Electrostatic Confinement of an Alkali-Metal Plasma

1971

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PHYSICAL REVIEW LETTERS 20 SEPTEMBER 1971 ary, though there is a small displacement of the minimum. Furthermore, as is evident from Fig. 3, it is possible to obtain an analytic representation for B y (x) valid very close to the point where B y = 0 in the plasma. If the B y (x) profile is symmetric, then by iteration the entire profile may be deduced from a numerical fit with the observed polarization results.For experiments in which narrower spatial density profiles are obtained, we expect increasing applicability of the method (of course, the upper hybrid resonance must remain accessible). Finally, we suggest an experiment that can indicate whether a local or an integrated effect is being measured for the wave polarization. In this experiment the relative phase of the second-harmonic ordinary and extraordinary waves is measured. A small phase difference implies |^|«1, and hence Eq. (8) is applicable (the difference must of course be less than 2n).We mention briefly another method, using an incident ordinary wave, that may be appropriate to experiments having sufficiently narrow density profiles.The frequency of the wave is chosen such that the ordinary wave must cross a point in the plasma, x 0 , where v = v co (cutoff frequency for the extraordinary wave), i.e., N x (x o )=0. The E ± component generated for x x 0 approach those of free space we again have a local determination of the magnetic field direction from a polar-Until quite recently, research aimed toward improving plasma confinement has concentrated largely on magnetic field geometries and schemes. Some attention has been given to electrostatic ization measurement of the transmitted wave, E y (b)/E g (b) = 0(x o ). The utility of this method is more restricted than the harmonic technique as free-space propagation is more readily obtained in the latter case for x>x 0 .The imposition of a hollow longitudinal beam of 2-kV electrons about a Q-machine potassium plasma column serves to deepen the radial potential well across that column. Transverse plasma flux is consequently decreased, while the peak ion density and endplate collector current rise an order of magnitude. A calculation is made of the transverse flux of ions in the plasma column with energy sufficient to surmount the potential well. 786

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Negatively Charged open-Ended Plasma to Strip and Confine Heavy Ions

Cited by 31 publications

References 10 publications

Toroidal Fusion Plasma with Powerful Negative Bias

Toroidal Fusion Plasma with Powerful Negative Bias

Mechanism of resonant electron acceleration at half gyrofrequency in non-neutral plasmas

Electrostatic Confinement of an Alkali-Metal Plasma

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