Self-consistency vanishes in the plateau regime of the bump-on-tail instability

Using the Vlasov-wave formalism, it is shown that self-consistency vanishes in the plateau regime of the bump-on-tail instability if the plateau is broad enough. This shows that, in contrast with the "turbulent trapping" Ansatz, a renormalization of the Landau growth rate or of the quasilinear diffusion coefficient is not necessarily related to the limit where the Landau growth time becomes large with respect to the time of spreading of the particle positions due to velocity diffusion

Uniform derivation of Coulomb collisional transport thanks to Debye shielding

The effective potential acting on particles in plasmas being essentially the Debye-shielded Coulomb potential, the particles collisional transport in thermal equilibrium is calculated for all impact parameters $b$, with a convergent expression reducing to Rutherford scattering for small $b$. No cutoff at the Debye length scale is needed, and the Coulomb logarithm is only slightly modified.Comment: arXiv admin note: text overlap with arXiv:1210.1546, arXiv:1310.309

New foundations and unification of basic plasma physics by means of classical mechanics

The derivation of Debye shielding and Landau damping from the $N$-body description of plasmas requires many pages of heavy kinetic calculations in classical textbooks and is done in distinct, unrelated chapters. Using Newton's second law for the $N$-body system, we perform this derivation in a few steps with elementary calculations using standard tools of calculus, and no probabilistic setting. Unexpectedly, Debye shielding is encountered on the way to Landau damping. The theory is extended to accommodate a correct description of trapping or chaos due to Langmuir waves, and to avoid the small amplitude assumption for the electrostatic potential. Using the shielded potential, collisional transport is computed for the first time by a convergent expression including the correct calculation of deflections for all impact parameters. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons.Comment: 28 pages, revTeX. arXiv admin note: substantial text overlap with arXiv:1210.154

Relevant heating of the quiet solar corona by Alfvén waves: a result of adiabaticity breakdown

International audienceIon heating by Alfvén waves has been considered for long as the mechanism explaining why thesolar corona has a temperature several orders of magnitude higher than the photosphere. Unfortu-nately, as the measured wave frequencies are much smaller than the ion cyclotron frequency, particleswere expected to behave adiabatically, impeding a direct wave-particle energy transfer to take place,except through decorrelating stochastic mechanisms related to broadband wave spectra. This paperproposes a new paradigm for this mechanism by showing it is actually much simpler, more general,and very efficient. Indeed, for measured wave amplitudes in the quiet corona, ion orbits are shownto cross quasi-periodically one or several slowly pulsating separatrices in phase space. Now, a sepa-ratrix is an orbit with an infinite period, thus much longer than the pulsation one. Therefore, eachseparatrix crossing cancels adiabatic invariance, and yields a very strong energy transfer from thewave, and thus particle heating. This occurs whatever be the wave spectrum, even a monochromaticone. The proposed mechanism is so efficient that it might lead to a self-organized picture of coronalheating: all Alfvén waves exceeding a threshold are immediately quenched and transfer their energyto the waves

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 work 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 wave and particle. The thresholdless chaotic mechanism considered here is likely to be applicable to other inhomogeneous systems

Closed-form solution of adiabatic particle trajectories in axis-symmetric magnetic fields

International audienceThe dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic-although possibly incommensurate-motions. The projection of the particle orbit along the two non-ignorable coordinates (x, y) may be expressed in terms of each other: y = y(x), yet-to our knowledge-such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x = x(t), y = y(t), and then one of the two relations is inverted, x(t) → t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle' orbit without the need to pass through the hourly law of motion

Breakdown of adiabatic invariance of fast ions in spherical tokamaks

Later version published: Nucl. Fusion 61 (2021) 106025 (7pp)The dynamics of fast particles corresponding to O(100) keV in NSTX, or of alpha particles in a properly rescaled reactor-grade spherical tokamak, is computed numerically through integration of the full equations of motion. The magnetic moment µ of these particles has large oscillations, and even chaotic ones, in a sizable domain of the machine. This has both practical and physical consequences. First, when µ has large oscillations, the use of guiding-center or gyrokinetic calculations for such orbits is questionable. Second, the capability of these particle to excite Alfvénic instabilities decreases, since the velocity of the particle fluctuates with respect to the phase-velocity of the Alfvén wave, which imposes a fluctuating sign to the energy exchanges with this wave. Even when chaotic orbits are present, the conservation of the toroidal momentum sets strong constraints about the volume available to the particles, and their radial diffusion stays bounded

A POWER-BALANCE MODEL OF L-MODE DENSITY LIMIT IN FUSION PLASMAS

A 1D cylindrical power-balance model of the radiation density limit gives a unified description of the phenomenon for stellarator, reversed field pinch and L-mode tokamak [P. Zanca et al, Nucl. Fusion 59 (2019) 126011]. The density limit scaling laws for the three different configurations are all derived by combination of just two equations: i) single-fluid heat-transport equation; ii) on-axis Ohm's law with Spitzer resistivity, taken in a suitable limit for the stellarator. Here, we present a refined version of the model, alongside further experimental evidences supporting its successful application

The Reversed Field Pinch

This paper reviews the research on the reversed field pinch (RFP) in the last three decades. Substantial experimental and theoretical progress and transformational changes have been achieved since the last review (Bodin 1990 Nucl. Fusion 30 1717-37). The experiments have been performed in devices with different sizes and capabilities. The largest are RFX-mod in Padova (Italy) and MST in Madison (USA). The experimental community includes also EXTRAP-T2R in Sweden, RELAX in Japan and KTX in China. Impressive improvements in the performance are the result of exploration of two lines: the high current operation (up to 2 MA) with the spontaneous occurrence of helical equilibria with good magnetic flux surfaces and the active control of the current profile. A crucial ingredient for the advancements obtained in the experiments has been the development of state-of-art active feedback control systems allowing the control of MHD instabilities in presence of a thin shell. The balance between achievements and still open issues leads us to the conclusion that the RFP can be a valuable and diverse contributor in the quest for fusion electricity