On the structure of the boundary layer in a Beklemishev diamagnetic bubble

The prospect of stabilization of the $m=1$ ``rigid'' ballooning mode in an open axially symmetric long-thin trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It was found that for effective wall stabilization, the beta parameter $\beta$ must exceed some critical value $\beta_{\text{crit}}$. The dependence of $\beta_{\text{crit}}$ on the mirror ratio, radial pressure profile, axial profile of the vacuum magnetic field, and the width of vacuum gap between plasma and lateral wall was studied. Minimal critical beta at the level of $70\%$ is achieved at zero vacuum gap, although stability zone at $\beta \to 1$ exists even at extremely wide vacuum gap. It is shown that when a conducting lateral wall is combined with conducting end plates simulating attachment of the end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values $0<\beta<1$.

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“…1 Equilibrium with β > 1 is still possible in systems where ionic Larmor radius is large in a certain sence, see [25,26].…”

Section: A Pressure Model A1mentioning

confidence: 99%

Wall stabilization of the rigid ballooning m = 1 mode in a long-thin mirror trap

Kotelnikov¹,

Prikhodko²,

Yakovlev³

et al. 2022

Nucl. Fusion

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“…Therefore, the kinetic effects are to be taken into account in future work. The first kinetic models of the diamagnetic bubble [6,7] show the thickness of the transition layer to be in the range of several ion Larmor radii calculated for the vacuum magnetic field. Confinement of high-β and β ≃ 1 plasma in mirror machines has already been discussed in the past.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, work has also been carried out on the construction of kinetic models of the diamagnetic confinement mode. In [6], Kotelnikov provides a fully kinetic description of the diamagnetic bubble equilibrium in cylindrical geometry. He shows the thickness of the transition layer to be in the range of several ion Larmor radii, calculated for the vacuum magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional MHD equilibria of diamagnetic bubble in gas-dynamic trap

Khristo¹,

Beklemishev²

2022

Plasma Phys. Control. Fusion

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This article presents a magnetohydrodynamic two-dimensional numerical model of diamagnetic bubble equilibria in an axisymmetric open trap. The theoretical model consists of the Grad-Shafranov equilibrium equation and the transport equation obtained within the resistive single-ﬂuid magnetohydrodynamics with isotropic pressure. Found are the numerical solutions corresponding to the diamagnetic conﬁnement mode. In particular, the equilibria of the diamagnetic bubble in the GDMT are calculated. We investigate the eﬀect of magnetic ﬁeld corrugation on the equilibrium; the corrugation of the vacuum ﬁeld is shown to lead to a rather moderate corrugation of the bubble boundary if the period of corrugation is suﬃciently small. A valuable numerical result is the distribution of the diamagnetic ﬁeld, which would be useful for optimizing the position of the wall-stabilization plates.

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