On the relativistic cold fluid radial equilibrium of a nonneutral plasma

Kotelnikov, I. A.; Romé, M.; Pozzoli, R.

doi:10.1016/j.physleta.2007.09.058

Cited by 8 publications

(9 citation statements)

References 21 publications

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“…In the case of slowly rotating non-neutral plasma equilibria, 11 the magnetic field can be described by a scalar magnetic potential = B ‫ء‬ with B ‫ء‬ = const, such that…”

Section: Curvilinear Coordinatesmentioning

confidence: 99%

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with quadrupole field errors

Akhmetov

Kotelnikov

2009

Physics of Plasmas

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“…In the case of slowly rotating non-neutral plasma equilibria, 11 the magnetic field can be described by a scalar magnetic potential = B ‫ء‬ with B ‫ء‬ = const, such that…”

Section: Curvilinear Coordinatesmentioning

confidence: 99%

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with quadrupole field errors

Akhmetov

Kotelnikov

2009

Physics of Plasmas

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“…In the equilibrium state, the time derivative vanishes. If the electron density is far below the Brillouin limit, n Ӷ n B , and the plasma column is the slow rotation state, 23 then the v · ٌv term is negligible in comparison with the other terms and the force balance equation reduces to…”

Section: A General Properties Of Non-neutral Plasma Equilibriamentioning

confidence: 99%

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with a weakly tilted magnetic field

Kotelnikov

Romé

2008

Physics of Plasmas

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The effect of small asymmetric magnetic perturbations on the equilibrium of a non-neutral plasma confined in a Malmberg-Penning trap is analyzed. A constraint, known in the theory of tandem mirrors as the condition of current closure, is derived for non-neutral plasmas. Together with Poisson's equation, this constraint provides a set of equations for determining self-consistent asymmetric equilibria of non-neutral plasmas in Malmberg-Penning traps. As an example of this approach, the non-neutral plasma equilibrium in the presence of a weak magnetic tilt is analyzed. Analytical and semianalytical solutions for the electric potential variations inside the trap are found in a paraxial limit for various radial density profiles of the plasma, including the case of global thermal equilibrium. The numerical procedure aimed to obtain self-consistent plasma equilibria for a magnetic field with a large asymmetry is also discussed. The newly developed method can be straightforwardly applied to determine plasma equilibria under the effect of the magnetic perturbations of higher multipolarity ͑such as, quadrupole or octupole fields͒.

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“…As it was argued in Ref. [8], performing the calculations in flux coordinates makes the interpretation of the plasma equilibrium much easier and provides the best approach to the problem of the error field mediated transport.The electric current produced by the flowing electrons confined in a MP trap produces a negligible change of the magnetic field, if the electron density n is far below the Brillouin limit [9] n B B 2 =8mc 2 (with m the particle mass and c the speed of light) except for the case of a fast rotating non-neutral plasma equilibrium [10]. The magnetic field can then be described by a scalar magnetic potential such that B ¼ r:…”

mentioning

confidence: 99%

“…The electric current produced by the flowing electrons confined in a MP trap produces a negligible change of the magnetic field, if the electron density n is far below the Brillouin limit [9] n B B 2 =8mc 2 (with m the particle mass and c the speed of light) except for the case of a fast rotating non-neutral plasma equilibrium [10]. The magnetic field can then be described by a scalar magnetic potential such that B ¼ r:…”

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confidence: 99%

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Admissible Equilibria of Non-neutral Plasmas in a Malmberg-Penning Trap

Kotelnikov

Romé

2008

Phys. Rev. Lett.

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A ''parallel current constraint'' is derived, that in combination with the Poisson equation allows one to select admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap in the presence of a nonuniform and nonaxisymmetric magnetic field. Asymmetry-induced currents (analogous to the PfirschSchlüter currents in Tokamaks) appearing in a non-neutral plasma even in the absence of magnetic drifts are explicitly computed in the case of a uniformly tilted magnetic field. The radial confinement of non-neutral plasmas in Malmberg-Penning (MP) traps is provided by a strong axial magnetic field. This field is assumed to be uniform in most theories that deal with plasma confinement. However, small perturbations of the magnetic field may play a crucial role in the transport of non-neutral plasmas in this kind of confinement devices [1]; see also the review paper [2] and references therein for further discussion of the problem of non-neutral plasma transport. On the other hand, it is well known that an accurate treatment of the plasma transport requires at first an analysis of the plasma equilibrium, as it is demonstrated by established theories for quasineutral plasma confined, e.g., in tandem mirrors [3].It may be wondered whether an equilibrium of a nonneutral plasma exists in an asymmetric magnetic field, since an asymmetry leads in general to plasma expansion. A positive answer to this question implies that the equilibrium is referred to a time interval shorter than the expansion time m . If the asymmetry is small, the latter is expected to be at least greater then the axial bounce time of the particles inside the trap b and the plasma azimuthal rotation time 2=! E , i.e., m ) ð b ; 2=! E Þ. In general, m / À2 , where the parameter characterizes the smallness on the magnetic field inhomogeneity. At this stage it can be assumed that $ B=B, where B represents the difference of the actual magnetic field from an ideal uniform magnetic field B Ã ¼ B Ã e z directed along the symmetry axis of the cylindrical confinement device. For the small values achieved in existing devices the expansion time can therefore be quite large, and for a shorter time interval, t ( m , it is possible to consider a slowly evolving plasma column as being in a static equilibrium.Systematic studies of nonaxisymmetric equilibria in a MP trap have been started in Refs. [4,5]. In Ref.[4] the equilibrium of a non-neutral plasma column in a weakly tilted magnetic field was simulated numerically. In Ref. [5] an electrostatic asymmetry was introduced by azimuthally sectored electrodes, and the analytical treatment was limited to the case of a cold plasma with a stepwise radial density profile. Later on, three-dimensional numerical particle-in-cell simulations of the non-neutral plasma equilibrium with quadrupole or mirror magnetic perturbations have been reported in Ref. [6]. However, similar numerical simulations are hardly able to uncover fine-structure effects that limit plasma lifetime in existing and future facilities designed to achieve im...

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On the relativistic cold fluid radial equilibrium of a nonneutral plasma

Cited by 8 publications

References 21 publications

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with quadrupole field errors

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with quadrupole field errors

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with a weakly tilted magnetic field

Admissible Equilibria of Non-neutral Plasmas in a Malmberg-Penning Trap

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