Physics

An adjoint method to calculate the gradient of island width in stellarators is presented and applied to a set of magnetic field configurations. The underlying method of calculation of the island width is that of Cary & Hanson (1991) (with a minor modification), and requires that the residue of the island centre be small. Therefore, the gradient of the residue is calculated in addition. Both the island width and the gradient calculations are verified using an analytical magnetic field configuration introduced in Reiman & Greenside (1986). The method is also applied to the calculation of the shape gradient of the width of a magnetic island in an NCSX vacuum configuration with respect to positions on a coil. A gradient-based optimization is applied to a magnetic field configuration studied in Hanson & Cary (1984) to minimize stochasticity by adding perturbations to a pair of helical coils. Although only vacuum magnetic fields and an analytical magnetic field model are considered in this work, the adjoint calculation of the island width gradient could also be applied to a magnetohydrodynamic (MHD) equilibrium if the derivative of the magnetic field with respect to the equilibrium parameters was known. Using the island width gradient calculation presented here, more general gradient-based optimization methods can be applied to design stellarators with small magnetic islands. Moreoever, the sensitivity of the island size may itself be optimized to ensure that coil tolerances with respect to island size are kept as high as possible.

We review experimental and theoretical cross sections for electron transport in α -tetrahydrofurfuryl alcohol (THFA) and, in doing so, propose a plausible complete set. To assess the accuracy and self-consistency of our proposed set, we use the pulsed-Townsend technique to measure drift velocities, longitudinal diffusion coefficients and effective Townsend first ionisation coefficients for electron swarms in admixtures of THFA in argon, across a range of density-reduced electric fields from 1 Td to 450 Td. These measurements are then compared to simulated values derived from our proposed set using a multi-term solution of Boltzmann's equation. We observe discrepancies between the simulation and experiment, which we attempt to address by employing a neural network model that is trained to solve the inverse swarm problem of unfolding the cross sections underpinning our experimental swarm measurements. What results from our neural network-based analysis is a refined set of electron-THFA cross sections, which we confirm is of higher consistency with our swarm measurements than that we initially proposed. We also use our data base to calculate electron transport coefficients in pure THFA, across a range of reduced electric fields from 0.001 Td to 10,000 Td.

The results of the analysis of the deviation of the force equilibrium for ions from the neoclassical theory prediction, calculated using the direct measurements of the radial electric field, in the view of its possible local and nonlocal correlation with the profiles of electron, Te, and ion, Ti, temperatures in the T-10 tokamak are presented. Local correlations are analyzed by means of the Pearson's correlation. Nonlocal correlations are treated with an inverse problem under the assumption of an integral equation relationship between the deviation and Te and Ti profiles. The discharges with zero, weak and strong auxiliary heating (electron cyclotron resonance heating) are analyzed. It is found that the electrons substantially (not less than ions) contribute to the deviation of the ion equilibrium from the neoclassical theory prediction both in the local and nonlocal models.

The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability ( 1??γ d / γ L ?? ) when effective collisions are much larger than the instability growth rate ( ν?��?). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk-Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk-Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag can not be varied independently of other key parameters in realistic scenarios. While the effect of drag is modest when the ratio of drag to scattering α/ν is very small, it can become substantial when α/ν??.5 , suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.

A coupled two frequency Hill's equation is solved. Analytically approximate solution correct up-to first order is derived using modified Lindstedt Poincare perturbation method. For a wide range of controlling parameters we compare the numerical and analytical solutions. The solution is the first step towards developing a comprehensive understanding of the electrodynamics of charged particles in a combinational ion trap utilizing both electrostatic DC and RF fields along with a constant static magnetic field with prospects of confining antimatter such as anti hydrogen for a reasonably long durations of time.

In non-inverted heating scenarios, a lower hybrid (LH) resonance can appear in the plasma edge of tokamaks. This resonance can lead to large edge power deposition when heating in the ion cyclotron resonance frequency (ICRF) range. In this paper, the edge power loss associated with this LH resonance is analytically computed for a cold plasma description using an asymptotic approach and analytical continuation. This power loss can be directly linked to the local radial electric field and is then compared to the corresponding power loss computed with the semi-analytical code ANTITER IV. This method offers the possibility to check the precision of the numerical integration made in ANTITER IV and gives insights in the physics underlying the edge power absorption. Finally, solutions to minimize this edge power absorption are investigated and applied to the case of ITER's ion cyclotron resonance heating (ICRH) launcher. This study is also of direct relevance to DEMO.

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscous-resistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

The description of electronic exchange--correlation effects is of paramount importance for many applications in physics, chemistry, and beyond. In a recent Letter, Dornheim \textit{et al.} [\textit{Phys. Rev. Lett.}~\textbf{125}, 235001 (2020)] have presented the \emph{effective static approximation} (ESA) to the local field correction (LFC), which allows for the highly accurate estimation of electronic properties such as the interaction energy and the static structure factor. In the present work, we give an analytical parametrization of the LFC within ESA that is valid for any wave number, and available for the entire range of densities ( 0.7??r s ??0 ) and temperatures ( 0?�θ≤4 ) that are relevant for applications both in the ground state and in the warm dense matter regime. A short implementation in Python is provided, which can easily be incorporated into existing codes. In addition, we present an extensive analysis of the performance of ESA regarding the estimation of various quantities like the dynamic structure factor, static dielectric function, the electronically screened ion-potential, and also stopping power in electronic medium. In summary, we find that the ESA gives an excellent description of all these quantities in the warm dense matter regime, and only becomes inaccurate when the electrons start to form a strongly correlated electron liquid ( r s ??0 ). Moreover, we note that the exact incorporation of exact asymptotic limits often leads to a superior accuracy compared to the neural-net representation of the static LFC [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)].

An impact of neutrals on anomalous edge plasma transport and zonal flow (ZF) is considered. As an example, it is assumed that edge plasma turbulence is driven by the resistive drift wave (RDW) instability. It is found that the actual effect of neutrals is not related to a suppression of the instability \textit{per se}, but due to an impact on the ZF. Particularly, it is shown that, whereas the neutrals make very little impact on the linear growth rate of the RDW instability, they can largely reduce the zonal flow generation in the nonlinear stage, which results in an enhancement of the overall anomalous plasma transport. Even though only RDW instability is considered, it seems that such an impact of neutrals on anomalous edge plasma transport has a very generic feature. It is conceivable that such neutral induced enhancement of anomalous plasma transport is observed experimentally in a detached divertor regime, which is accompanied by a strong increase of neutral density.

This paper presents the application of two classical models to high-resolution electric field measurements carried out in a hollow cathode discharge operated in pure hydrogen plasma. The electric field determination has been done via the Stark shifting and splitting of the 2S level of hydrogen, followed by optogalvanic detection. Two classical models, Rickards' and Wro{ń}ski's, are applied to these measurements with the objective of obtaining a first estimation on the discharge dynamics. The chosen models provide an idea of the ions movement, their energy and their mean free path at the cathode fall region, as well as the electric field strength behaviour depending on the discharge characteristics.