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Register a new userTwo-parameter Radial Equilibrium Models for Field-Reversed Configurations
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A new equilibrium pressure profile extending the Rigid-Rotor (RR) model with a simple unified expression $P=P(psi;beta_{s},alpha, sigma)$ 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 $beta_sequiv P_s/2mu_0B_e^2$ and $delta_sequiv L_{ps}/R_s$, 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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A new tool (GSEQ-FRC) for solving two-dimensional (2D) equilibrium of field-reversed configuration (FRC) based on fixed boundary and free boundary conditions with external coils included is developed. Benefiting from the two-parameter modified rigid rotor (MRR) radial equilibrium model and the numerical approaches presented by [Ma et al, Nucl. Fusion, 61, 036046, 2021], GSEQ-FRC are used to study the equilibrium properties of FRC quantitatively and will be used for fast FRC equilibrium reconstruction. In GSEQ-FRC, the FRC equilibrium can be conveniently determined by two parameters, i.e., the ratio between thermal pressure and magnetic pressure at the seperatrix $beta_s$, and the normalized scrape of layer (SOL) width $delta_s$. Examples with fixed and free boundary conditions are given to demonstrate the capability of GSEQ-FRC in the equilibrium calculations. This new tool is used to quantitatively study the factors affecting the shape of the FRC separatrix, revealing how the FRC changes from racetrack-like to ellipse-like.
The Multi-region Relaxed MHD (MRxMHD) has been successful in the construction of equilibria in three-dimensional (3D) configurations. In MRxMHD, the plasma is sliced into sub-volumes separated by ideal interfaces, each undergoing relaxation, allowing the formation of islands and chaos. The resulting equilibrium has a stepped pressure profile across sub-volumes. The Stepped Pressure Equilibrium Code (SPEC) [S.R. Hudson et al., Phys. Plasmas 19, 112502 (2012)] was developed to calculate MRxMHD equilibria numerically. In this work, we have extended the SPEC code to compute MRxMHD equilibria with field-aligned flow and rotation, following the theoretical development to incorporate cross-helicity and angular momentum constraints. The code has been verified for convergence and compared to a Grad-Shafranov solver in 2D. We apply our new tool to study the flow profile change before and after the sawtooth crash of a reversed-field pinch discharge, in which data of the parallel flow is available. We find the promising result that under the constraints of cross-helicity and angular momentum, the parallel flow profile in post-crash SPEC equilibrium is flat in the plasma core and the amplitude of the flow matches experimental observations. Finally, we provide an example equilibrium with a 3D helical field structure as the favoured lower energy state. This will be the first 3D numerical equilibrium in which the flow effects are self-consistently calculated.
In the reversed field pinch RFX-mod strong electron temperature gradients develop when the Single-Helical-Axis regime is achieved. Gyrokinetic calculations show that in the region of the strong temperature gradients microtearing instabilities are the dominant turbulent mechanism acting on the ion Larmor radius scale. The quasi-linear evaluation of the electron thermal conductivity is in good agreement with the experimental estimates.
Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principle simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum distribution of beam particles depends on the observation radius and is neither separable, nor Gaussian.
Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the gravitational force contrasts with the underlying assumptions of Boltzmann statistics where the interactions among particles are assumed to be short ranged. A particular generalization of the classical Boltzmann formalism is available within the nonextensive context of Tsallis q -statistics, subject to non -additivity of the entropies of sub - systems. Assuming stationarity and isotropy in the velocity space, it is possible solving the generalized collsionless Boltzmann equation to derive the galaxy distribution function and density profile. We present a particular set of nonextensive models and investigate their dynamical and observable properties. As a test of the viability of this generalized context, we fit the rotation curve of M33 showing that the proposed approach leads to dark matter haloes in excellent agreement with the observed data.
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