Two-dimensional kinetic field-reversed equilibria

Webster, Robert B.; Schwarzmeier, James L.; Lewis, Harry R.; Choi, Chan Young; Terry, William S.

doi:10.1063/1.859831

Cited by 8 publications

(5 citation statements)

References 8 publications

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“…where B θ = 0 is assumed, and ψ = Ψ p /2π = r 0 B z rdr is the normalized radial magnetic flux, J θ is the toroidal current density of plasma, P ′ is the derivative of pressure with respect to ψ and µ 0 is the vacuum permeability. Studies have shown that in present experiments kinetic effects of the equilibrium is small [7], and the FRC experimental study confirmed the applicability of the G-S equation [1,8], at least for the inner region of FRCs.…”

Section: Introductionsupporting

confidence: 84%

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Two-parameter Radial Equilibrium Models for Field-Reversed Configurations

Ma,

Xie,

Bai

et al. 2020

Preprint

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A new equilibrium pressure profile extending the Rigid-Rotor (RR) model with a simple unified expression P = P(ψ;β s ,α,σ) for both inside and outside the separatrix is proposed, in which the radial normalized field-reversed configuration (FRC) equilibrium profiles for pressure, magnetic field, and current can be determined by only two dimensionless parameters β s ≡ P s /2µ 0 B 2 e and δ s ≡ L ps /R s , where P s is the thermal pressure at the separatrix, B e is the external magnetic field strength, L ps is the pressure profile scale length at the separatrix, and R s is the separatrix radius. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate the narrow scrape of layer (SOL) width and hollow current density profiles, and can be used to fit experimental measurements satisfactorily. Detailed one-dimensional (1D) characteristics of the new MRR model are investigated analytically and numerically, and the results are also confirmed in two-dimensional (2D) numerical equilibrium solutions.

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Section: Introductionsupporting

confidence: 84%

“…In Eqs. (7) and (8) b s is the normalized magnetic field b ≡ B(r)/B e at the separatrix, σ and α are free parameters. In the 2PE and 3PE models [Eqs.…”

Section: The Mrr Equilibrium Modelmentioning

confidence: 99%

Two-parameter Radial Equilibrium Models for Field-Reversed Configurations

Ma,

Xie,

Bai

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…where B θ = 0 is assumed, and ψ = Ψ p /2π = r 0 B z r dr is the normalized poloidal magnetic flux, J θ is the toroidal current density of the plasma, P is the derivative of pressure with respect to ψ and μ 0 is the permeability of vacuum. Studies have shown that at equilibrium, kinetic effects are negligible in a standard FRC [10], and an FRC experimental study confirmed the applicability of the G-S equation [1,11], at least for the inner region of FRCs.…”

Section: Introductionmentioning

confidence: 67%

“…In terms of the normalized parameters defined above, equation ( 16) can be written in different forms for each model described by equations ( 4)- (10):…”

Section: A Step-by-step Methods For a Quasi-1d Equilibrium Solutionmentioning

confidence: 99%

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Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

Ma¹,

Xie²,

Bai³

et al. 2021

Nucl. Fusion

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A new equilibrium pressure profile is proposed that extends the rigid rotor (RR) model with a simple unified expression P = P(ψ; β s, α, σ) for both inside and outside the separatrix. A new method is described for solving the field-reversed configuration (FRC) one-dimensional (1D) equilibrium with only two parameters. The radial normalized FRC equilibrium profiles for pressure, magnetic field, and current density can be uniquely determined by the dimensionless parameters of β s ≡ P s / B e 2 / 2 μ 0 and δ s ≡ L ps/R s. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate narrow scrape-off layer (SOL) widths and hollow current density profiles, and can be used to fit experimental measurements. A database of 1D plasma equilibria in the (β s, δ s) space is provided for the convenience of real-time approximate FRC equilibrium reconstruction. The detailed one-dimensional (1D) characteristics of the equilibrium models are investigated analytically and numerically. The 1D results from the MRR models are also validated using two-dimensional (2D) Grad–Shafranov (G–S) equilibrium solutions.

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Profile consistency of an elongated field-reversed configuration. I. Asymptotic theory

Barnes

2001

Physics of Plasmas

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An asymptotic theory of field-reversed configuration (FRC) equilibrium is developed, where the small expansion parameter is the square of the inverse elongation of the separatrix. It is shown that equilibrium alone completely determines the closed-field pressure profile of an elongated FRC in terms of the open-field profile. Examples show that the closed profile is insensitive to details of the open profile. A surprising result is that the open outflow plasma (axially beyond closed region) is always totally diamagnetic on the axis (β=1, where β is measured in the θ-pinch sense). The separatrix shape (axial variation) depends uniquely on the first-order pressure profile, and any separatrix shape may be realized within the limitations of the asymptotic theory. This sensitive dependence of shape on pressure profile explains extreme stiffness of the FRC equilibrium problem which was reported earlier. These results are compared favorably with experimental observations.

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Two-dimensional kinetic field-reversed equilibria

Cited by 8 publications

References 8 publications

Two-parameter Radial Equilibrium Models for Field-Reversed Configurations

Two-parameter Radial Equilibrium Models for Field-Reversed Configurations

Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

Profile consistency of an elongated field-reversed configuration. I. Asymptotic theory

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