Thresholdless stochastic particle heating by a single wave

Stochastic heating is a well-known mechanism through which magnetized particles may be energized by low-frequency electromagnetic waves. In its simplest version, under spatially homogeneous conditions, it is known to be operative only above a threshold in the normalized wave amplitude, which may be a demanding requisite in actual scenarios, severely restricting its range of applicability. In this paper we show, by numerical simulations supported by inspection of the particle Hamiltonian, that allowing for even a very weak spatial inhomogeneity completely removes the threshold, trading the requirement upon the wave amplitude with a requisite upon the duration of the interaction between the wave and particle. The thresholdless chaotic mechanism considered here is likely to be applicable to other inhomogeneous systems.

Alfvénic propagation: a key to nonlocal effects in magnetized plasmas

A long-standing puzzle in fusion research comes from experiments where a sudden peripheral electron temperature perturbation is accompanied by an almost simultaneous opposite change in central temperature, in a way incompatible with local transport models. This Letter shows that these experiments and similar ones are fairly well quantitatively reproduced, when induction effects are incorporated in the total plasma response, alongside standard local diffusive transport, as suggested in earlier work [Plasma Phys. Controlled Fusion 54, 124036 (2012).

Experimental-like helical self-organization in reversed-field pinch modeling

We report the first nonlinear three-dimensional magnetohydrodynamic (MHD) numerical simulations of the reversed-field pinch (RFP) that exhibit a systematic repetition of quasisingle helicity states with the same dominant mode in between reconnection events. This distinctive feature of experimental self-organized helical RFP plasmas is reproduced in MHD simulations at low dissipation by allowing a helical modulation of the plasma magnetic boundary similar to the experimental one. Realistic mode amplitudes and magnetic topology are also found.

Calculation of transport coefficient profiles in modulation experiments as an inverse problem

The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusion model where these issues are related to the vanishing of the determinant of a 2×2 matrix. This sheds light on the accuracy of calculations with transport codes, and provides a path for a more precise assessment of the profiles and of the related uncertainty.

Vanishing magnetic shear and electron transport barriers in the RFX-mod reversed field pinch

We define the safety factor q for the helical plasmas of the experiment RFX-mod by accounting for the actual three-dimensional nature of the magnetic flux surfaces. Such a profile is not monotonic but goes through a maximum located in the vicinity of the electron transport barriers measured by a high resolution Thomson scattering diagnostic. Helical states with a single axis obtained in viscoresistive magnetohydrodynamic numerical simulations exhibit similar nonmonotonic q profiles provided that the final states are preceded by a magnetic island phase, like in the experiment.

When can the Fokker-Planck equation describe anomalous or chaotic transport?

The Fokker-Planck equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced perturbations. It can be justified for generic particle transport provided that there is enough randomness in the Hamiltonian describing the dynamics. Then, except for 1 degree of freedom, the two transport coefficients are largely independent. Depending on the statistics of interest, the same dynamical system may be found diffusive or dominated by its Lévy flights.

Transport barrier inside the reversal surface in the chaotic regime of the reversed-field pinch

Magnetic field lines and the corresponding particle orbits are computed for a typical chaotic magnetic field provided by a magnetohydrodynamics numerical simulation of the reversed-field pinch. The m = 1 modes are phase locked and produce a toroidally localized bulging of the plasma which increases particle transport. The m = 0 and m = 1 modes produce magnetic chaos implying poor confinement. However, they also allow for the formation of magnetic islands which induce transport barriers inside the reversal surface.

Dominant electrostatic nature of the reversed field pinch dynamo

The origin of the dynamo velocity field of the reversed field pinch within the visco-resistive MHD modeling is uncovered. The main component of this field is an electrostatic drift. The corresponding electrostatic field is related to a small charge separation which is consistent with the quasineutrality approximation, and which should be present in real plasmas, too. While quite natural in the stationary single helicity state, this analysis is shown to extend also to the nonstationary multiple helicity regime. Numerical simulations provide the spatial distribution of fields and of charge separation.

Experimental observation of nonlinear synchronization due to a single wave

A test electron beam is propagated in a specially designed traveling wave tube. It interacts with a nonresonant wave, and its energy distribution is recorded at the tube output. We report the direct experimental observation of the spatially periodic electron velocity bunching, and of a nonlinear effect on the electron velocity modulation: the synchronization of the particles with the wave responsible for Landau damping in plasma physics. The results are explained by second order perturbation theory in the wave amplitude.

Bifurcation in viscoresistive MHD: the hartmann number and the reversed field pinch

A scaling approach to the simplest viscoresistive MHD model reveals that the Prandtl number acts only through the inertia term. When this term is negligible the dynamics is ruled by the Hartmann number H only. This occurs for the reversed field pinch dynamics as seen by numerical simulation of the model. When H is large the system is in a multiple helicity state. In the vicinity of H = 2500 the system displays temporal intermittency with laminar phases of quasi-single-helicity (SH) type. For lower H's two basins of SH are shown to coexist. SH regimes are of interest because of their nonchaotic magnetic field.

Chaos healing by separatrix disappearance and quasisingle helicity states of the reversed field pinch

The resilience to chaotic perturbations of one-parameter one-degree-of-freedom Hamiltonian dynamics is shown to increase when its corresponding separatrix vanishes due to a saddle-node bifurcation. This is first highlighted for the magnetic chaos related to quasisingle helicity (QSH) states of the reversed field pinch. It provides a rationale for the confinement improvement of helical structures experimentally found for QSH plasmas; such a feature would not be expected from the classical resonance overlap picture as the separatrix disappearance occurs when the amplitude of the dominant mode increases.

Quasi-single-helicity reversed-field-pinch plasmas

The reversed field pinch (RFP) is a configuration for plasma magnetic confinement. It has been traditionally viewed as dominated by a bath of MHD instabilities producing magnetic chaos and high energy transport. We report experimental results which go beyond this view. They show a decrease of magnetic chaos and the formation of a coherent helical structure in the plasma, whose imaging and temperature profile are provided for the first time. These quasi-single-helicity states are observed both transiently and in stationary conditions. The last case is consistent with a theoretically predicted bifurcation. Our results set a new frame for improving confinement in high current nonchaotic RFP's.